Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze52.0ms (0.4%)

Memory

8.5MiB live, 53.7MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50.6%	49.4%	0%	0%	0%	0
0%	0%	50.6%	49.4%	0%	0%	0%	1
0%	0%	50.6%	49.4%	0%	0%	0%	2
0%	0%	25.3%	49.4%	0%	25.3%	0%	3
0%	0%	25.3%	49.4%	0%	25.3%	0%	4
0%	0%	19%	49.4%	0%	31.6%	0%	5
0%	0%	15.8%	49.4%	0%	34.8%	0%	6
0%	0%	11.1%	49.4%	0%	39.5%	0%	7
0%	0%	8.7%	49.4%	0%	41.9%	0%	8
0%	0%	5.9%	49.4%	0%	44.6%	0%	9
0%	0%	4.5%	49.4%	0%	46%	0%	10
0%	0%	3.1%	49.4%	0%	47.5%	0%	11
0%	0%	2.7%	49.4%	0%	47.9%	0%	12

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample7.5s (54.1%)

Memory

186.6MiB live, 7 380.2MiB allocated

Samples

4.1s	25 993×	0	invalid
1.0s	2 762×	1	valid
681.0ms	5 494×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 4.0s

const: 841.0ms (21.3% of total)

ival-add: 820.0ms (20.7% of total)

ival-tan: 623.0ms (15.8% of total)

ival-<=: 356.0ms (9% of total)

ival-fabs: 302.0ms (7.6% of total)

ival-sub: 267.0ms (6.8% of total)

ival-mult: 253.0ms (6.4% of total)

ival-<: 215.0ms (5.4% of total)

ival-and: 116.0ms (2.9% of total)

adjust: 100.0ms (2.5% of total)

exact: 47.0ms (1.2% of total)

ival-assert: 14.0ms (0.4% of total)

Bogosity

explain89.0ms (0.6%)

Memory

33.0MiB live, 149.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
221	2	(-6.887226976773675e-96 2.8680079236547454e-98)	3	(-5.044773938705592e-97 6.3670843752180895e-99)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
1	0	-	0	-	`(tan.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(tan.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`	cancellation	220	8
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	218	3
-	2	33

Precision

0.990909090909091

Recall

0.9864253393665159

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	218	3	0
-	2	5	28

Precision?

0.9692982456140351

Recall?

1.0

Freqs

test

number	freq
0	36
1	219
2	1

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

23.0ms	202×	1	valid
16.0ms	310×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-tan: 10.0ms (43.8% of total)

adjust: 4.0ms (17.5% of total)

ival-add: 4.0ms (17.5% of total)

ival-sub: 3.0ms (13.2% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

preprocess25.0ms (0.2%)

Memory

-4.0MiB live, 38.1MiB allocated

Algorithm

1×	egg-herbie

Rules

102×	`sub-neg`
80×	`lower-fma.f64`
80×	`lower-fma.f32`
68×	`cancel-sign-sub-inv`
64×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Outputs
#<batchref>
#<batchref>

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify26.0ms (0.2%)

Memory

-31.9MiB live, 6.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(tan.f64 x)
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`
36×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(tan.f64 x)

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

localize25.0ms (0.2%)

Memory

26.5MiB live, 26.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(tan.f64 x)
accuracy	0.08163815908213547	(tan.f64 (+.f64 x eps))
accuracy	24.735122395798246	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

11.0ms	101×	1	valid
8.0ms	155×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-tan: 5.0ms (46.1% of total)

adjust: 2.0ms (18.4% of total)

ival-sub: 2.0ms (18.4% of total)

ival-add: 2.0ms (18.4% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series26.0ms (0.2%)

Memory

-23.8MiB live, 14.2MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
15.0ms	x	@	-inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
3.0ms	x	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	eps	@	inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	eps	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	eps	@	-inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))

simplify197.0ms (1.4%)

Memory

38.2MiB live, 239.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14 592×	`lower-fma.f64`
14 592×	`lower-fma.f32`
5 316×	`lower-*.f64`
5 316×	`lower-*.f32`
2 664×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	1351
1	464	1285
2	1534	1274
3	5964	1242
0	8538	1195

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

Inputs
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
x
(+ eps x)
(+ eps x)
(+ eps x)
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (cos eps))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))

Outputs
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rewrite203.0ms (1.5%)

Memory

-25.2MiB live, 220.9MiB allocated

Rules

3 740×	`lower-/.f64`
3 740×	`lower-/.f32`
3 736×	`lower-*.f64`
3 736×	`lower-*.f32`
3 166×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	1538
0	157	1143
1	1204	887
0	8644	849

Stop Event

1×	iter limit
1×	node limit
1×	saturated

Counts

4 → 8

Calls

Call 1

Inputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
(tan.f64 x)

Outputs
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eval12.0ms (0.1%)

Memory: -13.3MiB live, 24.9MiB allocated
Compiler: Compiled 1 561 to 151 computations (90.3% saved)

prune9.0ms (0.1%)

Memory

22.3MiB live, 22.3MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	77	8	85
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	9	86

Accuracy

99.9%

Counts

86 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	5.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (+ x eps) (+.f64 eps x)))
	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))))
▶	59.7%	(-.f64 #s(approx (+ x eps) (+.f64 eps x)) (tan.f64 x))
▶	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
▶	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
▶	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
▶	98.0%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
	61.2%	#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))))

Compiler

Compiled 485 to 204 computations (57.9% saved)

simplify273.0ms (2%)

Memory

-17.1MiB live, 276.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 eps (cos.f64 x))
cost-diff	0	(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
cost-diff	19072	(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
cost-diff	0	(pow.f64 (sin.f64 x) #s(literal 2 binary64))
cost-diff	0	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(sin.f64 eps)
cost-diff	0	(/.f64 (sin.f64 eps) (cos.f64 eps))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
cost-diff	0	(tan.f64 x)
cost-diff	0	(+.f64 eps x)
cost-diff	0	#s(approx (+ x eps) (+.f64 eps x))
cost-diff	0	(-.f64 #s(approx (+ x eps) (+.f64 eps x)) (tan.f64 x))
cost-diff	192	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
cost-diff	19072	(fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
cost-diff	26816	(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
cost-diff	86336	(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))

Rules

33 558×	`lower-fma.f32`
33 536×	`lower-fma.f64`
4 346×	`lower-+.f32`
4 342×	`lower-+.f64`
3 732×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	1268
0	97	1268
1	166	1128
2	385	1104
3	1383	964
4	6700	939
0	8318	911

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))))
(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
#s(literal -1/6 binary64)
(-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin.f64 x)
x
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 1/6 binary64)
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
(/.f64 (sin.f64 x) (cos.f64 x))
(*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
#s(literal 1/3 binary64)
(/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
#s(literal 3 binary64)
eps
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) (tan.f64 x))
#s(approx (+ x eps) (+.f64 eps x))
(+.f64 eps x)
eps
x
(tan.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin.f64 eps)
eps
(cos.f64 eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin.f64 x)
x
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
eps
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 eps (cos.f64 x))
eps
(cos.f64 x)
x
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(sin.f64 x)
#s(literal 3 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))

Outputs
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localize321.0ms (2.3%)

Memory

-1.4MiB live, 353.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
accuracy	0.025722509768442016	(pow.f64 (sin.f64 x) #s(literal 3 binary64))
accuracy	0.109375	(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.5070900891804948	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
accuracy	0.00390625	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy	0.0078125	(pow.f64 (sin.f64 x) #s(literal 2 binary64))
accuracy	0.0078125	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
accuracy	0.7093718546349276	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
accuracy	0	(sin.f64 eps)
accuracy	0	(cos.f64 eps)
accuracy	0.0078125	(/.f64 (sin.f64 eps) (cos.f64 eps))
accuracy	1.2742688909564484	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
accuracy	0	(+.f64 eps x)
accuracy	0	(tan.f64 x)
accuracy	0	#s(approx (+ x eps) (+.f64 eps x))
accuracy	24.320478714078178	(-.f64 #s(approx (+ x eps) (+.f64 eps x)) (tan.f64 x))
accuracy	0.12890625	(fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.30078125	(*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
accuracy	0.35912655670525323	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
accuracy	0.978847509768442	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))

Samples

171.0ms	99×	1	valid
93.0ms	156×	0	valid
3.0ms	1×	3	valid

Compiler

Compiled 1 123 to 59 computations (94.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 232.0ms

ival-mult: 106.0ms (45.7% of total)

ival-add: 25.0ms (10.8% of total)

ival-div: 20.0ms (8.6% of total)

ival-pow2: 19.0ms (8.2% of total)

ival-pow: 14.0ms (6% of total)

adjust: 13.0ms (5.6% of total)

const: 12.0ms (5.2% of total)

ival-sub: 6.0ms (2.6% of total)

ival-tan: 5.0ms (2.2% of total)

ival-cos: 5.0ms (2.2% of total)

ival-sin: 5.0ms (2.2% of total)

exact: 1.0ms (0.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series132.0ms (0.9%)

Memory

9.4MiB live, 127.6MiB allocated

Counts

25 → 456

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 #s(approx (+ x eps) (+.f64 eps x)) (tan.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (+ x eps) (+.f64 eps x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (+.f64 eps x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (sin.f64 eps) (cos.f64 eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (cos.f64 eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())

Outputs
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#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
48.0ms	eps	@	-inf	((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (+ x eps) (tan x)) (+ x eps) (+ eps x) (tan x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (/ eps (cos x)) (- (tan (+ x eps)) (tan x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (pow (cos x) 2) (pow (sin x) 3) (/ (pow (sin x) 3) (pow (cos x) 2)))
19.0ms	x	@	-inf	((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (+ x eps) (tan x)) (+ x eps) (+ eps x) (tan x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (/ eps (cos x)) (- (tan (+ x eps)) (tan x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (pow (cos x) 2) (pow (sin x) 3) (/ (pow (sin x) 3) (pow (cos x) 2)))
17.0ms	x	@	inf	((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (+ x eps) (tan x)) (+ x eps) (+ eps x) (tan x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (/ eps (cos x)) (- (tan (+ x eps)) (tan x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (pow (cos x) 2) (pow (sin x) 3) (/ (pow (sin x) 3) (pow (cos x) 2)))
11.0ms	eps	@	0	((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (+ x eps) (tan x)) (+ x eps) (+ eps x) (tan x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (/ eps (cos x)) (- (tan (+ x eps)) (tan x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (pow (cos x) 2) (pow (sin x) 3) (/ (pow (sin x) 3) (pow (cos x) 2)))
8.0ms	eps	@	inf	((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (+ x eps) (tan x)) (+ x eps) (+ eps x) (tan x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (/ eps (cos x)) (- (tan (+ x eps)) (tan x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (pow (cos x) 2) (pow (sin x) 3) (/ (pow (sin x) 3) (pow (cos x) 2)))

simplify277.0ms (2%)

Memory

8.4MiB live, 237.4MiB allocated

Algorithm

1×	egg-herbie

Rules

11 770×	`lower-fma.f64`
11 770×	`lower-fma.f32`
6 668×	`lower-*.f64`
6 668×	`lower-*.f32`
4 688×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	599	10510
1	1919	10202
2	6562	10020
0	8517	9590

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 433

Calls

Call 1

Inputs
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(- x (/ (sin x) (cos x)))
(- (+ eps x) (/ (sin x) (cos x)))
(- (+ eps x) (/ (sin x) (cos x)))
(- (+ eps x) (/ (sin x) (cos x)))
x
(+ eps x)
(+ eps x)
(+ eps x)
x
(+ eps x)
(+ eps x)
(+ eps x)
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
eps
(* eps (- (+ 1 (/ x eps)) (/ (sin x) (* eps (cos x)))))
(* eps (- (+ 1 (/ x eps)) (/ (sin x) (* eps (cos x)))))
(* eps (- (+ 1 (/ x eps)) (/ (sin x) (* eps (cos x)))))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* (pow eps 2) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
eps
(* -1 (* eps (- (* -1 (/ (- x (/ (sin x) (cos x))) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- x (/ (sin x) (cos x))) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- x (/ (sin x) (cos x))) eps)) 1)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x))
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
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(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
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1/3
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-1/2
(- (* -1/3 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)
(* 1/3 (pow eps 2))
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1/3
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eps
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eps
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(+ eps x)
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eps
(+ eps x)
(+ eps x)
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x
(* x (+ 1 (* 1/3 (pow x 2))))
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(/ (sin eps) (cos eps))
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(/ (sin eps) (cos eps))
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eps
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(* eps x)
(* x (+ eps x))
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(* x (+ eps (* x (+ 1 (* x (- (+ (* 2/3 x) (* 5/6 eps)) (* -1/2 eps)))))))
(/ (sin eps) (cos eps))
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eps
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eps
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(/ (sin eps) (cos eps))
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(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(* 1/3 x)
(* x (+ 1/3 (* 4/9 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* 17/45 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* (pow x 2) (+ 17/45 (* 248/945 (pow x 2))))))))
1
(+ 1 (* -1 (pow x 2)))
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(pow x 3)
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(* (pow x 3) (+ 1 (* (pow x 2) (- (* 13/120 (pow x 2)) 1/2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 13/120 (* -41/3024 (pow x 2)))) 1/2))))
(pow x 3)
(* (pow x 3) (+ 1 (* 1/2 (pow x 2))))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1/2 (* 11/40 (pow x 2))))))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 11/40 (* 421/3024 (pow x 2))))))))
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(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
x
(* x (- (+ 1 (/ eps x)) (/ (sin x) (* x (cos x)))))
(* x (- (+ 1 (/ eps x)) (/ (sin x) (* x (cos x)))))
(* x (- (+ 1 (/ eps x)) (/ (sin x) (* x (cos x)))))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
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(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
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(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
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(pow (cos x) 2)
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(/ (pow (sin x) 3) (pow (cos x) 2))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
x
(* -1 (* x (- (* -1 (/ (- eps (/ (sin x) (cos x))) x)) 1)))
(* -1 (* x (- (* -1 (/ (- eps (/ (sin x) (cos x))) x)) 1)))
(* -1 (* x (- (* -1 (/ (- eps (/ (sin x) (cos x))) x)) 1)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(/ (pow (sin x) 3) (pow (cos x) 2))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/ (pow (sin x) 3) (pow (cos x) 2))

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rewrite258.0ms (1.8%)

Memory

4.6MiB live, 253.9MiB allocated

Rules

8 888×	`lower-*.f64`
8 888×	`lower-*.f32`
4 496×	`lower-fma.f64`
4 496×	`lower-fma.f32`
3 918×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	599	11890
0	599	9769
1	4673	9613
0	10985	9171

Stop Event

1×	iter limit
1×	node limit
1×	saturated

Counts

25 → 131

Calls

Call 1

Inputs
(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) (tan.f64 x))
#s(approx (+ x eps) (+.f64 eps x))
(+.f64 eps x)
(tan.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin.f64 eps)
(cos.f64 eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(/.f64 eps (cos.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))

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eval566.0ms (4.1%)

Memory: -10.1MiB live, 308.5MiB allocated
Compiler: Compiled 88 196 to 2 368 computations (97.3% saved)

prune61.0ms (0.4%)

Memory

21.0MiB live, 98.1MiB allocated

Pruning

27 alts after pruning (25 fresh and 2 done)

	Pruned	Kept	Total
New	1 038	22	1 060
Fresh	0	3	3
Picked	4	1	5
Done	0	1	1
Total	1 042	27	1 069

Accuracy

99.9%

Counts

1 069 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	5.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (+ x eps) (+.f64 eps x)))
	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))))
	2.5%	(-.f64 #s(approx (+ x eps) (+.f64 eps x)) #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
	8.1%	(+.f64 eps x)
▶	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
▶	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
✓	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
	96.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
▶	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) x eps) x)) eps eps))
	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps)) eps eps))
	97.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))
	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
	96.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
	61.2%	#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) eps)))
▶	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
	5.3%	#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)))
▶	8.1%	x

Compiler

Compiled 1 200 to 606 computations (49.5% saved)

simplify185.0ms (1.3%)

Memory

-26.2MiB live, 214.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 eps (cos.f64 x))
cost-diff	0	(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
cost-diff	6464	(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
cost-diff	320	(fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps))
cost-diff	384	(fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps))
cost-diff	512	(-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
cost-diff	0	(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
cost-diff	64	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
cost-diff	192	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
cost-diff	26816	(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))

Rules

18 264×	`lower-fma.f32`
18 230×	`lower-fma.f64`
4 474×	`lower-+.f32`
4 470×	`lower-+.f64`
3 448×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	1489
0	132	1468
1	245	1364
2	552	1352
3	1913	1347
0	8545	1321

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))))
(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
#s(literal -1/6 binary64)
(-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin.f64 x)
x
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 1/6 binary64)
(fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))
#s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
(*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
#s(literal 1/3 binary64)
(/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
#s(literal 3 binary64)
eps
(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))
x
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
(*.f64 x x)
x
eps
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)
(fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps)
(fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps))
(-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps))
(fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps))
#s(literal 2/45 binary64)
eps
(*.f64 #s(literal -1/3 binary64) eps)
#s(literal -1/3 binary64)
(*.f64 #s(literal -2/3 binary64) eps)
#s(literal -2/3 binary64)
(*.f64 x x)
x
(*.f64 #s(literal 2/3 binary64) eps)
#s(literal 2/3 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 eps (cos.f64 x))
eps
(cos.f64 x)
x
(+.f64 eps (sin.f64 x))
(sin.f64 x)
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))

Outputs
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localize384.0ms (2.8%)

Memory

2.8MiB live, 374.8MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
accuracy	0.01171875	(+.f64 eps (sin.f64 x))
accuracy	0.11328125	(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.6872103832404486	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
accuracy	0.32421875	(*.f64 #s(literal -2/3 binary64) eps)
accuracy	0.46875	(-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps))
accuracy	0.7093718546349276	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
accuracy	1.1121015985151494	#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps))
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
accuracy	0.7093718546349276	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
accuracy	1.277990941455913	#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
accuracy	0.30078125	(*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
accuracy	0.34911580985818597	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
accuracy	0.94921875	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
accuracy	0.978847509768442	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))

Samples

151.0ms	99×	1	valid
131.0ms	156×	0	valid
3.0ms	1×	3	valid

Compiler

Compiled 1 245 to 77 computations (93.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 247.0ms

ival-add: 72.0ms (29.1% of total)

ival-mult: 42.0ms (17% of total)

ival-div: 41.0ms (16.6% of total)

const: 33.0ms (13.4% of total)

adjust: 19.0ms (7.7% of total)

ival-pow: 10.0ms (4% of total)

ival-sub: 9.0ms (3.6% of total)

ival-tan: 8.0ms (3.2% of total)

ival-pow2: 7.0ms (2.8% of total)

ival-cos: 3.0ms (1.2% of total)

ival-sin: 3.0ms (1.2% of total)

exact: 1.0ms (0.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series52.0ms (0.4%)

Memory

4.6MiB live, 84.3MiB allocated

Counts

21 → 384

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal -2/3 binary64) eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (+.f64 eps (sin.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) #<representation binary64>) () ())) ())
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Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	x	@	-inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (+ (* 2/45 eps) (* -1/3 eps)) (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ eps (cos x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (* -2/3 eps) (+ eps (sin x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
8.0ms	eps	@	inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (+ (* 2/45 eps) (* -1/3 eps)) (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ eps (cos x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (* -2/3 eps) (+ eps (sin x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
6.0ms	x	@	inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (+ (* 2/45 eps) (* -1/3 eps)) (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ eps (cos x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (* -2/3 eps) (+ eps (sin x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
5.0ms	eps	@	0	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (+ (* 2/45 eps) (* -1/3 eps)) (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ eps (cos x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (* -2/3 eps) (+ eps (sin x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
4.0ms	eps	@	-inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (+ (* 2/45 eps) (* -1/3 eps)) (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ eps (cos x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (* -2/3 eps) (+ eps (sin x)) (/ (pow (sin x) 2) (pow (cos x) 2)))

simplify572.0ms (4.1%)

Memory

-10.2MiB live, 254.2MiB allocated

Algorithm

1×	egg-herbie

Rules

11 748×	`lower-fma.f64`
11 748×	`lower-fma.f32`
7 318×	`lower-*.f64`
7 318×	`lower-*.f32`
4 932×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	394	6503
1	1188	6213
2	3681	5990
0	9158	5703

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 378

Calls

Call 1

Inputs
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* 17/45 eps)
(* 17/45 eps)
(* 17/45 eps)
(* 17/45 eps)
(* -13/45 eps)
(* -13/45 eps)
(* -13/45 eps)
(* -13/45 eps)
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (/ (* eps (sin x)) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (/ eps (cos x)) (/ (sin x) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (/ eps (cos x)) (/ (sin x) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (/ (* eps (sin x)) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (/ eps (cos x)) (/ (sin x) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (/ eps (cos x)) (/ (sin x) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -2/3 eps)
(* -2/3 eps)
(* -2/3 eps)
(* -2/3 eps)
(sin x)
(+ eps (sin x))
(+ eps (sin x))
(+ eps (sin x))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* 17/45 eps)
(* 17/45 eps)
(* 17/45 eps)
(* 17/45 eps)
(* -13/45 eps)
(* -13/45 eps)
(* -13/45 eps)
(* -13/45 eps)
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (pow eps 3) (cos x))
(* (pow eps 3) (+ (/ 1 (cos x)) (/ (sin x) (* eps (cos x)))))
(* (pow eps 3) (+ (/ 1 (cos x)) (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))))
(* (pow eps 3) (+ (/ 1 (cos x)) (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (pow eps 2) (cos x))
(* (pow eps 2) (+ (/ 1 (cos x)) (/ (sin x) (* eps (cos x)))))
(* (pow eps 2) (+ (/ 1 (cos x)) (+ (/ (sin x) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))
(* (pow eps 2) (+ (/ 1 (cos x)) (+ (/ (sin x) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -2/3 eps)
(* -2/3 eps)
(* -2/3 eps)
(* -2/3 eps)
eps
(* eps (+ 1 (/ (sin x) eps)))
(* eps (+ 1 (/ (sin x) eps)))
(* eps (+ 1 (/ (sin x) eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* 17/45 eps)
(* 17/45 eps)
(* 17/45 eps)
(* 17/45 eps)
(* -13/45 eps)
(* -13/45 eps)
(* -13/45 eps)
(* -13/45 eps)
(* -1 (* eps (- (* -17/45 (pow x 2)) 2/3)))
(* -1 (* eps (- (* -17/45 (pow x 2)) 2/3)))
(* -1 (* eps (- (* -17/45 (pow x 2)) 2/3)))
(* -1 (* eps (- (* -17/45 (pow x 2)) 2/3)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (pow eps 3) (cos x))
(* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* eps (cos x)))) (/ 1 (cos x)))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (sin x) (cos x))) eps)) (/ 1 (cos x)))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (sin x) (cos x))) eps)) (/ 1 (cos x)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (pow eps 2) (cos x))
(* (pow eps 2) (+ (/ 1 (cos x)) (/ (sin x) (* eps (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ 1 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ 1 (cos x))))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -2/3 eps)
(* -2/3 eps)
(* -2/3 eps)
(* -2/3 eps)
eps
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(* -1 (* eps (- (* -1 (/ (sin x) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (sin x) eps)) 1)))
-1/2
(- (* -1/3 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)
1/3
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(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
1/3
(+ 1/3 (* 1/2 x))
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(/ (sin eps) (cos eps))
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(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
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(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
eps
(+ eps (* eps (pow x 2)))
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(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(pow x 2)
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(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(pow x 2)
(pow x 2)
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(/ (sin eps) (cos eps))
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eps
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(* 1/3 x)
(* x (+ 1/3 (* 4/9 (pow x 2))))
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(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* (pow x 2) (+ 17/45 (* 248/945 (pow x 2))))))))
eps
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(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
eps
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(+ eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (- (+ (* -1/3 eps) (* 2/45 eps)) (* -2/3 eps)))
(* (pow x 2) (- (+ (* -1/3 eps) (+ (* 2/45 eps) (* 2/3 (/ eps (pow x 2))))) (* -2/3 eps)))
(* (pow x 2) (- (+ (* -1/3 eps) (+ (* 2/45 eps) (* 2/3 (/ eps (pow x 2))))) (* -2/3 eps)))
(* (pow x 2) (- (+ (* -1/3 eps) (+ (* 2/45 eps) (* 2/3 (/ eps (pow x 2))))) (* -2/3 eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ eps (* eps (+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (sin x))
(+ eps (sin x))
(+ eps (sin x))
(+ eps (sin x))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
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(* (pow x 2) (- (+ (* -1/3 eps) (+ (* 2/45 eps) (* 2/3 (/ eps (pow x 2))))) (* -2/3 eps)))
(* (pow x 2) (- (+ (* -1/3 eps) (+ (* 2/45 eps) (* 2/3 (/ eps (pow x 2))))) (* -2/3 eps)))
(* (pow x 2) (- (+ (* -1/3 eps) (+ (* 2/45 eps) (* 2/3 (/ eps (pow x 2))))) (* -2/3 eps)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(+ eps (* eps (+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ eps (sin x))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (sin x))
(+ eps (sin x))
(+ eps (sin x))
(+ eps (sin x))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))

Outputs
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rewrite160.0ms (1.1%)

Memory

25.3MiB live, 145.5MiB allocated

Rules

6 394×	`lower-*.f64`
6 394×	`lower-*.f32`
3 400×	`lower-/.f64`
3 400×	`lower-/.f32`
2 762×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	394	7078
0	394	5910
1	3002	4724
0	8285	4507

Stop Event

1×	iter limit
1×	node limit
1×	saturated

Counts

21 → 96

Calls

Call 1

Inputs
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
(*.f64 x x)
(-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps))
(fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal -1/3 binary64) eps))
(fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 eps (cos.f64 x))
(*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps))
(*.f64 #s(literal -2/3 binary64) eps)
(+.f64 eps (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))

Outputs
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eval125.0ms (0.9%)

Memory: -29.7MiB live, 136.5MiB allocated
Compiler: Compiled 30 682 to 1 071 computations (96.5% saved)

prune35.0ms (0.3%)

Memory

28.7MiB live, 67.9MiB allocated

Pruning

28 alts after pruning (24 fresh and 4 done)

	Pruned	Kept	Total
New	585	11	596
Fresh	7	13	20
Picked	3	2	5
Done	0	2	2
Total	595	28	623

Accuracy

99.9%

Counts

623 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))))
▶	8.1%	(+.f64 eps x)
	18.0%	(*.f64 #s(literal 17/45 binary64) eps)
▶	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps #s(approx (- -1/6 (- (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
▶	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
▶	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
	98.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 2/45 eps) (* -1/3 eps)) (*.f64 #s(literal -13/45 binary64) eps)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
✓	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
	96.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
	98.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) eps eps))
✓	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) x eps) x)) eps eps))
	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps)) eps eps))
	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
	96.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
	61.2%	#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))))
	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
▶	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
	56.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (fma.f64 #s(literal 2/3 binary64) eps (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 2/3 binary64) (.f64 #s(literal -13/45 binary64) eps))) x) x)) (.f64 x x) eps) (.f64 x x) eps)))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (.f64 x x) eps) #s(literal 17/45 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
✓	8.1%	x

Compiler

Compiled 1 323 to 674 computations (49.1% saved)

simplify166.0ms (1.2%)

Memory

-28.8MiB live, 125.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 eps (cos.f64 x))
cost-diff	0	(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
cost-diff	6464	(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
cost-diff	0	(/.f64 eps (cos.f64 x))
cost-diff	0	(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))))
cost-diff	0	(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
cost-diff	0	(.f64 (.f64 x x) eps)
cost-diff	0	(fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps)
cost-diff	0	#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
cost-diff	0	(+.f64 eps x)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps #s(approx (- -1/6 (- (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
cost-diff	192	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
cost-diff	6464	(fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))))
cost-diff	26752	(fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))

Rules

17 876×	`lower-fma.f32`
17 838×	`lower-fma.f64`
3 842×	`lower-*.f32`
3 836×	`lower-*.f64`
3 074×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	1832
0	167	1832
1	303	1697
2	698	1685
3	2009	1685
4	6361	1679
0	8090	1634

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps #s(approx (- -1/6 (- (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps #s(approx (- -1/6 (- (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps #s(approx (- -1/6 (- (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps #s(approx (- -1/6 (- (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps #s(approx (- -1/6 (- (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))))
(fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))))
(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
#s(literal -1/6 binary64)
(-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin.f64 x)
x
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 1/6 binary64)
(fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))
#s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
(*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
#s(literal 1/3 binary64)
(/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
#s(literal 3 binary64)
eps
#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))
(fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(pow.f64 (cos.f64 x) #s(literal 4 binary64))
(+.f64 eps x)
eps
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)
(fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps)
(.f64 (.f64 x x) eps)
(*.f64 x x)
x
eps
#s(literal 2/3 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps)
(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))))
(/.f64 eps (cos.f64 x))
eps
(cos.f64 x)
x
(+.f64 eps (sin.f64 x))
(sin.f64 x)
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))
(pow.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)
(fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64))
(fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64))
#s(literal 62/315 binary64)
(*.f64 x x)
#s(literal 17/45 binary64)
#s(literal 2/3 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 eps (cos.f64 x))
eps
(cos.f64 x)
x
(+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x))
#s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)
(sin.f64 x)
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))

Outputs
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localize380.0ms (2.7%)

Memory

30.9MiB live, 428.7MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x))
accuracy	0.109375	(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.5070900891804948	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
accuracy	1.3608552699347698	#s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64)))
accuracy	0.01171875	(+.f64 eps (sin.f64 x))
accuracy	0.11328125	(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))))
accuracy	0.6872103832404486	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
accuracy	1.1383297028172281	#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))
accuracy	0.01171875	(fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps)
accuracy	0.078125	(.f64 (.f64 x x) eps)
accuracy	0.7093718546349276	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
accuracy	1.163331925040916	#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps))
accuracy	0	(+.f64 eps x)
accuracy	0.1328125	(fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps #s(approx (- -1/6 (- (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.30078125	(*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
accuracy	0.34911580985818597	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps #s(approx (- -1/6 (- (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
accuracy	0.94921875	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))

Samples

163.0ms	99×	1	valid
115.0ms	156×	0	valid
4.0ms	1×	3	valid

Compiler

Compiled 1 302 to 90 computations (93.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 238.0ms

ival-add: 55.0ms (23.1% of total)

ival-mult: 46.0ms (19.3% of total)

const: 36.0ms (15.1% of total)

adjust: 26.0ms (10.9% of total)

ival-div: 26.0ms (10.9% of total)

ival-pow: 21.0ms (8.8% of total)

ival-sub: 8.0ms (3.4% of total)

ival-pow2: 7.0ms (2.9% of total)

ival-tan: 5.0ms (2.1% of total)

ival-cos: 3.0ms (1.3% of total)

ival-sin: 3.0ms (1.3% of total)

exact: 1.0ms (0.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series164.0ms (1.2%)

Memory

-6.4MiB live, 68.9MiB allocated

Counts

22 → 444

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps #s(approx (- -1/6 (- (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (+.f64 eps x) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 x x) eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps #s(approx (- -1/6 (- (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (+.f64 eps (sin.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) #<representation binary64>) () ())

Outputs
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Calls

6 calls:

Time	Variable		Point	Expression
104.0ms	eps	@	inf	((+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (* (* x x) eps) 2/3) eps) (* (* x x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ eps (cos x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ eps (sin x)) (/ (pow (sin x) 3) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)))
11.0ms	x	@	inf	((+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (* (* x x) eps) 2/3) eps) (* (* x x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ eps (cos x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ eps (sin x)) (/ (pow (sin x) 3) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)))
11.0ms	x	@	-inf	((+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (* (* x x) eps) 2/3) eps) (* (* x x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ eps (cos x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ eps (sin x)) (/ (pow (sin x) 3) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)))
6.0ms	eps	@	-inf	((+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (* (* x x) eps) 2/3) eps) (* (* x x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ eps (cos x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ eps (sin x)) (/ (pow (sin x) 3) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)))
6.0ms	eps	@	0	((+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (* (* x x) eps) 2/3) eps) (* (* x x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ eps (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ eps (cos x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ eps (sin x)) (/ (pow (sin x) 3) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)))

simplify204.0ms (1.5%)

Memory

12.3MiB live, 210.8MiB allocated

Algorithm

1×	egg-herbie

Rules

11 038×	`lower-fma.f64`
11 038×	`lower-fma.f32`
6 382×	`lower-*.f64`
6 382×	`lower-*.f32`
4 174×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	589	10263
1	1964	9786
2	6661	9692
0	8036	9282

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 430

Calls

Call 1

Inputs
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
x
(+ eps x)
(+ eps x)
(+ eps x)
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (/ (* eps (sin x)) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (/ eps (cos x)) (/ (sin x) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (/ eps (cos x)) (/ (sin x) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (/ (* eps (sin x)) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (/ eps (cos x)) (/ (sin x) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (/ eps (cos x)) (/ (sin x) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(sin x)
(+ eps (sin x))
(+ eps (sin x))
(+ eps (sin x))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* eps (pow x 2))
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(* eps (pow x 2))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (pow eps 3) (cos x))
(* (pow eps 3) (+ (/ 1 (cos x)) (/ (sin x) (* eps (cos x)))))
(* (pow eps 3) (+ (/ 1 (cos x)) (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))))
(* (pow eps 3) (+ (/ 1 (cos x)) (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))))
(/ (pow eps 2) (cos x))
(* (pow eps 2) (+ (/ 1 (cos x)) (/ (sin x) (* eps (cos x)))))
(* (pow eps 2) (+ (/ 1 (cos x)) (+ (/ (sin x) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))
(* (pow eps 2) (+ (/ 1 (cos x)) (+ (/ (sin x) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(* (pow eps 2) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
eps
(* eps (+ 1 (/ (sin x) eps)))
(* eps (+ 1 (/ (sin x) eps)))
(* eps (+ 1 (/ (sin x) eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
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(* eps (pow x 2))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
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(/ (pow eps 3) (cos x))
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(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (sin x) (cos x))) eps)) (/ 1 (cos x)))))
(/ (pow eps 2) (cos x))
(* (pow eps 2) (+ (/ 1 (cos x)) (/ (sin x) (* eps (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ 1 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ 1 (cos x))))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(* (pow eps 2) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x))
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
eps
(* -1 (* eps (- (* -1 (/ (sin x) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (sin x) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (sin x) eps)) 1)))
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(* 2/3 x)
(* x (+ 2/3 (* 1/2 x)))
(* x (+ 2/3 (* x (+ 1/2 (* 25/18 x)))))
(* x (+ 2/3 (* x (+ 1/2 (* x (+ 25/18 (* 1/3 x)))))))
1/3
(+ 1/3 (* 1/2 x))
(+ 1/3 (* x (+ 1/2 (* 5/6 x))))
(+ 1/3 (* x (+ 1/2 (* x (+ 5/6 (* 1/6 x))))))
(/ (sin eps) (cos eps))
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(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
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(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
eps
(+ eps (* 2/3 (* eps (pow x 2))))
(+ eps (* 2/3 (* eps (pow x 2))))
(+ eps (* 2/3 (* eps (pow x 2))))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ eps (pow eps 3))
(+ eps (+ (* (pow eps 2) x) (pow eps 3)))
(+ eps (+ (* x (+ (* eps (* x (- 1 (* -1/2 (pow eps 2))))) (pow eps 2))) (pow eps 3)))
(+ eps (+ (* x (+ (* x (+ (* eps (* x (- (* -1/6 eps) (* -1/2 eps)))) (* eps (- 1 (* -1/2 (pow eps 2)))))) (pow eps 2))) (pow eps 3)))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(+ (* x (+ eps (* x (- 1 (* -1/2 (pow eps 2)))))) (pow eps 2))
(+ (* x (+ eps (* x (- (+ 1 (* x (- (* -1/6 eps) (* -1/2 eps)))) (* -1/2 (pow eps 2)))))) (pow eps 2))
eps
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eps
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eps
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x
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(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (sin x) (cos x))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ eps (sin x))
(+ eps (sin x))
(+ eps (sin x))
(+ eps (sin x))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/ (pow (sin x) 3) (pow (cos x) 2))
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))

Outputs
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rewrite291.0ms (2.1%)

Memory

4.1MiB live, 228.2MiB allocated

Rules

9 744×	`lower-*.f64`
9 744×	`lower-*.f32`
5 284×	`lower-fma.f64`
5 284×	`lower-fma.f32`
4 442×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	589	10824
0	589	9490
1	4789	9334
0	12135	8872

Stop Event

1×	iter limit
1×	node limit
1×	saturated

Counts

22 → 89

Calls

Call 1

Inputs
(fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))
(fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))))
(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps #s(approx (- -1/6 (- (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps))
(fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps)
(.f64 (.f64 x x) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps)
(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))))
(/.f64 eps (cos.f64 x))
(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps #s(approx (- -1/6 (- (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))
(+.f64 eps (sin.f64 x))
#s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64)))
(+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x))

Outputs
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eval138.0ms (1%)

Memory: -12.1MiB live, 124.4MiB allocated
Compiler: Compiled 20 849 to 1 043 computations (95% saved)

prune78.0ms (0.6%)

Memory

8.7MiB live, 83.7MiB allocated

Pruning

32 alts after pruning (26 fresh and 6 done)

	Pruned	Kept	Total
New	537	11	548
Fresh	4	15	19
Picked	3	2	5
Done	0	4	4
Total	544	32	576

Accuracy

99.9%

Counts

576 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))))
✓	8.1%	(+.f64 eps x)
	18.0%	(*.f64 #s(literal 17/45 binary64) eps)
	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 5/6 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	98.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 2/45 eps) (* -1/3 eps)) (*.f64 #s(literal -13/45 binary64) eps)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
✓	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
	96.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
	97.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps) eps eps))
	98.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) eps eps))
✓	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
	20.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 5/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64))) eps eps))
	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps)) eps eps))
	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) #s(literal 1/3 binary64)) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
	96.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
	61.2%	#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))))
	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) eps) (fma.f64 #s(literal -2/3 binary64) eps (.f64 #s(literal 1/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
✓	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (.f64 x x) eps) #s(literal 17/45 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
	98.0%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 #s(approx (+ (* (* (* x x) eps) 2/3) eps) (.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64))) (.f64 x x) eps)))
	8.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
	5.3%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
	8.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ eps (sin x)) (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))))
	6.4%	#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
✓	8.1%	x

Compiler

Compiled 1 983 to 649 computations (67.3% saved)

regimes94.0ms (0.7%)

Memory

-10.2MiB live, 66.8MiB allocated

Counts

53 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
(*.f64 #s(literal 17/45 binary64) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 5/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 #s(approx (+ (* (* (* x x) eps) 2/3) eps) (.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64))) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (.f64 x x) eps) #s(literal 17/45 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) eps) (fma.f64 #s(literal -2/3 binary64) eps (.f64 #s(literal 1/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (fma.f64 #s(literal 2/3 binary64) eps (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 2/3 binary64) (.f64 #s(literal -13/45 binary64) eps))) x) x)) (.f64 x x) eps) (.f64 x x) eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (+ x eps) (+.f64 eps x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ eps (sin x)) (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 2/45 eps) (* -1/3 eps)) (*.f64 #s(literal -13/45 binary64) eps)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 5/6 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) #s(literal 1/3 binary64)) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps #s(approx (- -1/6 (- (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) #s(literal 1/3 binary64)) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))

Calls

3 calls:

56.0ms	x
20.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
14.0ms	eps

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`eps`
99.4%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes52.0ms (0.4%)

Memory

-3.2MiB live, 70.1MiB allocated

Counts

48 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
(*.f64 #s(literal 17/45 binary64) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 5/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 #s(approx (+ (* (* (* x x) eps) 2/3) eps) (.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64))) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (.f64 x x) eps) #s(literal 17/45 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) eps) (fma.f64 #s(literal -2/3 binary64) eps (.f64 #s(literal 1/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (fma.f64 #s(literal 2/3 binary64) eps (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 2/3 binary64) (.f64 #s(literal -13/45 binary64) eps))) x) x)) (.f64 x x) eps) (.f64 x x) eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (+ x eps) (+.f64 eps x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ eps (sin x)) (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 2/45 eps) (* -1/3 eps)) (*.f64 #s(literal -13/45 binary64) eps)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 5/6 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))

Calls

3 calls:

21.0ms	eps
13.0ms	x
13.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`eps`
99.2%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes43.0ms (0.3%)

Memory

26.4MiB live, 73.8MiB allocated

Counts

45 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
(*.f64 #s(literal 17/45 binary64) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 5/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 #s(approx (+ (* (* (* x x) eps) 2/3) eps) (.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64))) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (.f64 x x) eps) #s(literal 17/45 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) eps) (fma.f64 #s(literal -2/3 binary64) eps (.f64 #s(literal 1/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (fma.f64 #s(literal 2/3 binary64) eps (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 2/3 binary64) (.f64 #s(literal -13/45 binary64) eps))) x) x)) (.f64 x x) eps) (.f64 x x) eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (+ x eps) (+.f64 eps x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ eps (sin x)) (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 2/45 eps) (* -1/3 eps)) (*.f64 #s(literal -13/45 binary64) eps)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 5/6 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))

Calls

3 calls:

17.0ms	eps
12.0ms	x
12.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`eps`
99.0%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes300.0ms (2.2%)

Memory

-8.0MiB live, 102.9MiB allocated

Counts

44 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
(*.f64 #s(literal 17/45 binary64) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 5/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 #s(approx (+ (* (* (* x x) eps) 2/3) eps) (.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64))) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (.f64 x x) eps) #s(literal 17/45 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) eps) (fma.f64 #s(literal -2/3 binary64) eps (.f64 #s(literal 1/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (fma.f64 #s(literal 2/3 binary64) eps (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 2/3 binary64) (.f64 #s(literal -13/45 binary64) eps))) x) x)) (.f64 x x) eps) (.f64 x x) eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (+ x eps) (+.f64 eps x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ eps (sin x)) (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 2/45 eps) (* -1/3 eps)) (*.f64 #s(literal -13/45 binary64) eps)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 5/6 binary64) x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 #s(approx (/ (pow (sin x) 3) (pow (cos x) 2)) (pow.f64 x #s(literal 3 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))

Calls

3 calls:

269.0ms	x
15.0ms	eps
14.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`eps`
98.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes37.0ms (0.3%)

Memory

-5.7MiB live, 43.7MiB allocated

Counts

40 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
(*.f64 #s(literal 17/45 binary64) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 5/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 #s(approx (+ (* (* (* x x) eps) 2/3) eps) (.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64))) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (.f64 x x) eps) #s(literal 17/45 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) eps) (fma.f64 #s(literal -2/3 binary64) eps (.f64 #s(literal 1/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (fma.f64 #s(literal 2/3 binary64) eps (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 2/3 binary64) (.f64 #s(literal -13/45 binary64) eps))) x) x)) (.f64 x x) eps) (.f64 x x) eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (+ x eps) (+.f64 eps x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ eps (sin x)) (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 2/45 eps) (* -1/3 eps)) (*.f64 #s(literal -13/45 binary64) eps)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))

Calls

3 calls:

13.0ms	eps
11.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
11.0ms	x

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`eps`
98.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes34.0ms (0.2%)

Memory

14.2MiB live, 52.3MiB allocated

Counts

38 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
(*.f64 #s(literal 17/45 binary64) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 5/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 #s(approx (+ (* (* (* x x) eps) 2/3) eps) (.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64))) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (.f64 x x) eps) #s(literal 17/45 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) eps) (fma.f64 #s(literal -2/3 binary64) eps (.f64 #s(literal 1/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (fma.f64 #s(literal 2/3 binary64) eps (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 2/3 binary64) (.f64 #s(literal -13/45 binary64) eps))) x) x)) (.f64 x x) eps) (.f64 x x) eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (+ x eps) (+.f64 eps x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ eps (sin x)) (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 2/45 eps) (* -1/3 eps)) (*.f64 #s(literal -13/45 binary64) eps)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))

Calls

3 calls:

10.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
10.0ms	eps
10.0ms	x

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`eps`
98.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes32.0ms (0.2%)

Memory

4.4MiB live, 43.0MiB allocated

Counts

35 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
(*.f64 #s(literal 17/45 binary64) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 5/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 #s(approx (+ (* (* (* x x) eps) 2/3) eps) (.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64))) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (.f64 x x) eps) #s(literal 17/45 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) eps) (fma.f64 #s(literal -2/3 binary64) eps (.f64 #s(literal 1/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (.f64 #s(literal -1/3 binary64) eps)) (.f64 #s(literal -2/3 binary64) eps)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (fma.f64 #s(literal 2/3 binary64) eps (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 2/3 binary64) (.f64 #s(literal -13/45 binary64) eps))) x) x)) (.f64 x x) eps) (.f64 x x) eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (+ x eps) (+.f64 eps x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ eps (sin x)) (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (+.f64 eps x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))) eps eps))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) eps) (fma.f64 #s(literal -2/3 binary64) eps (*.f64 #s(literal 1/3 binary64) eps))) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps)))

Calls

3 calls:

11.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
10.0ms	x
10.0ms	eps

Results

Accuracy	Segments	Branch
98.3%	1	`x`
98.3%	1	`eps`
98.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.2%)

Memory

-9.4MiB live, 29.4MiB allocated

Counts

22 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
(*.f64 #s(literal 17/45 binary64) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 5/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 #s(approx (+ (* (* (* x x) eps) 2/3) eps) (.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64))) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (.f64 x x) eps) #s(literal 17/45 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)))

Calls

3 calls:

8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms	x
6.0ms	eps

Results

Accuracy	Segments	Branch
98.3%	1	`x`
98.3%	1	`eps`
98.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes31.0ms (0.2%)

Memory

-40.2MiB live, 22.0MiB allocated

Counts

21 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
(*.f64 #s(literal 17/45 binary64) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 5/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 #s(approx (+ (* (* (* x x) eps) 2/3) eps) (.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64))) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 #s(approx (+ (* (- (+ (* 2/45 eps) (* -1/3 eps)) (* -2/3 eps)) (* x x)) (* 2/3 eps)) (.f64 (.f64 (.f64 x x) eps) #s(literal 17/45 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))

Calls

3 calls:

17.0ms	eps
6.0ms	x
6.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
98.2%	1	`x`
98.2%	1	`eps`
98.2%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.1%)

Memory

18.3MiB live, 18.3MiB allocated

Counts

18 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
(*.f64 #s(literal 17/45 binary64) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
(-.f64 #s(approx (+ x eps) (+.f64 eps x)) #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 5/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 #s(approx (+ (* (* (* x x) eps) 2/3) eps) (.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64))) (.f64 x x) eps)))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))

Calls

3 calls:

6.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
6.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
98.1%	1	`x`
98.1%	1	`eps`
98.1%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.1%)

Memory

-14.5MiB live, 24.3MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
(*.f64 #s(literal 17/45 binary64) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) eps eps))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))

Calls

3 calls:

6.0ms	eps
4.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	x

Results

Accuracy	Segments	Branch
98.1%	1	`x`
98.1%	1	`eps`
98.1%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.1%)

Memory

16.6MiB live, 16.6MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
(*.f64 #s(literal 17/45 binary64) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))

Calls

3 calls:

4.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	x
4.0ms	eps

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`eps`
97.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes36.0ms (0.3%)

Memory

-23.1MiB live, 16.2MiB allocated

Counts

9 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
(*.f64 #s(literal 17/45 binary64) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 eps x) eps eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))

Calls

3 calls:

28.0ms	x
4.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms	eps

Results

Accuracy	Segments	Branch
96.8%	1	`x`
96.8%	1	`eps`
96.8%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
(*.f64 #s(literal 17/45 binary64) eps)

Outputs
(*.f64 #s(literal 17/45 binary64) eps)

Calls

3 calls:

3.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
18.0%	1	`x`
18.0%	1	`eps`
18.0%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))
(+.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))

Calls

3 calls:

2.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
8.2%	1	`x`
8.2%	1	`eps`
8.2%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

11.0MiB live, 11.0MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) #s(literal 1/3 binary64)))

(+.f64 eps x)

Outputs
x

Calls

3 calls:

2.0ms	x
2.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms	eps

Results

Accuracy	Segments	Branch
8.1%	1	`x`
8.1%	1	`eps`
8.1%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify46.0ms (0.3%)

Memory

-25.2MiB live, 54.6MiB allocated

Algorithm

1×	egg-herbie

Rules

26×	`-commutative-binary64-.f64`
22×	`+-commutative-binary64-+.f64`
8×	`sub-neg-binary64-neg.f64-+.f64--.f64`
4×	`neg-sub0-binary64--.f64-neg.f64`
4×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	155	784
1	180	784
2	187	784
3	191	784
4	193	784

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) #s(literal 1/3 binary64)) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) #s(approx (+ eps (sin x)) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (*.f64 #s(literal 17/45 binary64) eps) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) eps) (fma.f64 #s(literal -2/3 binary64) eps (.f64 #s(literal 1/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x eps eps))
(*.f64 #s(literal 17/45 binary64) eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (tan x) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) (*.f64 #s(literal 2/3 binary64) x)))
x

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

soundness126.0ms (0.9%)

Memory

2.7MiB live, 41.3MiB allocated

Rules

6 394×	`lower-*.f64`
6 394×	`lower-*.f32`
3 400×	`lower-/.f64`
3 400×	`lower-/.f32`
2 762×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	394	7078
0	394	5910
1	3002	4724
0	8285	4507

Stop Event

1×	iter limit
1×	node limit
1×	saturated

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

start0.0ms (0%)

analyze52.0ms (0.4%)

sample7.5s (54.1%)

explain89.0ms (0.6%)

preprocess25.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify26.0ms (0.2%)

localize25.0ms (0.2%)

series26.0ms (0.2%)

simplify197.0ms (1.4%)

rewrite203.0ms (1.5%)

eval12.0ms (0.1%)

prune9.0ms (0.1%)

simplify273.0ms (2%)

localize321.0ms (2.3%)

series132.0ms (0.9%)

simplify277.0ms (2%)

rewrite258.0ms (1.8%)

eval566.0ms (4.1%)

prune61.0ms (0.4%)

simplify185.0ms (1.3%)

localize384.0ms (2.8%)

series52.0ms (0.4%)

simplify572.0ms (4.1%)

rewrite160.0ms (1.1%)

eval125.0ms (0.9%)

prune35.0ms (0.3%)

simplify166.0ms (1.2%)

localize380.0ms (2.7%)

series164.0ms (1.2%)

simplify204.0ms (1.5%)

rewrite291.0ms (2.1%)

eval138.0ms (1%)

prune78.0ms (0.6%)

regimes94.0ms (0.7%)

regimes52.0ms (0.4%)

regimes43.0ms (0.3%)

regimes300.0ms (2.2%)

regimes37.0ms (0.3%)

regimes34.0ms (0.2%)

regimes32.0ms (0.2%)

regimes22.0ms (0.2%)

regimes31.0ms (0.2%)

regimes18.0ms (0.1%)

regimes16.0ms (0.1%)

regimes12.0ms (0.1%)

regimes36.0ms (0.3%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0%)

simplify46.0ms (0.3%)

soundness126.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18