Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze51.0ms (0.4%)

Memory

24.2MiB live, 62.3MiB 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)

sample6.6s (49.8%)

Memory

-119.8MiB live, 6 456.8MiB allocated

Samples

2.9s	25 608×	0	invalid
674.0ms	5 457×	0	valid
561.0ms	2 799×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 2.9s

const: 655.0ms (22.4% of total)

ival-tan: 594.0ms (20.3% of total)

ival-mult: 275.0ms (9.4% of total)

ival-fabs: 270.0ms (9.2% of total)

ival-<: 238.0ms (8.1% of total)

ival-add: 227.0ms (7.7% of total)

ival-<=: 215.0ms (7.3% of total)

ival-sub: 191.0ms (6.5% of total)

ival-and: 110.0ms (3.8% of total)

adjust: 97.0ms (3.3% of total)

exact: 46.0ms (1.6% of total)

ival-assert: 13.0ms (0.4% of total)

Bogosity

explain99.0ms (0.7%)

Memory

-14.2MiB live, 146.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
233	3	(3.894231937328039e-146 3.6986299966733965e-148)	2	(1.0345554415759243e-25 2.1468675942902987e-27)	`(-.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	234	6
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	231	2
-	3	20

Precision

0.9871794871794872

Recall

0.9914163090128756

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	231	2	0
-	3	4	16

Precision?

0.9708333333333333

Recall?

1.0

Freqs

test

number	freq
0	22
1	233
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

19.0ms	180×	1	valid
16.0ms	332×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-tan: 9.0ms (44.4% of total)

adjust: 4.0ms (19.7% of total)

ival-sub: 3.0ms (14.8% of total)

ival-add: 3.0ms (14.8% of total)

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

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

preprocess275.0ms (2.1%)

Memory

-4.6MiB live, 189.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	43
1	35	43
2	62	43
3	109	43
4	184	43
5	328	43
6	654	43
7	1492	43
8	3439	43
9	4340	43
10	6665	43
11	7416	43
12	7872	43
0	6	7
0	10	7
1	16	7
2	25	7
3	41	7
4	66	7
5	117	7
6	211	7
7	474	7
8	1311	7
9	2274	7
10	3303	7
11	3588	7
12	3771	7
13	3850	7
14	3868	7
15	3874	7
16	3880	7
17	3886	7
18	3892	7
19	3898	7
20	3904	7
21	3910	7
22	3916	7
23	3922	7
24	3928	7
25	7779	7
0	8041	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB 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
▶	60.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify212.0ms (1.6%)

Memory

17.9MiB live, 139.7MiB 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))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	16	18
2	25	18
3	41	18
4	66	18
5	117	18
6	211	18
7	474	18
8	1311	18
9	2274	18
10	3303	18
11	3588	18
12	3771	18
13	3850	18
14	3868	18
15	3874	18
16	3880	18
17	3886	18
18	3892	18
19	3898	18
20	3904	18
21	3910	18
22	3916	18
23	3922	18
24	3928	18
25	7779	18
0	8041	18

Stop Event

1×	iter limit
1×	node limit
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
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(tan.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
(tan.f64 x)

localize26.0ms (0.2%)

Memory

-8.0MiB live, 30.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(tan.f64 x)
accuracy	0.06623300745128272	(tan.f64 (+.f64 x eps))
accuracy	25.320212751734758	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

13.0ms	90×	1	valid
8.0ms	166×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-sub: 5.0ms (37.2% of total)

ival-tan: 5.0ms (37.2% of total)

adjust: 2.0ms (14.9% of total)

ival-add: 2.0ms (14.9% of total)

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

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

series11.0ms (0.1%)

Memory

15.9MiB live, 15.9MiB allocated

Counts

4 → 31

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
(/ (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)))
(+ (* 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)
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)))
(* x (+ 1 (/ eps 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))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* 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))))) (/ (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)))
(* eps (+ 1 (/ x eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	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))
1.0ms	eps	@	-inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
1.0ms	x	@	inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))

simplify180.0ms (1.4%)

Memory

-15.2MiB live, 144.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	970
1	488	910
2	1845	849
0	8454	797

Stop Event

1×	iter limit
1×	node limit

Counts

31 → 29

Calls

Call 1

Inputs
(/ (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)))
(+ (* 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)
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)))
(* x (+ 1 (/ eps 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))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* 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))))) (/ (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)))
(* eps (+ 1 (/ x eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))

Outputs
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(/.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (cos.f64 eps)) (sin.f64 eps)) (cos.f64 eps))
(+ (* 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)))
(fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (cos.f64 eps)) x (/.f64 (sin.f64 eps) (cos.f64 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)))
(fma.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/2 binary64)) x) x (/.f64 (fma.f64 (fma.f64 (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (cos.f64 eps))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 x (/.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (cos.f64 eps)) (sin.f64 eps)) (cos.f64 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)))
(fma.f64 (+.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (cos.f64 eps)) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 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)))
(fma.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) x) x (+.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (cos.f64 eps)) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
eps
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(* x (+ 1 (/ eps x)))
(fma.f64 (/.f64 eps x) x x)
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* 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)))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps eps)
(* 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)))))
(fma.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps)
(* 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)))))
(fma.f64 (fma.f64 (.f64 (-.f64 (.f64 (neg.f64 eps) (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) #s(literal -1/3 binary64) (fma.f64 (.f64 (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (sin.f64 x) (.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) #s(literal -1/3 binary64)))) (cos.f64 x))) (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (+.f64 (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64)))) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps)
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 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)))
(+.f64 (fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps eps) (/.f64 (sin.f64 x) (cos.f64 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)))
(fma.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (+.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) #s(literal 1 binary64))) eps (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))

rewrite214.0ms (1.6%)

Memory

-11.3MiB live, 146.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	53	16
2	440	16
3	6608	16
0	8588	16

Stop Event

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

Counts

4 → 158

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
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64)) (sin.f64 x) (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)))) (*.f64 (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64)) (cos.f64 x)))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 (+.f64 (+.f64 eps x) x))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x))))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64))))
(*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (/.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))))
(*.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (/.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(/.f64 (/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (.f64 (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64)) (sin.f64 x))) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
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(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 (-.f64 eps x) eps (.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (.f64 x x))))
(fma.f64 (fabs.f64 x) (/.f64 (fabs.f64 x) (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(fma.f64 (neg.f64 x) (/.f64 (neg.f64 x) (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(fma.f64 (.f64 eps eps) (/.f64 eps (fma.f64 (-.f64 eps x) eps (.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (.f64 x x) (/.f64 x (fma.f64 (-.f64 eps x) eps (.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 eps (/.f64 (.f64 eps eps) (fma.f64 (-.f64 eps x) eps (.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(fma.f64 x (/.f64 (.f64 x x) (fma.f64 (-.f64 eps x) eps (.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 (.f64 x (/.f64 x (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (.f64 x x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (.f64 x x))))
(+.f64 (.f64 x (/.f64 x (-.f64 x eps))) (/.f64 (.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(+.f64 eps x)
(+.f64 x eps)
(/.f64 (neg.f64 (+.f64 #s(literal 0 binary64) (tan.f64 x))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 x))) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (sin.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64))) (cos.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64))))
(/.f64 (+.f64 #s(literal 0 binary64) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 x))))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
(neg.f64 (neg.f64 (tan.f64 x)))
(tan.f64 (+.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64)) (PI.f64)))
(tan.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64)))
(tan.f64 (+.f64 (PI.f64) x))
(tan.f64 x)
(+.f64 (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (tan.f64 x)))) (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (tan.f64 x)))))

eval25.0ms (0.2%)

Memory: 31.6MiB live, 31.6MiB allocated
Compiler: Compiled 5 935 to 840 computations (85.8% saved)

prune12.0ms (0.1%)

Memory

-16.4MiB live, 20.9MiB allocated

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	172	11	183
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	172	12	184

Accuracy

100.0%

Counts

184 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	36.8%	(fma.f64 (tan.f64 (+.f64 eps x)) (/.f64 (tan.f64 (+.f64 eps x)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (/.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))))
▶	60.4%	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
	60.3%	(/.f64 (-.f64 (.f64 (+.f64 #s(literal 0 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (tan.f64 (+.f64 eps x)))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 (+.f64 eps x)))) (cos.f64 x)))
▶	60.3%	(/.f64 (-.f64 (.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
	60.4%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	59.7%	(-.f64 (tan.f64 (-.f64 (.f64 x (/.f64 x (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x))
▶	60.4%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	60.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	100.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))
	99.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps eps))
	99.2%	#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))
▶	97.9%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 605 to 316 computations (47.8% saved)

simplify144.0ms (1.1%)

Memory

19.3MiB live, 137.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 (+.f64 eps x))
cost-diff	0	(*.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x)))
cost-diff	2	(-.f64 (.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x))))
cost-diff	9	(/.f64 (-.f64 (.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
cost-diff	0	(sin.f64 (-.f64 (+.f64 eps x) x))
cost-diff	0	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x)))
cost-diff	0	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
cost-diff	4	(-.f64 (+.f64 eps x) x)
cost-diff	0	(/.f64 (sin.f64 x) (cos.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)) (/.f64 (sin.f64 x) (cos.f64 x)))
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	1	(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64))
cost-diff	1	(fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64))
cost-diff	6	(fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
cost-diff	10	(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	740
0	107	732
1	197	694
2	536	658
3	2392	585
0	8629	584

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

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

localize234.0ms (1.8%)

Memory

-8.6MiB live, 227.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(*.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x)))
accuracy	0.03904044311272992	(cos.f64 (+.f64 eps x))
accuracy	0.04460098638627304	(sin.f64 (+.f64 eps x))
accuracy	25.314335112939414	(-.f64 (.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x))))
accuracy	0.0078125	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x)))
accuracy	0.01171875	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
accuracy	0.03904044311272992	(cos.f64 (+.f64 eps x))
accuracy	25.379876922698482	(-.f64 (+.f64 eps x) x)
accuracy	0.0	(cos.f64 x)
accuracy	0.01171875	(/.f64 (sin.f64 x) (cos.f64 x))
accuracy	0.06623300745128272	(tan.f64 (+.f64 x eps))
accuracy	25.320212751734758	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
accuracy	0.0	(/.f64 (sin.f64 eps) (cos.f64 eps))
accuracy	0.0	(sin.f64 eps)
accuracy	0.0	(cos.f64 eps)
accuracy	1.3696263764930934	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
accuracy	0.1875	(fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
accuracy	0.21484375	(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
accuracy	0.34765625	(.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps)
accuracy	0.98046875	(fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64))

Samples

113.0ms	99×	1	valid
67.0ms	156×	0	valid
2.0ms	1×	2	valid

Compiler

Compiled 701 to 63 computations (91% saved)

Precisions

Click to see histograms. Total time spent on operations: 147.0ms

ival-div: 45.0ms (30.7% of total)

ival-mult: 28.0ms (19.1% of total)

ival-add: 16.0ms (10.9% of total)

adjust: 12.0ms (8.2% of total)

ival-sin: 9.0ms (6.1% of total)

ival-cos: 8.0ms (5.4% of total)

const: 7.0ms (4.8% of total)

ival-pow2: 7.0ms (4.8% of total)

ival-sub: 6.0ms (4.1% of total)

ival-tan: 5.0ms (3.4% of total)

ival-neg: 3.0ms (2% of total)

exact: 1.0ms (0.7% of total)

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

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

series121.0ms (0.9%)

Memory

-9.2MiB live, 71.7MiB allocated

Counts

24 → 145

Calls

Call 1

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

Outputs
-1/2
(- (* -4/3 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)
(* -5/6 (pow x 2))
(* (pow x 2) (- (* -13/18 (pow x 2)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* -10/27 (pow x 2)) 13/18)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -373/1890 (pow x 2)) 10/27)) 13/18)) 5/6))
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)))))))
-1
(- (* -1 (pow x 2)) 1)
(- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1)) 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)))
(+ (* 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)
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))))))))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(+ (* x (+ (* x (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ (* x (+ (* x (+ (* -1 (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (cos eps)) (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(* -1 (sin eps))
(+ (* -1 (sin eps)) (* (pow x 4) (- (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* -1/3 (sin eps)))))
(+ (* -1 (sin eps)) (* (pow x 4) (- (+ (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* (pow x 2) (- (* -1 (+ (* -1/24 (sin eps)) (* -1/360 (sin eps)))) (* -1 (+ (* -1/36 (sin eps)) (* -1/60 (sin eps))))))) (* -1/3 (sin eps)))))
(+ (* -1 (sin eps)) (* (pow x 4) (- (+ (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* (pow x 2) (- (+ (* -1 (+ (* -1/24 (sin eps)) (* -1/360 (sin eps)))) (* (pow x 2) (- (* -1 (+ (* 1/20160 (sin eps)) (+ (* 1/720 (sin eps)) (* 1/576 (sin eps))))) (* -1 (+ (* 1/2520 (sin eps)) (* 1/360 (sin eps))))))) (* -1 (+ (* -1/36 (sin eps)) (* -1/60 (sin eps))))))) (* -1/3 (sin eps)))))
(+ (* -1 (sin eps)) (* -1 (* x (cos eps))))
(+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (sin eps)))))
(+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (* x (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))))))))))
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps))))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/135 (pow x 2)) 1/18))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/135 (* -1/1890 (pow x 2)))) 1/18))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))
(+ (* 1/6 (pow (sin x) 2)) (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)
(- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin x) (cos x))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (cos (+ eps x)))
(* -1 (/ (- (* -1 (* (cos x) (sin (+ eps x)))) (* -1 (* (cos (+ eps x)) (sin x)))) (* (cos x) (cos (+ eps x)))))
(- (* -1 (* (cos x) (sin (+ eps x)))) (* -1 (* (cos (+ eps x)) (sin x))))
(* -1 (* (cos x) (sin (+ eps x))))
(sin (+ eps x))
(* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
(* 1/6 (pow (sin x) 2))
(cos x)
(cos (+ eps x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (cos (- eps (* -1 x))))
(* -1 (/ (- (* -1 (* (cos x) (sin (- eps (* -1 x))))) (* -1 (* (cos (- eps (* -1 x))) (sin x)))) (* (cos x) (cos (- eps (* -1 x))))))
(- (* -1 (* (cos x) (sin (- eps (* -1 x))))) (* -1 (* (cos (- eps (* -1 x))) (sin x))))
(* -1 (* (cos x) (sin (- eps (* -1 x)))))
(sin (- eps (* -1 x)))
(cos (- eps (* -1 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 (* 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 (+ 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 (* -1/2 (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))))) (/ (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)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (cos x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* -1 (/ (* eps (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 2)))
(* eps (+ (* -1 (/ (* eps (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)))) (pow (cos x) 3))) (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))))
(* eps (+ (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* eps (+ (* -1 (* eps (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3)))))))
(* eps (+ (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* eps (+ (* -1 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))) (* eps (+ (* -1 (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (* -1 (/ (* (sin x) (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))) (* 1/6 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))))))))))))
(* eps (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)))
(* eps (- (+ (* -1 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))) (pow (sin x) 2)))
(* eps (- (+ (* -1 (pow (cos x) 2)) (* (pow eps 2) (- (+ (* 1/6 (pow (cos x) 2)) (* (pow eps 2) (- (* -1/120 (pow (cos x) 2)) (* 1/120 (pow (sin x) 2))))) (* -1/6 (pow (sin x) 2))))) (pow (sin x) 2)))
(* eps (- (+ (* -1 (pow (cos x) 2)) (* (pow eps 2) (- (+ (* 1/6 (pow (cos x) 2)) (* (pow eps 2) (- (+ (* -1/120 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/5040 (pow (cos x) 2)) (* -1/5040 (pow (sin x) 2))))) (* 1/120 (pow (sin x) 2))))) (* -1/6 (pow (sin x) 2))))) (pow (sin x) 2)))
(* -1 (* (cos x) (sin x)))
(+ (* -1 (* eps (pow (cos x) 2))) (* -1 (* (cos x) (sin x))))
(+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (cos x) 2)) (* 1/2 (* eps (* (cos x) (sin x)))))))
(+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (cos x) 2)) (* eps (+ (* 1/6 (* eps (pow (cos x) 2))) (* 1/2 (* (cos x) (sin x))))))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(* eps (+ 1 (/ x eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(sin (neg (* -1 eps)))
(* -1 (/ (- (* -1 (* (cos x) (sin (- x (* -1 eps))))) (* -1 (* (cos (- x (* -1 eps))) (sin x)))) (* (cos x) (cos (- x (* -1 eps))))))
(- (* -1 (* (cos x) (sin (- x (* -1 eps))))) (* -1 (* (cos (- x (* -1 eps))) (sin x))))
(* -1 (* (cos x) (sin (- x (* -1 eps)))))
(sin (- x (* -1 eps)))
(cos (- x (* -1 eps)))

Calls

6 calls:

Time	Variable		Point	Expression
63.0ms	x	@	inf	((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (+ eps x) x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (sin (+ eps x)) (neg (cos x))) (sin (+ eps x)) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (* (pow (sin x) 2) 1/6) (cos x) (cos (+ eps x)))
16.0ms	eps	@	0	((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (+ eps x) x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (sin (+ eps x)) (neg (cos x))) (sin (+ eps x)) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (* (pow (sin x) 2) 1/6) (cos x) (cos (+ eps x)))
14.0ms	eps	@	-inf	((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (+ eps x) x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (sin (+ eps x)) (neg (cos x))) (sin (+ eps x)) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (* (pow (sin x) 2) 1/6) (cos x) (cos (+ eps x)))
9.0ms	x	@	-inf	((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (+ eps x) x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (sin (+ eps x)) (neg (cos x))) (sin (+ eps x)) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (* (pow (sin x) 2) 1/6) (cos x) (cos (+ eps x)))
9.0ms	x	@	0	((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (+ eps x) x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (sin (+ eps x)) (neg (cos x))) (sin (+ eps x)) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (* (pow (sin x) 2) 1/6) (cos x) (cos (+ eps x)))

simplify201.0ms (1.5%)

Memory

18.8MiB live, 135.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	716	3417
1	2383	3212
0	8665	3041

Stop Event

1×	iter limit
1×	node limit

Counts

145 → 143

Calls

Call 1

Inputs
-1/2
(- (* -4/3 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)
(* -5/6 (pow x 2))
(* (pow x 2) (- (* -13/18 (pow x 2)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* -10/27 (pow x 2)) 13/18)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -373/1890 (pow x 2)) 10/27)) 13/18)) 5/6))
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)))))))
-1
(- (* -1 (pow x 2)) 1)
(- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1)) 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)))
(+ (* 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)
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))))))))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(+ (* x (+ (* x (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ (* x (+ (* x (+ (* -1 (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (cos eps)) (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(* -1 (sin eps))
(+ (* -1 (sin eps)) (* (pow x 4) (- (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* -1/3 (sin eps)))))
(+ (* -1 (sin eps)) (* (pow x 4) (- (+ (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* (pow x 2) (- (* -1 (+ (* -1/24 (sin eps)) (* -1/360 (sin eps)))) (* -1 (+ (* -1/36 (sin eps)) (* -1/60 (sin eps))))))) (* -1/3 (sin eps)))))
(+ (* -1 (sin eps)) (* (pow x 4) (- (+ (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* (pow x 2) (- (+ (* -1 (+ (* -1/24 (sin eps)) (* -1/360 (sin eps)))) (* (pow x 2) (- (* -1 (+ (* 1/20160 (sin eps)) (+ (* 1/720 (sin eps)) (* 1/576 (sin eps))))) (* -1 (+ (* 1/2520 (sin eps)) (* 1/360 (sin eps))))))) (* -1 (+ (* -1/36 (sin eps)) (* -1/60 (sin eps))))))) (* -1/3 (sin eps)))))
(+ (* -1 (sin eps)) (* -1 (* x (cos eps))))
(+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (sin eps)))))
(+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (* x (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))))))))))
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps))))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/135 (pow x 2)) 1/18))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/135 (* -1/1890 (pow x 2)))) 1/18))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))
(+ (* 1/6 (pow (sin x) 2)) (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)
(- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin x) (cos x))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (cos (+ eps x)))
(* -1 (/ (- (* -1 (* (cos x) (sin (+ eps x)))) (* -1 (* (cos (+ eps x)) (sin x)))) (* (cos x) (cos (+ eps x)))))
(- (* -1 (* (cos x) (sin (+ eps x)))) (* -1 (* (cos (+ eps x)) (sin x))))
(* -1 (* (cos x) (sin (+ eps x))))
(sin (+ eps x))
(* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
(* 1/6 (pow (sin x) 2))
(cos x)
(cos (+ eps x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (cos (- eps (* -1 x))))
(* -1 (/ (- (* -1 (* (cos x) (sin (- eps (* -1 x))))) (* -1 (* (cos (- eps (* -1 x))) (sin x)))) (* (cos x) (cos (- eps (* -1 x))))))
(- (* -1 (* (cos x) (sin (- eps (* -1 x))))) (* -1 (* (cos (- eps (* -1 x))) (sin x))))
(* -1 (* (cos x) (sin (- eps (* -1 x)))))
(sin (- eps (* -1 x)))
(cos (- eps (* -1 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 (* 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 (+ 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 (* -1/2 (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))))) (/ (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)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (cos x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* -1 (/ (* eps (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 2)))
(* eps (+ (* -1 (/ (* eps (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)))) (pow (cos x) 3))) (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))))
(* eps (+ (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* eps (+ (* -1 (* eps (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3)))))))
(* eps (+ (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* eps (+ (* -1 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))) (* eps (+ (* -1 (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (* -1 (/ (* (sin x) (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))) (* 1/6 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))))))))))))
(* eps (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)))
(* eps (- (+ (* -1 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))) (pow (sin x) 2)))
(* eps (- (+ (* -1 (pow (cos x) 2)) (* (pow eps 2) (- (+ (* 1/6 (pow (cos x) 2)) (* (pow eps 2) (- (* -1/120 (pow (cos x) 2)) (* 1/120 (pow (sin x) 2))))) (* -1/6 (pow (sin x) 2))))) (pow (sin x) 2)))
(* eps (- (+ (* -1 (pow (cos x) 2)) (* (pow eps 2) (- (+ (* 1/6 (pow (cos x) 2)) (* (pow eps 2) (- (+ (* -1/120 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/5040 (pow (cos x) 2)) (* -1/5040 (pow (sin x) 2))))) (* 1/120 (pow (sin x) 2))))) (* -1/6 (pow (sin x) 2))))) (pow (sin x) 2)))
(* -1 (* (cos x) (sin x)))
(+ (* -1 (* eps (pow (cos x) 2))) (* -1 (* (cos x) (sin x))))
(+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (cos x) 2)) (* 1/2 (* eps (* (cos x) (sin x)))))))
(+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (cos x) 2)) (* eps (+ (* 1/6 (* eps (pow (cos x) 2))) (* 1/2 (* (cos x) (sin x))))))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(* eps (+ 1 (/ x eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(sin (neg (* -1 eps)))
(* -1 (/ (- (* -1 (* (cos x) (sin (- x (* -1 eps))))) (* -1 (* (cos (- x (* -1 eps))) (sin x)))) (* (cos x) (cos (- x (* -1 eps))))))
(- (* -1 (* (cos x) (sin (- x (* -1 eps))))) (* -1 (* (cos (- x (* -1 eps))) (sin x))))
(* -1 (* (cos x) (sin (- x (* -1 eps)))))
(sin (- x (* -1 eps)))
(cos (- x (* -1 eps)))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* -4/3 (pow x 2)) 1/2)
(-.f64 (.f64 (.f64 x x) #s(literal -4/3 binary64)) #s(literal 1/2 binary64))
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)
(-.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -17/9 binary64) (.f64 x x)) #s(literal 4/3 binary64)) x) x) #s(literal 1/2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)
(-.f64 (.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -248/135 binary64) (.f64 x x)) #s(literal 17/9 binary64)) x) x) #s(literal 4/3 binary64)) (.f64 x x)) #s(literal 1/2 binary64))
(* -5/6 (pow x 2))
(.f64 #s(literal -5/6 binary64) (.f64 x x))
(* (pow x 2) (- (* -13/18 (pow x 2)) 5/6))
(.f64 (.f64 (-.f64 (.f64 #s(literal -13/18 binary64) (.f64 x x)) #s(literal 5/6 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (- (* -10/27 (pow x 2)) 13/18)) 5/6))
(.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -10/27 binary64) (.f64 x x)) #s(literal 13/18 binary64)) x) x) #s(literal 5/6 binary64)) (.f64 x x))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -373/1890 (pow x 2)) 10/27)) 13/18)) 5/6))
(.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -373/1890 binary64) (.f64 x x)) #s(literal 10/27 binary64)) x) x) #s(literal 13/18 binary64)) (.f64 x x)) #s(literal 5/6 binary64)) (.f64 x x))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 4/3 (pow x 2)))
(fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 248/135 binary64) (.f64 x x) #s(literal 17/9 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
-1
#s(literal -1 binary64)
(- (* -1 (pow x 2)) 1)
(-.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)
(-.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -2/3 binary64) (.f64 x x)) #s(literal 1 binary64)) x) x) #s(literal 1 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1)) 1)
(-.f64 (.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -17/45 binary64) (.f64 x x)) #s(literal 2/3 binary64)) x) x) #s(literal 1 binary64)) (.f64 x x)) #s(literal 1 binary64))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* 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)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 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)))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) #s(literal 1/2 binary64))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 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)))
(fma.f64 (fma.f64 x (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) x (/.f64 (sin.f64 eps) (cos.f64 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)))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) #s(literal 1/6 binary64))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps))) x (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
eps
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (*.f64 (fma.f64 (sin.f64 eps) (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 #s(literal 2/3 binary64) (cos.f64 eps)) (/.f64 (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (cos.f64 eps))) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x) (/.f64 (sin.f64 eps) (cos.f64 eps))) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal -1/2 binary64) (pow.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (-.f64 (fma.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal -1/3 binary64) (/.f64 (.f64 (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal -1/2 binary64) (pow.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) #s(literal 3 binary64))) (sin.f64 eps)) (cos.f64 eps))) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 (.f64 (sin.f64 eps) #s(literal -1/2 binary64)) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(sin eps)
(sin.f64 eps)
(+ (* x (+ (* x (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (+ (* x (+ (* x (+ (* -1 (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (cos eps)) (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
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(+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (sin eps)))))
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(*.f64 #s(literal 1/3 binary64) eps)
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(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* -1/18 (pow x 2))))
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(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/135 (* -1/1890 (pow x 2)))) 1/18))))
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1
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(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(* x (+ 1 (/ eps x)))
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(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
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(/ (sin eps) (cos (+ eps x)))
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(* -1 (* (cos x) (sin (+ eps x))))
(*.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x)))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
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(* 1/6 (pow (sin x) 2))
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
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(cos.f64 x)
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
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(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/ (sin eps) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 eps x)))
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(- (* -1 (* (cos x) (sin (- eps (* -1 x))))) (* -1 (* (cos (- eps (* -1 x))) (sin x))))
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(* -1 (* (cos x) (sin (- eps (* -1 x)))))
(*.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x)))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
(* 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)))))
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(* 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)))))
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(* 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)))))
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(* eps (+ 1 (* 1/3 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
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(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
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(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
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(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
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(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 x)))
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(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
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(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
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(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
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(/ eps (cos x))
(/.f64 eps (cos.f64 x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
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(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
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(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
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(* -1 (/ (* eps (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 2)))
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(* eps (+ (* -1 (/ (* eps (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)))) (pow (cos x) 3))) (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))))
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(* eps (+ (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* eps (+ (* -1 (* eps (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3)))))))
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(* eps (+ (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* eps (+ (* -1 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))) (* eps (+ (* -1 (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (* -1 (/ (* (sin x) (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))) (* 1/6 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))))))))))))
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(* eps (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)))
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(* eps (- (+ (* -1 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))) (pow (sin x) 2)))
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(* eps (- (+ (* -1 (pow (cos x) 2)) (* (pow eps 2) (- (+ (* 1/6 (pow (cos x) 2)) (* (pow eps 2) (- (* -1/120 (pow (cos x) 2)) (* 1/120 (pow (sin x) 2))))) (* -1/6 (pow (sin x) 2))))) (pow (sin x) 2)))
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(* eps (- (+ (* -1 (pow (cos x) 2)) (* (pow eps 2) (- (+ (* 1/6 (pow (cos x) 2)) (* (pow eps 2) (- (+ (* -1/120 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/5040 (pow (cos x) 2)) (* -1/5040 (pow (sin x) 2))))) (* 1/120 (pow (sin x) 2))))) (* -1/6 (pow (sin x) 2))))) (pow (sin x) 2)))
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(* -1 (* (cos x) (sin x)))
(*.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
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(+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (cos x) 2)) (* 1/2 (* eps (* (cos x) (sin x)))))))
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(+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (cos x) 2)) (* eps (+ (* 1/6 (* eps (pow (cos x) 2))) (* 1/2 (* (cos x) (sin x))))))))
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(sin x)
(sin.f64 x)
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(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (-.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps (cos.f64 x))
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(* eps (+ 1 (/ x eps)))
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(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
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(* -1 (* eps (- (* -1 (/ x eps)) 1)))
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(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 eps x)))
(sin (neg (* -1 eps)))
(sin.f64 eps)
(* -1 (/ (- (* -1 (* (cos x) (sin (- x (* -1 eps))))) (* -1 (* (cos (- x (* -1 eps))) (sin x)))) (* (cos x) (cos (- x (* -1 eps))))))
(/.f64 (neg.f64 (/.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x)) (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x))) (cos.f64 x))) (cos.f64 (+.f64 eps x)))
(- (* -1 (* (cos x) (sin (- x (* -1 eps))))) (* -1 (* (cos (- x (* -1 eps))) (sin x))))
(fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x)) (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)))
(* -1 (* (cos x) (sin (- x (* -1 eps)))))
(*.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x)))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))

rewrite173.0ms (1.3%)

Memory

-3.3MiB live, 190.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	313
0	88	275
1	322	229
2	2674	229
0	8568	223

Stop Event

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

Counts

24 → 440

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (pow.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)))) (neg.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64))) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.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)) (cos.f64 x)) (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (/.f64 (pow.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))
(-.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal 1/2 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))))
(-.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (.f64 (neg.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) #s(literal -1/2 binary64)))
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eval150.0ms (1.1%)

Memory: 20.3MiB live, 208.3MiB allocated
Compiler: Compiled 41 612 to 4 080 computations (90.2% saved)

prune52.0ms (0.4%)

Memory

-43.2MiB live, 67.3MiB allocated

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	768	15	783
Fresh	6	0	6
Picked	4	1	5
Done	0	1	1
Total	778	17	795

Accuracy

100.0%

Counts

795 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.1%	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
	60.0%	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
▶	99.9%	(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
	99.2%	(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) (cos.f64 x))
✓	60.4%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
▶	59.9%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
✓	60.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	59.9%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
	59.8%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
	59.5%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)))
	99.9%	#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
	99.2%	#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	99.8%	#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (*.f64 (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
▶	3.6%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
	3.7%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
	97.9%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
▶	97.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))

Compiler

Compiled 647 to 442 computations (31.7% saved)

simplify129.0ms (1%)

Memory

15.5MiB live, 127.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
cost-diff	2	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
cost-diff	0	(+.f64 eps (PI.f64))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
cost-diff	1	(+.f64 (+.f64 eps (PI.f64)) (PI.f64))
cost-diff	3	(tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64)))
cost-diff	0	(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
cost-diff	2	(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
cost-diff	0	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x)))
cost-diff	0	(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	356
0	86	352
1	151	342
2	358	336
3	1100	330
4	4217	330
5	7925	330
0	8001	323

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
eps
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
x
(cos.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
(*.f64 eps eps)
eps
#s(literal 1/3 binary64)
#s(literal 1 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
(tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64)))
(+.f64 (+.f64 eps (PI.f64)) (PI.f64))
(+.f64 eps (PI.f64))
eps
(PI.f64)
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64))
#s(literal 17/315 binary64)
(*.f64 x x)
#s(literal 2/15 binary64)
#s(literal 1/3 binary64)
#s(literal 1 binary64)
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(sin.f64 x)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
#s(literal 1 binary64)

Outputs
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 x eps)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
eps
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 x eps))
(+.f64 eps x)
(+.f64 x eps)
x
(cos.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))
#s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
#s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(*.f64 eps eps)
eps
#s(literal 1/3 binary64)
#s(literal 1 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64)))
(tan.f64 eps)
(+.f64 (+.f64 eps (PI.f64)) (PI.f64))
(fma.f64 #s(literal 2 binary64) (PI.f64) eps)
(+.f64 eps (PI.f64))
(+.f64 (PI.f64) eps)
eps
(PI.f64)
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (/ (sin x) (cos x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64))
(fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))
#s(literal 17/315 binary64)
(*.f64 x x)
#s(literal 2/15 binary64)
#s(literal 1/3 binary64)
#s(literal 1 binary64)
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(sin.f64 x)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
#s(literal 1 binary64)

localize598.0ms (4.5%)

Memory

-3.6MiB live, 517.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.06623300745128272	(tan.f64 (+.f64 x eps))
accuracy	0.2265625	(.f64 #s(literal 1/24 binary64) (.f64 x x))
accuracy	0.5866142723295996	#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy	25.320212751734758	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
accuracy	0.01953125	(fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64))
accuracy	0.06623300745128272	(tan.f64 (+.f64 x eps))
accuracy	0.6099429427736986	#s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
accuracy	25.320212751734758	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
accuracy	0.0078125	(+.f64 (+.f64 eps (PI.f64)) (PI.f64))
accuracy	0.01171875	(+.f64 eps (PI.f64))
accuracy	1.3696263764930934	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
accuracy	61.29208674699038	(tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64)))
accuracy	0.0	(*.f64 eps eps)
accuracy	0.0	#s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
accuracy	0.0078125	(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)
accuracy	1.3696263764930934	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
accuracy	0.0	#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
accuracy	0.0078125	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x)))
accuracy	0.01171875	(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
accuracy	0.03904044311272992	(cos.f64 (+.f64 eps x))

Samples

381.0ms	101×	2	valid
172.0ms	149×	1	valid
2.0ms	6×	0	valid

Compiler

Compiled 253 to 47 computations (81.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 471.0ms

ival-tan: 319.0ms (67.7% of total)

adjust: 52.0ms (11% of total)

ival-add: 24.0ms (5.1% of total)

ival-mult: 22.0ms (4.7% of total)

const: 20.0ms (4.2% of total)

ival-div: 9.0ms (1.9% of total)

ival-cos: 8.0ms (1.7% of total)

ival-sub: 7.0ms (1.5% of total)

ival-sin: 7.0ms (1.5% of total)

ival-pi: 3.0ms (0.6% of total)

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

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

exact: 0.0ms (0% of total)

series19.0ms (0.1%)

Memory

23.8MiB live, 23.8MiB allocated

Counts

24 → 105

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
(tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64)))
(+.f64 (+.f64 eps (PI.f64)) (PI.f64))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
(+.f64 eps (PI.f64))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(cos.f64 (+.f64 eps x))
(*.f64 eps eps)
#s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
(fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(.f64 #s(literal 1/24 binary64) (.f64 x x))

Outputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(+ (* 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)))
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))))))))
(+ (* 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)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
1/3
(+ 1/3 (* 2/15 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* 1/24 (pow x 2))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (cos (+ eps x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* 17/315 (pow x 7))
(* (pow x 7) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 17/315 (+ (/ 1/3 (pow x 4)) (+ (* 2/15 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin x) (cos x))
(cos (+ eps x))
(* 17/315 (pow x 4))
(* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))
(cos x)
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (cos (- eps (* -1 x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 2/15 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 17/315)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/3 (/ 1 (pow x 2))) (pow x 4))) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(cos (- eps (* -1 x)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (cos x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* 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))))
(* eps (+ 1 (* 1/3 (pow eps 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 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))))))))
(+ 1 (* 1/3 (pow eps 2)))
(/ (sin (* 2 (PI))) (cos (* 2 (PI))))
(+ (* eps (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
(+ (* eps (- (+ 1 (/ (* eps (* (sin (* 2 (PI))) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2)))))) (cos (* 2 (PI))))) (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin (* 2 (PI))) 2) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (pow (cos (* 2 (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (* 1/6 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2)))))))) (* -1 (/ (* (sin (* 2 (PI))) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (cos (* 2 (PI)))))))) (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
(* 2 (PI))
(+ eps (* 2 (PI)))
(PI)
(+ eps (PI))
(+ (* 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)))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(pow eps 2)
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* 1/3 (pow eps 2))
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2))))
(/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI)))))
(* eps (+ 1 (* 2 (/ (PI) eps))))
(* eps (+ 1 (/ (PI) eps)))
(* eps (+ 1 (/ x eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(sin (neg (* -1 eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- (* 2 (PI)) (* -1 eps))) (cos (- (* 2 (PI)) (* -1 eps))))
(* -1 (* eps (- (* -2 (/ (PI) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (PI) eps)) 1)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(cos (- x (* -1 eps)))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	-inf	((/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (tan (+ (+ eps (PI)) (PI))) (+ (+ eps (PI)) (PI)) (- (tan (+ x eps)) (tan x)) (+ eps (PI)) (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (/ (sin x) (cos x)) (cos (+ eps x)) (* eps eps) (/ (sin x) (cos x)) (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (cos x) (* 1/24 (* x x)))
3.0ms	eps	@	inf	((/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (tan (+ (+ eps (PI)) (PI))) (+ (+ eps (PI)) (PI)) (- (tan (+ x eps)) (tan x)) (+ eps (PI)) (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (/ (sin x) (cos x)) (cos (+ eps x)) (* eps eps) (/ (sin x) (cos x)) (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (cos x) (* 1/24 (* x x)))
3.0ms	x	@	inf	((/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (tan (+ (+ eps (PI)) (PI))) (+ (+ eps (PI)) (PI)) (- (tan (+ x eps)) (tan x)) (+ eps (PI)) (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (/ (sin x) (cos x)) (cos (+ eps x)) (* eps eps) (/ (sin x) (cos x)) (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (cos x) (* 1/24 (* x x)))
3.0ms	eps	@	0	((/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (tan (+ (+ eps (PI)) (PI))) (+ (+ eps (PI)) (PI)) (- (tan (+ x eps)) (tan x)) (+ eps (PI)) (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (/ (sin x) (cos x)) (cos (+ eps x)) (* eps eps) (/ (sin x) (cos x)) (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (cos x) (* 1/24 (* x x)))
3.0ms	x	@	-inf	((/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (tan (+ (+ eps (PI)) (PI))) (+ (+ eps (PI)) (PI)) (- (tan (+ x eps)) (tan x)) (+ eps (PI)) (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (- (tan (+ x eps)) (/ (sin x) (cos x))) (/ (sin x) (cos x)) (cos (+ eps x)) (* eps eps) (/ (sin x) (cos x)) (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (cos x) (* 1/24 (* x x)))

simplify194.0ms (1.5%)

Memory

-10.0MiB live, 144.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	466	2298
1	1497	2149
2	5330	1926
0	8474	1828

Stop Event

1×	iter limit
1×	node limit

Counts

105 → 103

Calls

Call 1

Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(+ (* 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)))
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))))))))
(+ (* 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)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
1/3
(+ 1/3 (* 2/15 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* 1/24 (pow x 2))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (cos (+ eps x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* 17/315 (pow x 7))
(* (pow x 7) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 17/315 (+ (/ 1/3 (pow x 4)) (+ (* 2/15 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin x) (cos x))
(cos (+ eps x))
(* 17/315 (pow x 4))
(* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))
(cos x)
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (cos (- eps (* -1 x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 2/15 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 17/315)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/3 (/ 1 (pow x 2))) (pow x 4))) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(cos (- eps (* -1 x)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (cos x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* 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))))
(* eps (+ 1 (* 1/3 (pow eps 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 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))))))))
(+ 1 (* 1/3 (pow eps 2)))
(/ (sin (* 2 (PI))) (cos (* 2 (PI))))
(+ (* eps (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
(+ (* eps (- (+ 1 (/ (* eps (* (sin (* 2 (PI))) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2)))))) (cos (* 2 (PI))))) (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin (* 2 (PI))) 2) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (pow (cos (* 2 (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (* 1/6 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2)))))))) (* -1 (/ (* (sin (* 2 (PI))) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (cos (* 2 (PI)))))))) (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
(* 2 (PI))
(+ eps (* 2 (PI)))
(PI)
(+ eps (PI))
(+ (* 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)))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(pow eps 2)
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* 1/3 (pow eps 2))
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2))))
(/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI)))))
(* eps (+ 1 (* 2 (/ (PI) eps))))
(* eps (+ 1 (/ (PI) eps)))
(* eps (+ 1 (/ x eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(sin (neg (* -1 eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- (* 2 (PI)) (* -1 eps))) (cos (- (* 2 (PI)) (* -1 eps))))
(* -1 (* eps (- (* -2 (/ (PI) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (PI) eps)) 1)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(cos (- x (* -1 eps)))

Outputs
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (cos.f64 eps)) (sin.f64 eps)) (cos.f64 eps))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (*.f64 (fma.f64 (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 2/3 binary64) (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x) (/.f64 (sin.f64 eps) (cos.f64 eps))) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (neg.f64 x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (-.f64 (fma.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal -1/3 binary64) (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(sin eps)
(sin.f64 eps)
(+ (* 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)))
(fma.f64 (/.f64 (fma.f64 (*.f64 (sin.f64 eps) x) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (cos.f64 eps)) x (/.f64 (sin.f64 eps) (cos.f64 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)))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 eps)) (sin.f64 eps) (.f64 (neg.f64 x) (+.f64 (fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 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)))
(fma.f64 (+.f64 (/.f64 (fma.f64 (*.f64 (sin.f64 eps) x) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (cos.f64 eps)) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 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)))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 eps)) (sin.f64 eps) (.f64 (neg.f64 x) (+.f64 (fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal 1/6 binary64)))) x (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
eps
(+ eps x)
(+.f64 x eps)
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(fma.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 eps)) x) (sin.f64 eps)) x (cos.f64 eps))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) x) (sin.f64 eps)) x (cos.f64 eps))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 2/15 (pow x 2)))
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64))
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(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps (cos.f64 x))
(pow eps 2)
(*.f64 eps eps)
(* 1/3 (pow eps 3))
(*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2))))
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
(/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI)))))
(/.f64 (sin.f64 eps) (neg.f64 (neg.f64 (cos.f64 eps))))
(* eps (+ 1 (* 2 (/ (PI) eps))))
(*.f64 (fma.f64 (/.f64 (PI.f64) eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (/ (PI) eps)))
(fma.f64 (/.f64 (PI.f64) eps) eps eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps)))
(sin (neg (* -1 eps)))
(sin.f64 eps)
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin (- (* 2 (PI)) (* -1 eps))) (cos (- (* 2 (PI)) (* -1 eps))))
(/.f64 (sin.f64 eps) (neg.f64 (neg.f64 (cos.f64 eps))))
(* -1 (* eps (- (* -2 (/ (PI) eps)) 1)))
(.f64 (neg.f64 eps) (-.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) eps)) #s(literal 1 binary64)))
(* -1 (* eps (- (* -1 (/ (PI) eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 (PI.f64)) eps) #s(literal 1 binary64)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))

rewrite226.0ms (1.7%)

Memory

6.9MiB live, 163.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	277
0	86	261
1	361	251
2	2992	251
0	8212	250

Stop Event

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

Counts

24 → 320

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
(tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64)))
(+.f64 (+.f64 eps (PI.f64)) (PI.f64))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
(+.f64 eps (PI.f64))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(cos.f64 (+.f64 eps x))
(*.f64 eps eps)
#s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
(fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(.f64 #s(literal 1/24 binary64) (.f64 x x))

Outputs
(/.f64 (/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (cos.f64 (+.f64 x eps))) (neg.f64 (cos.f64 x)))
(/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (cos.f64 x)))
(/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (neg.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 x eps))) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(neg.f64 (/.f64 (/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (cos.f64 (+.f64 x eps))) (cos.f64 x)))
(neg.f64 (/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 x eps))) (neg.f64 (cos.f64 x))))
(/.f64 (neg.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)))) (neg.f64 (neg.f64 (cos.f64 (+.f64 x eps)))))
(/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (neg.f64 (cos.f64 (+.f64 x eps))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (cos.f64 (+.f64 x eps))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
(.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)
(.f64 eps (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 2 binary64)) #s(literal 1 binary64)) eps) (-.f64 (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/27 binary64) #s(literal 1 binary64)) eps) (fma.f64 (pow.f64 (.f64 eps eps) #s(literal 2 binary64)) #s(literal 1/9 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))))
(/.f64 (.f64 eps (-.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) #s(literal 1 binary64)))
(/.f64 (.f64 eps (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/27 binary64) #s(literal 1 binary64))) (fma.f64 (pow.f64 (.f64 eps eps) #s(literal 2 binary64)) #s(literal 1/9 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))))
(fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))
(fma.f64 #s(literal 1 binary64) eps (.f64 (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps))
(fma.f64 eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (*.f64 eps #s(literal 1 binary64)))
(fma.f64 eps #s(literal 1 binary64) (.f64 eps (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(+.f64 (.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) eps) (.f64 #s(literal 1 binary64) eps))
(+.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) eps))
(+.f64 (.f64 eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) (.f64 eps #s(literal 1 binary64)))
(+.f64 (.f64 eps #s(literal 1 binary64)) (.f64 eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/27 binary64) #s(literal 1 binary64))) (neg.f64 (fma.f64 (pow.f64 (.f64 eps eps) #s(literal 2 binary64)) #s(literal 1/9 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 1 binary64)))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/27 binary64) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 2 binary64)) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/27 binary64) #s(literal 1 binary64)) (fma.f64 (pow.f64 (.f64 eps eps) #s(literal 2 binary64)) #s(literal 1/9 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(fma.f64 (*.f64 #s(literal 1/3 binary64) (fabs.f64 eps)) (fabs.f64 eps) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1/3 binary64) (neg.f64 eps)) (neg.f64 eps) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64))
(fma.f64 (fabs.f64 eps) (*.f64 (fabs.f64 eps) #s(literal 1/3 binary64)) #s(literal 1 binary64))
(fma.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal 1/3 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 1 binary64))
(fma.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))
(fma.f64 eps (.f64 (.f64 #s(literal 1/3 binary64) eps) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 eps (*.f64 #s(literal 1/3 binary64) eps) #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 1 binary64))) (pow.f64 (-.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))
(-.f64 #s(literal 1 binary64) (.f64 (neg.f64 (.f64 eps eps)) #s(literal 1/3 binary64)))
(-.f64 #s(literal 1 binary64) (.f64 (neg.f64 eps) (.f64 #s(literal 1/3 binary64) eps)))
(+.f64 (/.f64 (.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/27 binary64)) (fma.f64 (pow.f64 (.f64 eps eps) #s(literal 2 binary64)) #s(literal 1/9 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (pow.f64 (fma.f64 (pow.f64 (.f64 eps eps) #s(literal 2 binary64)) #s(literal 1/9 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) #s(literal -1 binary64)))
(+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) (PI.f64))))))
(/.f64 (+.f64 (tan.f64 (/.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64))))) (tan.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64)))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (/.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64))))) (tan.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64))))))))
(/.f64 (+.f64 (tan.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) eps) (.f64 eps eps)))) (tan.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) eps) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) eps) (.f64 eps eps)))) (tan.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) eps) (*.f64 eps eps)))))))
(/.f64 (sin.f64 (+.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) eps) (PI.f64)) (PI.f64))) (cos.f64 (+.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) eps) (PI.f64)) (PI.f64))))
(/.f64 (neg.f64 (+.f64 #s(literal 0 binary64) (tan.f64 eps))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 eps)))))
(/.f64 (neg.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps))) (neg.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps))))
(/.f64 (+.f64 #s(literal 0 binary64) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 eps))))
(/.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (cos.f64 eps)))
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 #s(literal 0 binary64) eps)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(neg.f64 (/.f64 (sin.f64 eps) (neg.f64 (cos.f64 eps))))
(neg.f64 (neg.f64 (tan.f64 eps)))
(tan.f64 (+.f64 (+.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) eps) (PI.f64)) (PI.f64)) (PI.f64)))
(tan.f64 (+.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) eps) (PI.f64)) (PI.f64)))
(tan.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) eps) (PI.f64)))
(tan.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) eps))
(tan.f64 (+.f64 (PI.f64) eps))
(tan.f64 eps)
(+.f64 (/.f64 (tan.f64 eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (tan.f64 eps)))) (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (tan.f64 eps)))))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64))) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)))
(/.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 2 binary64))) (-.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal 8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 2 binary64)) (.f64 eps (.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 (+.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64)) (*.f64 (+.f64 (PI.f64) eps) (PI.f64)))))
(/.f64 (+.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64)))) (neg.f64 (-.f64 (+.f64 (PI.f64) eps) (PI.f64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64)))))
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(cos.f64 (neg.f64 (+.f64 x eps)))
(cos.f64 (+.f64 x eps))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (.f64 (sin.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x)))) (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 eps x)))))
(+.f64 (.f64 (neg.f64 (sin.f64 (+.f64 x eps))) #s(literal 0 binary64)) (.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (.f64 #s(literal 0 binary64) (sin.f64 (+.f64 x eps))))
(+.f64 (.f64 (sin.f64 eps) (neg.f64 (sin.f64 x))) (.f64 (cos.f64 eps) (cos.f64 x)))
(+.f64 (.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (.f64 (cos.f64 eps) (cos.f64 x)))
(+.f64 (.f64 (sin.f64 (+.f64 x eps)) #s(literal 0 binary64)) (.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(*.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)))
(*.f64 (neg.f64 (fabs.f64 eps)) (neg.f64 (fabs.f64 eps)))
(*.f64 (fabs.f64 (fabs.f64 eps)) (fabs.f64 (fabs.f64 eps)))
(*.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 eps)))
(*.f64 (fabs.f64 eps) (fabs.f64 eps))
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 eps eps)
(pow.f64 (pow.f64 eps #s(literal 1 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (fabs.f64 eps)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 (fabs.f64 eps)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 eps)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 eps) #s(literal 2 binary64))
(pow.f64 (neg.f64 eps) #s(literal 2 binary64))
(pow.f64 eps #s(literal 2 binary64))
(neg.f64 (*.f64 eps (neg.f64 eps)))
(neg.f64 (*.f64 (neg.f64 eps) eps))
(fabs.f64 (*.f64 eps eps))
(+.f64 (cosh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (fabs.f64 eps)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 eps)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
#s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
(/.f64 (-.f64 #s(literal 1/9 binary64) (pow.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x) #s(literal 2 binary64))) (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x) #s(literal 2 binary64)) #s(literal 1/9 binary64))) (neg.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x) #s(literal 1/3 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/27 binary64))) (neg.f64 (+.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) (.f64 x #s(literal 1/3 binary64)))) (pow.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x) #s(literal 2 binary64)) #s(literal 1/9 binary64)) (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x) #s(literal 1/3 binary64)))
(/.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/27 binary64)) (+.f64 #s(literal 1/9 binary64) (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x) #s(literal 2 binary64)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) (.f64 x #s(literal 1/3 binary64))))))
(/.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/27 binary64)) (+.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) (.f64 x #s(literal 1/3 binary64)))) (pow.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x) #s(literal 2 binary64))))
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) (fabs.f64 x)) (fabs.f64 x) #s(literal 1/3 binary64))
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) (neg.f64 x)) (neg.f64 x) #s(literal 1/3 binary64))
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x #s(literal 1/3 binary64))
(fma.f64 (fabs.f64 x) (.f64 (fabs.f64 x) (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64))
(fma.f64 (neg.f64 x) (.f64 (neg.f64 x) (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 1/3 binary64))
(fma.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) #s(literal 1/3 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x) #s(literal 1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x) #s(literal 1/3 binary64))))
(-.f64 #s(literal 1/3 binary64) (.f64 (neg.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x)) x))
(-.f64 #s(literal 1/3 binary64) (.f64 (neg.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) (*.f64 x x)))
(-.f64 #s(literal 1/3 binary64) (.f64 (neg.f64 (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))))
(+.f64 (/.f64 (.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) (.f64 x #s(literal 1/3 binary64)))) (pow.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x) #s(literal 2 binary64)))) (/.f64 #s(literal 1/27 binary64) (+.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) (.f64 x #s(literal 1/3 binary64)))) (pow.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x) #s(literal 2 binary64)))))
(+.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x) #s(literal 1/3 binary64))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64)) x) x))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1/24 binary64) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 #s(literal 1/24 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 1/24 binary64) x) x)
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 1/24 binary64)))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1/24 binary64)))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(.f64 x (.f64 #s(literal 1/24 binary64) x))

eval96.0ms (0.7%)

Memory: -1.6MiB live, 104.9MiB allocated
Compiler: Compiled 15 963 to 2 015 computations (87.4% saved)

prune22.0ms (0.2%)

Memory

-12.1MiB live, 41.5MiB allocated

Pruning

22 alts after pruning (15 fresh and 7 done)

	Pruned	Kept	Total
New	465	10	475
Fresh	5	5	10
Picked	0	5	5
Done	0	2	2
Total	470	22	492

Accuracy

100.0%

Counts

492 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.1%	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
▶	60.0%	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	99.9%	(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps) x))) (cos.f64 x))
✓	99.9%	(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
	99.8%	(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))) (cos.f64 x))
	99.2%	(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) (cos.f64 x))
▶	99.9%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
✓	60.4%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	59.9%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
✓	60.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	59.9%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
▶	59.8%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
	59.5%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
	99.2%	#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	99.8%	#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (.f64 (/.f64 (+.f64 (/.f64 (.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
✓	3.6%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
▶	3.7%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
	3.8%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 #s(approx (+ (+ eps (PI)) (PI)) (*.f64 (fma.f64 (/.f64 (PI.f64) eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))))
	97.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
✓	97.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
	97.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) (+.f64 #s(literal 0 binary64) eps)))
▶	5.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))

Compiler

Compiled 786 to 547 computations (30.4% saved)

simplify140.0ms (1.1%)

Memory

-7.7MiB live, 188.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 (-.f64 (+.f64 eps x) x))
cost-diff	0	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x)))
cost-diff	0	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
cost-diff	4	(-.f64 (+.f64 eps x) x)
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
cost-diff	2	(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
cost-diff	0	(PI.f64)
cost-diff	0	(+.f64 (PI.f64) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
cost-diff	2	(tan.f64 (+.f64 (PI.f64) eps))
cost-diff	0	#s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))
cost-diff	0	(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
cost-diff	0	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	252
0	75	240
1	131	224
2	259	216
3	681	213
4	2147	213
5	4988	213
6	7498	213
0	8012	210

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
eps
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(cos.f64 x)
x
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))
#s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
(tan.f64 (+.f64 (PI.f64) eps))
(+.f64 (PI.f64) eps)
(PI.f64)
eps
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64))
#s(literal 2/15 binary64)
(*.f64 x x)
#s(literal 1/3 binary64)
#s(literal 1 binary64)
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x)))
(sin.f64 (-.f64 (+.f64 eps x) x))
(-.f64 (+.f64 eps x) x)
(+.f64 eps x)
eps
x
(cos.f64 (+.f64 eps x))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)

Outputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
eps
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos.f64 x)
x
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))
#s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(tan.f64 (+.f64 (PI.f64) eps))
(tan.f64 eps)
(+.f64 (PI.f64) eps)
(PI.f64)
eps
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/15 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (/ (sin x) (cos x)) (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/15 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/15 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64))
#s(literal 2/15 binary64)
(*.f64 x x)
#s(literal 1/3 binary64)
#s(literal 1 binary64)
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x)))
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps)))
(sin.f64 (-.f64 (+.f64 eps x) x))
(sin.f64 eps)
(-.f64 (+.f64 eps x) x)
eps
(+.f64 eps x)
(+.f64 x eps)
eps
x
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 x eps))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)

localize962.0ms (7.3%)

Memory

9.7MiB live, 523.0MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
accuracy	0.03904044311272992	(cos.f64 (+.f64 eps x))
accuracy	0.8371770197139548	#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	25.379876922698482	(-.f64 (+.f64 eps x) x)
accuracy	0.0078125	(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
accuracy	0.06623300745128272	(tan.f64 (+.f64 x eps))
accuracy	0.6468585266256394	#s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
accuracy	25.320212751734758	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
accuracy	0.0	(PI.f64)
accuracy	0.01171875	(+.f64 (PI.f64) eps)
accuracy	1.3696263764930934	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
accuracy	61.18689628909194	(tan.f64 (+.f64 (PI.f64) eps))
accuracy	1.3696263764930934	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))
accuracy	60.436808034487	#s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64))
accuracy	0.0	(cos.f64 x)
accuracy	0.0	#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
accuracy	0.015625	(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
accuracy	0.03904044311272992	(cos.f64 (+.f64 x eps))

Samples

750.0ms	101×	2	valid
164.0ms	149×	1	valid
2.0ms	6×	0	valid

Compiler

Compiled 196 to 41 computations (79.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 839.0ms

ival-tan: 725.0ms (86.4% of total)

adjust: 36.0ms (4.3% of total)

ival-add: 18.0ms (2.1% of total)

ival-mult: 14.0ms (1.7% of total)

const: 11.0ms (1.3% of total)

ival-div: 10.0ms (1.2% of total)

ival-cos: 8.0ms (1% of total)

ival-sin: 7.0ms (0.8% of total)

ival-sub: 6.0ms (0.7% of total)

ival-pi: 3.0ms (0.4% of total)

exact: 1.0ms (0.1% of total)

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

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

series18.0ms (0.1%)

Memory

16.4MiB live, 16.4MiB allocated

Counts

23 → 98

Calls

Call 1

Inputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))
#s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64))
(tan.f64 (+.f64 (PI.f64) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
(+.f64 (PI.f64) eps)
(PI.f64)
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
(-.f64 (+.f64 eps x) x)
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x)))
(sin.f64 (-.f64 (+.f64 eps x) x))
(cos.f64 (+.f64 x eps))
(cos.f64 x)
#s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(cos.f64 (+.f64 eps x))

Outputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ (* 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)))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(+ (* 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)
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(* (cos x) (cos (+ eps x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* 2/15 (pow x 5))
(* (pow x 5) (+ 2/15 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/15 (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin eps) (cos (+ eps x)))
(cos (+ eps x))
(cos x)
(/ (sin x) (cos x))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/3 (/ 1 (pow x 2))) (pow x 2))) 2/15)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (sin eps) (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* 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))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (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)))))
(/ (sin (* 2 (PI))) (cos (* 2 (PI))))
(+ (* eps (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
(+ (* eps (- (+ 1 (/ (* eps (* (sin (* 2 (PI))) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2)))))) (cos (* 2 (PI))))) (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin (* 2 (PI))) 2) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (pow (cos (* 2 (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (* 1/6 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2)))))))) (* -1 (/ (* (sin (* 2 (PI))) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (cos (* 2 (PI)))))))) (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
(/ (sin (PI)) (cos (PI)))
(+ (* eps (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))
(+ (* eps (- (+ 1 (/ (* eps (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))) (cos (PI)))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin (PI)) 2) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (pow (cos (PI)) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (* 1/6 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))))) (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI))))))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))
(PI)
(+ eps (PI))
(+ (* 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)))
(/ eps (cos x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI)))))
(/ (sin (+ eps (PI))) (cos (+ eps (PI))))
(* eps (+ 1 (/ (PI) eps)))
(* eps (+ 1 (/ x eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- (* 2 (PI)) (* -1 eps))) (cos (- (* 2 (PI)) (* -1 eps))))
(/ (sin (- (PI) (* -1 eps))) (cos (- (PI) (* -1 eps))))
(* -1 (* eps (- (* -1 (/ (PI) eps)) 1)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(cos (- x (* -1 eps)))

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	-inf	((/ (sin (- (+ eps x) x)) (* (cos x) (cos (+ x eps)))) (sin (- (+ eps x) x)) (sin eps) (* (cos x) (cos (+ x eps))) (- (tan (+ x eps)) (tan x)) (tan (+ (+ eps (PI)) (PI))) (tan (+ (PI) eps)) (- (tan (+ x eps)) (tan x)) (+ (PI) eps) (PI) (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (- (+ eps x) x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (cos (+ x eps)) (cos x) (/ (sin x) (cos x)) (cos x) (cos (+ eps x)))
3.0ms	eps	@	inf	((/ (sin (- (+ eps x) x)) (* (cos x) (cos (+ x eps)))) (sin (- (+ eps x) x)) (sin eps) (* (cos x) (cos (+ x eps))) (- (tan (+ x eps)) (tan x)) (tan (+ (+ eps (PI)) (PI))) (tan (+ (PI) eps)) (- (tan (+ x eps)) (tan x)) (+ (PI) eps) (PI) (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (- (+ eps x) x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (cos (+ x eps)) (cos x) (/ (sin x) (cos x)) (cos x) (cos (+ eps x)))
2.0ms	eps	@	0	((/ (sin (- (+ eps x) x)) (* (cos x) (cos (+ x eps)))) (sin (- (+ eps x) x)) (sin eps) (* (cos x) (cos (+ x eps))) (- (tan (+ x eps)) (tan x)) (tan (+ (+ eps (PI)) (PI))) (tan (+ (PI) eps)) (- (tan (+ x eps)) (tan x)) (+ (PI) eps) (PI) (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (- (+ eps x) x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (cos (+ x eps)) (cos x) (/ (sin x) (cos x)) (cos x) (cos (+ eps x)))
2.0ms	x	@	-inf	((/ (sin (- (+ eps x) x)) (* (cos x) (cos (+ x eps)))) (sin (- (+ eps x) x)) (sin eps) (* (cos x) (cos (+ x eps))) (- (tan (+ x eps)) (tan x)) (tan (+ (+ eps (PI)) (PI))) (tan (+ (PI) eps)) (- (tan (+ x eps)) (tan x)) (+ (PI) eps) (PI) (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (- (+ eps x) x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (cos (+ x eps)) (cos x) (/ (sin x) (cos x)) (cos x) (cos (+ eps x)))
2.0ms	x	@	inf	((/ (sin (- (+ eps x) x)) (* (cos x) (cos (+ x eps)))) (sin (- (+ eps x) x)) (sin eps) (* (cos x) (cos (+ x eps))) (- (tan (+ x eps)) (tan x)) (tan (+ (+ eps (PI)) (PI))) (tan (+ (PI) eps)) (- (tan (+ x eps)) (tan x)) (+ (PI) eps) (PI) (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (- (+ eps x) x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (sin (- (+ eps x) x)) (cos (+ x eps)) (cos x) (/ (sin x) (cos x)) (cos x) (cos (+ eps x)))

simplify194.0ms (1.5%)

Memory

6.8MiB live, 92.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	491	2282
1	1644	1926
2	5786	1856
0	8028	1765

Stop Event

1×	iter limit
1×	node limit

Counts

98 → 96

Calls

Call 1

Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ (* 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)))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(+ (* 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)
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(* (cos x) (cos (+ eps x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* 2/15 (pow x 5))
(* (pow x 5) (+ 2/15 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/15 (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin eps) (cos (+ eps x)))
(cos (+ eps x))
(cos x)
(/ (sin x) (cos x))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/3 (/ 1 (pow x 2))) (pow x 2))) 2/15)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (sin eps) (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* 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))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (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)))))
(/ (sin (* 2 (PI))) (cos (* 2 (PI))))
(+ (* eps (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
(+ (* eps (- (+ 1 (/ (* eps (* (sin (* 2 (PI))) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2)))))) (cos (* 2 (PI))))) (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin (* 2 (PI))) 2) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (pow (cos (* 2 (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (* 1/6 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2)))))))) (* -1 (/ (* (sin (* 2 (PI))) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (cos (* 2 (PI)))))))) (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
(/ (sin (PI)) (cos (PI)))
(+ (* eps (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))
(+ (* eps (- (+ 1 (/ (* eps (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))) (cos (PI)))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin (PI)) 2) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (pow (cos (PI)) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (* 1/6 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))))) (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI))))))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))
(PI)
(+ eps (PI))
(+ (* 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)))
(/ eps (cos x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI)))))
(/ (sin (+ eps (PI))) (cos (+ eps (PI))))
(* eps (+ 1 (/ (PI) eps)))
(* eps (+ 1 (/ x eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- (* 2 (PI)) (* -1 eps))) (cos (- (* 2 (PI)) (* -1 eps))))
(/ (sin (- (PI) (* -1 eps))) (cos (- (PI) (* -1 eps))))
(* -1 (* eps (- (* -1 (/ (PI) eps)) 1)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(cos (- x (* -1 eps)))

Outputs
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (cos.f64 eps)) (sin.f64 eps)) (cos.f64 eps))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (cos.f64 eps)) (sin.f64 eps) (/.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 2/3 binary64) (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x) (/.f64 (sin.f64 eps) (cos.f64 eps))) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(sin eps)
(sin.f64 eps)
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(fma.f64 (neg.f64 x) (fma.f64 (cos.f64 eps) x (sin.f64 eps)) (cos.f64 eps))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 2/3 binary64) (neg.f64 (cos.f64 eps))) x (neg.f64 (sin.f64 eps))) x (cos.f64 eps))
(+ (* 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)))
(fma.f64 (/.f64 (fma.f64 (+.f64 x (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (cos.f64 eps)) x (/.f64 (sin.f64 eps) (cos.f64 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)))
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x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
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eps
(+ eps x)
(+.f64 x eps)
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
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(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
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(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
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(* 2/15 (pow x 5))
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(/ (sin eps) (cos (+ eps x)))
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(cos x)
(cos.f64 x)
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
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(* -1 (* x (- (* -1 (/ eps x)) 1)))
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(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
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(* eps (+ 1 (* -1/6 (pow eps 2))))
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(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
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(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
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(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
(* 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)))))
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(* 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)))))
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(/ (sin (* 2 (PI))) (cos (* 2 (PI))))
#s(literal 0 binary64)
(+ (* eps (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
eps
(+ (* eps (- (+ 1 (/ (* eps (* (sin (* 2 (PI))) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2)))))) (cos (* 2 (PI))))) (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
eps
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin (* 2 (PI))) 2) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (pow (cos (* 2 (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (* 1/6 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2)))))))) (* -1 (/ (* (sin (* 2 (PI))) (- 1 (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (cos (* 2 (PI)))))))) (* -1 (/ (pow (sin (* 2 (PI))) 2) (pow (cos (* 2 (PI))) 2))))) (/ (sin (* 2 (PI))) (cos (* 2 (PI)))))
(.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64)) eps)
(/ (sin (PI)) (cos (PI)))
#s(literal 0 binary64)
(+ (* eps (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))
eps
(+ (* eps (- (+ 1 (/ (* eps (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))) (cos (PI)))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))
eps
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin (PI)) 2) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (pow (cos (PI)) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (* 1/6 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))))) (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI))))))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))
(.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64)) eps)
(PI)
(PI.f64)
(+ eps (PI))
(+.f64 (PI.f64) eps)
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 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)))
(fma.f64 (+.f64 (/.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (sin.f64 x) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 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)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x) (.f64 (neg.f64 eps) (+.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64) (.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64)))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps (/.f64 (sin.f64 x) (cos.f64 x)))
(/ eps (cos x))
(/.f64 eps (cos.f64 x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(.f64 (/.f64 (+.f64 (/.f64 (.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) (cos.f64 x)) eps)
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(fma.f64 (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (cos.f64 x)))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) eps (/.f64 eps (cos.f64 x)))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(fma.f64 (.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (cos.f64 x)))) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (cos.f64 x))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) eps (/.f64 eps (cos.f64 x)))
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps (cos.f64 x))
(/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI)))))
(/.f64 (sin.f64 eps) (neg.f64 (neg.f64 (cos.f64 eps))))
(/ (sin (+ eps (PI))) (cos (+ eps (PI))))
(/.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (cos.f64 eps)))
(* eps (+ 1 (/ (PI) eps)))
(fma.f64 (/.f64 (PI.f64) eps) eps eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(sin (neg (* -1 eps)))
(sin.f64 eps)
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin (- (* 2 (PI)) (* -1 eps))) (cos (- (* 2 (PI)) (* -1 eps))))
(/.f64 (sin.f64 eps) (neg.f64 (neg.f64 (cos.f64 eps))))
(/ (sin (- (PI) (* -1 eps))) (cos (- (PI) (* -1 eps))))
(/.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (cos.f64 eps)))
(* -1 (* eps (- (* -1 (/ (PI) eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 (PI.f64)) eps) #s(literal 1 binary64)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps)))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))

rewrite205.0ms (1.6%)

Memory

-14.1MiB live, 96.2MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	49	204
0	75	194
1	324	174
2	2575	174
0	8197	174

Stop Event

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

Counts

23 → 361

Calls

Call 1

Inputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))
#s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64))
(tan.f64 (+.f64 (PI.f64) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
(+.f64 (PI.f64) eps)
(PI.f64)
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
(-.f64 (+.f64 eps x) x)
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x)))
(sin.f64 (-.f64 (+.f64 eps x) x))
(cos.f64 (+.f64 x eps))
(cos.f64 x)
#s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(cos.f64 (+.f64 eps x))

Outputs
(*.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (+.f64 (cos.f64 (-.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 x eps) x)))) #s(literal 2 binary64))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (neg.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 x))) (neg.f64 (cos.f64 (+.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)))) (neg.f64 (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (cos.f64 x))))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(neg.f64 (/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(neg.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (cos.f64 x))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 x)))) (sin.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 x))) (sin.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) x)) (sin.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (neg.f64 (neg.f64 x)))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 (+.f64 x eps))))) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (+.f64 x eps)))) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 x eps))) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (neg.f64 (+.f64 x eps))))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)))) (cos.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 x eps))) (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 x eps))) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 x eps))) (neg.f64 x))) (cos.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 x eps))) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 x eps))) x)) (cos.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 x eps))) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (+.f64 x eps)) (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 (neg.f64 (+.f64 x eps)) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 x eps) (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 (+.f64 x eps) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (+.f64 x eps))))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 (+.f64 x eps)))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (neg.f64 (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (+.f64 x eps))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (neg.f64 (neg.f64 (+.f64 x eps))))) (cos.f64 (-.f64 (neg.f64 x) (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (neg.f64 (neg.f64 (+.f64 x eps))))) (cos.f64 (-.f64 x (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
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(-.f64 (.f64 (sin.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (+.f64 (+.f64 x eps) x))) (cos.f64 (/.f64 (.f64 x x) (+.f64 (+.f64 x eps) x)))) (.f64 (cos.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (+.f64 (+.f64 x eps) x))) (sin.f64 (/.f64 (.f64 x x) (+.f64 (+.f64 x eps) x)))))
(-.f64 (.f64 (sin.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (fma.f64 x (+.f64 (+.f64 x eps) x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))))) (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 (+.f64 x eps) x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (.f64 (cos.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (fma.f64 x (+.f64 (+.f64 x eps) x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))))) (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 (+.f64 x eps) x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))))))
(-.f64 (.f64 (sin.f64 (/.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64)) (-.f64 (+.f64 (PI.f64) eps) (PI.f64)))) (cos.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (-.f64 (+.f64 (PI.f64) eps) (PI.f64))))) (.f64 (cos.f64 (/.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64)) (-.f64 (+.f64 (PI.f64) eps) (PI.f64)))) (sin.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (-.f64 (+.f64 (PI.f64) eps) (PI.f64))))))
(-.f64 (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))))) (.f64 (neg.f64 (cos.f64 eps)) (sin.f64 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))))))
(-.f64 (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 (.f64 (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64))))) (.f64 (neg.f64 (cos.f64 eps)) (sin.f64 (.f64 (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64))))))
(-.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (.f64 (cos.f64 (+.f64 x eps)) (sin.f64 x)))
(cos.f64 (+.f64 (+.f64 (PI.f64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))))
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(+.f64 (.f64 (sin.f64 eps) #s(literal 1 binary64)) (.f64 (cos.f64 eps) #s(literal 0 binary64)))
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(+.f64 (.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 eps))) (.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 eps))))
(+.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64))) (cos.f64 (-.f64 eps x)))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))))
(fma.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x))) (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 eps x)))))
(fma.f64 (cos.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))) (.f64 (sin.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))))
(fma.f64 (neg.f64 (sin.f64 (+.f64 x eps))) #s(literal 0 binary64) (*.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)))
(fma.f64 (sin.f64 (+.f64 x eps)) #s(literal 0 binary64) (*.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)) (*.f64 #s(literal 0 binary64) (sin.f64 (+.f64 x eps))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(sin.f64 (+.f64 (-.f64 (neg.f64 x) eps) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 x eps))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)))
(-.f64 (.f64 (cos.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))) (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x eps) (.f64 eps eps))))) (.f64 (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))) (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x eps) (.f64 eps eps))))))
(-.f64 (.f64 (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x)))) (cos.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))) (.f64 (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x)))) (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (sin.f64 x))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 eps))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
(cos.f64 (neg.f64 (-.f64 (neg.f64 x) eps)))
(cos.f64 (neg.f64 (neg.f64 (neg.f64 (+.f64 x eps)))))
(cos.f64 (neg.f64 (neg.f64 (+.f64 x eps))))
(cos.f64 (-.f64 (neg.f64 x) eps))
(cos.f64 (neg.f64 (+.f64 x eps)))
(cos.f64 (+.f64 x eps))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x)))) (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 eps x)))))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (.f64 (sin.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))))
(+.f64 (.f64 (neg.f64 (sin.f64 (+.f64 x eps))) #s(literal 0 binary64)) (.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)))
(+.f64 (.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (.f64 (cos.f64 eps) (cos.f64 x)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (.f64 #s(literal 0 binary64) (sin.f64 (+.f64 x eps))))
(+.f64 (.f64 (sin.f64 eps) (neg.f64 (sin.f64 x))) (.f64 (cos.f64 eps) (cos.f64 x)))
(+.f64 (.f64 (sin.f64 (+.f64 x eps)) #s(literal 0 binary64)) (.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(sin.f64 (+.f64 (neg.f64 (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(cos.f64 (neg.f64 (neg.f64 (neg.f64 x))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64)))
#s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64))) (cos.f64 (-.f64 eps x)))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))))
(fma.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x))) (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 eps x)))))
(fma.f64 (cos.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))) (.f64 (sin.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))))
(fma.f64 (neg.f64 (sin.f64 (+.f64 x eps))) #s(literal 0 binary64) (*.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)))
(fma.f64 (sin.f64 (+.f64 x eps)) #s(literal 0 binary64) (*.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)) (*.f64 #s(literal 0 binary64) (sin.f64 (+.f64 x eps))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(sin.f64 (+.f64 (-.f64 (neg.f64 x) eps) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 x eps))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)))
(-.f64 (.f64 (cos.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))) (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x eps) (.f64 eps eps))))) (.f64 (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))) (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x eps) (.f64 eps eps))))))
(-.f64 (.f64 (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x)))) (cos.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))) (.f64 (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x)))) (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (sin.f64 x))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 eps))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
(cos.f64 (neg.f64 (-.f64 (neg.f64 x) eps)))
(cos.f64 (neg.f64 (neg.f64 (neg.f64 (+.f64 x eps)))))
(cos.f64 (neg.f64 (neg.f64 (+.f64 x eps))))
(cos.f64 (-.f64 (neg.f64 x) eps))
(cos.f64 (neg.f64 (+.f64 x eps)))
(cos.f64 (+.f64 x eps))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x)))) (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 eps x)))))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (.f64 (sin.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))))
(+.f64 (.f64 (neg.f64 (sin.f64 (+.f64 x eps))) #s(literal 0 binary64)) (.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)))
(+.f64 (.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (.f64 (cos.f64 eps) (cos.f64 x)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (.f64 #s(literal 0 binary64) (sin.f64 (+.f64 x eps))))
(+.f64 (.f64 (sin.f64 eps) (neg.f64 (sin.f64 x))) (.f64 (cos.f64 eps) (cos.f64 x)))
(+.f64 (.f64 (sin.f64 (+.f64 x eps)) #s(literal 0 binary64)) (.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))

eval78.0ms (0.6%)

Memory: -12.3MiB live, 73.9MiB allocated
Compiler: Compiled 12 870 to 1 942 computations (84.9% saved)

prune23.0ms (0.2%)

Memory

17.8MiB live, 55.0MiB allocated

Pruning

20 alts after pruning (11 fresh and 9 done)

	Pruned	Kept	Total
New	413	6	419
Fresh	5	5	10
Picked	2	3	5
Done	1	6	7
Total	421	20	441

Accuracy

100.0%

Counts

441 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
	99.2%	(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) (cos.f64 x))
	98.5%	(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	99.9%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (cos.f64 (+.f64 x eps))))
✓	99.9%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	99.8%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) #s(approx (cos (+ x eps)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))))
	99.1%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
	98.7%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
✓	60.4%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	60.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	59.9%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
✓	59.8%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
	59.5%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
	99.2%	#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
✓	3.6%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
✓	3.7%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
	3.8%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 #s(approx (+ (+ eps (PI)) (PI)) (*.f64 (fma.f64 (/.f64 (PI.f64) eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))))
	97.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
✓	97.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
	97.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) eps))

Compiler

Compiled 1 397 to 522 computations (62.6% saved)

regimes37.0ms (0.3%)

Memory

-14.0MiB live, 71.0MiB allocated

Counts

43 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) (+.f64 #s(literal 0 binary64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 #s(approx (+ (+ eps (PI)) (PI)) (*.f64 (fma.f64 (/.f64 (PI.f64) eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
(-.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 (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
(-.f64 (tan.f64 (-.f64 (.f64 x (/.f64 x (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (cos.f64 (+.f64 x eps))))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps) x))) (cos.f64 x))
#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))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) #s(approx (cos (+ x eps)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))) (cos.f64 x))
#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (.f64 (/.f64 (+.f64 (/.f64 (.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (*.f64 (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
(/.f64 (-.f64 (.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 0 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (tan.f64 (+.f64 eps x)))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 (+.f64 eps x)))) (cos.f64 x)))
(fma.f64 (tan.f64 (+.f64 eps x)) (/.f64 (tan.f64 (+.f64 eps x)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (/.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))

Outputs

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

Calls

3 calls:

13.0ms	x
12.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
10.0ms	eps

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes34.0ms (0.3%)

Memory

27.3MiB live, 65.7MiB allocated

Counts

42 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) (+.f64 #s(literal 0 binary64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 #s(approx (+ (+ eps (PI)) (PI)) (*.f64 (fma.f64 (/.f64 (PI.f64) eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
(-.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 (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
(-.f64 (tan.f64 (-.f64 (.f64 x (/.f64 x (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (cos.f64 (+.f64 x eps))))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps) x))) (cos.f64 x))
#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))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) #s(approx (cos (+ x eps)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))) (cos.f64 x))
#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (.f64 (/.f64 (+.f64 (/.f64 (.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (*.f64 (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
(/.f64 (-.f64 (.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 0 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (tan.f64 (+.f64 eps x)))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 (+.f64 eps x)))) (cos.f64 x)))
(fma.f64 (tan.f64 (+.f64 eps x)) (/.f64 (tan.f64 (+.f64 eps x)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (/.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps eps))

Outputs
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`eps`
99.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes27.0ms (0.2%)

Memory

-20.0MiB live, 55.8MiB allocated

Counts

29 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) (+.f64 #s(literal 0 binary64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 #s(approx (+ (+ eps (PI)) (PI)) (*.f64 (fma.f64 (/.f64 (PI.f64) eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
(-.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 (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
(-.f64 (tan.f64 (-.f64 (.f64 x (/.f64 x (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

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

Calls

3 calls:

9.0ms	x
9.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms	eps

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`eps`
99.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes23.0ms (0.2%)

Memory

12.9MiB live, 58.3MiB allocated

Counts

26 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) (+.f64 #s(literal 0 binary64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 #s(approx (+ (+ eps (PI)) (PI)) (*.f64 (fma.f64 (/.f64 (PI.f64) eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
(-.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 (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
(-.f64 (tan.f64 (-.f64 (.f64 x (/.f64 x (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))

Outputs
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) (cos.f64 x))

Calls

3 calls:

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

regimes17.0ms (0.1%)

Memory

-7.9MiB live, 31.0MiB allocated

Counts

18 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) (+.f64 #s(literal 0 binary64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 #s(approx (+ (+ eps (PI)) (PI)) (*.f64 (fma.f64 (/.f64 (PI.f64) eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
(-.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 (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))

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

Calls

3 calls:

5.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	eps
5.0ms	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)

regimes16.0ms (0.1%)

Memory

-8.7MiB live, 30.7MiB allocated

Counts

17 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) (+.f64 #s(literal 0 binary64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 #s(approx (+ (+ eps (PI)) (PI)) (*.f64 (fma.f64 (/.f64 (PI.f64) eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

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

Calls

3 calls:

6.0ms	eps
5.0ms	x
5.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
98.5%	1	`eps`
98.5%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.5%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.1%)

Memory

26.2MiB live, 26.2MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) (+.f64 #s(literal 0 binary64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 eps (PI.f64)) (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 #s(approx (+ (+ eps (PI)) (PI)) (*.f64 (fma.f64 (/.f64 (PI.f64) eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ (sin x) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))

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

Calls

3 calls:

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

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)

regimes6.0ms (0%)

Memory

-26.2MiB live, 13.2MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))

#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) eps))

#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) (+.f64 #s(literal 0 binary64) eps)))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) eps))

Calls

3 calls:

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

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)

regimes4.0ms (0%)

Memory

10.1MiB live, 10.1MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))

Calls

3 calls:

1.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.0ms	x
1.0ms	eps

Results

Accuracy	Segments	Branch
5.6%	1	`x`
5.6%	1	`eps`
5.6%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify86.0ms (0.7%)

Memory

6.2MiB live, 57.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	242
1	109	228
2	150	218
3	205	218
4	428	218
5	1488	218
6	2709	218
7	4964	218
8	7128	218

Stop Event

1×	node limit

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) (cos.f64 x))
#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) (cos.f64 x))
#s(approx (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(approx (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (/.f64 eps (cos.f64 x))) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan (+ (+ eps (PI)) (PI))) #s(literal 0 binary64)))

soundness1.1s (8.6%)

Memory

9.2MiB live, 479.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	491	2282
1	1644	1926
2	5786	1856
0	8028	1765
0	716	3417
1	2383	3212
0	8665	3041
0	157	970
1	488	910
2	1845	849
0	8454	797
0	466	2298
1	1497	2149
2	5330	1926
0	8474	1828
0	48	313
0	88	275
1	322	229
2	2674	229
0	8568	223
0	6	16
0	10	16
1	53	16
2	440	16
3	6608	16
0	8588	16

Stop Event

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

Compiler

Compiled 457 to 233 computations (49% saved)

preprocess156.0ms (1.2%)

Memory: -19.8MiB live, 55.8MiB allocated
Compiler: Compiled 524 to 178 computations (66% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze51.0ms (0.4%)

sample6.6s (49.8%)

explain99.0ms (0.7%)

preprocess275.0ms (2.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify212.0ms (1.6%)

localize26.0ms (0.2%)

series11.0ms (0.1%)

simplify180.0ms (1.4%)

rewrite214.0ms (1.6%)

eval25.0ms (0.2%)

prune12.0ms (0.1%)

simplify144.0ms (1.1%)

localize234.0ms (1.8%)

series121.0ms (0.9%)

simplify201.0ms (1.5%)

rewrite173.0ms (1.3%)

eval150.0ms (1.1%)

prune52.0ms (0.4%)

simplify129.0ms (1%)

localize598.0ms (4.5%)

series19.0ms (0.1%)

simplify194.0ms (1.5%)

rewrite226.0ms (1.7%)

eval96.0ms (0.7%)

prune22.0ms (0.2%)

simplify140.0ms (1.1%)

localize962.0ms (7.3%)

series18.0ms (0.1%)

simplify194.0ms (1.5%)

rewrite205.0ms (1.6%)

eval78.0ms (0.6%)

prune23.0ms (0.2%)

regimes37.0ms (0.3%)

regimes34.0ms (0.3%)

regimes27.0ms (0.2%)

regimes23.0ms (0.2%)

regimes17.0ms (0.1%)

regimes16.0ms (0.1%)

regimes12.0ms (0.1%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify86.0ms (0.7%)

soundness1.1s (8.6%)

preprocess156.0ms (1.2%)

end0.0ms (0%)

Profiling