Metrics for invcot (example 3.9)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze9.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.7%	50.3%	0%	0%	0%	0
0%	0%	49.7%	50.3%	0%	0%	0%	1
0%	0%	49.7%	50.3%	0%	0%	0%	2
25%	12.4%	37.3%	50.3%	0%	0%	0%	3
62.5%	31.1%	18.6%	50.3%	0%	0%	0%	4
81.3%	40.4%	9.3%	50.3%	0%	0%	0%	5
90.6%	45%	4.7%	50.3%	0%	0%	0%	6
95.3%	47.4%	2.3%	50.3%	0%	0%	0%	7
97.7%	48.5%	1.2%	50.3%	0%	0%	0%	8
98.8%	49.1%	0.6%	50.3%	0%	0%	0%	9
99.4%	49.4%	0.3%	50.3%	0%	0%	0%	10
99.7%	49.5%	0.1%	50.3%	0%	0%	0%	11
99.9%	49.6%	0.1%	50.3%	0%	0%	0%	12

Compiler

Compiled 16 to 12 computations (25% saved)

sample10.2s (62.3%)

Memory

-11.9MiB live, 8 370.7MiB allocated

Samples

7.5s	3 868×	2	valid
1.9s	4 313×	1	valid
7.0ms	75×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 8.9s

ival-tan: 7.3s (82.4% of total)

ival-div: 449.0ms (5.1% of total)

const: 439.0ms (5% of total)

adjust: 433.0ms (4.9% of total)

ival-sub: 165.0ms (1.9% of total)

ival-<: 49.0ms (0.6% of total)

ival-and: 13.0ms (0.1% of total)

exact: 5.0ms (0.1% of total)

ival-assert: 4.0ms (0% of total)

Bogosity

explain747.0ms (4.6%)

Memory

-11.0MiB live, 628.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
256	-	-	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`
0	-	-	`(/.f64 #s(literal 1 binary64) x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(tan.f64 x)`
0	-	-	`(/.f64 #s(literal 1 binary64) (tan.f64 x))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`	cancellation	256	0

Confusion

	Predicted +	Predicted -
+	256	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	256	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	256

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

627.0ms	254×	2	valid
64.0ms	250×	1	valid
0.0ms	8×	0	valid

Compiler

Compiled 69 to 28 computations (59.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 669.0ms

ival-tan: 553.0ms (82.7% of total)

ival-div: 97.0ms (14.5% of total)

adjust: 11.0ms (1.6% of total)

ival-sub: 6.0ms (0.9% of total)

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

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

exact: 0.0ms (0% of total)

preprocess35.0ms (0.2%)

Memory

-9.5MiB live, 31.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Outputs
(-.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) x))

Symmetry

(negabs x)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.7%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify8.0ms (0%)

Memory

13.6MiB live, 13.6MiB 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 #s(literal 1 binary64) (tan.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)

Outputs
(-.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)

localize242.0ms (1.5%)

Memory

23.4MiB live, 337.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0	(tan.f64 x)
accuracy	0.015625	(/.f64 #s(literal 1 binary64) (tan.f64 x))
accuracy	59.639913169424005	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Samples

203.0ms	127×	2	valid
30.0ms	125×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 40 to 14 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 222.0ms

ival-tan: 200.0ms (90.1% of total)

ival-div: 10.0ms (4.5% of total)

adjust: 8.0ms (3.6% of total)

ival-sub: 3.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0%)

Memory

-27.1MiB live, 10.8MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((- (/ 1 x) (/ 1 (tan x))) (/ 1 x) (/ 1 (tan x)) (tan x))
1.0ms	x	@	-inf	((- (/ 1 x) (/ 1 (tan x))) (/ 1 x) (/ 1 (tan x)) (tan x))
1.0ms	x	@	0	((- (/ 1 x) (/ 1 (tan x))) (/ 1 x) (/ 1 (tan x)) (tan x))

simplify198.0ms (1.2%)

Memory

5.9MiB live, 236.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	324
1	179	324
2	458	318
3	1332	318
4	2094	318
5	3093	318
6	3681	318
7	3948	318
8	5088	318
9	7270	318
0	8431	300

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) 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))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))

Outputs
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) x)
(/.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/45 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 -2/945 binary64) (.f64 x x) #s(literal -1/45 binary64)) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
x
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 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 (pow.f64 x #s(literal 5 binary64)) (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) x)
(/.f64 (cos.f64 x) (sin.f64 x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) x)
(/.f64 (cos.f64 x) (sin.f64 x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 (sin.f64 x) (cos.f64 x))

rewrite103.0ms (0.6%)

Memory

26.8MiB live, 187.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	17
1	49	17
2	454	17
3	5706	17
0	9203	17

Stop Event

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

Counts

4 → 277

Calls

Call 1

Inputs
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan.f64 x)

Outputs
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eval49.0ms (0.3%)

Memory: -4.1MiB live, 115.2MiB allocated
Compiler: Compiled 5 644 to 767 computations (86.4% saved)

prune7.0ms (0%)

Memory

-16.1MiB live, 22.4MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	321	3	324
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	322	3	325

Accuracy

99.4%

Counts

325 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
▶	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
▶	98.7%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Status

Accuracy

Program

▶

99.4%

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))

▶

99.3%

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))

▶

98.7%

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 51 to 35 computations (31.4% saved)

simplify119.0ms (0.7%)

Memory

17.9MiB live, 103.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
cost-diff	0	(*.f64 #s(literal 1/3 binary64) x)
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	113
0	29	113
1	48	113
2	83	113
3	145	113
4	237	113
5	263	113
6	305	113
7	337	113
8	588	113
9	1987	113
10	2697	113
11	2789	113
12	2789	113
13	2791	113
14	2792	113
0	2792	113

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
x
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
x
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) x)
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)

localize309.0ms (1.9%)

Memory

11.6MiB live, 366.2MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
accuracy	0.00390625	(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
accuracy	0.00390625	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
accuracy	0.3515625	(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
accuracy	0.10621703111186122	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
accuracy	0.34765625	(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
accuracy	0.35546875	(*.f64 #s(literal 1/3 binary64) x)
accuracy	0.49720355326799853	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Samples

224.0ms	127×	2	valid
67.0ms	125×	1	valid
1.0ms	4×	0	valid

Compiler

Compiled 208 to 40 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 265.0ms

ival-tan: 192.0ms (72.5% of total)

const: 18.0ms (6.8% of total)

ival-mult: 18.0ms (6.8% of total)

ival-div: 14.0ms (5.3% of total)

adjust: 13.0ms (4.9% of total)

ival-add: 6.0ms (2.3% of total)

ival-sub: 3.0ms (1.1% of total)

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.1%)

Memory

-17.9MiB live, 17.5MiB allocated

Counts

10 → 120

Calls

Call 1

Inputs
#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
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Calls

3 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	((- (/ 1 x) (/ 1 (tan x))) (* 1/3 x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (+ (* 2/945 (* x x)) 1/45))
2.0ms	x	@	inf	((- (/ 1 x) (/ 1 (tan x))) (* 1/3 x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (+ (* 2/945 (* x x)) 1/45))
2.0ms	x	@	-inf	((- (/ 1 x) (/ 1 (tan x))) (* 1/3 x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (+ (* 2/945 (* x x)) 1/45))

Time

Variable

Point

Expression

6.0ms

((- (/ 1 x) (/ 1 (tan x))) (* 1/3 x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (+ (* 2/945 (* x x)) 1/45))

2.0ms

inf

((- (/ 1 x) (/ 1 (tan x))) (* 1/3 x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (+ (* 2/945 (* x x)) 1/45))

2.0ms

-inf

((- (/ 1 x) (/ 1 (tan x))) (* 1/3 x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (* x x) 1/45) 1/3) x) (+ (* (* x x) 1/45) 1/3) (* x x) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (+ (* 2/945 (* x x)) 1/45))

simplify284.0ms (1.7%)

Memory

-29.8MiB live, 143.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	908
1	185	908
2	478	908
3	1158	908
4	2335	908
5	5653	908
0	8092	833

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
1/45
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* 2/945 (pow x 2)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 2))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 2))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))

Outputs
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
#s(literal 1/3 binary64)
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
#s(literal 1/3 binary64)
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
#s(literal 1/45 binary64)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/945 binary64))
(.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x)
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(.f64 #s(literal 2/945 binary64) (.f64 x x))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/945 binary64))
(.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x)
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(.f64 #s(literal 2/945 binary64) (.f64 x x))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))

rewrite168.0ms (1%)

Memory

-4.3MiB live, 185.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	101
0	29	101
1	123	101
2	933	101
0	8743	101

Stop Event

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

Counts

10 → 309

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) x)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(*.f64 x x)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval76.0ms (0.5%)

Memory: 9.7MiB live, 130.0MiB allocated
Compiler: Compiled 14 198 to 1 415 computations (90% saved)

prune28.0ms (0.2%)

Memory

-17.7MiB live, 62.1MiB allocated

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	473	6	479
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	473	9	482

Accuracy

100.0%

Counts

482 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
▶	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
▶	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
▶	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
▶	99.8%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
✓	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/945 binary64))) x))
✓	98.7%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 335 to 233 computations (30.4% saved)

simplify128.0ms (0.8%)

Memory

16.3MiB live, 94.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
cost-diff	6848	(/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))
cost-diff	0	(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
cost-diff	0	(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x)
cost-diff	0	(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
cost-diff	0	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
cost-diff	0	(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
cost-diff	320	(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))
cost-diff	0	(*.f64 #s(literal 1/45 binary64) x)
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
cost-diff	320	(fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
cost-diff	0	(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
cost-diff	1088	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	292
0	61	292
1	98	276
2	154	276
3	275	276
4	403	276
5	517	276
6	646	276
7	804	276
8	1404	276
9	4615	276
10	6074	276
11	6690	276
12	6847	276
13	7154	276
14	7472	276
0	8020	276

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
x
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 x x)
x
(*.f64 #s(literal 1/45 binary64) x)
#s(literal 1/45 binary64)
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
#s(literal 1/2025 binary64)
#s(literal -1/9 binary64)
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal -1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
(/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
(pow.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
x
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)))
#s(literal 1 binary64)
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(*.f64 x x)
x
(*.f64 #s(literal 1/45 binary64) x)
#s(literal 1/45 binary64)
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))))
(.f64 (/.f64 x (fma.f64 (.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/2025 binary64) (*.f64 #s(literal -1/9 binary64) x))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
#s(literal 1/2025 binary64)
#s(literal -1/9 binary64)
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal -1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x)
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
(pow.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)

localize477.0ms (2.9%)

Memory

-13.7MiB live, 413.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
accuracy	0.00390625	(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
accuracy	0.00390625	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
accuracy	0.3984375	(/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))
accuracy	0.01171875	(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))
accuracy	0.10621703111186122	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
accuracy	0.39453125	(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x)
accuracy	0.453125	(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))
accuracy	0.00390625	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
accuracy	0.01171875	(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))
accuracy	0.22265625	(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
accuracy	0.35546875	(*.f64 #s(literal 1/3 binary64) x)
accuracy	0.0078125	(fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
accuracy	0.10621703111186122	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
accuracy	0.21875	(*.f64 #s(literal 1/45 binary64) x)
accuracy	0.35546875	(*.f64 #s(literal 1/3 binary64) x)
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
accuracy	0.0078125	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
accuracy	0.10621703111186122	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))

Samples

318.0ms	127×	2	valid
105.0ms	125×	1	valid
1.0ms	4×	0	valid

Compiler

Compiled 534 to 78 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 379.0ms

ival-tan: 178.0ms (46.9% of total)

ival-add: 58.0ms (15.3% of total)

const: 56.0ms (14.8% of total)

ival-mult: 28.0ms (7.4% of total)

adjust: 26.0ms (6.9% of total)

ival-div: 24.0ms (6.3% of total)

ival-pow: 6.0ms (1.6% of total)

ival-sub: 3.0ms (0.8% of total)

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

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

exact: 0.0ms (0% of total)

series25.0ms (0.2%)

Memory

6.5MiB live, 43.3MiB allocated

Counts

21 → 252

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal 1/45 binary64) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/45 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/45 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/45 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/45 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

inf

((/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* 1/45 (* x x)) 1/3) (+ (* (* x x) (* 1/45 x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* x x) (* 1/45 x) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) (* x x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* 2/945 (* x x)) 1/45) x) (+ (* 2/945 (* x x)) 1/45) (- (/ 1 x) (/ 1 (tan x))) (/ (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* 1/45 (* x x)) -1/3)) (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* (pow x 4) 1/2025) -1/9) (/ (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (pow x -1)) (- (/ 1 x) (/ 1 (tan x))) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (* 1/3 x) (+ (* 1/45 (* x x)) -1/3))

4.0ms

-inf

((/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* 1/45 (* x x)) 1/3) (+ (* (* x x) (* 1/45 x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* x x) (* 1/45 x) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) (* x x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* 2/945 (* x x)) 1/45) x) (+ (* 2/945 (* x x)) 1/45) (- (/ 1 x) (/ 1 (tan x))) (/ (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* 1/45 (* x x)) -1/3)) (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* (pow x 4) 1/2025) -1/9) (/ (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (pow x -1)) (- (/ 1 x) (/ 1 (tan x))) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (* 1/3 x) (+ (* 1/45 (* x x)) -1/3))

4.0ms

((/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* 1/45 (* x x)) 1/3) (+ (* (* x x) (* 1/45 x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* x x) (* 1/45 x) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) (* x x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* 2/945 (* x x)) 1/45) x) (+ (* 2/945 (* x x)) 1/45) (- (/ 1 x) (/ 1 (tan x))) (/ (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* 1/45 (* x x)) -1/3)) (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* (pow x 4) 1/2025) -1/9) (/ (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (pow x -1)) (- (/ 1 x) (/ 1 (tan x))) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (* 1/3 x) (+ (* 1/45 (* x x)) -1/3))

simplify141.0ms (0.9%)

Memory

35.9MiB live, 190.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	2018
1	334	2014
2	838	2014
3	1987	2010
4	4664	2010
0	8129	1866

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/45 x)
(* x (+ 1/45 (* 2/945 (pow x 2))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
1/45
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* 2/945 (pow x 2)))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* -1/9 x)
(* x (- (* 1/2025 (pow x 4)) 1/9))
(* x (- (* 1/2025 (pow x 4)) 1/9))
(* x (- (* 1/2025 (pow x 4)) 1/9))
-1/9
(- (* 1/2025 (pow x 4)) 1/9)
(- (* 1/2025 (pow x 4)) 1/9)
(- (* 1/2025 (pow x 4)) 1/9)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
-1/3
(- (* 1/45 (pow x 2)) 1/3)
(- (* 1/45 (pow x 2)) 1/3)
(- (* 1/45 (pow x 2)) 1/3)
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 2/945 (pow x 3))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* 2/945 (pow x 2))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/2025 (pow x 5))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/45 (pow x 2))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 2/945 (pow x 3))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* 2/945 (pow x 2))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/2025 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/45 (pow x 2))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))

Outputs
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
#s(literal 3 binary64)
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(fma.f64 (fma.f64 #s(literal 1/75 binary64) (.f64 x x) #s(literal -1/5 binary64)) (.f64 x x) #s(literal 3 binary64))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/1125 binary64) (.f64 x x) #s(literal 1/75 binary64)) (.f64 x x) #s(literal -1/5 binary64)) (*.f64 x x) #s(literal 3 binary64))
#s(literal 1/3 binary64)
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 #s(literal 1/45 binary64) x)
(*.f64 #s(literal 1/45 binary64) x)
(*.f64 #s(literal 1/45 binary64) x)
(*.f64 #s(literal 1/45 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
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(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))

rewrite219.0ms (1.3%)

Memory

-9.1MiB live, 274.2MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	243
0	61	233
1	252	213
2	1872	213
0	8477	213

Stop Event

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

Counts

21 → 813

Calls

Call 1

Inputs
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
(*.f64 x x)
(*.f64 #s(literal 1/45 binary64) x)
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))

Outputs
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eval172.0ms (1.1%)

Memory: 11.6MiB live, 243.2MiB allocated
Compiler: Compiled 39 994 to 2 624 computations (93.4% saved)

prune183.0ms (1.1%)

Memory

-14.5MiB live, 65.7MiB allocated

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	1 252	5	1 257
Fresh	1	0	1
Picked	3	2	5
Done	0	3	3
Total	1 256	10	1 266

Accuracy

100.0%

Counts

1 266 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
▶	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
▶	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)))
▶	99.9%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
▶	99.2%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
▶	99.0%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))))
✓	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
✓	98.7%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 348 to 249 computations (28.4% saved)

simplify181.0ms (1.1%)

Memory

13.5MiB live, 51.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 x #s(literal -1 binary64))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))))
cost-diff	1792	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))))
cost-diff	5760	(/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))
cost-diff	0	(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
cost-diff	0	(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)))
cost-diff	7232	(/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x))
cost-diff	0	#s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x)
cost-diff	0	(/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
cost-diff	0	#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
cost-diff	0	(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
cost-diff	0	(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
cost-diff	0	#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
cost-diff	0	(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	383
0	67	381
1	105	381
2	187	369
3	441	369
4	1501	369
5	3874	369
6	5773	369
7	7134	369
8	7832	369
0	8010	358

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
#s(literal -1/5 binary64)
(*.f64 x x)
#s(literal 3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
#s(literal 3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
(/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))
(.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x)
#s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64))
#s(literal -1/9 binary64)
x
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal -1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)))
(/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x))
(neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))))
#s(literal 1 binary64)
(/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))
(pow.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))
#s(literal -1/5 binary64)
(*.f64 x x)
#s(literal 3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
#s(literal 3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (/.f64 x (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal -1/3 binary64))) #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64))))
(.f64 (/.f64 x (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal -1/3 binary64))) #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)))
(.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x)
#s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64))
#s(literal -1/9 binary64)
x
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal -1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal -1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x)
(fma.f64 #s(literal -2/945 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x))
(.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x)
#s(literal 1 binary64)
(/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) x)
(pow.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)

localize934.0ms (5.7%)

Memory

-0.6MiB live, 273.1MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
accuracy	0.22265625	(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
accuracy	0.43014340516871985	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))))
accuracy	0.4453125	(/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))
accuracy	0.00390625	(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
accuracy	0.00390625	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
accuracy	0.22265625	(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
accuracy	0.3984375	(/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x))
accuracy	0.09897078940174665	#s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64))
accuracy	0.10621703111186122	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
accuracy	0.39453125	(.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x)
accuracy	0.453125	(/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))
accuracy	0.0078125	(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
accuracy	0.10621703111186122	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
accuracy	0.49490682071700154	#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
accuracy	0.09630810821123671	#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
accuracy	0.10621703111186122	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))

Samples

559.0ms	127×	2	valid
336.0ms	125×	1	valid
1.0ms	4×	0	valid

Compiler

Compiled 676 to 93 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 670.0ms

ival-tan: 411.0ms (61.4% of total)

const: 155.0ms (23.1% of total)

ival-div: 31.0ms (4.6% of total)

adjust: 25.0ms (3.7% of total)

ival-mult: 23.0ms (3.4% of total)

ival-add: 12.0ms (1.8% of total)

ival-pow: 6.0ms (0.9% of total)

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

ival-neg: 2.0ms (0.3% of total)

exact: 1.0ms (0.1% of total)

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

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

series25.0ms (0.2%)

Memory

-16.1MiB live, 21.5MiB allocated

Counts

21 → 252

Calls

Call 1

Inputs
#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (pow.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())

Outputs
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Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

((- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* -1/5 (* x x)) 3) (- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (- (/ 1 x) (/ 1 (tan x))) (/ (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* 1/45 (* x x)) -1/3)) (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* (pow x 4) 1/2025) -1/9) (/ (neg (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/ -1 x)) (- (/ 1 x) (/ 1 (tan x))) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3) (* (+ (* 2/945 (* x x)) 1/45) x) (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/ 1 (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (pow x -1) (* x x) (+ (* 2/945 (* x x)) 1/45))

3.0ms

inf

((- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* -1/5 (* x x)) 3) (- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (- (/ 1 x) (/ 1 (tan x))) (/ (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* 1/45 (* x x)) -1/3)) (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* (pow x 4) 1/2025) -1/9) (/ (neg (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/ -1 x)) (- (/ 1 x) (/ 1 (tan x))) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3) (* (+ (* 2/945 (* x x)) 1/45) x) (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/ 1 (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (pow x -1) (* x x) (+ (* 2/945 (* x x)) 1/45))

2.0ms

((- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* -1/5 (* x x)) 3) (- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (- (/ 1 x) (/ 1 (tan x))) (/ (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* 1/45 (* x x)) -1/3)) (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* (pow x 4) 1/2025) -1/9) (/ (neg (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/ -1 x)) (- (/ 1 x) (/ 1 (tan x))) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3) (* (+ (* 2/945 (* x x)) 1/45) x) (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/ 1 (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (pow x -1) (* x x) (+ (* 2/945 (* x x)) 1/45))

simplify170.0ms (1%)

Memory

14.8MiB live, 129.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	163	2222
1	441	2220
2	1108	2216
3	2669	2212
4	5756	2212
0	8233	2073

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* -1/9 x)
(* x (- (* 1/2025 (pow x 4)) 1/9))
(* x (- (* 1/2025 (pow x 4)) 1/9))
(* x (- (* 1/2025 (pow x 4)) 1/9))
-1/9
(- (* 1/2025 (pow x 4)) 1/9)
(- (* 1/2025 (pow x 4)) 1/9)
(- (* 1/2025 (pow x 4)) 1/9)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(* 1/45 x)
(* x (+ 1/45 (* 2/945 (pow x 2))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(/ 3 x)
(/ (+ 3 (* -1/5 (pow x 2))) x)
(/ (+ 3 (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5))) x)
(/ (+ 3 (* (pow x 2) (- (* (pow x 2) (- (* 13/7875 (pow x 2)) 1/175)) 1/5))) x)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/45
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* 2/945 (pow x 2)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/2025 (pow x 5))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 3))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(/ 945/2 (pow x 5))
(/ (- 945/2 (* 19845/4 (/ 1 (pow x 2)))) (pow x 5))
(/ (+ 945/2 (* -1 (/ (+ 19845/4 (* 178605/8 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 5))
(/ (- (+ 945/2 (* 16253055/16 (/ 1 (pow x 6)))) (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4)))) (pow x 5))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2/945 (pow x 2))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/2025 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 3))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(/ 945/2 (pow x 5))
(* -1 (/ (- (* 19845/4 (/ 1 (pow x 2))) 945/2) (pow x 5)))
(* -1 (/ (- (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4))) 945/2) (pow x 5)))
(* -1 (/ (- (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4))) (+ 945/2 (* 16253055/16 (/ 1 (pow x 6))))) (pow x 5)))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2/945 (pow x 2))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))

Outputs
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
#s(literal 3 binary64)
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(fma.f64 (fma.f64 #s(literal 1/75 binary64) (.f64 x x) #s(literal -1/5 binary64)) (.f64 x x) #s(literal 3 binary64))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/1125 binary64) (.f64 x x) #s(literal 1/75 binary64)) (.f64 x x) #s(literal -1/5 binary64)) (*.f64 x x) #s(literal 3 binary64))
#s(literal 3 binary64)
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
#s(literal 3 binary64)
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(fma.f64 (fma.f64 #s(literal 1/75 binary64) (.f64 x x) #s(literal -1/5 binary64)) (.f64 x x) #s(literal 3 binary64))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/1125 binary64) (.f64 x x) #s(literal 1/75 binary64)) (.f64 x x) #s(literal -1/5 binary64)) (*.f64 x x) #s(literal 3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(*.f64 #s(literal -1/9 binary64) x)
(*.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/9 binary64)) x)
(*.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/9 binary64)) x)
(*.f64 (fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/9 binary64)) x)
#s(literal -1/9 binary64)
(fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/9 binary64))
(fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/9 binary64))
(fma.f64 #s(literal 1/2025 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/9 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
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(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(.f64 #s(literal 2/945 binary64) (.f64 x x))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))

rewrite157.0ms (1%)

Memory

7.0MiB live, 238.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	308
0	67	306
1	274	294
2	1857	294
0	8288	284

Stop Event

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

Counts

21 → 547

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
(/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))
(.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x)
#s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64))
(/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)))
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))))
(pow.f64 x #s(literal -1 binary64))
(*.f64 x x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))

Outputs
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eval155.0ms (0.9%)

Memory: -0.1MiB live, 276.0MiB allocated
Compiler: Compiled 34 358 to 2 610 computations (92.4% saved)

prune24.0ms (0.1%)

Memory

-8.8MiB live, 76.5MiB allocated

Pruning

10 alts after pruning (1 fresh and 9 done)

	Pruned	Kept	Total
New	993	1	994
Fresh	0	0	0
Picked	1	4	5
Done	0	5	5
Total	994	10	1 004

Accuracy

100.0%

Counts

1 004 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
✓	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
✓	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)))
✓	99.9%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
✓	99.2%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) #s(approx (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/175 binary64) (.f64 x x) #s(literal -1/5 binary64)) (.f64 x x) #s(literal 3 binary64)) x))))
✓	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
✓	98.7%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 607 to 271 computations (55.4% saved)

regimes10.0ms (0.1%)

Memory

23.8MiB live, 23.8MiB allocated

Counts

16 → 1

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) #s(approx (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/175 binary64) (.f64 x x) #s(literal -1/5 binary64)) (.f64 x x) #s(literal 3 binary64)) x))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/945 binary64))) x))

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))

Calls

2 calls:

5.0ms	x
4.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes4.0ms (0%)

Memory

10.6MiB live, 10.6MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes5.0ms (0%)

Memory

-29.1MiB live, 9.9MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))

#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))

Calls

2 calls:

2.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
2.0ms	x

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes3.0ms (0%)

Memory

8.3MiB live, 8.3MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))

Calls

2 calls:

2.0ms	x
1.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes2.0ms (0%)

Memory

6.5MiB live, 6.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Calls

2 calls:

1.0ms	x
1.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify24.0ms (0.1%)

Memory

-20.6MiB live, 57.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	97
1	36	97

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

soundness666.0ms (4.1%)

Memory

44.2MiB live, 434.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	101
0	29	101
1	123	101
2	933	101
0	8743	101
0	67	324
1	179	324
2	458	318
3	1332	318
4	2094	318
5	3093	318
6	3681	318
7	3948	318
8	5088	318
9	7270	318
0	8431	300
0	119	2018
1	334	2014
2	838	2014
3	1987	2010
4	4664	2010
0	8129	1866

Stop Event

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

Compiler

Compiled 195 to 105 computations (46.2% saved)

preprocess56.0ms (0.3%)

Memory: -27.6MiB live, 90.9MiB allocated
Remove: (negabs x)
Compiler: Compiled 312 to 148 computations (52.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19

start0.0ms (0%)

analyze9.0ms (0.1%)

sample10.2s (62.3%)

explain747.0ms (4.6%)

preprocess35.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0%)

localize242.0ms (1.5%)

series7.0ms (0%)

simplify198.0ms (1.2%)

rewrite103.0ms (0.6%)

eval49.0ms (0.3%)

prune7.0ms (0%)

simplify119.0ms (0.7%)

localize309.0ms (1.9%)

series15.0ms (0.1%)

simplify284.0ms (1.7%)

rewrite168.0ms (1%)

eval76.0ms (0.5%)

prune28.0ms (0.2%)

simplify128.0ms (0.8%)

localize477.0ms (2.9%)

series25.0ms (0.2%)

simplify141.0ms (0.9%)

rewrite219.0ms (1.3%)

eval172.0ms (1.1%)

prune183.0ms (1.1%)

simplify181.0ms (1.1%)

localize934.0ms (5.7%)

series25.0ms (0.2%)

simplify170.0ms (1%)

rewrite157.0ms (1%)

eval155.0ms (0.9%)

prune24.0ms (0.1%)

regimes10.0ms (0.1%)

regimes4.0ms (0%)

regimes5.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

simplify24.0ms (0.1%)

soundness666.0ms (4.1%)

preprocess56.0ms (0.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19