Metrics for cos2 (problem 3.4.1)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample1.8s (23.1%)

Memory

49.0MiB live, 1 866.0MiB allocated

Samples

663.0ms	2 202×	2	valid
490.0ms	4 232×	0	valid
208.0ms	570×	3	valid
153.0ms	1 252×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

ival-cos: 811.0ms (69.1% of total)

ival-div: 100.0ms (8.5% of total)

adjust: 94.0ms (8% of total)

ival-sub: 90.0ms (7.7% of total)

ival-mult: 65.0ms (5.5% of total)

ival-true: 6.0ms (0.5% of total)

exact: 5.0ms (0.4% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain193.0ms (2.5%)

Memory

8.9MiB live, 201.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
85	1	(6.548636514882421e+268)	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
56	1	(4.494148365799654e+161)	-	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`(*.f64 x x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	86	5
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`	u/u	54	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	54
↳	`(*.f64 x x)`	underflow	54
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`	n/o	3	0
↳	`(*.f64 x x)`	overflow	69

Confusion

	Predicted +	Predicted -
+	138	0
-	5	113

Precision

0.965034965034965

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	138	0	0
-	5	5	108

Precision?

0.9324324324324325

Recall?

1.0

Freqs

test

number	freq
0	113
1	143

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

45.0ms	154×	2	valid
34.0ms	22×	3	valid
23.0ms	244×	0	valid
10.0ms	92×	1	valid

Compiler

Compiled 50 to 22 computations (56% saved)

Precisions

Click to see histograms. Total time spent on operations: 92.0ms

ival-cos: 70.0ms (76.4% of total)

ival-div: 6.0ms (6.5% of total)

adjust: 6.0ms (6.5% of total)

ival-sub: 5.0ms (5.5% of total)

ival-mult: 4.0ms (4.4% of total)

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

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

exact: 0.0ms (0% of total)

preprocess79.0ms (1%)

Memory

-8.9MiB live, 40.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	32	17
2	102	16
3	300	16
4	772	16
5	1212	16
6	1321	16
7	1337	16
0	6	8
0	10	8
1	19	8
2	30	8
3	46	8
4	82	8
5	131	8
6	188	8
7	324	8
8	629	8
9	1047	8
10	1179	8
0	1179	8

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.0%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify27.0ms (0.3%)

Memory

-4.3MiB live, 33.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(cos.f64 x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
0	10	19
1	19	19
2	30	19
3	46	19
4	82	19
5	131	19
6	188	19
7	324	19
8	629	19
9	1047	19
10	1179	19
0	1179	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize51.0ms (0.6%)

Memory

9.2MiB live, 82.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(cos.f64 x)
accuracy	13.406095877945296	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
accuracy	18.70036259678346	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

21.0ms	77×	2	valid
13.0ms	122×	0	valid
5.0ms	46×	1	valid
3.0ms	11×	3	valid

Compiler

Compiled 21 to 8 computations (61.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-cos: 19.0ms (63.8% of total)

ival-div: 3.0ms (10.1% of total)

adjust: 3.0ms (10.1% of total)

ival-sub: 3.0ms (10.1% of total)

ival-mult: 2.0ms (6.7% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0%)

Memory

6.6MiB live, 6.6MiB allocated

Counts

4 → 16

Calls

Call 1

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

Outputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(pow x 2)
(/ (- 1 (cos x)) (pow x 2))
(- 1 (cos x))
(cos x)

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((/ (- 1 (cos x)) (* x x)) (- 1 (cos x)) (cos x) (* x x))
1.0ms	x	@	0	((/ (- 1 (cos x)) (* x x)) (- 1 (cos x)) (cos x) (* x x))
1.0ms	x	@	inf	((/ (- 1 (cos x)) (* x x)) (- 1 (cos x)) (cos x) (* x x))

simplify217.0ms (2.8%)

Memory

9.5MiB live, 166.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	153
1	105	153
2	258	153
3	601	153
4	1281	153
5	1981	153
6	2536	153
7	3409	153
8	4960	153
9	6581	153
10	7480	153
11	7690	153
12	7708	153
13	7710	153
0	8119	135

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 16

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(pow x 2)
(/ (- 1 (cos x)) (pow x 2))
(- 1 (cos x))
(cos x)

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/720 binary64) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)

rewrite260.0ms (3.3%)

Memory

-5.8MiB live, 204.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	17
1	40	17
2	270	17
3	2843	17
0	9915	17

Stop Event

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

Counts

4 → 629

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (/.f64 (.f64 (neg.f64 x) x) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x))) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
(.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 x #s(literal -2 binary64))) (pow.f64 x #s(literal -4 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (pow.f64 (pow.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -4 binary64)))
(*.f64 (pow.f64 (/.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 x (-.f64 (cos.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 x (-.f64 (cos.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (pow.f64 x #s(literal -2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 x (-.f64 (cos.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x))
(*.f64 (pow.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (/.f64 x (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) x) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64))))
(.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)) (pow.f64 (.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 x (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 x (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 x (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 x #s(literal -2 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)))
(.f64 (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 x #s(literal -2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 x #s(literal -2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)))
(.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 x #s(literal -2 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 (cos.f64 x) #s(literal 1 binary64))) (neg.f64 (pow.f64 x #s(literal -2 binary64))))
(.f64 (pow.f64 (.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x) #s(literal -1/2 binary64)))
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) x) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) x))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) x) (/.f64 (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64)) x))
(*.f64 (pow.f64 (pow.f64 (/.f64 x (sin.f64 x)) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64)))
(.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 x #s(literal -2 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 x #s(literal -2 binary64))) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64)))
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(.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)
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(*.f64 x x)
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eval125.0ms (1.6%)

Memory: 12.7MiB live, 85.8MiB allocated
Compiler: Compiled 13 688 to 1 661 computations (87.9% saved)

prune100.0ms (1.3%)

Memory

3.9MiB live, 41.6MiB allocated

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	631	14	645
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	631	15	646

Accuracy

100.0%

Counts

646 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	21.4%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
	49.1%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	49.0%	(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (/.f64 (cos.f64 x) x))) (neg.f64 x))
	13.4%	(/.f64 (-.f64 (.f64 (neg.f64 x) x) (.f64 (.f64 (neg.f64 x) x) (cos.f64 x))) (.f64 (.f64 (neg.f64 x) x) (.f64 x x)))
	17.6%	(/.f64 (-.f64 (neg.f64 x) (.f64 (.f64 (neg.f64 x) x) (/.f64 (cos.f64 x) x))) (.f64 (.f64 (neg.f64 x) x) x))
	43.4%	(/.f64 (-.f64 x (*.f64 x (cos.f64 x))) (pow.f64 x #s(literal 3 binary64)))
	47.9%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))
✓	48.0%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	28.6%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
▶	78.3%	(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
▶	48.6%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
	49.0%	(*.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
▶	53.8%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
	53.4%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
▶	54.5%	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Compiler

Compiled 376 to 240 computations (36.2% saved)

simplify246.0ms (3.1%)

Memory

-9.0MiB live, 107.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
cost-diff	2	(-.f64 (.f64 x x) (.f64 (*.f64 x x) (cos.f64 x)))
cost-diff	8	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x))
cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
cost-diff	0	(/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
cost-diff	0	(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)
cost-diff	2	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
cost-diff	0	(tan.f64 (/.f64 x #s(literal 2 binary64)))
cost-diff	0	(sin.f64 x)
cost-diff	0	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
cost-diff	0	(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	173
0	47	155
1	93	153
2	191	153
3	486	149
4	1448	149
5	2950	149
6	4318	149
0	8034	149

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(sin.f64 x)
x
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 x x)
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
#s(literal 1/720 binary64)
(*.f64 x x)
x
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
#s(literal 1 binary64)
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)
(/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
x
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x))
(-.f64 (.f64 x x) (.f64 (*.f64 x x) (cos.f64 x)))
(*.f64 x x)
x
(.f64 (.f64 x x) (cos.f64 x))
(cos.f64 x)

Outputs
(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
(*.f64 (/.f64 (/.f64 (sin.f64 x) x) x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x))
(sin.f64 x)
x
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 x x)
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
#s(literal 1/720 binary64)
(*.f64 x x)
x
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
#s(literal 1 binary64)
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)
(/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
x
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(-.f64 (.f64 x x) (.f64 (*.f64 x x) (cos.f64 x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(*.f64 x x)
x
(.f64 (.f64 x x) (cos.f64 x))
(.f64 (.f64 (cos.f64 x) x) x)
(cos.f64 x)

localize208.0ms (2.7%)

Memory

-33.3MiB live, 242.3MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.05078125	(.f64 (.f64 x x) (cos.f64 x))
accuracy	13.406095877945296	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
accuracy	15.174618810789458	(-.f64 (.f64 x x) (.f64 (*.f64 x x) (cos.f64 x)))
accuracy	40.689114722080554	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x))
accuracy	0.12890625	(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)
accuracy	0.3158066750940733	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
accuracy	13.1363510167756	(/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
accuracy	18.70036259678346	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	0.0	(*.f64 x x)
accuracy	0.03125	(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.03125	(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
accuracy	29.54902509315436	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
accuracy	29.12704441130743	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
accuracy	0.0	(tan.f64 (/.f64 x #s(literal 2 binary64)))
accuracy	0.0	(sin.f64 x)
accuracy	0.15234375	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
accuracy	13.406095877945296	(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))

Samples

106.0ms	122×	0	valid
50.0ms	77×	2	valid
18.0ms	47×	1	valid
8.0ms	10×	3	valid

Compiler

Compiled 164 to 28 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 117.0ms

ival-div: 33.0ms (28.3% of total)

ival-mult: 23.0ms (19.7% of total)

ival-cos: 20.0ms (17.1% of total)

adjust: 10.0ms (8.6% of total)

ival-sin: 9.0ms (7.7% of total)

const: 8.0ms (6.9% of total)

ival-sub: 5.0ms (4.3% of total)

ival-tan: 5.0ms (4.3% of total)

ival-add: 4.0ms (3.4% of total)

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

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

exact: 0.0ms (0% of total)

series12.0ms (0.2%)

Memory

13.8MiB live, 13.8MiB allocated

Counts

17 → 49

Calls

Call 1

Inputs
(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(sin.f64 x)
(tan.f64 (/.f64 x #s(literal 2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(*.f64 x x)
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)
(/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x))
(-.f64 (.f64 x x) (.f64 (*.f64 x x) (cos.f64 x)))
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
(.f64 (.f64 x x) (cos.f64 x))

Outputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
-1/24
(- (* 1/720 (pow x 2)) 1/24)
(pow x 2)
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))
(/ 2 x)
(/ (+ 2 (* 1/6 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))) x)
(/ (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2))))))) x)
(* 1/2 (pow x 4))
(* (pow x 4) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* (pow x 2) (+ 1 (* -1/2 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(sin x)
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (- 1 (cos x)) (pow x 2))
(* 1/720 (pow x 4))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 2))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(/ (pow x 2) (- 1 (cos x)))
(/ x (- 1 (cos x)))
(- 1 (cos x))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (cos x))

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((/ (* (sin x) (tan (/ x 2))) (* x x)) (* (sin x) (tan (/ x 2))) (sin x) (tan (/ x 2)) (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x)) (+ (* (+ (* 1/720 (* x x)) -1/24) (* x x)) 1/2) (+ (* 1/720 (* x x)) -1/24) (* x x) (/ 1 (* (/ x (- 1 (cos x))) x)) (* (/ x (- 1 (cos x))) x) (/ x (- 1 (cos x))) (- 1 (cos x)) (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (- (* x x) (* (* x x) (cos x))) (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (* (* x x) (cos x)))
4.0ms	x	@	inf	((/ (* (sin x) (tan (/ x 2))) (* x x)) (* (sin x) (tan (/ x 2))) (sin x) (tan (/ x 2)) (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x)) (+ (* (+ (* 1/720 (* x x)) -1/24) (* x x)) 1/2) (+ (* 1/720 (* x x)) -1/24) (* x x) (/ 1 (* (/ x (- 1 (cos x))) x)) (* (/ x (- 1 (cos x))) x) (/ x (- 1 (cos x))) (- 1 (cos x)) (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (- (* x x) (* (* x x) (cos x))) (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (* (* x x) (cos x)))
2.0ms	x	@	0	((/ (* (sin x) (tan (/ x 2))) (* x x)) (* (sin x) (tan (/ x 2))) (sin x) (tan (/ x 2)) (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x)) (+ (* (+ (* 1/720 (* x x)) -1/24) (* x x)) 1/2) (+ (* 1/720 (* x x)) -1/24) (* x x) (/ 1 (* (/ x (- 1 (cos x))) x)) (* (/ x (- 1 (cos x))) x) (/ x (- 1 (cos x))) (- 1 (cos x)) (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (- (* x x) (* (* x x) (cos x))) (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (* (* x x) (cos x)))

Time

Variable

Point

Expression

5.0ms

-inf

((/ (* (sin x) (tan (/ x 2))) (* x x)) (* (sin x) (tan (/ x 2))) (sin x) (tan (/ x 2)) (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x)) (+ (* (+ (* 1/720 (* x x)) -1/24) (* x x)) 1/2) (+ (* 1/720 (* x x)) -1/24) (* x x) (/ 1 (* (/ x (- 1 (cos x))) x)) (* (/ x (- 1 (cos x))) x) (/ x (- 1 (cos x))) (- 1 (cos x)) (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (- (* x x) (* (* x x) (cos x))) (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (* (* x x) (cos x)))

4.0ms

inf

((/ (* (sin x) (tan (/ x 2))) (* x x)) (* (sin x) (tan (/ x 2))) (sin x) (tan (/ x 2)) (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x)) (+ (* (+ (* 1/720 (* x x)) -1/24) (* x x)) 1/2) (+ (* 1/720 (* x x)) -1/24) (* x x) (/ 1 (* (/ x (- 1 (cos x))) x)) (* (/ x (- 1 (cos x))) x) (/ x (- 1 (cos x))) (- 1 (cos x)) (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (- (* x x) (* (* x x) (cos x))) (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (* (* x x) (cos x)))

2.0ms

((/ (* (sin x) (tan (/ x 2))) (* x x)) (* (sin x) (tan (/ x 2))) (sin x) (tan (/ x 2)) (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x)) (+ (* (+ (* 1/720 (* x x)) -1/24) (* x x)) 1/2) (+ (* 1/720 (* x x)) -1/24) (* x x) (/ 1 (* (/ x (- 1 (cos x))) x)) (* (/ x (- 1 (cos x))) x) (/ x (- 1 (cos x))) (- 1 (cos x)) (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (- (* x x) (* (* x x) (cos x))) (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (* (* x x) (cos x)))

simplify155.0ms (2%)

Memory

2.2MiB live, 157.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	125	516
1	356	516
2	923	504
3	2974	504
4	5615	504
5	7113	504
0	8080	451

Stop Event

1×	iter limit
1×	node limit

Counts

49 → 48

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
-1/24
(- (* 1/720 (pow x 2)) 1/24)
(pow x 2)
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))
(/ 2 x)
(/ (+ 2 (* 1/6 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))) x)
(/ (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2))))))) x)
(* 1/2 (pow x 4))
(* (pow x 4) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* (pow x 2) (+ 1 (* -1/2 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(sin x)
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (- 1 (cos x)) (pow x 2))
(* 1/720 (pow x 4))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 2))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(/ (pow x 2) (- 1 (cos x)))
(/ x (- 1 (cos x)))
(- 1 (cos x))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (cos x))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
-1/24
#s(literal -1/24 binary64)
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(pow x 2)
(*.f64 x x)
2
#s(literal 2 binary64)
(+ 2 (* 1/6 (pow x 2)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/3024 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 2 binary64))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* 1/6 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2))))))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/3024 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(* 1/2 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(* (pow x 4) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1 (* -1/2 (pow x 2))))
(fma.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x) x)
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 x x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(.f64 (/.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) x)))
(sin x)
(sin.f64 x)
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* 1/720 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/720 binary64))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)) x) x)
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(* 1/720 (pow x 2))
(.f64 #s(literal 1/720 binary64) (.f64 x x))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(/ (pow x 2) (- 1 (cos x)))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)
(/ x (- 1 (cos x)))
(/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* (pow x 2) (- 1 (cos x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* (pow x 2) (cos x))
(.f64 (.f64 (cos.f64 x) x) x)

rewrite174.0ms (2.2%)

Memory

-14.8MiB live, 252.9MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	150
0	47	128
1	189	126
2	1242	126
0	8593	126

Stop Event

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

Counts

17 → 1 252

Calls

Call 1

Inputs
(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(sin.f64 x)
(tan.f64 (/.f64 x #s(literal 2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(*.f64 x x)
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)
(/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x))
(-.f64 (.f64 x x) (.f64 (*.f64 x x) (cos.f64 x)))
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
(.f64 (.f64 x x) (cos.f64 x))

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

eval129.0ms (1.6%)

Memory: 18.8MiB live, 168.4MiB allocated
Compiler: Compiled 23 822 to 3 219 computations (86.5% saved)

prune48.0ms (0.6%)

Memory

3.4MiB live, 92.5MiB allocated

Pruning

18 alts after pruning (13 fresh and 5 done)

	Pruned	Kept	Total
New	953	9	962
Fresh	5	4	9
Picked	1	4	5
Done	0	1	1
Total	959	18	977

Accuracy

100.0%

Counts

977 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	21.5%	(/.f64 (/.f64 (fma.f64 (neg.f64 x) (.f64 (cos.f64 x) x) (.f64 x x)) (.f64 x x)) (.f64 x x))
▶	21.4%	(/.f64 (/.f64 (fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)) (.f64 x x)) (.f64 x x))
✓	21.4%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
	49.1%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	21.4%	(/.f64 (/.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x))) (.f64 x x)) (.f64 x x))
	21.4%	(/.f64 (/.f64 #s(approx (- (* x x) (* (* x x) (cos x))) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)) (.f64 x x)) (.f64 x x))
	49.0%	(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (/.f64 (cos.f64 x) x))) (neg.f64 x))
✓	48.0%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	28.6%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
	78.3%	(/.f64 (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 x)) (*.f64 x x))
▶	13.4%	(/.f64 (neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x)))) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
✓	48.6%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
	82.3%	(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ x (- 1 (cos x))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 2 binary64)) x)) x))
▶	82.5%	(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))
▶	47.9%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
✓	53.8%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
▶	53.4%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
✓	54.5%	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Compiler

Compiled 464 to 291 computations (37.3% saved)

simplify602.0ms (7.7%)

Memory

-37.1MiB live, 172.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)
cost-diff	0	(/.f64 (/.f64 (fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)) (.f64 x x)) (.f64 x x))
cost-diff	2	(fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x))
cost-diff	8	(/.f64 (fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)) (*.f64 x x))
cost-diff	1	(neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x))))
cost-diff	2	(.f64 x (.f64 (neg.f64 x) x))
cost-diff	2	(.f64 (.f64 x (*.f64 (neg.f64 x) x)) x)
cost-diff	5	(/.f64 (neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x)))) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
cost-diff	0	(+.f64 #s(literal -1 binary64) (cos.f64 x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 #s(literal -1 binary64) (*.f64 x x))
cost-diff	2	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))
cost-diff	0	#s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64)))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	230
0	61	210
1	130	204
2	317	195
3	1138	189
4	3287	189
5	5026	189
6	6101	189
7	7245	189
0	8031	189

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))
#s(literal 1 binary64)
#s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))
#s(literal 1/6 binary64)
(*.f64 x x)
x
#s(literal 2 binary64)
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
#s(literal -1 binary64)
(*.f64 x x)
x
(+.f64 #s(literal -1 binary64) (cos.f64 x))
(cos.f64 x)
(/.f64 (neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x)))) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
(neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x))))
(.f64 x (-.f64 x (.f64 (cos.f64 x) x)))
x
(-.f64 x (*.f64 (cos.f64 x) x))
(*.f64 (cos.f64 x) x)
(cos.f64 x)
(.f64 (.f64 x (*.f64 (neg.f64 x) x)) x)
(.f64 x (.f64 (neg.f64 x) x))
(*.f64 (neg.f64 x) x)
(neg.f64 x)
(/.f64 (/.f64 (fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)) (.f64 x x)) (.f64 x x))
(/.f64 (fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)) (*.f64 x x))
(fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x))
x
(.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)
(neg.f64 (*.f64 (cos.f64 x) x))
(*.f64 (cos.f64 x) x)
(cos.f64 x)
(*.f64 x x)

Outputs
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 2 binary64))))
#s(literal 1 binary64)
#s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64)))
#s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 2 binary64)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 2 binary64))
#s(literal 1/6 binary64)
(*.f64 x x)
x
#s(literal 2 binary64)
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/.f64 #s(literal -1 binary64) (*.f64 x x))
#s(literal -1 binary64)
(*.f64 x x)
x
(+.f64 #s(literal -1 binary64) (cos.f64 x))
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(cos.f64 x)
(/.f64 (neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x)))) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x))))
(.f64 (.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) x)
(.f64 x (-.f64 x (.f64 (cos.f64 x) x)))
(.f64 (-.f64 x (.f64 (cos.f64 x) x)) x)
x
(-.f64 x (*.f64 (cos.f64 x) x))
(*.f64 (cos.f64 x) x)
(cos.f64 x)
(.f64 (.f64 x (*.f64 (neg.f64 x) x)) x)
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(.f64 x (.f64 (neg.f64 x) x))
(pow.f64 (neg.f64 x) #s(literal 3 binary64))
(*.f64 (neg.f64 x) x)
(neg.f64 x)
(/.f64 (/.f64 (fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/.f64 (fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)) (*.f64 x x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x))
(.f64 (-.f64 x (.f64 (cos.f64 x) x)) x)
x
(.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)
(.f64 (.f64 (neg.f64 x) (cos.f64 x)) x)
(neg.f64 (*.f64 (cos.f64 x) x))
(*.f64 (neg.f64 x) (cos.f64 x))
(*.f64 (cos.f64 x) x)
(cos.f64 x)
(*.f64 x x)

localize207.0ms (2.6%)

Memory

26.6MiB live, 299.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.10546875	(*.f64 (cos.f64 x) x)
accuracy	13.406095877945296	(/.f64 (/.f64 (fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)) (.f64 x x)) (.f64 x x))
accuracy	26.554180137786545	(fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x))
accuracy	40.689114722080554	(/.f64 (fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)) (*.f64 x x))
accuracy	0.08984375	(.f64 x (-.f64 x (.f64 (cos.f64 x) x)))
accuracy	0.10546875	(*.f64 (cos.f64 x) x)
accuracy	12.151854836780505	(-.f64 x (*.f64 (cos.f64 x) x))
accuracy	46.430361408022684	(/.f64 (neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x)))) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
accuracy	0.0	(cos.f64 x)
accuracy	0.38962206650090925	(/.f64 #s(literal -1 binary64) (*.f64 x x))
accuracy	14.41453545664796	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
accuracy	18.70036259678346	(+.f64 #s(literal -1 binary64) (cos.f64 x))
accuracy	0.0	(*.f64 x x)
accuracy	0.08984375	(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
accuracy	29.82369706853706	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
accuracy	0.0	(*.f64 x x)
accuracy	0.08984375	(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))
accuracy	0.3158066750940733	(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))
accuracy	10.936090955450958	#s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64)))

Samples

70.0ms	77×	2	valid
36.0ms	122×	0	valid
26.0ms	47×	1	valid
11.0ms	10×	3	valid

Compiler

Compiled 216 to 37 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 110.0ms

ival-mult: 27.0ms (24.6% of total)

ival-cos: 23.0ms (21% of total)

ival-div: 18.0ms (16.4% of total)

adjust: 14.0ms (12.8% of total)

ival-sub: 9.0ms (8.2% of total)

ival-add: 8.0ms (7.3% of total)

const: 6.0ms (5.5% of total)

ival-neg: 5.0ms (4.6% of total)

exact: 1.0ms (0.9% of total)

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

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

series18.0ms (0.2%)

Memory

-4.3MiB live, 32.1MiB allocated

Counts

21 → 63

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))
#s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(+.f64 #s(literal -1 binary64) (cos.f64 x))
(/.f64 (neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x)))) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
(.f64 (.f64 x (*.f64 (neg.f64 x) x)) x)
(.f64 x (.f64 (neg.f64 x) x))
(neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x))))
(/.f64 (fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)) (*.f64 x x))
(fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x))
(/.f64 (/.f64 (fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)) (.f64 x x)) (.f64 x x))
(.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)
(cos.f64 x)
(-.f64 x (*.f64 (cos.f64 x) x))
(*.f64 (cos.f64 x) x)
(.f64 x (-.f64 x (.f64 (cos.f64 x) x)))

Outputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))
(pow x 2)
(/ -1 (pow x 2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(* -1 (pow x 4))
(* -1 (pow x 3))
(* -1/2 (pow x 4))
(* (pow x 4) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* 1/2 (pow x 4))
(* (pow x 4) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* -1 (pow x 2))
(* (pow x 2) (- (* 1/2 (pow x 2)) 1))
(* (pow x 2) (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1))
(* (pow x 2) (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* 1/2 (pow x 3))
(* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
x
(* x (+ 1 (* -1/2 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(/ (- 1 (cos x)) (pow x 2))
(/ (pow x 2) (- 1 (cos x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(- (cos x) 1)
(* (pow x 2) (- (cos x) 1))
(+ 1 (* -1 (cos x)))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(* -1 (* (pow x 2) (cos x)))
(cos x)
(* x (- 1 (cos x)))
(* x (cos x))
(* (pow x 2) (- 1 (cos x)))
(* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))
(* x (+ 1 (* -1 (cos x))))

Calls

3 calls:

Time

Variable

Point

Expression

10.0ms

-inf

((/ 1 (* (/ x (- 1 (cos x))) x)) (* (/ x (- 1 (cos x))) x) (+ (* 1/6 (* x x)) 2) (* x x) (/ (- 1 (cos x)) (* x x)) (+ (* (* x x) -1/24) 1/2) (* (/ -1 (* x x)) (+ -1 (cos x))) (/ -1 (* x x)) (+ -1 (cos x)) (/ (neg (* x (- x (* (cos x) x)))) (* (* x (* (neg x) x)) x)) (* (* x (* (neg x) x)) x) (* x (* (neg x) x)) (neg (* x (- x (* (cos x) x)))) (/ (+ (* x x) (* (neg (* (cos x) x)) x)) (* x x)) (+ (* x x) (* (neg (* (cos x) x)) x)) (/ (/ (+ (* x x) (* (neg (* (cos x) x)) x)) (* x x)) (* x x)) (* (neg (* (cos x) x)) x) (cos x) (- x (* (cos x) x)) (* (cos x) x) (* x (- x (* (cos x) x))))

4.0ms

inf

((/ 1 (* (/ x (- 1 (cos x))) x)) (* (/ x (- 1 (cos x))) x) (+ (* 1/6 (* x x)) 2) (* x x) (/ (- 1 (cos x)) (* x x)) (+ (* (* x x) -1/24) 1/2) (* (/ -1 (* x x)) (+ -1 (cos x))) (/ -1 (* x x)) (+ -1 (cos x)) (/ (neg (* x (- x (* (cos x) x)))) (* (* x (* (neg x) x)) x)) (* (* x (* (neg x) x)) x) (* x (* (neg x) x)) (neg (* x (- x (* (cos x) x)))) (/ (+ (* x x) (* (neg (* (cos x) x)) x)) (* x x)) (+ (* x x) (* (neg (* (cos x) x)) x)) (/ (/ (+ (* x x) (* (neg (* (cos x) x)) x)) (* x x)) (* x x)) (* (neg (* (cos x) x)) x) (cos x) (- x (* (cos x) x)) (* (cos x) x) (* x (- x (* (cos x) x))))

3.0ms

((/ 1 (* (/ x (- 1 (cos x))) x)) (* (/ x (- 1 (cos x))) x) (+ (* 1/6 (* x x)) 2) (* x x) (/ (- 1 (cos x)) (* x x)) (+ (* (* x x) -1/24) 1/2) (* (/ -1 (* x x)) (+ -1 (cos x))) (/ -1 (* x x)) (+ -1 (cos x)) (/ (neg (* x (- x (* (cos x) x)))) (* (* x (* (neg x) x)) x)) (* (* x (* (neg x) x)) x) (* x (* (neg x) x)) (neg (* x (- x (* (cos x) x)))) (/ (+ (* x x) (* (neg (* (cos x) x)) x)) (* x x)) (+ (* x x) (* (neg (* (cos x) x)) x)) (/ (/ (+ (* x x) (* (neg (* (cos x) x)) x)) (* x x)) (* x x)) (* (neg (* (cos x) x)) x) (cos x) (- x (* (cos x) x)) (* (cos x) x) (* x (- x (* (cos x) x))))

simplify223.0ms (2.8%)

Memory

-11.5MiB live, 191.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	118	638
1	341	632
2	893	626
3	2885	626
4	4156	626
5	6965	626
0	8071	567

Stop Event

1×	iter limit
1×	node limit

Counts

63 → 62

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))
(pow x 2)
(/ -1 (pow x 2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(* -1 (pow x 4))
(* -1 (pow x 3))
(* -1/2 (pow x 4))
(* (pow x 4) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* 1/2 (pow x 4))
(* (pow x 4) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* -1 (pow x 2))
(* (pow x 2) (- (* 1/2 (pow x 2)) 1))
(* (pow x 2) (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1))
(* (pow x 2) (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* 1/2 (pow x 3))
(* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
x
(* x (+ 1 (* -1/2 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(/ (- 1 (cos x)) (pow x 2))
(/ (pow x 2) (- 1 (cos x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(- (cos x) 1)
(* (pow x 2) (- (cos x) 1))
(+ 1 (* -1 (cos x)))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(* -1 (* (pow x 2) (cos x)))
(cos x)
(* x (- 1 (cos x)))
(* x (cos x))
(* (pow x 2) (- 1 (cos x)))
(* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))
(* x (+ 1 (* -1 (cos x))))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
2
#s(literal 2 binary64)
(+ 2 (* 1/6 (pow x 2)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/3024 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 2 binary64))
(pow x 2)
(*.f64 x x)
(/ -1 (pow x 2))
(/.f64 (/.f64 #s(literal -1 binary64) x) x)
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 x x) #s(literal -1/720 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x) x)
(* -1 (pow x 4))
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(* -1 (pow x 3))
(pow.f64 (neg.f64 x) #s(literal 3 binary64))
(* -1/2 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64))
(* (pow x 4) (- (* 1/24 (pow x 2)) 1/2))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))
(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 x x) #s(literal -1/720 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* 1/2 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(* (pow x 4) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (* 1/2 (pow x 2)) 1))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64) (neg.f64 x)) x)
(* (pow x 2) (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1))
(*.f64 (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/24 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64) (neg.f64 x))) x)
(* (pow x 2) (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64) (neg.f64 x)) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(* 1/2 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64))
(* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
x
(* x (+ 1 (* -1/2 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (pow x 2) (- 1 (cos x)))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(- (cos x) 1)
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(* (pow x 2) (- (cos x) 1))
(.f64 (.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) x)
(+ 1 (* -1 (cos x)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* -1 (* (pow x 2) (cos x)))
(.f64 (neg.f64 x) (.f64 (cos.f64 x) x))
(cos x)
(cos.f64 x)
(* x (- 1 (cos x)))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(* x (cos x))
(*.f64 (cos.f64 x) x)
(* (pow x 2) (- 1 (cos x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))
(.f64 (.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) x)
(* x (+ 1 (* -1 (cos x))))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)

rewrite164.0ms (2.1%)

Memory

14.4MiB live, 210.3MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	191
0	61	171
1	247	160
2	1727	154
0	8740	154

Stop Event

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

Counts

21 → 1 434

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))
#s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(+.f64 #s(literal -1 binary64) (cos.f64 x))
(/.f64 (neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x)))) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
(.f64 (.f64 x (*.f64 (neg.f64 x) x)) x)
(.f64 x (.f64 (neg.f64 x) x))
(neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x))))
(/.f64 (fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)) (*.f64 x x))
(fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x))
(/.f64 (/.f64 (fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)) (.f64 x x)) (.f64 x x))
(.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)
(cos.f64 x)
(-.f64 x (*.f64 (cos.f64 x) x))
(*.f64 (cos.f64 x) x)
(.f64 x (-.f64 x (.f64 (cos.f64 x) x)))

Outputs
(.f64 (pow.f64 #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 2 binary64)))))
(.f64 (pow.f64 #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (pow.f64 #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 2 binary64))) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 2 binary64))))) #s(literal -1 binary64))
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(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 x (fma.f64 (cos.f64 x) x x))) (.f64 (.f64 x (fma.f64 (cos.f64 x) x x)) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 (.f64 x (fma.f64 (cos.f64 x) x x)) (.f64 x (fma.f64 (cos.f64 x) x x))))
(/.f64 (.f64 (-.f64 (.f64 x x) (pow.f64 (*.f64 (cos.f64 x) x) #s(literal 2 binary64))) x) (fma.f64 (cos.f64 x) x x))
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(/.f64 (.f64 x (-.f64 (.f64 x x) (pow.f64 (*.f64 (cos.f64 x) x) #s(literal 2 binary64)))) (fma.f64 (cos.f64 x) x x))
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(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 x (fma.f64 (cos.f64 x) x x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 x) x) x) #s(literal 3 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 (neg.f64 x) (cos.f64 x))))))
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(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (.f64 (-.f64 x (.f64 (cos.f64 x) x)) x) #s(literal -1 binary64))))
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (cos.f64 x) x) (fma.f64 (cos.f64 x) x x) (.f64 x x)) (.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) x) #s(literal 3 binary64))))))
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(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 (*.f64 (neg.f64 x) (cos.f64 x)) x))
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(fma.f64 x x (.f64 (.f64 (neg.f64 x) (cos.f64 x)) x))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (*.f64 (neg.f64 x) (cos.f64 x)) x))
(-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (neg.f64 (cos.f64 x)) (.f64 x x) (.f64 (neg.f64 x) x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 (cos.f64 x)) (.f64 x x) (*.f64 (neg.f64 x) x))))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (cos.f64 x) #s(literal -1 binary64)) (.f64 x x))) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 x (fma.f64 (cos.f64 x) x x))))
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(-.f64 (.f64 x x) (.f64 (*.f64 (cos.f64 x) x) x))
(+.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (cos.f64 x) #s(literal -1 binary64)) (.f64 x x))) (neg.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 x (fma.f64 (cos.f64 x) x x)))))
(+.f64 #s(literal 0 binary64) (.f64 (-.f64 x (.f64 (cos.f64 x) x)) x))
(+.f64 (.f64 (.f64 (neg.f64 x) (cos.f64 x)) x) (*.f64 x x))
(+.f64 (.f64 x x) (.f64 (*.f64 (neg.f64 x) (cos.f64 x)) x))

eval97.0ms (1.2%)

Memory: 16.2MiB live, 172.7MiB allocated
Compiler: Compiled 22 993 to 3 006 computations (86.9% saved)

prune32.0ms (0.4%)

Memory

-13.9MiB live, 70.8MiB allocated

Pruning

22 alts after pruning (13 fresh and 9 done)

	Pruned	Kept	Total
New	958	9	967
Fresh	4	4	8
Picked	1	4	5
Done	0	5	5
Total	963	22	985

Accuracy

100.0%

Counts

985 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.4%	(/.f64 (fma.f64 (/.f64 (cos.f64 x) (neg.f64 x)) x #s(literal 1 binary64)) (*.f64 x x))
▶	13.8%	(/.f64 (fma.f64 (.f64 (cos.f64 x) x) x (.f64 (neg.f64 x) x)) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
	13.9%	(/.f64 (fma.f64 (neg.f64 x) x (.f64 (.f64 (cos.f64 x) x) x)) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
	21.5%	(/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) (cos.f64 x)) x (.f64 x x)) (.f64 x x)) (.f64 x x))
✓	21.4%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
	49.1%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	21.4%	(/.f64 (/.f64 #s(approx (- (* x x) (* (* x x) (cos x))) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)) (.f64 x x)) (.f64 x x))
	13.4%	(/.f64 (-.f64 (.f64 (.f64 (cos.f64 x) x) x) (.f64 x x)) (.f64 (.f64 x (.f64 (neg.f64 x) x)) x))
✓	48.0%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
▶	28.6%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
▶	49.0%	(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (cos.f64 x) #s(literal -1 binary64))) x)
	78.3%	(/.f64 (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 x)) (*.f64 x x))
✓	13.4%	(/.f64 (neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x)))) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
✓	48.6%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
▶	82.5%	(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))))
✓	82.5%	(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))
	32.1%	(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* 1/6 (* x x)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
▶	47.9%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64)))))
✓	47.9%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
✓	53.8%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
✓	54.5%	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Compiler

Compiled 542 to 339 computations (37.5% saved)

simplify79.0ms (1%)

Memory

15.1MiB live, 88.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	2	(.f64 x (.f64 (neg.f64 x) x))
cost-diff	2	(.f64 (.f64 x (*.f64 (neg.f64 x) x)) x)
cost-diff	2	(fma.f64 (.f64 (cos.f64 x) x) x (.f64 (neg.f64 x) x))
cost-diff	5	(/.f64 (fma.f64 (.f64 (cos.f64 x) x) x (.f64 (neg.f64 x) x)) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 #s(literal -1 binary64) (*.f64 x x))
cost-diff	2	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64)))))
cost-diff	4	(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
cost-diff	0	(+.f64 (cos.f64 x) #s(literal -1 binary64))
cost-diff	0	(/.f64 #s(literal -1 binary64) x)
cost-diff	0	(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (cos.f64 x) #s(literal -1 binary64))) x)
cost-diff	2	(*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (cos x) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
cost-diff	0	(*.f64 #s(literal 1/6 binary64) x)
cost-diff	0	(fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))
cost-diff	0	#s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	199
0	58	181
1	111	172
2	213	168
3	554	166
4	2236	166
5	5364	166
0	8001	166

Stop Event

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

Calls

Call 1

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

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

localize249.0ms (3.2%)

Memory

7.2MiB live, 251.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.08203125	(.f64 x (.f64 (neg.f64 x) x))
accuracy	0.10546875	(*.f64 (cos.f64 x) x)
accuracy	17.365901303770272	(fma.f64 (.f64 (cos.f64 x) x) x (.f64 (neg.f64 x) x))
accuracy	46.430361408022684	(/.f64 (fma.f64 (.f64 (cos.f64 x) x) x (.f64 (neg.f64 x) x)) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
accuracy	0.38962206650090925	(/.f64 #s(literal -1 binary64) (*.f64 x x))
accuracy	0.8439631129039368	(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
accuracy	14.41453545664796	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64)))))
accuracy	18.70036259678346	(+.f64 (cos.f64 x) #s(literal -1 binary64))
accuracy	0.0	(cos.f64 x)
accuracy	0.0546875	(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (cos.f64 x) #s(literal -1 binary64))) x)
accuracy	13.232771452681884	(*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
accuracy	18.70036259678346	(+.f64 (cos.f64 x) #s(literal -1 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	13.406095877945296	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
accuracy	18.70036259678346	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	26.761033988133995	#s(approx (cos x) #s(literal 1 binary64))
accuracy	0.03125	(fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))
accuracy	0.3158066750940733	(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))))
accuracy	0.32421875	(*.f64 #s(literal 1/6 binary64) x)
accuracy	10.936090955450958	#s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))

Samples

94.0ms	77×	2	valid
81.0ms	122×	0	valid
27.0ms	11×	3	valid
19.0ms	46×	1	valid

Compiler

Compiled 184 to 33 computations (82.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 149.0ms

ival-cos: 43.0ms (28.8% of total)

ival-sub: 29.0ms (19.4% of total)

ival-mult: 29.0ms (19.4% of total)

ival-div: 20.0ms (13.4% of total)

ival-add: 15.0ms (10% of total)

adjust: 8.0ms (5.4% of total)

const: 4.0ms (2.7% of total)

ival-neg: 1.0ms (0.7% of total)

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

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

exact: 0.0ms (0% of total)

series18.0ms (0.2%)

Memory

-10.9MiB live, 25.7MiB allocated

Counts

21 → 49

Calls

Call 1

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

Outputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))
(* 1/6 x)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(pow x 2)
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(/ -1 x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(/ -1 (pow x 2))
(* -1/2 (pow x 4))
(* (pow x 4) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(* -1 (pow x 4))
(* -1 (pow x 3))
x
(* x (+ 1 (* -1/2 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(/ (- 1 (cos x)) (pow x 2))
(/ (pow x 2) (- 1 (cos x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(- 1 (cos x))
(cos x)
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(- (cos x) 1)
(* (pow x 2) (- (cos x) 1))
(* x (cos x))

Calls

3 calls:

Time

Variable

Point

Expression

8.0ms

((/ 1 (* (/ x (- 1 (cos x))) x)) (* (/ x (- 1 (cos x))) x) (+ (* (* 1/6 x) x) 2) (* 1/6 x) (/ (- 1 (cos x)) (* x x)) (- 1 (cos x)) (cos x) (* x x) (* (/ -1 x) (+ (cos x) -1)) (/ (* (/ -1 x) (+ (cos x) -1)) x) (/ -1 x) (+ (cos x) -1) (/ -1 (/ -1 (+ (cos x) -1))) (* (/ -1 (* x x)) (/ -1 (/ -1 (+ (cos x) -1)))) (/ -1 (* x x)) (/ (+ (* (* (cos x) x) x) (* (neg x) x)) (* (* x (* (neg x) x)) x)) (+ (* (* (cos x) x) x) (* (neg x) x)) (* (* x (* (neg x) x)) x) (* x (* (neg x) x)) (cos x) (* (cos x) x))

6.0ms

inf

((/ 1 (* (/ x (- 1 (cos x))) x)) (* (/ x (- 1 (cos x))) x) (+ (* (* 1/6 x) x) 2) (* 1/6 x) (/ (- 1 (cos x)) (* x x)) (- 1 (cos x)) (cos x) (* x x) (* (/ -1 x) (+ (cos x) -1)) (/ (* (/ -1 x) (+ (cos x) -1)) x) (/ -1 x) (+ (cos x) -1) (/ -1 (/ -1 (+ (cos x) -1))) (* (/ -1 (* x x)) (/ -1 (/ -1 (+ (cos x) -1)))) (/ -1 (* x x)) (/ (+ (* (* (cos x) x) x) (* (neg x) x)) (* (* x (* (neg x) x)) x)) (+ (* (* (cos x) x) x) (* (neg x) x)) (* (* x (* (neg x) x)) x) (* x (* (neg x) x)) (cos x) (* (cos x) x))

3.0ms

-inf

((/ 1 (* (/ x (- 1 (cos x))) x)) (* (/ x (- 1 (cos x))) x) (+ (* (* 1/6 x) x) 2) (* 1/6 x) (/ (- 1 (cos x)) (* x x)) (- 1 (cos x)) (cos x) (* x x) (* (/ -1 x) (+ (cos x) -1)) (/ (* (/ -1 x) (+ (cos x) -1)) x) (/ -1 x) (+ (cos x) -1) (/ -1 (/ -1 (+ (cos x) -1))) (* (/ -1 (* x x)) (/ -1 (/ -1 (+ (cos x) -1)))) (/ -1 (* x x)) (/ (+ (* (* (cos x) x) x) (* (neg x) x)) (* (* x (* (neg x) x)) x)) (+ (* (* (cos x) x) x) (* (neg x) x)) (* (* x (* (neg x) x)) x) (* x (* (neg x) x)) (cos x) (* (cos x) x))

simplify168.0ms (2.1%)

Memory

-8.8MiB live, 181.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	98	469
1	272	462
2	650	462
3	1954	462
4	3885	462
5	5167	462
6	7749	462
0	8069	413

Stop Event

1×	iter limit
1×	node limit

Counts

49 → 48

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))
(* 1/6 x)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(pow x 2)
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(/ -1 x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(/ -1 (pow x 2))
(* -1/2 (pow x 4))
(* (pow x 4) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(* -1 (pow x 4))
(* -1 (pow x 3))
x
(* x (+ 1 (* -1/2 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(/ (- 1 (cos x)) (pow x 2))
(/ (pow x 2) (- 1 (cos x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(- 1 (cos x))
(cos x)
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(- (cos x) 1)
(* (pow x 2) (- (cos x) 1))
(* x (cos x))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
2
#s(literal 2 binary64)
(+ 2 (* 1/6 (pow x 2)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/3024 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 2 binary64))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 x x) #s(literal -1/720 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x) x)
(/ -1 (pow x 2))
(/.f64 (/.f64 #s(literal -1 binary64) x) x)
(* -1/2 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64))
(* (pow x 4) (- (* 1/24 (pow x 2)) 1/2))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/24 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64)))
(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))
(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 x x) #s(literal -1/720 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)))
(* -1 (pow x 4))
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(* -1 (pow x 3))
(pow.f64 (neg.f64 x) #s(literal 3 binary64))
x
(* x (+ 1 (* -1/2 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (pow x 2) (- 1 (cos x)))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)
(* -1 (/ (- (cos x) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(- (cos x) 1)
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(* (pow x 2) (- (cos x) 1))
(.f64 (.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) x)
(* x (cos x))
(*.f64 (cos.f64 x) x)

rewrite257.0ms (3.3%)

Memory

-9.4MiB live, 318.3MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	165
0	58	147
1	227	137
2	1575	131
0	8639	131

Stop Event

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

Counts

21 → 1 506

Calls

Call 1

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

Outputs
(.f64 (pow.f64 #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))))
(.f64 (pow.f64 #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (pow.f64 #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))))) #s(literal -1 binary64))
(pow.f64 (.f64 #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))) #s(literal -1 binary64)))
(.f64 (neg.f64 #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))))
(.f64 #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))))
(pow.f64 (pow.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal 1 binary64))
#s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))
(/.f64 (neg.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal -1 binary64))))
(/.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal -1 binary64)))
(neg.f64 (neg.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))))
(exp.f64 (neg.f64 (.f64 (log.f64 #s(approx ( (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))) #s(literal -1 binary64))))
(.f64 (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -2 binary64)))))
(.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/216 binary64) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64)))))))
(.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -4 binary64)) (pow.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -2 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/216 binary64) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))))))
(.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/216 binary64) #s(literal 8 binary64)) (pow.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))) #s(literal -1 binary64))
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(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) x) x) #s(literal 2 binary64)) (.f64 x (fma.f64 (cos.f64 x) x x))) (.f64 (.f64 x (fma.f64 (cos.f64 x) x x)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (.f64 x (fma.f64 (cos.f64 x) x x)) (*.f64 x (fma.f64 (cos.f64 x) x x))))
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(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (.f64 (.f64 x (-.f64 (cos.f64 x) #s(literal 1 binary64))) x) #s(literal -1 binary64))))
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(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) x) x) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (neg.f64 (pow.f64 x #s(literal 4 binary64)))))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (neg.f64 (pow.f64 x #s(literal 6 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 (.f64 x (-.f64 (cos.f64 x) #s(literal 1 binary64))) x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 x (-.f64 (cos.f64 x) #s(literal 1 binary64))) x) #s(literal -1 binary64)))
(neg.f64 (.f64 (neg.f64 x) (.f64 x (-.f64 (cos.f64 x) #s(literal 1 binary64)))))
(fma.f64 (/.f64 (.f64 (.f64 (.f64 (cos.f64 x) x) x) (.f64 (cos.f64 x) x)) x) (/.f64 x (fma.f64 (cos.f64 x) x x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x (fma.f64 (cos.f64 x) x x)))))
(fma.f64 (/.f64 (.f64 (.f64 (.f64 (cos.f64 x) x) x) (cos.f64 x)) x) (/.f64 (.f64 x x) (fma.f64 (cos.f64 x) x x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x (fma.f64 (cos.f64 x) x x)))))
(fma.f64 (/.f64 (.f64 (.f64 (.f64 (cos.f64 x) x) x) x) x) (/.f64 (.f64 (cos.f64 x) x) (fma.f64 (cos.f64 x) x x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x (fma.f64 (cos.f64 x) x x)))))
(fma.f64 (/.f64 (pow.f64 (.f64 (cos.f64 x) x) #s(literal 2 binary64)) x) (/.f64 (.f64 x x) (fma.f64 (cos.f64 x) x x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x (fma.f64 (cos.f64 x) x x)))))
(fma.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) x) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (cos.f64 x) x x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x (fma.f64 (cos.f64 x) x x)))))
(fma.f64 (/.f64 (.f64 x x) x) (/.f64 (pow.f64 (.f64 (cos.f64 x) x) #s(literal 2 binary64)) (fma.f64 (cos.f64 x) x x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x (fma.f64 (cos.f64 x) x x)))))
(fma.f64 (/.f64 (.f64 (.f64 (cos.f64 x) x) x) x) (/.f64 (.f64 (.f64 (cos.f64 x) x) x) (fma.f64 (cos.f64 x) x x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x (fma.f64 (cos.f64 x) x x)))))
(fma.f64 (/.f64 (.f64 (cos.f64 x) x) x) (/.f64 (.f64 x (.f64 (.f64 (cos.f64 x) x) x)) (fma.f64 (cos.f64 x) x x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x (fma.f64 (cos.f64 x) x x)))))
(fma.f64 (/.f64 (cos.f64 x) x) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 (cos.f64 x) x) x)) (fma.f64 (cos.f64 x) x x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x (fma.f64 (cos.f64 x) x x)))))
(fma.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) x) x) #s(literal 2 binary64)) (pow.f64 (.f64 x (fma.f64 (cos.f64 x) x x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 x (fma.f64 (cos.f64 x) x x)))))
(fma.f64 (.f64 (neg.f64 x) x) #s(literal 1 binary64) (.f64 (*.f64 (cos.f64 x) x) x))
(fma.f64 (neg.f64 x) x (.f64 (.f64 (cos.f64 x) x) x))
(fma.f64 (.f64 (cos.f64 x) x) x (.f64 (neg.f64 x) x))
(fma.f64 (cos.f64 x) (.f64 x x) (.f64 (neg.f64 x) x))
(fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 (*.f64 (cos.f64 x) x) x))
(fma.f64 (.f64 x x) (cos.f64 x) (.f64 (neg.f64 x) x))
(fma.f64 (.f64 x x) #s(literal -1 binary64) (.f64 (*.f64 (cos.f64 x) x) x))
(fma.f64 x (neg.f64 x) (.f64 (.f64 (cos.f64 x) x) x))
(fma.f64 x (.f64 (cos.f64 x) x) (.f64 (neg.f64 x) x))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (cos.f64 x) x) (.f64 (.f64 (cos.f64 x) x) x)) (fma.f64 (cos.f64 x) x x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x (fma.f64 (cos.f64 x) x x)))))
(fma.f64 #s(literal 1 binary64) (.f64 (neg.f64 x) x) (.f64 (*.f64 (cos.f64 x) x) x))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 (neg.f64 x) x) (.f64 (.f64 (cos.f64 x) x) x))) (/.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) x) x) #s(literal 2 binary64)) (-.f64 (.f64 (neg.f64 x) x) (.f64 (.f64 (cos.f64 x) x) x))))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) x) x) #s(literal 2 binary64)) (.f64 x (fma.f64 (cos.f64 x) x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 x (fma.f64 (cos.f64 x) x x))))
(-.f64 #s(literal 0 binary64) (.f64 (neg.f64 x) (.f64 x (-.f64 (cos.f64 x) #s(literal 1 binary64)))))
(-.f64 (.f64 (.f64 (cos.f64 x) x) x) (*.f64 x x))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) x) x) #s(literal 2 binary64)) (.f64 x (fma.f64 (cos.f64 x) x x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 x (fma.f64 (cos.f64 x) x x)))))
(+.f64 (.f64 (.f64 (cos.f64 x) x) x) (*.f64 (neg.f64 x) x))
(+.f64 (.f64 (neg.f64 x) x) (.f64 (*.f64 (cos.f64 x) x) x))
(*.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) x)
(.f64 (.f64 (neg.f64 x) x) (*.f64 x x))
(*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))
(.f64 (.f64 x x) (*.f64 (neg.f64 x) x))
(*.f64 x (pow.f64 (neg.f64 x) #s(literal 3 binary64)))
(/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))
(/.f64 (*.f64 x x) (neg.f64 (pow.f64 x #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))))
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3/2 binary64)) (pow.f64 (neg.f64 x) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64))
(.f64 (.f64 (neg.f64 x) x) x)
(.f64 (neg.f64 x) (.f64 x x))
(*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))
(.f64 (.f64 x x) (neg.f64 x))
(.f64 x (.f64 (neg.f64 x) x))
(pow.f64 (neg.f64 x) #s(literal 3 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 (pow.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 3 binary64)))
(/.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (neg.f64 (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 3 binary64)))
(/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64))
(/.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) x))
(/.f64 x (neg.f64 (pow.f64 x #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 3 binary64)))
(neg.f64 (pow.f64 x #s(literal 3 binary64)))
(fma.f64 #s(literal 0 binary64) (*.f64 x x) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))
(fma.f64 (*.f64 x x) #s(literal 0 binary64) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))
(-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64)))
(+.f64 (.f64 (.f64 x x) #s(literal 0 binary64)) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 x x)) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))
(+.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 3 binary64)))
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x)))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(neg.f64 (neg.f64 (cos.f64 x)))
(-.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 x)))
(cos.f64 x)
(*.f64 (cos.f64 x) x)
(*.f64 x (cos.f64 x))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) x) #s(literal 2 binary64)) #s(literal 0 binary64)) (-.f64 (.f64 (cos.f64 x) x) #s(literal 0 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) x) #s(literal 3 binary64)) #s(literal 0 binary64)) (+.f64 (pow.f64 (.f64 (cos.f64 x) x) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (.f64 (.f64 (cos.f64 x) x) #s(literal 0 binary64)))))
(fma.f64 (cos.f64 x) x #s(literal 0 binary64))
(fma.f64 x (cos.f64 x) #s(literal 0 binary64))
(+.f64 (*.f64 (cos.f64 x) x) #s(literal 0 binary64))

eval116.0ms (1.5%)

Memory: 6.4MiB live, 206.9MiB allocated
Compiler: Compiled 21 994 to 2 829 computations (87.1% saved)

prune33.0ms (0.4%)

Memory

4.6MiB live, 81.7MiB allocated

Pruning

23 alts after pruning (10 fresh and 13 done)

	Pruned	Kept	Total
New	1 061	3	1 064
Fresh	1	7	8
Picked	1	4	5
Done	0	9	9
Total	1 063	23	1 086

Accuracy

100.0%

Counts

1 086 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.4%	(/.f64 (fma.f64 (/.f64 (cos.f64 x) (neg.f64 x)) x #s(literal 1 binary64)) (*.f64 x x))
✓	13.8%	(/.f64 (fma.f64 (.f64 (cos.f64 x) x) x (.f64 (neg.f64 x) x)) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
	13.9%	(/.f64 (fma.f64 (neg.f64 x) x (.f64 (.f64 (cos.f64 x) x) x)) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
	21.5%	(/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) (cos.f64 x)) x (.f64 x x)) (.f64 x x)) (.f64 x x))
	48.0%	(/.f64 (/.f64 (fma.f64 (neg.f64 (cos.f64 x)) x x) (*.f64 x x)) x)
✓	21.4%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
	49.1%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	21.4%	(/.f64 (/.f64 #s(approx (- (* x x) (* (* x x) (cos x))) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)) (.f64 x x)) (.f64 x x))
	13.4%	(/.f64 (-.f64 (.f64 (.f64 (cos.f64 x) x) x) (.f64 x x)) (.f64 (.f64 x (.f64 (neg.f64 x) x)) x))
✓	48.0%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
✓	28.6%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
✓	49.0%	(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (cos.f64 x) #s(literal -1 binary64))) x)
	78.3%	(/.f64 (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 x)) (*.f64 x x))
✓	13.4%	(/.f64 (neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x)))) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
✓	48.6%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
✓	82.5%	(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))))
✓	82.5%	(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))
	32.1%	(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* (* 1/6 x) x) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
	47.9%	(/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 x) #s(literal 1 binary64))) (.f64 (neg.f64 x) x)))
✓	47.9%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
✓	53.8%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
✓	54.5%	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Compiler

Compiled 892 to 371 computations (58.4% saved)

regimes25.0ms (0.3%)

Memory

-1.9MiB live, 35.3MiB allocated

Counts

36 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* 1/6 (* x x)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* (* 1/6 x) x) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ x (- 1 (cos x))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 2 binary64)) x)) x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(*.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (cos.f64 x) #s(literal -1 binary64))) x)
(/.f64 (/.f64 (fma.f64 (neg.f64 (cos.f64 x)) x x) (*.f64 x x)) x)
(/.f64 (fma.f64 (/.f64 (cos.f64 x) (neg.f64 x)) x #s(literal 1 binary64)) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 x) #s(literal 1 binary64))) (.f64 (neg.f64 x) x)))
(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (/.f64 (cos.f64 x) x))) (neg.f64 x))
(/.f64 (neg.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x)))) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
(/.f64 (/.f64 #s(approx (- (* x x) (* (* x x) (cos x))) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x))) (.f64 x x)) (.f64 x x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 x) x) x) (.f64 x x)) (.f64 (.f64 x (.f64 (neg.f64 x) x)) x))
(/.f64 (fma.f64 (neg.f64 x) x (.f64 (.f64 (cos.f64 x) x) x)) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
(/.f64 (fma.f64 (.f64 (cos.f64 x) x) x (.f64 (neg.f64 x) x)) (.f64 (.f64 x (*.f64 (neg.f64 x) x)) x))
(/.f64 (-.f64 (.f64 (neg.f64 x) x) (.f64 (.f64 (neg.f64 x) x) (cos.f64 x))) (.f64 (.f64 (neg.f64 x) x) (.f64 x x)))
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
(/.f64 (/.f64 (fma.f64 x x (.f64 (neg.f64 (.f64 (cos.f64 x) x)) x)) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (fma.f64 (neg.f64 x) (.f64 (cos.f64 x) x) (.f64 x x)) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) (cos.f64 x)) x (.f64 x x)) (.f64 x x)) (.f64 x x))
(/.f64 (-.f64 (neg.f64 x) (.f64 (.f64 (neg.f64 x) x) (/.f64 (cos.f64 x) x))) (.f64 (.f64 (neg.f64 x) x) x))
(/.f64 (-.f64 x (*.f64 x (cos.f64 x))) (pow.f64 x #s(literal 3 binary64)))
(/.f64 (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 x)) (*.f64 x x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)))

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

Calls

2 calls:

14.0ms	x
9.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Results

Accuracy	Segments	Branch
99.7%	2	`x`
99.4%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes7.0ms (0.1%)

Memory

14.0MiB live, 14.0MiB allocated

Counts

11 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* 1/6 (* x x)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* (* 1/6 x) x) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ x (- 1 (cos x))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 2 binary64)) x)) x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (cos.f64 x)))

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)))

(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Calls

2 calls:

4.0ms	x
3.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Results

Accuracy	Segments	Branch
99.3%	3	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
99.3%	2	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes6.0ms (0.1%)

Memory

12.2MiB live, 12.2MiB allocated

Counts

9 → 1

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* 1/6 (* x x)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* (* 1/6 x) x) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ x (- 1 (cos x))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 2 binary64)) x)) x))

Outputs
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))

Calls

2 calls:

3.0ms	x
3.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Results

Accuracy	Segments	Branch
82.5%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
82.5%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes9.0ms (0.1%)

Memory

-37.1MiB live, 9.7MiB allocated

Counts

6 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* 1/6 (* x x)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* (* 1/6 x) x) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)))

(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* 1/6 (* x x)) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
54.5%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
82.6%	2	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes3.0ms (0%)

Memory

5.4MiB live, 5.4MiB allocated

Counts

5 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* 1/6 (* x x)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* (* 1/6 x) x) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))

(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* 1/6 (* x x)) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
82.5%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0%)

Memory

4.2MiB live, 4.2MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
80.5%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes3.0ms (0%)

Memory

6.3MiB live, 6.3MiB allocated

Accuracy

Total -0.8b remaining (-2.7%)

Threshold costs -0.8b (-2.7%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))

Outputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
54.5%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
54.5%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

bsearch14.0ms (0.2%)

Memory

21.8MiB live, 21.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.003701350455776986	28086.917873572314

Samples

7.0ms

144×

valid

Compiler

Compiled 263 to 199 computations (24.3% saved)

Precisions

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

ival-cos: 2.0ms (45.3% of total)

ival-sub: 1.0ms (22.7% of total)

ival-div: 1.0ms (22.7% of total)

ival-mult: 1.0ms (22.7% of total)

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

exact: 0.0ms (0% of total)

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

bsearch5.0ms (0.1%)

Memory

-35.5MiB live, 2.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
5.0ms	0.003701350455776986	28086.917873572314

Compiler

Compiled 263 to 199 computations (24.3% saved)

bsearch14.0ms (0.2%)

Memory

21.2MiB live, 21.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.003701350455776986	28086.917873572314

Samples

8.0ms

112×

valid

Compiler

Compiled 407 to 307 computations (24.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-cos: 4.0ms (72.3% of total)

ival-sub: 1.0ms (18.1% of total)

ival-div: 1.0ms (18.1% of total)

ival-mult: 1.0ms (18.1% of total)

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

exact: 0.0ms (0% of total)

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

bsearch10.0ms (0.1%)

Memory

15.3MiB live, 15.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	0.003701350455776986	28086.917873572314

Samples

5.0ms

80×

valid

Compiler

Compiled 362 to 289 computations (20.2% saved)

Precisions

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

ival-cos: 2.0ms (51.6% of total)

ival-mult: 1.0ms (25.8% of total)

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

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

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

exact: 0.0ms (0% of total)

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

bsearch20.0ms (0.3%)

Memory

-13.7MiB live, 23.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	8.3274586875623e+73	1.576529846123247e+77

Samples

9.0ms

128×

valid

Compiler

Compiled 171 to 146 computations (14.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-cos: 5.0ms (71.6% of total)

ival-sub: 1.0ms (14.3% of total)

ival-div: 1.0ms (14.3% of total)

ival-mult: 1.0ms (14.3% of total)

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

exact: 0.0ms (0% of total)

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

simplify84.0ms (1.1%)

Memory

6.3MiB live, 44.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	206
1	72	206
2	91	206
3	114	206
4	162	206
5	225	206
6	351	206
7	927	206
8	2510	206
9	4414	206
10	6930	206

Stop Event

1×	node limit

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 1116892707587883/36028797018963968 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x))
(if (<=.f64 x #s(literal 1116892707587883/36028797018963968 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))
(if (<=.f64 x #s(literal 2589569785738035/562949953421312 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* 1/6 (* x x)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x))))))
(if (<=.f64 x #s(literal 3715469692580659/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) #s(approx ( (/ x (- 1 (cos x))) x) #s(approx (+ (* 1/6 (* x x)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x))))))
(if (<=.f64 x #s(literal 76000000000000004862120657096007909209422644572716475826280587491460964679680 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x)))
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Outputs
(if (<=.f64 x #s(literal 1116892707587883/36028797018963968 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x))
(if (<=.f64 x #s(literal 1116892707587883/36028797018963968 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))))
(pow.f64 #s(approx (* (/ x (- 1 (cos x))) x) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))) #s(literal -1 binary64))
(if (<=.f64 x #s(literal 2589569785738035/562949953421312 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* 1/6 (* x x)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x))))))
(if (<=.f64 x #s(literal 2589569785738035/562949953421312 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))) (pow.f64 #s(approx (* (/ x (- 1 (cos x))) x) #s(approx (+ (* 1/6 (* x x)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x)))) #s(literal -1 binary64)))
(if (<=.f64 x #s(literal 3715469692580659/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) #s(approx ( (/ x (- 1 (cos x))) x) #s(approx (+ (* 1/6 (* x x)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x))))))
(if (<=.f64 x #s(literal 3715469692580659/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(approx ( (/ x (- 1 (cos x))) x) #s(approx (+ (* 1/6 (* x x)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x x)))) #s(literal -1 binary64)))
(if (<=.f64 x #s(literal 76000000000000004862120657096007909209422644572716475826280587491460964679680 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x)))
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

soundness1.5s (18.6%)

Memory

-8.9MiB live, 626.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	17
1	40	17
2	270	17
3	2843	17
0	9915	17
0	118	638
1	341	632
2	893	626
3	2885	626
4	4156	626
5	6965	626
0	8071	567
0	125	516
1	356	516
2	923	504
3	2974	504
4	5615	504
5	7113	504
0	8080	451
0	42	153
1	105	153
2	258	153
3	601	153
4	1281	153
5	1981	153
6	2536	153
7	3409	153
8	4960	153
9	6581	153
10	7480	153
11	7690	153
12	7708	153
13	7710	153
0	8119	135

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
1×	node limit
1×	iter limit

Compiler

Compiled 278 to 112 computations (59.7% saved)

preprocess82.0ms (1%)

Memory: 8.2MiB live, 130.4MiB allocated
Compiler: Compiled 556 to 204 computations (63.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze2.0ms (0%)

sample1.8s (23.1%)

explain193.0ms (2.5%)

preprocess79.0ms (1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify27.0ms (0.3%)

localize51.0ms (0.6%)

series3.0ms (0%)

simplify217.0ms (2.8%)

rewrite260.0ms (3.3%)

eval125.0ms (1.6%)

prune100.0ms (1.3%)

simplify246.0ms (3.1%)

localize208.0ms (2.7%)

series12.0ms (0.2%)

simplify155.0ms (2%)

rewrite174.0ms (2.2%)

eval129.0ms (1.6%)

prune48.0ms (0.6%)

simplify602.0ms (7.7%)

localize207.0ms (2.6%)

series18.0ms (0.2%)

simplify223.0ms (2.8%)

rewrite164.0ms (2.1%)

eval97.0ms (1.2%)

prune32.0ms (0.4%)

simplify79.0ms (1%)

localize249.0ms (3.2%)

series18.0ms (0.2%)

simplify168.0ms (2.1%)

rewrite257.0ms (3.3%)

eval116.0ms (1.5%)

prune33.0ms (0.4%)

regimes25.0ms (0.3%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes9.0ms (0.1%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes3.0ms (0%)

bsearch14.0ms (0.2%)

bsearch5.0ms (0.1%)

bsearch14.0ms (0.2%)

bsearch10.0ms (0.1%)

bsearch20.0ms (0.3%)

simplify84.0ms (1.1%)

soundness1.5s (18.6%)

preprocess82.0ms (1%)

end0.0ms (0%)

Profiling