Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze107.0ms (2.1%)

Memory

13.3MiB live, 129.6MiB 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
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
37.5%	37.5%	62.5%	0%	0%	0%	0%	4
43.8%	43.7%	56.2%	0%	0%	0%	0%	5
46.9%	46.9%	53.1%	0%	0%	0%	0%	6
48.4%	48.4%	51.5%	0%	0%	0%	0%	7
49.2%	49.2%	50.8%	0%	0%	0%	0%	8
49.6%	49.6%	50.4%	0%	0%	0%	0%	9
49.8%	49.8%	50.2%	0%	0%	0%	0%	10
49.9%	49.9%	50.1%	0%	0%	0%	0%	11
50%	49.9%	50%	0%	0%	0%	0%	12

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.9s (38.4%)

Memory

64.8MiB live, 1 664.5MiB allocated

Samples

592.0ms	2 182×	2	valid
553.0ms	4 257×	0	valid
239.0ms	602×	3	valid
176.0ms	1 213×	1	valid
2.0ms	2×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-cos: 820.0ms (60.8% of total)

ival-sin: 175.0ms (13% of total)

ival-sub: 124.0ms (9.2% of total)

adjust: 111.0ms (8.2% of total)

ival-div: 105.0ms (7.8% of total)

ival-true: 6.0ms (0.4% of total)

exact: 5.0ms (0.4% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

explain174.0ms (3.5%)

Memory

-30.1MiB live, 132.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
72	1	(2.233511361333238e+66)	1	(-2.122452999747606e+63)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
72	0	-	0	-	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	72	9
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	72	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	72

Confusion

	Predicted +	Predicted -
+	143	2
-	1	110

Precision

0.9930555555555556

Recall

0.9862068965517241

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	143	2	0
-	1	7	103

Precision?

0.9477124183006536

Recall?

1.0

Freqs

test

number	freq
0	112
1	144

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

43.0ms	60×	1	valid
41.0ms	154×	2	valid
31.0ms	252×	0	valid
16.0ms	46×	3	valid

Compiler

Compiled 62 to 28 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 112.0ms

ival-cos: 43.0ms (38.3% of total)

ival-sub: 32.0ms (28.5% of total)

ival-div: 18.0ms (16.1% of total)

ival-sin: 11.0ms (9.8% of total)

adjust: 7.0ms (6.2% of total)

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

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

exact: 0.0ms (0% of total)

preprocess80.0ms (1.6%)

Memory

-13.9MiB live, 32.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

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)) (sin.f64 x))

Outputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))

Symmetry

(negabs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune2.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.5%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify22.0ms (0.4%)

Memory

15.3MiB live, 15.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 x)
cost-diff	0	(cos.f64 x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
cost-diff	6592	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)

localize65.0ms (1.3%)

Memory

16.6MiB live, 53.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sin.f64 x)
accuracy	0	(cos.f64 x)
accuracy	14.702661555645198	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	16.867090233349177	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Samples

34.0ms	77×	2	valid
13.0ms	126×	0	valid
8.0ms	23×	3	valid
3.0ms	30×	1	valid

Compiler

Compiled 36 to 14 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-cos: 22.0ms (44.5% of total)

ival-div: 15.0ms (30.4% of total)

adjust: 5.0ms (10.1% of total)

ival-sin: 5.0ms (10.1% of total)

ival-sub: 3.0ms (6.1% of total)

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

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

exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory

3.7MiB live, 3.7MiB allocated

Counts

4 → 48

Calls

Call 1

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

Outputs
(* 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))))))))
(* 1/2 (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)))
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 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(sin x)
(sin x)
(sin x)
(sin x)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(sin x)
(sin x)
(sin x)
(sin x)

Calls

3 calls:

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

simplify225.0ms (4.5%)

Memory

-21.4MiB live, 132.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	286
1	224	286
2	555	280
3	1661	280
4	3000	280
5	4247	280
6	4597	280
7	5328	280
8	6820	280
0	8376	256

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

Inputs
(* 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))))))))
(* 1/2 (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)))
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 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(sin x)
(sin x)
(sin x)
(sin x)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(sin x)
(sin x)
(sin x)
(sin x)

Outputs
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.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)
(.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)
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(.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)
(.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)
#s(literal 1 binary64)
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(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))
x
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(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)
(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)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(sin.f64 x)
(sin.f64 x)
(sin.f64 x)
(sin.f64 x)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(sin.f64 x)
(sin.f64 x)
(sin.f64 x)
(sin.f64 x)

rewrite227.0ms (4.5%)

Memory

27.3MiB live, 259.2MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11

Stop Event

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

Counts

4 → 615

Calls

Call 1

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

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

eval84.0ms (1.7%)

Memory: -1.9MiB live, 153.1MiB allocated
Compiler: Compiled 13 342 to 1 647 computations (87.7% saved)

prune17.0ms (0.3%)

Memory

-9.3MiB live, 36.0MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	658	4	662
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	659	4	663

Accuracy

100.0%

Counts

663 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.9%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
▶	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶	53.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	53.2%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 34 to 29 computations (14.7% saved)

simplify30.0ms (0.6%)

Memory

-1.2MiB live, 33.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score
cost-diff	6464	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) 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	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	66
0	24	58
1	40	58
2	55	58
3	72	58
4	96	58
5	120	58
6	153	58
7	227	58
8	350	58
9	558	58
10	600	58
11	603	58
12	611	58
13	616	58
14	620	58
15	627	58
16	660	58
17	682	58
18	684	58
0	684	58

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize99.0ms (2%)

Memory

-2.2MiB live, 121.1MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
accuracy	0	(*.f64 x x)
accuracy	0.04296875	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.09375	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy	30.050614278630103	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	29.940780754014934	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Samples

31.0ms	77×	2	valid
26.0ms	126×	0	valid
24.0ms	23×	3	valid
6.0ms	30×	1	valid

Compiler

Compiled 123 to 36 computations (70.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-cos: 23.0ms (31.6% of total)

ival-mult: 16.0ms (22% of total)

adjust: 9.0ms (12.4% of total)

ival-tan: 5.0ms (6.9% of total)

ival-sin: 5.0ms (6.9% of total)

const: 4.0ms (5.5% of total)

ival-div: 3.0ms (4.1% of total)

ival-sub: 3.0ms (4.1% of total)

ival-pow: 3.0ms (4.1% of total)

ival-add: 1.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated

Counts

8 → 84

Calls

Call 1

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

Outputs
(* 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))))))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 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))))))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 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 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((/ (- 1 (cos x)) (sin x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (tan (* 1/2 x)) (pow 1 -1/2))
2.0ms	x	@	-inf	((/ (- 1 (cos x)) (sin x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (tan (* 1/2 x)) (pow 1 -1/2))
1.0ms	x	@	0	((/ (- 1 (cos x)) (sin x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (tan (* 1/2 x)) (pow 1 -1/2))

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify167.0ms (3.3%)

Memory

33.1MiB live, 105.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	520
1	114	520
2	285	520
3	660	520
4	1224	520
5	2800	520
6	3632	520
7	4484	520
8	4907	520
9	5454	520
10	6074	520
11	6831	520
12	7406	520
0	8141	484

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(* 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))))))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 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))))))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 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 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))

Outputs
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.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)
(.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)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.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)
(.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)
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
#s(literal 1/2 binary64)
(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))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.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)
(.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)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(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))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(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))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))

rewrite215.0ms (4.3%)

Memory

-31.2MiB live, 169.4MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	54
0	24	49
1	83	49
2	452	49
3	3932	37
0	11568	37

Stop Event

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

Counts

8 → 163

Calls

Call 1

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

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) x)))
(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(neg.f64 (/.f64 x #s(literal -2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) x) (-.f64 (.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/331776 binary64)) (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))) (-.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/48 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) x) (fma.f64 #s(literal 1/191102976 binary64) (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal 3 binary64)))) (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/331776 binary64) (.f64 (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) x) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) x) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(.f64 (.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) x) (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) x) (pow.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (/.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))))
(.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (.f64 (pow.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal -1 binary64)) x))
(.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (/.f64 x (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))))
(.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (.f64 (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) #s(literal -1 binary64)) x))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) x)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)))) x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(/.f64 (.f64 (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))) x) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (.f64 (neg.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) x) (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) x) (pow.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(/.f64 (.f64 x (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)))) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (.f64 x (neg.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))))
(/.f64 (.f64 x #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(/.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -2 binary64)) (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (+.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -2 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) (.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64))) (+.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -2 binary64)) (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) x)) (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) x) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))))
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(/.f64 (.f64 (fma.f64 #s(literal 1/2641807540224 binary64) (pow.f64 x #s(literal 18 binary64)) #s(literal 1/512 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/191102976 binary64) (pow.f64 x #s(literal 12 binary64)) (-.f64 #s(literal 1/64 binary64) (.f64 #s(literal 1/110592 binary64) (pow.f64 x #s(literal 6 binary64))))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/331776 binary64) #s(literal -1/16 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(/.f64 (fma.f64 #s(literal 1/191102976 binary64) (pow.f64 x #s(literal 12 binary64)) #s(literal -1/64 binary64)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/331776 binary64) (fma.f64 #s(literal 1/2304 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/16 binary64)))))
(/.f64 (fma.f64 #s(literal 1/191102976 binary64) (pow.f64 x #s(literal 12 binary64)) #s(literal -1/64 binary64)) (.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64))))
(/.f64 (fma.f64 #s(literal 1/2641807540224 binary64) (pow.f64 x #s(literal 18 binary64)) #s(literal 1/512 binary64)) (.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) (fma.f64 #s(literal 1/191102976 binary64) (pow.f64 x #s(literal 12 binary64)) (-.f64 #s(literal 1/64 binary64) (*.f64 #s(literal 1/110592 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(/.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))
(/.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))))))
(fma.f64 (exp.f64 (log.f64 #s(literal 1/24 binary64))) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (exp.f64 (log.f64 (*.f64 #s(literal 1/24 binary64) x))) x #s(literal 1/2 binary64))
(fma.f64 (pow.f64 (*.f64 #s(literal 1/24 binary64) x) #s(literal 1 binary64)) x #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/48 binary64) (.f64 x x) #s(literal 1/4 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) (/.f64 #s(literal 1/24 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (/.f64 (.f64 #s(literal 1/24 binary64) x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1/576 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (/.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64))
(fma.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1/24 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) (exp.f64 (log.f64 #s(literal 1/24 binary64))) #s(literal 1/2 binary64))
(fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (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 x (exp.f64 (log.f64 (*.f64 #s(literal 1/24 binary64) x))) #s(literal 1/2 binary64))
(fma.f64 x (pow.f64 (*.f64 #s(literal 1/24 binary64) x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 1/24 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 x (*.f64 #s(literal 1/24 binary64) x) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
(+.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
#s(literal 1 binary64)
#s(literal 1 binary64)

eval30.0ms (0.6%)

Memory: 25.5MiB live, 25.5MiB allocated
Compiler: Compiled 6 160 to 755 computations (87.7% saved)

prune37.0ms (0.7%)

Memory

-19.8MiB live, 34.8MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	272	2	274
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	273	5	278

Accuracy

100.0%

Counts

278 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶	53.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
✓	53.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	53.2%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
▶	6.9%	#s(literal 1 binary64)

Compiler

Compiled 50 to 40 computations (20% saved)

simplify30.0ms (0.6%)

Memory

-15.9MiB live, 18.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal 1/24 binary64) x)
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
cost-diff	320	(fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	41
0	18	38
1	36	36
2	58	36
3	73	36
4	94	36
5	118	36
6	151	36
7	225	36
8	349	36
9	555	36
10	597	36
11	600	36
12	608	36
13	614	36
14	618	36
15	625	36
16	658	36
17	676	36
18	678	36
0	678	34

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize78.0ms (1.6%)

Memory

38.1MiB live, 110.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.05078125	(fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.359375	(*.f64 #s(literal 1/24 binary64) x)
accuracy	30.050614278630103	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))

Samples

26.0ms	77×	2	valid
25.0ms	126×	0	valid
10.0ms	22×	3	valid
5.0ms	30×	1	valid
1.0ms	1×	5	exit

Compiler

Compiled 74 to 29 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-cos: 23.0ms (44.8% of total)

ival-mult: 6.0ms (11.7% of total)

adjust: 5.0ms (9.7% of total)

ival-sin: 5.0ms (9.7% of total)

const: 4.0ms (7.8% of total)

ival-div: 3.0ms (5.8% of total)

ival-sub: 3.0ms (5.8% of total)

ival-add: 1.0ms (1.9% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.3%)

Memory

-45.7MiB live, 5.3MiB allocated

Counts

5 → 60

Calls

Call 1

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

Outputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* 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))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)

Calls

3 calls:

Time

Variable

Point

Expression

11.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify200.0ms (4%)

Memory

28.3MiB live, 176.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	282
1	106	282
2	259	282
3	595	282
4	995	282
5	1717	282
6	3040	282
7	4209	282
8	5167	282
9	5858	282
10	6747	282
11	7172	282
12	7953	282
0	8079	267

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* 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))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)

Outputs
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.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)
(.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)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)

rewrite183.0ms (3.7%)

Memory

1.4MiB live, 206.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	37
0	18	34
1	68	32
2	474	32
3	4836	31
0	8786	29

Stop Event

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

Counts

5 → 135

Calls

Call 1

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

Outputs
(.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal 1/4 binary64) x (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))))
(.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (-.f64 (pow.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64)) (pow.f64 (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (fma.f64 #s(literal 1/191102976 binary64) (pow.f64 x #s(literal 18 binary64)) (pow.f64 (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) #s(literal 3 binary64)))) (fma.f64 (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) (-.f64 (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x))
(.f64 (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) x) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x)
(.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x))) (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))))
(.f64 (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))))
(.f64 (neg.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))))) (pow.f64 (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)))
(.f64 (neg.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)))) (pow.f64 (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x))))
(.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))))
(.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x))
(.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x)))
(.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) x)))))
(.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) x) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x)))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 x x))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/191102976 binary64) (pow.f64 x #s(literal 18 binary64))) (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x)))) (+.f64 (fma.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 4 binary64))) (pow.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/191102976 binary64) (pow.f64 x #s(literal 18 binary64))) (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (.f64 (fma.f64 (pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 3 binary64)) #s(literal 1/2641807540224 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 9 binary64))) (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64))) (fma.f64 #s(literal 1/191102976 binary64) (pow.f64 x #s(literal 18 binary64)) (-.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/13824 binary64)) #s(literal 1/8 binary64)))))
(/.f64 (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) #s(literal 1 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (pow.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) #s(literal 2 binary64))) (fma.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (.f64 (.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))))) (neg.f64 (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) x))))
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(fma.f64 x (exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (log.f64 #s(literal 1/24 binary64)))) (*.f64 #s(literal 1/2 binary64) x))
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(fma.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 x (.f64 (.f64 #s(literal 1/24 binary64) x) x) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))
(-.f64 (.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(+.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) #s(literal -1 binary64))) #s(literal -1 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 x #s(literal 1/24 binary64))
(*.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) x)
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x (exp.f64 (log.f64 #s(literal 1/2 binary64))))
(*.f64 x #s(literal 1/2 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(/.f64 (exp.f64 (log.f64 (neg.f64 x))) (exp.f64 (log.f64 #s(literal -2 binary64))))
(/.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (exp.f64 (log.f64 (/.f64 #s(literal 2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 x (exp.f64 (log.f64 #s(literal 2 binary64))))
(/.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 #s(literal -1/2 binary64) x))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x)))

eval30.0ms (0.6%)

Memory: -12.7MiB live, 58.0MiB allocated
Compiler: Compiled 5 453 to 555 computations (89.8% saved)

prune6.0ms (0.1%)

Memory

26.7MiB live, 26.8MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	195	5	200

Accuracy

100.0%

Counts

200 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
✓	53.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
✓	53.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	53.2%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	6.9%	#s(literal 1 binary64)

Compiler

Compiled 110 to 65 computations (40.9% saved)

regimes16.0ms (0.3%)

Memory

-21.7MiB live, 23.6MiB allocated

Counts

7 → 1

Calls

Call 1

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

Outputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes5.0ms (0.1%)

Memory

14.8MiB live, 14.8MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
56.2%	2	`x`
56.0%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes2.0ms (0%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

#s(literal 1 binary64)

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

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
56.2%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes4.0ms (0.1%)

Memory

-22.6MiB live, 16.9MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
55.8%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
55.9%	2	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

15.6MiB live, 15.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
6.9%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
6.9%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch30.0ms (0.6%)

Memory

-5.8MiB live, 73.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
28.0ms	2.170259495541874e-5	50.44192046136823

Samples

21.0ms

144×

valid

Compiler

Compiled 181 to 163 computations (9.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-cos: 13.0ms (70.2% of total)

ival-sin: 4.0ms (21.6% of total)

ival-sub: 1.0ms (5.4% of total)

ival-div: 1.0ms (5.4% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.170259495541874e-5	50.44192046136823

Compiler

Compiled 163 to 154 computations (5.5% saved)

bsearch9.0ms (0.2%)

Memory

8.3MiB live, 8.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	2.170259495541874e-5	50.44192046136823

Samples

6.0ms

64×

valid

Compiler

Compiled 118 to 127 computations (-7.6% saved)

Precisions

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

ival-cos: 2.0ms (45.2% of total)

ival-sin: 2.0ms (45.2% 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)

simplify51.0ms (1%)

Memory

-3.7MiB live, 40.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	65
1	31	65

Stop Event

1×

saturated

Calls

Call 1

Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6530219459687219/4503599627370496 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6530219459687219/4503599627370496 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness732.0ms (14.6%)

Memory

-10.4MiB live, 361.7MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11
0	17	54
0	24	49
1	83	49
2	452	49
3	3932	37
0	11568	37
0	79	286
1	224	286
2	555	280
3	1661	280
4	3000	280
5	4247	280
6	4597	280
7	5328	280
8	6820	280
0	8376	256

Stop Event

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

Compiler

Compiled 155 to 98 computations (36.8% saved)

preprocess98.0ms (2%)

Memory: -18.6MiB live, 98.6MiB allocated
Remove: (negabs x)
Compiler: Compiled 168 to 88 computations (47.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	17	66
0	24	58
1	40	58
2	55	58
3	72	58
4	96	58
5	120	58
6	153	58
7	227	58
8	350	58
9	558	58
10	600	58
11	603	58
12	611	58
13	616	58
14	620	58
15	627	58
16	660	58
17	682	58
18	684	58
0	684	58

Iter	Nodes	Cost
0	13	41
0	18	38
1	36	36
2	58	36
3	73	36
4	94	36
5	118	36
6	151	36
7	225	36
8	349	36
9	555	36
10	597	36
11	600	36
12	608	36
13	614	36
14	618	36
15	625	36
16	658	36
17	676	36
18	678	36
0	678	34

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	17	66
0	24	58
1	40	58
2	55	58
3	72	58
4	96	58
5	120	58
6	153	58
7	227	58
8	350	58
9	558	58
10	600	58
11	603	58
12	611	58
13	616	58
14	620	58
15	627	58
16	660	58
17	682	58
18	684	58
0	684	58

Iter	Nodes	Cost
0	13	41
0	18	38
1	36	36
2	58	36
3	73	36
4	94	36
5	118	36
6	151	36
7	225	36
8	349	36
9	555	36
10	597	36
11	600	36
12	608	36
13	614	36
14	618	36
15	625	36
16	658	36
17	676	36
18	678	36
0	678	34

start0.0ms (0%)

analyze107.0ms (2.1%)

sample1.9s (38.4%)

explain174.0ms (3.5%)

preprocess80.0ms (1.6%)

eval0.0ms (0%)

prune2.0ms (0%)

simplify22.0ms (0.4%)

localize65.0ms (1.3%)

series2.0ms (0%)

simplify225.0ms (4.5%)

rewrite227.0ms (4.5%)

eval84.0ms (1.7%)

prune17.0ms (0.3%)

simplify30.0ms (0.6%)

localize99.0ms (2%)

series6.0ms (0.1%)

simplify167.0ms (3.3%)

rewrite215.0ms (4.3%)

eval30.0ms (0.6%)

prune37.0ms (0.7%)

simplify30.0ms (0.6%)

localize78.0ms (1.6%)

series13.0ms (0.3%)

simplify200.0ms (4%)

rewrite183.0ms (3.7%)

eval30.0ms (0.6%)

prune6.0ms (0.1%)

regimes16.0ms (0.3%)

regimes5.0ms (0.1%)

regimes2.0ms (0%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch30.0ms (0.6%)

bsearch1.0ms (0%)

bsearch9.0ms (0.2%)

simplify51.0ms (1%)

soundness732.0ms (14.6%)

preprocess98.0ms (2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	17	66
0	24	58
1	40	58
2	55	58
3	72	58
4	96	58
5	120	58
6	153	58
7	227	58
8	350	58
9	558	58
10	600	58
11	603	58
12	611	58
13	616	58
14	620	58
15	627	58
16	660	58
17	682	58
18	684	58
0	684	58

Iter	Nodes	Cost
0	13	41
0	18	38
1	36	36
2	58	36
3	73	36
4	94	36
5	118	36
6	151	36
7	225	36
8	349	36
9	555	36
10	597	36
11	600	36
12	608	36
13	614	36
14	618	36
15	625	36
16	658	36
17	676	36
18	678	36
0	678	34