Details

analyze153.0ms (1.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.3%	87.7%	0
0%	12.3%	87.7%	1
6.2%	6.2%	87.7%	2
6.2%	6.2%	87.7%	3
9.2%	3.1%	87.7%	4
9.2%	3.1%	87.7%	5
10.8%	1.5%	87.7%	6
10.8%	1.5%	87.7%	7
11.5%	0.8%	87.7%	8
11.5%	0.8%	87.7%	9
11.9%	0.4%	87.7%	10
11.9%	0.4%	87.7%	11
12.1%	0.2%	87.7%	12
12.1%	0.2%	87.7%	13
12.1%	0.1%	87.8%	14

Compiler

Compiled 36 to 28 computations (22.2% saved)

sample49.0ms (0.6%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 65 to 51 computations (21.5% saved)

simplify91.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary32`
384×	`unsub-neg_binary32`
362×	`unswap-sqr_binary32`
349×	`neg-mul-1_binary32`
329×	`div-sub_binary32`

Counts

1 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	45	37
2	104	35
3	240	35
4	561	35
5	2384	35
6	3153	35
7	4056	35
8	4874	35
9	4989	35
10	4799	35

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.4b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.4b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.6b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (/.f32 1 (sqrt.f32 PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Status

Error

Program

▶

0.4b

(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (*.f32 (sqrt.f32 PI.f32) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))

0.6b

(/.f32 1 (+.f32 (+.f32 1 c) (*.f32 (*.f32 (/.f32 1 (sqrt.f32 PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Compiler

Compiled 126 to 96 computations (23.8% saved)

localize62.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.1b	(-.f32 (-.f32 1 cosTheta) cosTheta)
0.3b	(/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
0.3b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
0.4b	(.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

rewrite210.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

57×	`*-un-lft-identity_binary32`
32×	`add-exp-log_binary32`
28×	`add-sqr-sqrt_binary32`
24×	`times-frac_binary32`
22×	`add-cube-cbrt_binary32`

Counts

4 → 127

Calls

4 calls:

18.0ms	(/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
14.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
9.0ms	(.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
8.0ms	(-.f32 (-.f32 1 cosTheta) cosTheta)

Compiler

Compiled 3651 to 1782 computations (51.2% saved)

series112.0ms (1.3%)

Error

0.2b

Counts

4 → 30

Calls

4 calls:

43.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
15.0ms	(.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
13.0ms	(/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
9.0ms	(-.f32 (-.f32 1 cosTheta) cosTheta)

Compiler

Compiled 2302 to 1626 computations (29.4% saved)

simplify135.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

458×	`distribute-rgt-in_binary32`
357×	`cancel-sign-sub-inv_binary32`
274×	`associate-r_binary32`
234×	`associate-l_binary32`
179×	`*-commutative_binary32`

Counts

157 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	332	4982
1	834	4638
2	2849	4497
3	5140	4497

prune114.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	122	9	131
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	124	9	133

Error

0.0b

Counts

133 → 9

Alt Table

Status	Error	Program
	0.7b	(/.f32 (/.f32 1 (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.9b	(/.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
▶	0.4b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32)))))))
	12.8b	(.f32 (/.f32 1 (-.f32 (.f32 (+.f32 1 c) (+.f32 1 c)) (/.f32 (-.f32 1 (+.f32 cosTheta cosTheta)) (.f32 (.f32 PI.f32 (.f32 cosTheta cosTheta)) (pow.f32 (exp.f32 cosTheta) (+.f32 cosTheta cosTheta)))))) (-.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.4b	(.f32 (/.f32 1 (+.f32 (.f32 (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (-.f32 1 (.f32 c c))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (-.f32 1 c)))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 PI.f32) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
	0.8b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (cbrt.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) (cbrt.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))) (cbrt.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (/.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 PI.f32)))))
	0.7b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))

Compiler

Compiled 3377 to 1799 computations (46.7% saved)

localize75.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.3b	(/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32)))))
0.3b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32)))))))
0.3b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32))))
0.5b	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32)))

rewrite226.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

54×	`add-exp-log_binary32`
52×	`*-un-lft-identity_binary32`
34×	`add-cbrt-cube_binary32`
31×	`prod-exp_binary32`
26×	`add-sqr-sqrt_binary32`

Counts

4 → 132

Calls

4 calls:

25.0ms	(/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32)))))
15.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32)))))))
14.0ms	(.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32))))
7.0ms	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32)))

Compiler

Compiled 5164 to 1858 computations (64% saved)

series131.0ms (1.5%)

Error

0.0b

Counts

4 → 30

Calls

4 calls:

46.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32)))))))
23.0ms	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32)))
16.0ms	(.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32))))
13.0ms	(/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32)))))

Compiler

Compiled 2518 to 1768 computations (29.8% saved)

simplify296.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

398×	`associate-r_binary32`
377×	`associate-l_binary32`
315×	`cancel-sign-sub-inv_binary32`
225×	`*-commutative_binary32`
187×	`unswap-sqr_binary32`

Counts

162 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	357	6723
1	914	5677
2	3246	5621
3	4757	5621
4	4940	5621
5	5000	5621
6	5000	5621
7	4933	5621

prune139.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Error

Counts

148 → 8

Alt Table

Status	Error	Program
	0.7b	(/.f32 (/.f32 1 (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.4b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (cbrt.f32 PI.f32)) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32))))))
	12.8b	(.f32 (/.f32 1 (-.f32 (.f32 (+.f32 1 c) (+.f32 1 c)) (/.f32 (-.f32 1 (+.f32 cosTheta cosTheta)) (.f32 (.f32 PI.f32 (.f32 cosTheta cosTheta)) (pow.f32 (exp.f32 cosTheta) (+.f32 cosTheta cosTheta)))))) (-.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.4b	(.f32 (/.f32 1 (+.f32 (.f32 (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (-.f32 1 (.f32 c c))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (-.f32 1 c)))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 PI.f32) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
▶	0.4b	(.f32 (/.f32 1 (+.f32 (.f32 (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3)) (-.f32 1 (.f32 c c))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (-.f32 1 c)))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32))))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (fabs.f32 (cbrt.f32 (cbrt.f32 PI.f32)))) (sqrt.f32 (cbrt.f32 (cbrt.f32 PI.f32))))))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (/.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 PI.f32)))))

Compiler

Compiled 3778 to 2018 computations (46.6% saved)

localize119.0ms (1.4%)

Local error

Found 4 expressions with local error:

0.3b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32))))
0.4b	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3))
0.5b	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32)))
1.0b	(pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3)

rewrite204.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

52×	`add-exp-log_binary32`
40×	`prod-exp_binary32`
34×	`associate-r_binary32`
31×	`sqrt-prod_binary32`
24×	`add-cbrt-cube_binary32`

Counts

4 → 134

Calls

4 calls:

15.0ms	(.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32))))
9.0ms	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3))
8.0ms	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32)))
3.0ms	(pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3)

Compiler

Compiled 6332 to 2326 computations (63.3% saved)

series91.0ms (1.1%)

Error

Counts

4 → 18

Calls

4 calls:

24.0ms	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32)))
19.0ms	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3))
16.0ms	(.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32))))
0.0ms	(pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3)

Compiler

Compiled 2184 to 1347 computations (38.3% saved)

simplify151.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

604×	`unswap-sqr_binary32`
489×	`log-prod_binary32`
419×	`exp-prod_binary32`
413×	`associate-r_binary32`
389×	`associate-l_binary32`

Counts

152 → 120

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	184	2883
1	430	2587
2	1661	2465
3	2907	2435
4	4633	2432
5	4935	2432

prune103.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	120	8	128

Error

Counts

128 → 8

Alt Table

Status	Error	Program
✓	0.4b	(.f32 (/.f32 1 (+.f32 (.f32 (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3)) (-.f32 1 (.f32 c c))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (-.f32 1 c)))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32))))))
	0.5b	(.f32 (/.f32 1 (+.f32 (.f32 (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3)) (-.f32 1 (.f32 c c))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (-.f32 1 c)))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (cbrt.f32 (cbrt.f32 PI.f32))) (cbrt.f32 (sqrt.f32 (cbrt.f32 PI.f32)))))))
	12.8b	(.f32 (/.f32 1 (-.f32 (.f32 (+.f32 1 c) (+.f32 1 c)) (/.f32 (-.f32 1 (+.f32 cosTheta cosTheta)) (.f32 (.f32 PI.f32 (.f32 cosTheta cosTheta)) (pow.f32 (exp.f32 cosTheta) (+.f32 cosTheta cosTheta)))))) (-.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.4b	(.f32 (/.f32 1 (+.f32 (.f32 (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (-.f32 1 (.f32 c c))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (-.f32 1 c)))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 PI.f32) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
▶	0.4b	(.f32 (/.f32 1 (+.f32 (.f32 (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3)) (-.f32 1 (.f32 c c))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (-.f32 1 c)))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (cbrt.f32 PI.f32)) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (cbrt.f32 PI.f32)))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (fabs.f32 (cbrt.f32 (cbrt.f32 PI.f32)))) (sqrt.f32 (cbrt.f32 (cbrt.f32 PI.f32))))))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (/.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 PI.f32)))))
	0.7b	(/.f32 (/.f32 1 (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))

Compiler

Compiled 3299 to 1543 computations (53.2% saved)

localize109.0ms (1.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (cbrt.f32 PI.f32))
0.4b	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3))
0.4b	(.f32 (sqrt.f32 (cbrt.f32 PI.f32)) (.f32 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (cbrt.f32 PI.f32)))
1.0b	(pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3)

rewrite231.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

52×	`add-exp-log_binary32`
40×	`prod-exp_binary32`
31×	`associate-r_binary32`
30×	`sqrt-prod_binary32`
23×	`*-un-lft-identity_binary32`

Counts

4 → 136

Calls

4 calls:

11.0ms	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3))
8.0ms	(.f32 (sqrt.f32 (cbrt.f32 PI.f32)) (.f32 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (cbrt.f32 PI.f32)))
6.0ms	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (cbrt.f32 PI.f32))
3.0ms	(pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3)

Compiler

Compiled 5940 to 2359 computations (60.3% saved)

series87.0ms (1%)

Error

Counts

4 → 18

Calls

4 calls:

23.0ms	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (cbrt.f32 PI.f32))
19.0ms	(.f32 (sqrt.f32 (cbrt.f32 PI.f32)) (.f32 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (cbrt.f32 PI.f32)))
17.0ms	(.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3))
0.0ms	(pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3)

Compiler

Compiled 2093 to 1313 computations (37.3% saved)

simplify150.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

497×	`log-prod_binary32`
453×	`associate-l_binary32`
452×	`associate-r_binary32`
393×	`exp-prod_binary32`
345×	`cube-prod_binary32`

Counts

154 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	179	3089
1	414	2640
2	2015	2416
3	2824	2354
4	4561	2354
5	4979	2354

prune149.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	134	8	142

Error

Counts

142 → 8

Alt Table

Status	Error	Program
	0.4b	(.f32 (/.f32 1 (+.f32 (.f32 (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3)) (-.f32 1 (.f32 c c))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (-.f32 1 c)))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (cbrt.f32 PI.f32))))))
	0.5b	(.f32 (/.f32 1 (+.f32 (.f32 (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3)) (-.f32 1 (.f32 c c))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (-.f32 1 c)))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (cbrt.f32 (cbrt.f32 PI.f32))) (cbrt.f32 (sqrt.f32 (cbrt.f32 PI.f32)))))))
	12.8b	(.f32 (/.f32 1 (-.f32 (.f32 (+.f32 1 c) (+.f32 1 c)) (/.f32 (-.f32 1 (+.f32 cosTheta cosTheta)) (.f32 (.f32 PI.f32 (.f32 cosTheta cosTheta)) (pow.f32 (exp.f32 cosTheta) (+.f32 cosTheta cosTheta)))))) (-.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.4b	(.f32 (/.f32 1 (+.f32 (.f32 (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (-.f32 1 (.f32 c c))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (-.f32 1 c)))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 PI.f32) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
	0.4b	(.f32 (/.f32 1 (+.f32 (.f32 (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 (cbrt.f32 PI.f32)) 3)) (-.f32 1 (.f32 c c))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (-.f32 1 c)))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (cbrt.f32 PI.f32)) (.f32 (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (cbrt.f32 PI.f32)))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (.f32 (.f32 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) (fabs.f32 (cbrt.f32 (cbrt.f32 PI.f32)))) (sqrt.f32 (cbrt.f32 (cbrt.f32 PI.f32))))))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (/.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 PI.f32)))))
	0.7b	(/.f32 (/.f32 1 (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))

Compiler

Compiled 3776 to 1799 computations (52.4% saved)

regimes3.6s (42.3%)

Accuracy

Total 0.4b remaining (93.1%)

Threshold costs 0.4b (93.1%)

Compiler

Compiled 84907 to 58864 computations (30.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary32`
8×	`+-commutative_binary32`
7×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	99
1	46	99
2	57	99
3	63	99
4	66	99
5	64	99

end1.0ms (0%)

Compiler: Compiled 60 to 30 computations (50% saved)

sample1.7s (20.3%)

Algorithm

1×

intervals

Results

895.0ms	8000×	body	128	valid
185.0ms	8000×	pre	128	true

Compiler

Compiled 469 to 292 computations (37.7% saved)

Details

analyze153.0ms (1.8%)

sample49.0ms (0.6%)

simplify91.0ms (1.1%)

prune5.0ms (0.1%)

localize62.0ms (0.7%)

rewrite210.0ms (2.5%)

series112.0ms (1.3%)

simplify135.0ms (1.6%)

prune114.0ms (1.3%)

localize75.0ms (0.9%)

rewrite226.0ms (2.6%)

series131.0ms (1.5%)

simplify296.0ms (3.5%)

prune139.0ms (1.6%)

localize119.0ms (1.4%)

rewrite204.0ms (2.4%)

series91.0ms (1.1%)

simplify151.0ms (1.8%)

prune103.0ms (1.2%)

localize109.0ms (1.3%)

rewrite231.0ms (2.7%)

series87.0ms (1%)

simplify150.0ms (1.8%)

prune149.0ms (1.7%)

regimes3.6s (42.3%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample1.7s (20.3%)

Profiling