Details

analyze158.0ms (0.6%)

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)

sample55.0ms (0.2%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 65 to 51 computations (21.5% saved)

simplify89.0ms (0.3%)

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

prune9.0ms (0%)

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)

localize74.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite282.0ms (1.1%)

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:

15.0ms	(/.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))))))
13.0ms	(/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
10.0ms	(-.f32 (-.f32 1 cosTheta) cosTheta)
6.0ms	(.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

Compiler

Compiled 3651 to 1782 computations (51.2% saved)

series175.0ms (0.7%)

Error

0.2b

Counts

4 → 30

Calls

4 calls:

62.0ms	(/.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))))))
23.0ms	(.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
22.0ms	(/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
15.0ms	(-.f32 (-.f32 1 cosTheta) cosTheta)

Compiler

Compiled 2302 to 1626 computations (29.4% saved)

simplify132.0ms (0.5%)

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

prune353.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	121	10	131
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	123	10	133

Error

0.0b

Counts

133 → 10

Alt Table

Status	Error	Program
	3.1b	(exp.f32 (neg.f32 (log.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))))))))
	0.7b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) (sqrt.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)))))
	0.8b	(.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)))))))) (/.f32 1 (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))))))))
	0.6b	(.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))))))))
	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))))))))
	0.7b	(/.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)))))))
	0.4b	(/.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)))))))
	14.4b	(.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 (pow.f32 c 3))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (+.f32 1 (-.f32 (.f32 c c) c))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

Compiler

Compiled 3419 to 1843 computations (46.1% saved)

localize138.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.f32 (/.f32 1 (+.f32 (.f32 (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (+.f32 1 (pow.f32 c 3))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (+.f32 1 (-.f32 (.f32 c c) c))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
0.1b	(/.f32 1 (+.f32 (.f32 (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (+.f32 1 (pow.f32 c 3))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (+.f32 1 (-.f32 (*.f32 c c) c)))))
0.3b	(.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
0.3b	(.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

rewrite633.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

120×	`add-exp-log_binary32`
86×	`prod-exp_binary32`
48×	`add-cbrt-cube_binary32`
43×	`associate-l_binary32`
42×	`associate-*r/_binary32`

Counts

4 → 173

Calls

4 calls:

33.0ms	(.f32 (/.f32 1 (+.f32 (.f32 (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (+.f32 1 (pow.f32 c 3))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (+.f32 1 (-.f32 (.f32 c c) c))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
16.0ms	(/.f32 1 (+.f32 (.f32 (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (+.f32 1 (pow.f32 c 3))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (+.f32 1 (-.f32 (*.f32 c c) c)))))
9.0ms	(.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
6.0ms	(.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

Compiler

Compiled 14399 to 6673 computations (53.7% saved)

series1.8s (6.6%)

Error

0.0b

Counts

4 → 34

Calls

4 calls:

1.0s	(.f32 (/.f32 1 (+.f32 (.f32 (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (+.f32 1 (pow.f32 c 3))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (+.f32 1 (-.f32 (.f32 c c) c))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
339.0ms	(/.f32 1 (+.f32 (.f32 (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (+.f32 1 (pow.f32 c 3))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (+.f32 1 (-.f32 (*.f32 c c) c)))))
30.0ms	(.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
29.0ms	(.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

Compiler

Compiled 16442 to 10955 computations (33.4% saved)

simplify336.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

532×	`distribute-rgt-in_binary32`
435×	`*-commutative_binary32`
331×	`+-commutative_binary32`
284×	`associate-+r+_binary32`
196×	`associate-r_binary32`

Counts

207 → 177

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1112	22269
1	3586	20517
2	5310	20517

prune667.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	179	8	187

Error

Counts

187 → 8

Alt Table

Status	Error	Program
▶	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)))))
	0.6b	(.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))))))))
	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))))))))
	0.7b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) (sqrt.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 PI.f32) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.6b	(.f32 (log.f32 (exp.f32 (/.f32 1 (+.f32 (.f32 (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (+.f32 1 (pow.f32 c 3))) (.f32 (-.f32 (+.f32 1 (.f32 c c)) c) (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta)))))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
	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)))))))
	14.4b	(.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 (pow.f32 c 3))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (+.f32 1 (-.f32 (.f32 c c) c))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

Compiler

Compiled 15964 to 8223 computations (48.5% saved)

localize79.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (/.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 PI.f32)))
0.1b	(-.f32 (-.f32 1 cosTheta) cosTheta)
0.3b	(/.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)))))
0.4b	(/.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 PI.f32))

rewrite653.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

294×	`times-frac_binary32`
198×	`add-sqr-sqrt_binary32`
172×	`*-un-lft-identity_binary32`
162×	`add-cube-cbrt_binary32`
96×	`sqrt-prod_binary32`

Counts

4 → 299

Calls

4 calls:

32.0ms	(.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (/.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 PI.f32)))
9.0ms	(/.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)))))
7.0ms	(/.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 PI.f32))
6.0ms	(-.f32 (-.f32 1 cosTheta) cosTheta)

Compiler

Compiled 10049 to 4129 computations (58.9% saved)

series204.0ms (0.8%)

Error

Counts

4 → 30

Calls

4 calls:

71.0ms	(/.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)))))
26.0ms	(/.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 PI.f32))
23.0ms	(.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) (/.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 PI.f32)))
17.0ms	(-.f32 (-.f32 1 cosTheta) cosTheta)

Compiler

Compiled 2556 to 1985 computations (22.3% saved)

simplify502.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

349×	`associate-r_binary32`
329×	`associate-l_binary32`
287×	`*-commutative_binary32`
205×	`associate-/l/_binary32`
191×	`associate-/l*_binary32`

Counts

329 → 313

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	530	12260
1	1347	11542
2	4338	11373
3	4763	11368
4	4958	11368
5	4996	11368
6	4936	11368

prune479.0ms (1.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	310	3	313
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	314	7	321

Error

Counts

321 → 7

Alt Table

Status	Error	Program
✓	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)))))
▶	0.5b	(.f32 (/.f32 1 (+.f32 (-.f32 1 (.f32 c c)) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 PI.f32))) (-.f32 1 c)))) (*.f32 (-.f32 1 c) (sqrt.f32 (+.f32 (-.f32 1 cosTheta) cosTheta))))
	0.7b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (sqrt.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (sqrt.f32 PI.f32)))) (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta)))) (sqrt.f32 (/.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 PI.f32))))))
	0.6b	(.f32 (log.f32 (exp.f32 (/.f32 1 (+.f32 (.f32 (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (+.f32 1 (pow.f32 c 3))) (.f32 (-.f32 (+.f32 1 (.f32 c c)) c) (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta)))))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (/.f32 (sqrt.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (fabs.f32 (cbrt.f32 PI.f32))) (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta)))) (/.f32 (/.f32 (sqrt.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta) (sqrt.f32 (cbrt.f32 PI.f32))))))
	14.4b	(.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 (pow.f32 c 3))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (+.f32 1 (-.f32 (.f32 c c) c))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

Compiler

Compiled 8158 to 3493 computations (57.2% saved)

localize125.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite1.2s (4.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

370×	`times-frac_binary32`
258×	`*-un-lft-identity_binary32`
197×	`add-sqr-sqrt_binary32`
151×	`sqrt-prod_binary32`
125×	`add-cube-cbrt_binary32`

Counts

4 → 362

Calls

4 calls:

35.0ms	(.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 PI.f32))) (-.f32 1 c))
23.0ms	(/.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 PI.f32)))
10.0ms	(/.f32 1 (+.f32 (-.f32 1 (.f32 c c)) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 PI.f32))) (-.f32 1 c))))
4.0ms	(*.f32 cosTheta (sqrt.f32 PI.f32))

Compiler

Compiled 16265 to 8659 computations (46.8% saved)

series621.0ms (2.3%)

Error

Counts

4 → 35

Calls

4 calls:

313.0ms	(/.f32 1 (+.f32 (-.f32 1 (.f32 c c)) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 PI.f32))) (-.f32 1 c))))
95.0ms	(.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 PI.f32))) (-.f32 1 c))
29.0ms	(/.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 PI.f32)))
18.0ms	(*.f32 cosTheta (sqrt.f32 PI.f32))

Compiler

Compiled 7489 to 5338 computations (28.7% saved)

simplify299.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

532×	`associate-/l*_binary32`
498×	`times-frac_binary32`
220×	`distribute-rgt-in_binary32`
217×	`distribute-lft-in_binary32`
209×	`*-commutative_binary32`

Counts

397 → 348

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	772	18228
1	2084	17075
2	5296	17075

prune1.0s (3.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	347	1	348
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	348	7	355

Error

Counts

355 → 7

Alt Table

Status	Error	Program
	0.6b	(.f32 (log.f32 (exp.f32 (/.f32 1 (+.f32 (.f32 (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (+.f32 1 (pow.f32 c 3))) (.f32 (-.f32 (+.f32 1 (.f32 c c)) c) (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta)))))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
	0.5b	(.f32 (/.f32 1 (+.f32 (-.f32 1 (.f32 c c)) (.f32 (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (sqrt.f32 PI.f32) cosTheta)) (.f32 (cbrt.f32 (-.f32 1 c)) (cbrt.f32 (-.f32 1 c)))) (cbrt.f32 (-.f32 1 c))))) (*.f32 (-.f32 1 c) (sqrt.f32 (+.f32 (-.f32 1 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)))))
	0.5b	(.f32 (/.f32 1 (+.f32 (-.f32 1 (.f32 c c)) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 PI.f32))) (-.f32 1 c)))) (*.f32 (-.f32 1 c) (sqrt.f32 (+.f32 (-.f32 1 cosTheta) cosTheta))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (/.f32 (sqrt.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (fabs.f32 (cbrt.f32 PI.f32))) (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta)))) (/.f32 (/.f32 (sqrt.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta) (sqrt.f32 (cbrt.f32 PI.f32))))))
	14.4b	(.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 (pow.f32 c 3))) (.f32 (sqrt.f32 (-.f32 1 (+.f32 cosTheta cosTheta))) (+.f32 1 (-.f32 (.f32 c c) c))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 PI.f32) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

Compiler

Compiled 13806 to 7821 computations (43.4% saved)

regimes14.5s (54.4%)

Accuracy

Total 0.4b remaining (92.9%)

Threshold costs 0.4b (92.9%)

Compiler

Compiled 189281 to 127407 computations (32.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	76
1	38	76
2	47	76
3	54	76
4	58	76
5	59	76
6	58	76

end2.0ms (0%)

Compiler: Compiled 50 to 28 computations (44% saved)

sample2.2s (8.1%)

Algorithm

1×

intervals

Results

954.0ms	8000×	body	128	valid
181.0ms	8001×	pre	128	true
0.0ms	1×	body	128	nan

Compiler

Compiled 409 to 277 computations (32.3% saved)

Details

analyze158.0ms (0.6%)

sample55.0ms (0.2%)

simplify89.0ms (0.3%)

prune9.0ms (0%)

localize74.0ms (0.3%)

rewrite282.0ms (1.1%)

series175.0ms (0.7%)

simplify132.0ms (0.5%)

prune353.0ms (1.3%)

localize138.0ms (0.5%)

rewrite633.0ms (2.4%)

series1.8s (6.6%)

simplify336.0ms (1.3%)

prune667.0ms (2.5%)

localize79.0ms (0.3%)

rewrite653.0ms (2.4%)

series204.0ms (0.8%)

simplify502.0ms (1.9%)

prune479.0ms (1.8%)

localize125.0ms (0.5%)

rewrite1.2s (4.3%)

series621.0ms (2.3%)

simplify299.0ms (1.1%)

prune1.0s (3.8%)

regimes14.5s (54.4%)

simplify5.0ms (0%)

end2.0ms (0%)

sample2.2s (8.1%)

Profiling