Details

analyze291.0ms (1.5%)

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 42 to 32 computations (23.8% saved)

sample96.0ms (0.5%)

Algorithm

1×

intervals

Results

53.0ms	256×	body	128	valid
12.0ms	256×	pre	128	true

Compiler

Compiled 71 to 55 computations (22.5% saved)

simplify58.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

940×	`fma-neg_binary32`
929×	`fma-def_binary32`
740×	`times-frac_binary32`
329×	`div-sub_binary32`
317×	`associate-l_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	45	35
2	107	35
3	264	33
4	605	33
5	2500	33
6	3754	33
7	5049	33

prune9.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.6b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.8b	(/.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

▶

0.6b

(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))

0.8b

(/.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 148 to 113 computations (23.6% saved)

localize114.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))
✓	0.2b	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
✓	0.3b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.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)))

series222.0ms (1.1%)

Counts

4 → 46

Calls

4 calls:

145.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
48.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
18.0ms	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
10.0ms	(*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))

rewrite72.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary32`
36×	`add-exp-log_binary32`
28×	`add-sqr-sqrt_binary32`
23×	`add-cube-cbrt_binary32`
22×	`add-cbrt-cube_binary32`

Counts

4 → 129

Calls

4 calls:

17.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
15.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
12.0ms	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
8.0ms	(*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))

simplify265.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

396×	`associate-r_binary32`
336×	`associate-l_binary32`
295×	`fma-def_binary32`
272×	`unswap-sqr_binary32`
226×	`*-commutative_binary32`

Counts

175 → 228

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	6018
1	1072	5539
2	4023	5523
3	4986	5523

prune688.0ms (3.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	217	11	228
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	219	11	230

Error

0.0b

Counts

230 → 11

Alt Table

Status	Error	Program
	0.8b	(/.f32 (/.f32 1 (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
▶	0.4b	(.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (-.f32 1 (.f32 c c)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c)))) (.f32 (-.f32 1 c) (.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 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.7b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 1 (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	1.0b	(.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))))) (/.f32 1 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))))
	0.6b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))
	0.8b	(/.f32 1 (+.f32 1 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta -2 1) (PI.f32))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))
	13.3b	(.f32 (/.f32 1 (-.f32 (.f32 (+.f32 1 c) (+.f32 1 c)) (/.f32 (fma.f32 cosTheta -2 1) (.f32 (PI.f32) (.f32 (.f32 cosTheta cosTheta) (pow.f32 (exp.f32 (.f32 cosTheta cosTheta)) 2)))))) (-.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	1.0b	(/.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	0.8b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) (sqrt.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))

Compiler

Compiled 8996 to 5111 computations (43.2% saved)

localize201.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (-.f32 1 (.f32 c c)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c)))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
✓	0.1b	(/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (-.f32 1 (.f32 c c)) (*.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c))))
✓	0.4b	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))
	0.4b	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

series1.8s (9.4%)

Counts

3 → 48

Calls

3 calls:

1.3s

(*.f32 (/.f32 1 (fma.f32 (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (-.f32 1 (*.f32 c c)) (*.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c)))) (*.f32 (-.f32 1 c) (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

483.0ms

(/.f32 1 (fma.f32 (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (-.f32 1 (*.f32 c c)) (*.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c))))

18.0ms

(*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))

rewrite90.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`add-exp-log_binary32`
75×	`prod-exp_binary32`
42×	`add-cbrt-cube_binary32`
23×	`cbrt-unprod_binary32`
20×	`*-un-lft-identity_binary32`

Counts

3 → 120

Calls

3 calls:

29.0ms

(*.f32 (/.f32 1 (fma.f32 (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (-.f32 1 (*.f32 c c)) (*.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c)))) (*.f32 (-.f32 1 c) (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

12.0ms

(*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))

5.0ms

(/.f32 1 (fma.f32 (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (-.f32 1 (*.f32 c c)) (*.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c))))

simplify412.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

705×	`fma-def_binary32`
627×	`times-frac_binary32`
513×	`associate-/l*_binary32`
271×	`*-commutative_binary32`
209×	`+-commutative_binary32`

Counts

168 → 229

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	763	15021
1	2419	13564
2	5441	13564

prune1.0s (5.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	270	2	272
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	277	6	283

Error

Counts

283 → 6

Alt Table

Status	Error	Program
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	1.0b	(.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))))) (/.f32 1 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.6b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))
▶	0.5b	(/.f32 (.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (-.f32 1 (.f32 c c)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c)))) (.f32 (-.f32 (.f32 1 1) (.f32 c c)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) (+.f32 1 c))
	0.6b	(.f32 (log.f32 (exp.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (-.f32 1 (.f32 c c)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c)))))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

Compiler

Compiled 21181 to 11079 computations (47.7% saved)

localize254.0ms (1.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (-.f32 1 (.f32 c c)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c)))) (.f32 (-.f32 (.f32 1 1) (.f32 c c)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
	0.1b	(/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (-.f32 1 (.f32 c c)) (*.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c))))
	0.4b	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))
	0.4b	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

series1.7s (9%)

Counts

1 → 18

Calls

1 calls:

1.7s

(*.f32 (/.f32 1 (fma.f32 (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (-.f32 1 (*.f32 c c)) (*.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c)))) (*.f32 (-.f32 (*.f32 1 1) (*.f32 c c)) (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

rewrite67.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-exp-log_binary32`
72×	`prod-exp_binary32`
33×	`add-cbrt-cube_binary32`
20×	`cbrt-unprod_binary32`
13×	`associate-l_binary32`

Counts

1 → 64

Calls

1 calls:

30.0ms

(*.f32 (/.f32 1 (fma.f32 (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (-.f32 1 (*.f32 c c)) (*.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c)))) (*.f32 (-.f32 (*.f32 1 1) (*.f32 c c)) (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

simplify250.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

551×	`fma-def_binary32`
516×	`times-frac_binary32`
484×	`associate-/l*_binary32`
391×	`associate-/r*_binary32`
223×	`*-commutative_binary32`

Counts

82 → 116

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	588	9977
1	1901	8793
2	4974	8793

prune1.0s (5.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	270	6	276

Error

Counts

276 → 6

Alt Table

Status	Error	Program
▶	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	1.0b	(.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))))) (/.f32 1 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.6b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))
✓	0.5b	(/.f32 (.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (-.f32 1 (.f32 c c)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c)))) (.f32 (-.f32 (.f32 1 1) (.f32 c c)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) (+.f32 1 c))
	0.6b	(.f32 (log.f32 (exp.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (-.f32 1 (.f32 c c)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c)))))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

Compiler

Compiled 24210 to 13133 computations (45.8% saved)

localize160.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
✓	0.3b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
✓	0.3b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
✓	0.4b	(.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

series504.0ms (2.6%)

Counts

4 → 46

Calls

4 calls:

287.0ms	(.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
152.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
46.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
19.0ms	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))

rewrite122.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

29.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
28.0ms	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
22.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
15.0ms	(.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

simplify299.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

445×	`associate-r_binary32`
372×	`associate-l_binary32`
300×	`unswap-sqr_binary32`
298×	`fma-def_binary32`
258×	`*-commutative_binary32`

Counts

178 → 233

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	404	7630
1	1128	6450
2	4163	6415
3	5227	6415

prune592.0ms (3.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	233	0	233
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	233	6	239

Error

Counts

239 → 6

Alt Table

Status	Error	Program
✓	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	1.0b	(.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))))) (/.f32 1 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.6b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))
✓	0.5b	(/.f32 (.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (-.f32 1 (.f32 c c)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c)))) (.f32 (-.f32 (.f32 1 1) (.f32 c c)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) (+.f32 1 c))
	0.6b	(.f32 (log.f32 (exp.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (-.f32 1 (.f32 c c)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (-.f32 1 c)))))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

Compiler

Compiled 10306 to 4922 computations (52.2% saved)

regimes7.2s (37.1%)

Accuracy

Total 0.4b remaining (90.4%)

Threshold costs 0.4b (90.4%)

Counts

496 → 1

Compiler

Compiled 131378 to 90869 computations (30.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary32`
5×	`+-commutative_binary32`
2×	`distribute-rgt-neg-in_binary32`
2×	`cancel-sign-sub-inv_binary32`
2×	`sub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	94
1	57	94
2	61	94
3	62	94
4	63	94
5	60	94

end1.0ms (0%)

Compiler: Compiled 60 to 40 computations (33.3% saved)

sample1.8s (9.2%)

Algorithm

1×

intervals

Results

947.0ms	8000×	body	128	valid
191.0ms	8000×	pre	128	true

Compiler

Compiled 391 to 264 computations (32.5% saved)

Details

analyze291.0ms (1.5%)

sample96.0ms (0.5%)

simplify58.0ms (0.3%)

prune9.0ms (0%)

localize114.0ms (0.6%)

series222.0ms (1.1%)

rewrite72.0ms (0.4%)

simplify265.0ms (1.4%)

prune688.0ms (3.6%)

localize201.0ms (1%)

series1.8s (9.4%)

rewrite90.0ms (0.5%)

simplify412.0ms (2.1%)

prune1.0s (5.3%)

localize254.0ms (1.3%)

series1.7s (9%)

rewrite67.0ms (0.3%)

simplify250.0ms (1.3%)

prune1.0s (5.4%)

localize160.0ms (0.8%)

series504.0ms (2.6%)

rewrite122.0ms (0.6%)

simplify299.0ms (1.5%)

prune592.0ms (3.1%)

regimes7.2s (37.1%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.8s (9.2%)

Profiling