Details

analyze165.0ms (2.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.6%	99.4%	0
0%	0.6%	99.4%	1
0%	0.6%	99.4%	2
0.3%	0.3%	99.4%	3
0.3%	0.3%	99.4%	4
0.5%	0.2%	99.4%	5
0.5%	0.2%	99.4%	6
0.6%	0.1%	99.4%	7
0.6%	0.1%	99.4%	8
0.6%	0%	99.4%	9
0.6%	0%	99.4%	10
0.6%	0%	99.4%	11
0.6%	0%	99.4%	12
0.6%	0%	99.4%	13
0.6%	0%	99.4%	14

Compiler

Compiled 41 to 27 computations (34.1% saved)

sample50.0ms (0.8%)

Algorithm

1×

intervals

Results

28.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify47.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-/l*_binary32`
462×	`associate-l_binary32`
382×	`associate-*l/_binary32`
363×	`associate-r_binary32`
360×	`distribute-lft-in_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	45	31
2	160	31
3	661	31
4	2791	31
5	4866	31
6	4978	31

prune4.0ms (0.1%)

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
	0.5b	(/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
▶	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Status

Error

Program

0.5b

(/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))

▶

0.5b

(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Compiler

Compiled 145 to 87 computations (40% saved)

localize44.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
✓	0.2b	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.4b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

series153.0ms (2.3%)

Counts

4 → 84

Calls

4 calls:

98.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
31.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
13.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
12.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cbrt-cube_binary32`
22×	`add-exp-log_binary32`
21×	`pow1_binary32`
18×	`add-sqr-sqrt_binary32`
15×	`associate-r_binary32`

Counts

4 → 111

Calls

4 calls:

12.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
9.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
6.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
5.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

simplify98.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

633×	`associate-l_binary32`
535×	`times-frac_binary32`
508×	`associate-/r*_binary32`
299×	`associate-/l*_binary32`
183×	`fma-def_binary32`

Counts

195 → 231

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	419	5485
1	1280	4813
2	5382	4813

prune320.0ms (4.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	223	8	231
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	225	8	233

Error

Counts

233 → 8

Alt Table

Status	Error	Program
▶	0.4b	(cbrt.f32 (/.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (.f32 alpha alpha) 1)) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha)))) (.f32 (.f32 (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))) (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))) (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.8b	(exp.f32 (log.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
	0.5b	(.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (-.f32 (.f32 alpha alpha) 1) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(/.f32 (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))) (+.f32 (.f32 alpha alpha) 1)))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))) (sqrt.f32 (/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))))

Compiler

Compiled 9207 to 4937 computations (46.4% saved)

localize89.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha)))
✓	0.5b	(.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (*.f32 alpha alpha) 1))
✓	0.5b	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
✓	1.0b	(*.f32 (PI.f32) (PI.f32))

series66.0ms (1%)

Counts

4 → 36

Calls

4 calls:

32.0ms	(.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha)))
30.0ms	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
3.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (*.f32 alpha alpha) 1))
0.0ms	(*.f32 (PI.f32) (PI.f32))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`pow1_binary32`
42×	`log-pow_binary32`
32×	`add-sqr-sqrt_binary32`
31×	`*-un-lft-identity_binary32`
28×	`swap-sqr_binary32`

Counts

4 → 181

Calls

4 calls:

10.0ms	(.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha)))
9.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (*.f32 alpha alpha) 1))
9.0ms	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
3.0ms	(*.f32 (PI.f32) (PI.f32))

simplify149.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

520×	`distribute-rgt-in_binary32`
466×	`distribute-lft-in_binary32`
392×	`fma-def_binary32`
389×	`fma-neg_binary32`
325×	`*-commutative_binary32`

Counts

217 → 218

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	3094
1	367	2456
2	1195	2224
3	3763	2176
4	4968	2176
5	5169	2176

prune395.0ms (6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	218	8	226

Error

Counts

226 → 8

Alt Table

Status	Error	Program
✓	0.4b	(cbrt.f32 (/.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (.f32 alpha alpha) 1)) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha)))) (.f32 (.f32 (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))) (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))) (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.8b	(exp.f32 (log.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
	0.5b	(.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (-.f32 (.f32 alpha alpha) 1) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(/.f32 (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))) (+.f32 (.f32 alpha alpha) 1)))
▶	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))) (sqrt.f32 (/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))))

Compiler

Compiled 18149 to 8452 computations (53.4% saved)

localize50.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
	0.2b	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	3.1b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series131.0ms (2%)

Counts

2 → 36

Calls

2 calls:

94.0ms

(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

37.0ms

(pow.f32 (*.f32 alpha alpha) (PI.f32))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary32`
10×	`pow1_binary32`
7×	`add-cbrt-cube_binary32`
7×	`*-un-lft-identity_binary32`
7×	`add-sqr-sqrt_binary32`

Counts

2 → 57

Calls

2 calls:

9.0ms

(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

3.0ms

(pow.f32 (*.f32 alpha alpha) (PI.f32))

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

467×	`associate-r_binary32`
452×	`associate-/r*_binary32`
414×	`times-frac_binary32`
406×	`associate-l_binary32`
265×	`associate-/l*_binary32`

Counts

93 → 121

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	360	4112
1	1120	3692
2	5116	3692

prune285.0ms (4.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	207	2	209
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	209	8	217

Error

Counts

217 → 8

Alt Table

Status	Error	Program
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(.f32 (/.f32 (.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (cbrt.f32 (-.f32 (.f32 alpha alpha) 1))) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.4b	(cbrt.f32 (/.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (.f32 alpha alpha) 1)) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha)))) (.f32 (.f32 (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))) (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))) (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.8b	(exp.f32 (log.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
▶	0.5b	(.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (-.f32 (.f32 alpha alpha) 1) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(/.f32 (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))) (+.f32 (*.f32 alpha alpha) 1)))

Compiler

Compiled 8370 to 4550 computations (45.6% saved)

localize70.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
✓	0.2b	(/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
✓	0.3b	(.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (-.f32 (.f32 alpha alpha) 1) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.4b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

series118.0ms (1.8%)

Counts

2 → 36

Calls

2 calls:

80.0ms

(*.f32 (/.f32 1 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 (-.f32 (*.f32 alpha alpha) 1) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

38.0ms

(/.f32 1 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-exp-log_binary32`
28×	`add-cbrt-cube_binary32`
25×	`times-frac_binary32`
24×	`associate-r_binary32`
24×	`add-sqr-sqrt_binary32`

Counts

2 → 97

Calls

2 calls:

19.0ms

(*.f32 (/.f32 1 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 (-.f32 (*.f32 alpha alpha) 1) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

5.0ms

(/.f32 1 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))

simplify95.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

428×	`associate-/r*_binary32`
418×	`associate-r_binary32`
350×	`associate-l_binary32`
297×	`times-frac_binary32`
243×	`associate-/l*_binary32`

Counts

133 → 184

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	391	5775
1	1211	4837
2	5044	4837

prune375.0ms (5.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	274	2	276
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	277	7	284

Error

Counts

284 → 7

Alt Table

Status	Error	Program
	0.6b	(.f32 (.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (+.f32 alpha 1) 1)) (/.f32 (-.f32 alpha 1) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(/.f32 (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))) (+.f32 (*.f32 alpha alpha) 1)))
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(.f32 (/.f32 (.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (cbrt.f32 (-.f32 (.f32 alpha alpha) 1))) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.4b	(cbrt.f32 (/.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (.f32 alpha alpha) 1)) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha)))) (.f32 (.f32 (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (-.f32 (.f32 alpha alpha) 1) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))

Compiler

Compiled 11097 to 6110 computations (44.9% saved)

regimes1.8s (28.2%)

Accuracy

Total 0.4b remaining (92.9%)

Threshold costs 0.4b (92.9%)

Counts

323 → 1

Compiler

Compiled 47564 to 30520 computations (35.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary32`
2×	`+-commutative_binary32`
1×	`sub-neg_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	112
1	38	112
2	39	112
3	37	112

end1.0ms (0%)

Compiler: Compiled 74 to 42 computations (43.2% saved)

sample1.8s (27.1%)

Algorithm

1×

intervals

Results

866.0ms	8000×	body	128	valid
232.0ms	8000×	pre	128	true

Compiler

Compiled 392 to 235 computations (40.1% saved)

Details

analyze165.0ms (2.5%)

sample50.0ms (0.8%)

simplify47.0ms (0.7%)

prune4.0ms (0.1%)

localize44.0ms (0.7%)

series153.0ms (2.3%)

rewrite38.0ms (0.6%)

simplify98.0ms (1.5%)

prune320.0ms (4.9%)

localize89.0ms (1.4%)

series66.0ms (1%)

rewrite48.0ms (0.7%)

simplify149.0ms (2.3%)

prune395.0ms (6%)

localize50.0ms (0.8%)

series131.0ms (2%)

rewrite16.0ms (0.2%)

simplify80.0ms (1.2%)

prune285.0ms (4.3%)

localize70.0ms (1.1%)

series118.0ms (1.8%)

rewrite37.0ms (0.6%)

simplify95.0ms (1.5%)

prune375.0ms (5.7%)

regimes1.8s (28.2%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.8s (27.1%)

Profiling