Details

analyze122.0ms (1.4%)

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)

sample96.0ms (1.1%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify46.0ms (0.5%)

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%)

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)

localize46.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(log.f32 (*.f32 alpha alpha))
✓	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)))

series136.0ms (1.6%)

Counts

4 → 72

Calls

4 calls:

75.0ms	(/.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))))
29.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
21.0ms	(log.f32 (*.f32 alpha alpha))
11.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`pow1_binary32`
20×	`add-exp-log_binary32`
17×	`add-sqr-sqrt_binary32`
17×	`add-cbrt-cube_binary32`
13×	`*-un-lft-identity_binary32`

Counts

4 → 107

Calls

4 calls:

11.0ms	(/.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))))
6.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
6.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
3.0ms	(log.f32 (*.f32 alpha alpha))

simplify97.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

570×	`associate-l_binary32`
566×	`times-frac_binary32`
530×	`associate-/r*_binary32`
299×	`associate-/l*_binary32`
181×	`fma-def_binary32`

Counts

179 → 215

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	405	5044
1	1237	4476
2	5353	4476

prune308.0ms (3.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	208	7	215
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	210	7	217

Error

Counts

217 → 7

Alt Table

Status	Error	Program
	0.7b	(/.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))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (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))))
	1.0b	(-.f32 (+.f32 (fma.f32 2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))) (fma.f32 4 (/.f32 (.f32 (pow.f32 alpha 6) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 3 (.f32 (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 4 (/.f32 (.f32 (.f32 alpha alpha) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))))))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (+.f32 (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 (pow.f32 cosTheta 4) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))) (fma.f32 (/.f32 (pow.f32 cosTheta 6) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 8) (PI.f32)) (fma.f32 6 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (+.f32 (/.f32 (pow.f32 cosTheta 6) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 3 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 4)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))))))))))
	0.7b	(.f32 (sqrt.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)))) (sqrt.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)))))
▶	0.4b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
	0.4b	(/.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))))

Compiler

Compiled 8751 to 4795 computations (45.2% saved)

localize70.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))
✓	0.7b	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
✓	0.8b	(pow.f32 (fma.f32 alpha alpha -1) 3)
✓	1.0b	(pow.f32 (PI.f32) 3)

series1.7s (19.8%)

Counts

4 → 48

Calls

4 calls:

1.7s	(/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))
29.0ms	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
3.0ms	(pow.f32 (fma.f32 alpha alpha -1) 3)
0.0ms	(pow.f32 (PI.f32) 3)

rewrite53.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

359×	`add-exp-log_binary32`
253×	`prod-exp_binary32`
173×	`pow-exp_binary32`
145×	`pow-to-exp_binary32`
120×	`div-exp_binary32`

Counts

4 → 234

Calls

4 calls:

10.0ms	(/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))
3.0ms	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
2.0ms	(pow.f32 (PI.f32) 3)
1.0ms	(pow.f32 (fma.f32 alpha alpha -1) 3)

simplify403.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

365×	`*-commutative_binary32`
319×	`+-commutative_binary32`
302×	`fma-def_binary32`
271×	`associate-+r+_binary32`
251×	`associate-/r*_binary32`

Counts

282 → 227

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1226	23961
1	4248	23692
2	4990	23692
3	4955	23692

prune691.0ms (7.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	227	7	234

Error

Counts

234 → 7

Alt Table

Status	Error	Program
	0.7b	(/.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))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (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))))
	1.0b	(-.f32 (+.f32 (fma.f32 2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))) (fma.f32 4 (/.f32 (.f32 (pow.f32 alpha 6) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 3 (.f32 (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 4 (/.f32 (.f32 (.f32 alpha alpha) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))))))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (+.f32 (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 (pow.f32 cosTheta 4) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))) (fma.f32 (/.f32 (pow.f32 cosTheta 6) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 8) (PI.f32)) (fma.f32 6 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 6)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (+.f32 (/.f32 (pow.f32 cosTheta 6) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 3 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 4)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))))))))))
	0.7b	(.f32 (sqrt.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)))) (sqrt.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)))))
✓	0.4b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
▶	0.4b	(/.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))))

Compiler

Compiled 26184 to 20281 computations (22.5% saved)

localize46.0ms (0.5%)

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))

series128.0ms (1.5%)

Counts

3 → 60

Calls

3 calls:

88.0ms

(/.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))))

24.0ms

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

15.0ms

(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary32`
16×	`pow1_binary32`
13×	`add-cbrt-cube_binary32`
9×	`*-un-lft-identity_binary32`
9×	`add-sqr-sqrt_binary32`

Counts

3 → 79

Calls

3 calls:

8.0ms

(/.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))))

6.0ms

(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)

3.0ms

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

simplify108.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

529×	`associate-l_binary32`
455×	`associate-/r*_binary32`
438×	`times-frac_binary32`
280×	`associate-/l*_binary32`
184×	`fma-def_binary32`

Counts

139 → 162

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	396	4747
1	1210	4233
2	4950	4233
3	5026	4233

prune238.0ms (2.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	208	2	210
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	211	6	217

Error

Counts

217 → 6

Alt Table

Status	Error	Program
▶	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))
✓	0.4b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
	0.7b	(/.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))))
	0.7b	(.f32 (sqrt.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)))) (sqrt.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)))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (-.f32 alpha 1) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.4b	(/.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))))

Compiler

Compiled 8189 to 4436 computations (45.8% saved)

localize57.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series237.0ms (2.7%)

Counts

2 → 48

Calls

2 calls:

152.0ms

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

85.0ms

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

rewrite46.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`prod-diff_binary32`
42×	`associate-/r/_binary32`
42×	`associate-*r/_binary32`
35×	`times-frac_binary32`
32×	`*-un-lft-identity_binary32`

Counts

2 → 126

Calls

2 calls:

12.0ms

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

6.0ms

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

simplify400.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

598×	`associate-/r*_binary32`
485×	`times-frac_binary32`
355×	`fma-def_binary32`
282×	`associate-/l*_binary32`
158×	`*-commutative_binary32`

Counts

174 → 244

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	571	20975
1	1760	14189
2	5125	14189

prune643.0ms (7.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	392	0	392
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	392	6	398

Error

Counts

398 → 6

Alt Table

Status	Error	Program
✓	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))
✓	0.4b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
	0.7b	(/.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))))
	0.7b	(.f32 (sqrt.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)))) (sqrt.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)))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (-.f32 alpha 1) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.4b	(/.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))))

Compiler

Compiled 29958 to 15633 computations (47.8% saved)

regimes1.3s (15.1%)

Accuracy

Total 0.4b remaining (91.9%)

Threshold costs 0.4b (91.9%)

Counts

206 → 1

Compiler

Compiled 31421 to 20055 computations (36.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	45
1	27	45
2	26	45

end1.0ms (0%)

Compiler: Compiled 32 to 25 computations (21.9% saved)

sample1.6s (18.7%)

Algorithm

1×

intervals

Results

812.0ms	8000×	body	128	valid
204.0ms	8000×	pre	128	true

Compiler

Compiled 286 to 187 computations (34.6% saved)

Details

analyze122.0ms (1.4%)

sample96.0ms (1.1%)

simplify46.0ms (0.5%)

prune4.0ms (0%)

localize46.0ms (0.5%)

series136.0ms (1.6%)

rewrite31.0ms (0.4%)

simplify97.0ms (1.1%)

prune308.0ms (3.5%)

localize70.0ms (0.8%)

series1.7s (19.8%)

rewrite53.0ms (0.6%)

simplify403.0ms (4.6%)

prune691.0ms (7.9%)

localize46.0ms (0.5%)

series128.0ms (1.5%)

rewrite23.0ms (0.3%)

simplify108.0ms (1.2%)

prune238.0ms (2.7%)

localize57.0ms (0.7%)

series237.0ms (2.7%)

rewrite46.0ms (0.5%)

simplify400.0ms (4.6%)

prune643.0ms (7.4%)

regimes1.3s (15.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.6s (18.7%)

Profiling