Details

analyze108.0ms (1.7%)

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)

sample98.0ms (1.5%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
6.0ms	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 (-.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))))
	0.5b	(/.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)))

Status

Error

Program

▶

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))))

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)))

Compiler

Compiled 145 to 87 computations (40% saved)

localize42.0ms (0.7%)

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)))

series315.0ms (4.9%)

Counts

4 → 72

Calls

4 calls:

253.0ms	(/.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)))
24.0ms	(log.f32 (*.f32 alpha alpha))
10.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite29.0ms (0.5%)

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:

10.0ms	(/.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))))
5.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
5.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
2.0ms	(log.f32 (*.f32 alpha alpha))

simplify87.0ms (1.4%)

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

prune327.0ms (5.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	205	10	215
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	207	10	217

Error

0.0b

Counts

217 → 10

Alt Table

Status	Error	Program
	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)))))
	0.8b	(/.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))))
	0.6b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 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))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.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 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (cbrt.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (cbrt.f32 (.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 alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.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)))))
▶	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (log.f32 (exp.f32 (.f32 cosTheta (fma.f32 alpha alpha -1)))) cosTheta))))
	0.7b	(.f32 (/.f32 (.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (cbrt.f32 (fma.f32 alpha alpha -1))) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))

Compiler

Compiled 8799 to 4807 computations (45.4% saved)

localize61.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f32 cosTheta (fma.f32 alpha alpha -1))
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (log.f32 (exp.f32 (.f32 cosTheta (fma.f32 alpha alpha -1)))) cosTheta))))
	0.4b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	25.8b	(log.f32 (exp.f32 (*.f32 cosTheta (fma.f32 alpha alpha -1))))

series95.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

74.0ms

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

12.0ms

(log.f32 (exp.f32 (*.f32 cosTheta (fma.f32 alpha alpha -1))))

10.0ms

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

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary32`
14×	`add-exp-log_binary32`
12×	`add-sqr-sqrt_binary32`
10×	`*-un-lft-identity_binary32`
8×	`add-cube-cbrt_binary32`

Counts

3 → 76

Calls

3 calls:

11.0ms

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

3.0ms

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

1.0ms

(log.f32 (exp.f32 (*.f32 cosTheta (fma.f32 alpha alpha -1))))

simplify81.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

442×	`associate-r_binary32`
442×	`associate-/r*_binary32`
425×	`times-frac_binary32`
419×	`associate-l_binary32`
268×	`associate-/l*_binary32`

Counts

148 → 155

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	403	4708
1	1190	4184
2	5120	4184

prune324.0ms (5.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	199	10	209

Error

0.0b

Counts

209 → 10

Alt Table

Status	Error	Program
	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)))))
	0.8b	(/.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))))
	0.6b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 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))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.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 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (cbrt.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (cbrt.f32 (.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 alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.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)))))
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (log.f32 (exp.f32 (.f32 cosTheta (fma.f32 alpha alpha -1)))) cosTheta))))
	0.7b	(.f32 (/.f32 (.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (cbrt.f32 (fma.f32 alpha alpha -1))) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))

Compiler

Compiled 8478 to 4820 computations (43.1% saved)

localize46.0ms (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 (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))

series126.0ms (2%)

Counts

3 → 60

Calls

3 calls:

85.0ms

(/.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))))

25.0ms

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

15.0ms

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

rewrite24.0ms (0.4%)

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:

9.0ms

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

7.0ms

(/.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))

simplify109.0ms (1.7%)

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

prune270.0ms (4.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	208	2	210
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	210	10	220

Error

0.0b

Counts

220 → 10

Alt Table

Status	Error	Program
	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)))))
	0.8b	(/.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))))
	0.6b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 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))))
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (log.f32 (exp.f32 (.f32 cosTheta (fma.f32 alpha alpha -1)))) cosTheta))))
	0.6b	(-.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)))))
	0.6b	(/.f32 (+.f32 alpha 1) (/.f32 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))) (-.f32 alpha 1)))
▶	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.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 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)))))
	0.7b	(.f32 (/.f32 (.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (cbrt.f32 (fma.f32 alpha alpha -1))) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))

Compiler

Compiled 8556 to 4657 computations (45.6% saved)

localize65.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.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 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.4b	(.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha)))
✓	0.5b	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
✓	1.0b	(*.f32 (PI.f32) (PI.f32))

series178.0ms (2.8%)

Counts

4 → 48

Calls

4 calls:

111.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.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 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
34.0ms	(.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha)))
32.0ms	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
0.0ms	(*.f32 (PI.f32) (PI.f32))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`pow1_binary32`
42×	`log-pow_binary32`
22×	`add-sqr-sqrt_binary32`
21×	`associate-r_binary32`
21×	`*-un-lft-identity_binary32`

Counts

4 → 155

Calls

4 calls:

12.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.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 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
9.0ms	(.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha)))
7.0ms	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
3.0ms	(*.f32 (PI.f32) (PI.f32))

simplify101.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

551×	`associate-l_binary32`
516×	`associate-/r*_binary32`
496×	`times-frac_binary32`
243×	`associate-/l*_binary32`
182×	`fma-def_binary32`

Counts

203 → 228

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	411	6724
1	1237	4967
2	5006	4967

prune322.0ms (5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	226	2	228
Fresh	2	5	7
Picked	0	1	1
Done	1	1	2
Total	229	9	238

Error

0.0b

Counts

238 → 9

Alt Table

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

Compiler

Compiled 11284 to 5297 computations (53.1% saved)

regimes1.8s (28.5%)

Accuracy

Total 0.4b remaining (95.3%)

Threshold costs 0.4b (95.3%)

Counts

275 → 1

Compiler

Compiled 41103 to 26521 computations (35.5% 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

end2.0ms (0%)

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

sample1.6s (25.8%)

Algorithm

1×

intervals

Results

797.0ms	8000×	body	128	valid
204.0ms	8000×	pre	128	true

Compiler

Compiled 467 to 289 computations (38.1% saved)

Details

analyze108.0ms (1.7%)

sample98.0ms (1.5%)

simplify47.0ms (0.7%)

prune4.0ms (0.1%)

localize42.0ms (0.7%)

series315.0ms (4.9%)

rewrite29.0ms (0.5%)

simplify87.0ms (1.4%)

prune327.0ms (5.1%)

localize61.0ms (0.9%)

series95.0ms (1.5%)

rewrite20.0ms (0.3%)

simplify81.0ms (1.3%)

prune324.0ms (5.1%)

localize46.0ms (0.7%)

series126.0ms (2%)

rewrite24.0ms (0.4%)

simplify109.0ms (1.7%)

prune270.0ms (4.2%)

localize65.0ms (1%)

series178.0ms (2.8%)

rewrite43.0ms (0.7%)

simplify101.0ms (1.6%)

prune322.0ms (5%)

regimes1.8s (28.5%)

simplify3.0ms (0%)

end2.0ms (0%)

sample1.6s (25.8%)

Profiling