Details

analyze177.0ms (2.4%)

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)

sample48.0ms (0.7%)

Algorithm

1×

intervals

Results

26.0ms	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)

localize44.0ms (0.6%)

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)
✓	0.4b	(/.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 (1.9%)

Counts

4 → 84

Calls

4 calls:

82.0ms	(/.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)))
13.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
11.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite35.0ms (0.5%)

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))))
6.0ms	(.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)))

simplify95.0ms (1.3%)

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

prune302.0ms (4.2%)

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

0.0b

Counts

233 → 8

Alt Table

Status	Error	Program
	0.5b	(/.f32 1 (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (fma.f32 alpha alpha -1) (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))))
	0.6b	(.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)))
	0.9b	(.f32 (.f32 (cbrt.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))))) (cbrt.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)))))) (cbrt.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))))))
	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))))
	0.5b	(/.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))))
	0.5b	(-.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)))
	0.6b	(-.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)))))

Compiler

Compiled 9147 to 4909 computations (46.3% saved)

localize67.0ms (0.9%)

Local error

Found 4 expressions with local error:

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

series81.0ms (1.1%)

Counts

4 → 36

Calls

4 calls:

47.0ms	(.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3))
31.0ms	(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)

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary32`
25×	`add-sqr-sqrt_binary32`
16×	`prod-exp_binary32`
15×	`*-un-lft-identity_binary32`
15×	`add-cube-cbrt_binary32`

Counts

4 → 126

Calls

4 calls:

6.0ms	(.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3))
3.0ms	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
2.0ms	(pow.f32 (PI.f32) 3)
2.0ms	(pow.f32 (fma.f32 alpha alpha -1) 3)

simplify108.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-def_binary32`
478×	`log-prod_binary32`
459×	`exp-prod_binary32`
268×	`associate-r_binary32`
264×	`associate-l_binary32`

Counts

162 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	2300
1	345	2209
2	1554	2043
3	3476	2037
4	4960	2037
5	5127	2037

prune217.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	173	7	180

Error

Counts

180 → 7

Alt Table

Status	Error	Program
	0.5b	(/.f32 1 (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (fma.f32 alpha alpha -1) (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))))
	0.7b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (.f32 (pow.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) 3) (pow.f32 (cbrt.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))))
	0.6b	(.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 (.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))))
	0.5b	(-.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)))
	1.2b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) (.f32 (cbrt.f32 3) (cbrt.f32 3))) (cbrt.f32 3)) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))

Compiler

Compiled 6533 to 4637 computations (29% saved)

localize68.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.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))

series140.0ms (1.9%)

Counts

4 → 48

Calls

4 calls:

82.0ms	(/.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))))
32.0ms	(.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha)))
26.0ms	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
0.0ms	(*.f32 (PI.f32) (PI.f32))

rewrite56.0ms (0.8%)

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:

13.0ms	(/.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))))
10.0ms	(.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha)))
8.0ms	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
3.0ms	(*.f32 (PI.f32) (PI.f32))

simplify111.0ms (1.5%)

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

prune261.0ms (3.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	226	2	228
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	228	7	235

Error

Counts

235 → 7

Alt Table

Status	Error	Program
✓	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 1) (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)))) (/.f32 (+.f32 alpha -1) (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))))
▶	0.5b	(/.f32 1 (/.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3))) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))
	0.5b	(-.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)))
	1.2b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) (.f32 (cbrt.f32 3) (cbrt.f32 3))) (cbrt.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	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (.f32 (pow.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) 3) (pow.f32 (cbrt.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))))

Compiler

Compiled 11325 to 5376 computations (52.5% saved)

localize64.0ms (0.9%)

Local error

Found 4 expressions with local error:

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

series127.0ms (1.7%)

Counts

1 → 24

Calls

1 calls:

127.0ms

(/.f32 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 2 (log.f32 alpha)) 3))) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`times-frac_binary32`
50×	`*-un-lft-identity_binary32`
50×	`add-sqr-sqrt_binary32`
50×	`add-cube-cbrt_binary32`
14×	`cbrt-prod_binary32`

Counts

1 → 86

Calls

1 calls:

6.0ms

(/.f32 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 2 (log.f32 alpha)) 3))) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))

simplify177.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

397×	`cancel-sign-sub-inv_binary32`
254×	`fma-neg_binary32`
195×	`div-sub_binary32`
178×	`*-commutative_binary32`
165×	`associate-/r/_binary32`

Counts

110 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	289	6856
1	761	6533
2	2877	6345
3	4627	6339
4	4972	6339

prune372.0ms (5.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	295	0	295
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	295	7	302

Error

Counts

302 → 7

Alt Table

Status	Error	Program
✓	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 1) (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)))) (/.f32 (+.f32 alpha -1) (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))))
✓	0.5b	(/.f32 1 (/.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3))) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))
	0.5b	(-.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)))
	1.2b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) (.f32 (cbrt.f32 3) (cbrt.f32 3))) (cbrt.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	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (.f32 (pow.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) 3) (pow.f32 (cbrt.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))))

Compiler

Compiled 12219 to 8400 computations (31.3% saved)

regimes1.6s (22.4%)

Accuracy

Total 0.4b remaining (93.4%)

Threshold costs 0.4b (93.4%)

Counts

276 → 1

Compiler

Compiled 40545 to 27442 computations (32.3% 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	23	52
1	29	52
2	28	52

end1.0ms (0%)

Compiler: Compiled 36 to 29 computations (19.4% saved)

sample2.9s (39.3%)

Algorithm

1×

intervals

Results

1.4s	8000×	body	128	valid
339.0ms	8000×	pre	128	true

Compiler

Compiled 332 to 238 computations (28.3% saved)

Details

analyze177.0ms (2.4%)

sample48.0ms (0.7%)

simplify47.0ms (0.7%)

prune4.0ms (0.1%)

localize44.0ms (0.6%)

series136.0ms (1.9%)

rewrite35.0ms (0.5%)

simplify95.0ms (1.3%)

prune302.0ms (4.2%)

localize67.0ms (0.9%)

series81.0ms (1.1%)

rewrite18.0ms (0.3%)

simplify108.0ms (1.5%)

prune217.0ms (3%)

localize68.0ms (0.9%)

series140.0ms (1.9%)

rewrite56.0ms (0.8%)

simplify111.0ms (1.5%)

prune261.0ms (3.6%)

localize64.0ms (0.9%)

series127.0ms (1.7%)

rewrite18.0ms (0.3%)

simplify177.0ms (2.4%)

prune372.0ms (5.1%)

regimes1.6s (22.4%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.9s (39.3%)

Profiling