Details

analyze184.0ms (1.8%)

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 35 to 23 computations (34.3% saved)

sample56.0ms (0.6%)

Algorithm

1×

intervals

Results

30.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 63 to 41 computations (34.9% saved)

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-/l*_binary32`
583×	`div-sub_binary32`
462×	`associate-l_binary32`
382×	`associate-*l/_binary32`
363×	`associate-r_binary32`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	37
1	44	37
2	154	37
3	628	37
4	2620	37
5	4665	37
6	5735	37

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.5b

Counts

2 → 1

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))))

Compiler

Compiled 78 to 48 computations (38.5% saved)

localize51.0ms (0.5%)

Local error

Found 4 expressions with local error:

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)))

rewrite187.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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 → 99

Calls

4 calls:

13.0ms	(/.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 alpha alpha) 1) cosTheta)
5.0ms	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))
2.0ms	(log.f32 (*.f32 alpha alpha))

Compiler

Compiled 2832 to 1300 computations (54.1% saved)

series225.0ms (2.2%)

Error

0.3b

Counts

4 → 28

Calls

4 calls:

100.0ms	(/.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 (-.f32 (.f32 alpha alpha) 1) cosTheta)
17.0ms	(log.f32 (*.f32 alpha alpha))
17.0ms	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))

Compiler

Compiled 2718 to 1944 computations (28.5% saved)

simplify112.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

544×	`times-frac_binary32`
396×	`associate-/r*_binary32`
380×	`associate-l_binary32`
356×	`associate-r_binary32`
293×	`associate-/l*_binary32`

Counts

127 → 105

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	301	3795
1	887	3325
2	4690	3325
3	4961	3325

prune175.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	95	10	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	10	106

Error

0.0b

Counts

106 → 10

Alt Table

Status	Error	Program
	0.6b	(/.f32 1 (/.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))
	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 alpha 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
▶	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 PI.f32 (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (.f32 (.f32 2 (log.f32 alpha)) (cbrt.f32 PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))))) (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 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))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.7b	(.f32 (/.f32 (.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (cbrt.f32 (+.f32 (.f32 alpha alpha) -1))) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.8b	(.f32 (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))

Compiler

Compiled 3521 to 1725 computations (51% saved)

localize56.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

rewrite170.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

27×	`pow1_binary32`
23×	`add-exp-log_binary32`
20×	`add-cbrt-cube_binary32`
14×	`add-sqr-sqrt_binary32`
12×	`log-pow_binary32`

Counts

4 → 95

Calls

4 calls:

15.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 PI.f32 (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta))))
5.0ms	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))
5.0ms	(.f32 cosTheta (.f32 alpha alpha))
2.0ms	(log.f32 (*.f32 alpha alpha))

Compiler

Compiled 2666 to 850 computations (68.1% saved)

series207.0ms (2.1%)

Error

0.0b

Counts

4 → 25

Calls

4 calls:

103.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 PI.f32 (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta))))
22.0ms	(.f32 cosTheta (.f32 alpha alpha))
19.0ms	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))
14.0ms	(log.f32 (*.f32 alpha alpha))

Compiler

Compiled 2606 to 1838 computations (29.5% saved)

simplify120.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

482×	`times-frac_binary32`
385×	`associate-/r*_binary32`
356×	`associate-l_binary32`
342×	`associate-r_binary32`
274×	`associate-/l*_binary32`

Counts

120 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	296	3640
1	874	3191
2	4487	3189
3	5007	3189

prune156.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	91	10	101

Error

0.0b

Counts

101 → 10

Alt Table

Status	Error	Program
	0.6b	(/.f32 1 (/.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))
▶	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 alpha 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 PI.f32 (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (.f32 (.f32 2 (log.f32 alpha)) (cbrt.f32 PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))))) (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 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))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.7b	(.f32 (/.f32 (.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (cbrt.f32 (+.f32 (.f32 alpha alpha) -1))) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.8b	(.f32 (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))

Compiler

Compiled 3074 to 1421 computations (53.8% saved)

localize55.0ms (0.5%)

Local error

Found 4 expressions with local error:

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))))
3.0b	(pow.f32 (*.f32 alpha alpha) PI.f32)

rewrite200.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 96

Calls

4 calls:

8.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
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))))
7.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
3.0ms	(pow.f32 (*.f32 alpha alpha) PI.f32)

Compiler

Compiled 2875 to 1347 computations (53.1% saved)

series522.0ms (5.2%)

Error

0.0b

Counts

4 → 34

Calls

4 calls:

287.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
114.0ms	(/.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	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
17.0ms	(pow.f32 (*.f32 alpha alpha) PI.f32)

Compiler

Compiled 3216 to 2367 computations (26.4% saved)

simplify132.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

390×	`unswap-sqr_binary32`
355×	`associate-l_binary32`
330×	`times-frac_binary32`
300×	`associate-r_binary32`
221×	`associate-/r*_binary32`

Counts

130 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	3846
1	761	3487
2	3762	3466
3	5130	3466

prune175.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	115	10	125

Error

0.0b

Counts

125 → 10

Alt Table

Status	Error	Program
	0.6b	(/.f32 1 (/.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))
✓	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 alpha 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 PI.f32 (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (.f32 (.f32 2 (log.f32 alpha)) (cbrt.f32 PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))))) (cbrt.f32 (.f32 2 (.f32 PI.f32 (log.f32 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))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.7b	(.f32 (/.f32 (.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (cbrt.f32 (+.f32 (.f32 alpha alpha) -1))) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.8b	(.f32 (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (sqrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))

Compiler

Compiled 3491 to 1651 computations (52.7% saved)

localize73.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 cosTheta (.f32 alpha alpha))
0.3b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
0.4b	(*.f32 PI.f32 (log.f32 alpha))
0.4b	(/.f32 (+.f32 alpha 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha))))

rewrite275.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

52×	`add-cbrt-cube_binary32`
52×	`add-exp-log_binary32`
34×	`*-un-lft-identity_binary32`
33×	`add-sqr-sqrt_binary32`
26×	`associate-r_binary32`

Counts

4 → 130

Calls

4 calls:

17.0ms	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
7.0ms	(/.f32 (+.f32 alpha 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha))))
6.0ms	(.f32 cosTheta (.f32 alpha alpha))
4.0ms	(*.f32 PI.f32 (log.f32 alpha))

Compiler

Compiled 4553 to 2103 computations (53.8% saved)

series246.0ms (2.4%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

127.0ms	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
27.0ms	(/.f32 (+.f32 alpha 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha))))
24.0ms	(.f32 cosTheta (.f32 alpha alpha))
16.0ms	(*.f32 PI.f32 (log.f32 alpha))

Compiler

Compiled 3061 to 2110 computations (31.1% saved)

simplify145.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

481×	`times-frac_binary32`
432×	`associate-/r*_binary32`
378×	`associate-l_binary32`
335×	`associate-/l*_binary32`
292×	`associate-*r/_binary32`

Counts

157 → 123

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	408	5736
1	1222	4775
2	4992	4775
3	5012	4775

prune194.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	2	5	7
Picked	1	0	1
Done	1	1	2
Total	124	9	133

Error

Counts

133 → 9

Alt Table

Status	Error	Program
	0.6b	(/.f32 1 (/.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))
	0.6b	(.f32 (cbrt.f32 (/.f32 (pow.f32 (+.f32 alpha 1) 3) (.f32 8 (.f32 (pow.f32 PI.f32 3) (pow.f32 (log.f32 alpha) 3))))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	1.0b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (+.f32 alpha 1) (.f32 (.f32 PI.f32 (log.f32 alpha)) 2))) (cbrt.f32 (/.f32 (+.f32 alpha 1) (.f32 (.f32 PI.f32 (log.f32 alpha)) 2)))) (cbrt.f32 (/.f32 (+.f32 alpha 1) (.f32 (.f32 PI.f32 (log.f32 alpha)) 2)))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (.f32 (.f32 2 (log.f32 alpha)) (cbrt.f32 PI.f32))) (+.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))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 PI.f32 (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta) cosTheta))))
	0.7b	(.f32 (/.f32 (.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (cbrt.f32 (+.f32 (.f32 alpha alpha) -1))) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (cbrt.f32 (+.f32 (.f32 alpha alpha) -1)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	1.0b	(.f32 (.f32 (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	0.6b	(.f32 (/.f32 (+.f32 (pow.f32 alpha 3) (pow.f32 1 3)) (.f32 (.f32 (.f32 PI.f32 (log.f32 alpha)) 2) (+.f32 (.f32 alpha alpha) (-.f32 1 alpha)))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))

Compiler

Compiled 3733 to 1749 computations (53.1% saved)

regimes4.2s (41.6%)

Accuracy

Total 0.5b remaining (94.7%)

Threshold costs 0.5b (94.7%)

Compiler

Compiled 47316 to 30168 computations (36.2% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary32`
4×	`+-commutative_binary32`
3×	`sub-neg_binary32`
1×	`neg-sub0_binary32`
1×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	28	40
2	32	40
3	34	40
4	35	40
5	33	40

end2.0ms (0%)

Compiler: Compiled 28 to 17 computations (39.3% saved)

sample2.1s (20.9%)

Algorithm

1×

intervals

Results

839.0ms	8000×	body	128	valid
202.0ms	8000×	pre	128	true

Compiler

Compiled 443 to 273 computations (38.4% saved)

Details

analyze184.0ms (1.8%)

sample56.0ms (0.6%)

simplify52.0ms (0.5%)

prune4.0ms (0%)

localize51.0ms (0.5%)

rewrite187.0ms (1.9%)

series225.0ms (2.2%)

simplify112.0ms (1.1%)

prune175.0ms (1.7%)

localize56.0ms (0.6%)

rewrite170.0ms (1.7%)

series207.0ms (2.1%)

simplify120.0ms (1.2%)

prune156.0ms (1.6%)

localize55.0ms (0.5%)

rewrite200.0ms (2%)

series522.0ms (5.2%)

simplify132.0ms (1.3%)

prune175.0ms (1.7%)

localize73.0ms (0.7%)

rewrite275.0ms (2.7%)

series246.0ms (2.4%)

simplify145.0ms (1.4%)

prune194.0ms (1.9%)

regimes4.2s (41.6%)

simplify5.0ms (0%)

end2.0ms (0%)

sample2.1s (20.9%)

Profiling