Details

analyze163.0ms (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 35 to 23 computations (34.3% saved)

sample47.0ms (0.7%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 63 to 41 computations (34.9% saved)

simplify48.0ms (0.7%)

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

prune2.0ms (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)

localize46.0ms (0.7%)

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)
0.4b	(/.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)))

rewrite136.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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 → 103

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))))
7.0ms	(.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)

Compiler

Compiled 3092 to 1407 computations (54.5% saved)

series161.0ms (2.4%)

Error

0.3b

Counts

4 → 34

Calls

4 calls:

72.0ms	(/.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))))
21.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
17.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
13.0ms	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))

Compiler

Compiled 2964 to 2115 computations (28.6% saved)

simplify115.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

513×	`times-frac_binary32`
450×	`associate-l_binary32`
385×	`associate-r_binary32`
374×	`associate-/r*_binary32`
293×	`associate-/l*_binary32`

Counts

137 → 122

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	315	4080
1	930	3614
2	4651	3614
3	5086	3614

prune108.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	113	9	122
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	113	10	123

Error

0.0b

Counts

123 → 10

Alt Table

Status	Error	Program
	0.6b	(/.f32 (-.f32 (pow.f32 (.f32 alpha alpha) 3) (pow.f32 1 3)) (.f32 (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 (pow.f32 alpha 4) (+.f32 1 (*.f32 alpha alpha)))))
	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 (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)))))))
▶	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))))
	0.8b	(/.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))))
✓	0.5b	(/.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))))
	0.7b	(/.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 alpha 1) (/.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) 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)))))
	0.8b	(exp.f32 (log.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 3612 to 1713 computations (52.6% saved)

localize49.0ms (0.7%)

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)
0.4b	(/.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))))
3.1b	(pow.f32 (*.f32 alpha alpha) PI.f32)

rewrite133.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

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:

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

Compiler

Compiled 2875 to 1347 computations (53.1% saved)

series179.0ms (2.6%)

Error

0.0b

Counts

4 → 34

Calls

4 calls:

81.0ms	(/.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))))
21.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
20.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
16.0ms	(pow.f32 (*.f32 alpha alpha) PI.f32)

Compiler

Compiled 3216 to 2367 computations (26.4% saved)

simplify112.0ms (1.6%)

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

prune106.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	115	10	125

Error

0.0b

Counts

125 → 10

Alt Table

Status	Error	Program
	0.6b	(/.f32 (-.f32 (pow.f32 (.f32 alpha alpha) 3) (pow.f32 1 3)) (.f32 (.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 (pow.f32 alpha 4) (+.f32 1 (*.f32 alpha alpha)))))
	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 (log.f32 (pow.f32 (/.f32 1 alpha) (.f32 PI.f32 -2))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(/.f32 (+.f32 alpha 1) (/.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta))))))
	0.7b	(.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)))))))
✓	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))))
	0.7b	(/.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))))
▶	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (.f32 (fabs.f32 (pow.f32 alpha PI.f32)) (fabs.f32 (pow.f32 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)))))
	0.8b	(exp.f32 (log.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 3391 to 1624 computations (52.1% saved)

localize61.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.4b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (.f32 (fabs.f32 (pow.f32 alpha PI.f32)) (fabs.f32 (pow.f32 alpha PI.f32)))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.5b	(*.f32 (fabs.f32 (pow.f32 alpha PI.f32)) (fabs.f32 (pow.f32 alpha PI.f32)))
2.3b	(pow.f32 alpha PI.f32)
2.3b	(pow.f32 alpha PI.f32)

rewrite306.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

102×	`add-sqr-sqrt_binary32`
70×	`fabs-mul_binary32`
54×	`fabs-sqr_binary32`
50×	`unpow-prod-down_binary32`
49×	`unswap-sqr_binary32`

Counts

4 → 171

Calls

4 calls:

12.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (.f32 (fabs.f32 (pow.f32 alpha PI.f32)) (fabs.f32 (pow.f32 alpha PI.f32)))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
10.0ms	(*.f32 (fabs.f32 (pow.f32 alpha PI.f32)) (fabs.f32 (pow.f32 alpha PI.f32)))
2.0ms	(pow.f32 alpha PI.f32)
2.0ms	(pow.f32 alpha PI.f32)

Compiler

Compiled 6007 to 2527 computations (57.9% saved)

series157.0ms (2.3%)

Error

0.0b

Counts

4 → 23

Calls

4 calls:

81.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (.f32 (fabs.f32 (pow.f32 alpha PI.f32)) (fabs.f32 (pow.f32 alpha PI.f32)))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
27.0ms	(pow.f32 alpha PI.f32)
12.0ms	(pow.f32 alpha PI.f32)
6.0ms	(*.f32 (fabs.f32 (pow.f32 alpha PI.f32)) (fabs.f32 (pow.f32 alpha PI.f32)))

Compiler

Compiled 2669 to 1823 computations (31.7% saved)

simplify181.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

313×	`associate-/l/_binary32`
240×	`associate-l_binary32`
226×	`associate-r_binary32`
211×	`unswap-sqr_binary32`
207×	`times-frac_binary32`

Counts

194 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	5256
1	743	4452
2	3073	4329
3	4963	4329

prune136.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	168	9	177

Error

Counts

177 → 9

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))))
	0.7b	(-.f32 (.f32 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 (pow.f32 alpha PI.f32)) 2)) (+.f32 (/.f32 1 (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 (.f32 cosTheta cosTheta) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2)))) (/.f32 1/2 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (log.f32 (pow.f32 alpha PI.f32)))))
▶	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (/.f32 1 alpha) (.f32 PI.f32 -2))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(/.f32 (+.f32 alpha 1) (/.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta))))))
	0.6b	(.f32 (/.f32 (.f32 (cbrt.f32 (+.f32 -1 (.f32 alpha alpha))) (cbrt.f32 (+.f32 -1 (.f32 alpha alpha)))) (.f32 (log.f32 (pow.f32 alpha PI.f32)) 2)) (/.f32 (cbrt.f32 (+.f32 -1 (.f32 alpha alpha))) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha)))))))
	0.8b	(exp.f32 (log.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (log.f32 (pow.f32 alpha PI.f32)) 2) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))))))
	0.7b	(/.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 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (log.f32 (pow.f32 alpha PI.f32)) 2) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))))) (sqrt.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (log.f32 (pow.f32 alpha PI.f32)) 2) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha)))))))))

Compiler

Compiled 3536 to 1842 computations (47.9% saved)

localize59.0ms (0.9%)

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)
0.4b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (/.f32 1 alpha) (.f32 PI.f32 -2))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
3.1b	(pow.f32 (/.f32 1 alpha) (*.f32 PI.f32 -2))

rewrite180.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

21×	`add-exp-log_binary32`
21×	`add-sqr-sqrt_binary32`
19×	`*-un-lft-identity_binary32`
16×	`add-cbrt-cube_binary32`
16×	`add-cube-cbrt_binary32`

Counts

4 → 105

Calls

4 calls:

9.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (/.f32 1 alpha) (.f32 PI.f32 -2))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
8.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
6.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
4.0ms	(pow.f32 (/.f32 1 alpha) (*.f32 PI.f32 -2))

Compiler

Compiled 3467 to 2169 computations (37.4% saved)

series183.0ms (2.7%)

Error

Counts

4 → 34

Calls

4 calls:

86.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (/.f32 1 alpha) (.f32 PI.f32 -2))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
24.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
19.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
12.0ms	(pow.f32 (/.f32 1 alpha) (*.f32 PI.f32 -2))

Compiler

Compiled 3427 to 2671 computations (22.1% saved)

simplify147.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

415×	`times-frac_binary32`
369×	`associate-l_binary32`
319×	`associate-r_binary32`
265×	`associate-/r*_binary32`
226×	`associate-/l*_binary32`

Counts

139 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	299	4320
1	780	3777
2	4146	3717
3	4974	3717
4	4964	3717

prune135.0ms (2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	123	9	132

Error

Counts

132 → 9

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))))
	0.7b	(-.f32 (.f32 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 (pow.f32 alpha PI.f32)) 2)) (+.f32 (/.f32 1 (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 (.f32 cosTheta cosTheta) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2)))) (/.f32 1/2 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (log.f32 (pow.f32 alpha PI.f32)))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (/.f32 1 alpha) (.f32 PI.f32 -2))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(/.f32 (+.f32 alpha 1) (/.f32 (.f32 2 (.f32 PI.f32 (log.f32 alpha))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta))))))
	0.6b	(.f32 (/.f32 (.f32 (cbrt.f32 (+.f32 -1 (.f32 alpha alpha))) (cbrt.f32 (+.f32 -1 (.f32 alpha alpha)))) (.f32 (log.f32 (pow.f32 alpha PI.f32)) 2)) (/.f32 (cbrt.f32 (+.f32 -1 (.f32 alpha alpha))) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha)))))))
	0.8b	(exp.f32 (log.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (log.f32 (pow.f32 alpha PI.f32)) 2) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))))))
	0.7b	(/.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 1) (.f32 2 (.f32 PI.f32 (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (log.f32 (pow.f32 alpha PI.f32)) 2) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))))) (sqrt.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (log.f32 (pow.f32 alpha PI.f32)) 2) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha)))))))))

Compiler

Compiled 3177 to 1635 computations (48.5% saved)

regimes2.0s (29%)

Accuracy

Total 0.4b remaining (94.7%)

Threshold costs 0.4b (94.7%)

Compiler

Compiled 41749 to 26753 computations (35.9% 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	23	117
1	37	117
2	38	117
3	36	117

end1.0ms (0%)

Compiler: Compiled 77 to 41 computations (46.8% saved)

sample1.9s (27.5%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
178.0ms	8000×	pre	128	true

Compiler

Compiled 424 to 270 computations (36.3% saved)

Details

analyze163.0ms (2.4%)

sample47.0ms (0.7%)

simplify48.0ms (0.7%)

prune2.0ms (0%)

localize46.0ms (0.7%)

rewrite136.0ms (2%)

series161.0ms (2.4%)

simplify115.0ms (1.7%)

prune108.0ms (1.6%)

localize49.0ms (0.7%)

rewrite133.0ms (2%)

series179.0ms (2.6%)

simplify112.0ms (1.6%)

prune106.0ms (1.6%)

localize61.0ms (0.9%)

rewrite306.0ms (4.5%)

series157.0ms (2.3%)

simplify181.0ms (2.7%)

prune136.0ms (2%)

localize59.0ms (0.9%)

rewrite180.0ms (2.7%)

series183.0ms (2.7%)

simplify147.0ms (2.2%)

prune135.0ms (2%)

regimes2.0s (29%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.9s (27.5%)

Profiling