Details

analyze150.0ms (1.5%)

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)

sample49.0ms (0.5%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
7.0ms	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

prune5.0ms (0.1%)

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)

localize45.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
0.2b	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
0.2b	(/.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)))

rewrite240.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

22×	`add-exp-log_binary32` `add-cbrt-cube_binary32`
21×	`pow1_binary32`
18×	`add-sqr-sqrt_binary32`
15×	`associate-r_binary32`
14×	`*-un-lft-identity_binary32`

Counts

4 → 103

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))))
10.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
8.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
7.0ms	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))

Compiler

Compiled 3092 to 1407 computations (54.5% saved)

series288.0ms (2.8%)

Error

0.3b

Counts

4 → 34

Calls

4 calls:

118.0ms	(/.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))))
42.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
35.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
20.0ms	(.f32 PI.f32 (log.f32 (.f32 alpha alpha)))

Compiler

Compiled 2964 to 2131 computations (28.1% saved)

simplify123.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

544×	`times-frac_binary32`
456×	`associate-l_binary32`
398×	`associate-/r*_binary32`
390×	`associate-r_binary32`
289×	`associate-/l*_binary32`

Counts

137 → 123

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	295	4077
1	906	3600
2	4675	3600
3	5004	3600

prune222.0ms (2.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	114	9	123
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	114	10	124

Error

0.0b

Counts

124 → 10

Alt Table

Status	Error	Program
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (sqrt.f32 PI.f32) (.f32 (.f32 2 (log.f32 alpha)) (sqrt.f32 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 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 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 1 (.f32 alpha alpha))))
▶	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))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)))))))
	0.6b	(/.f32 (-.f32 (pow.f32 (.f32 alpha alpha) 3) (pow.f32 1 3)) (.f32 (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 (pow.f32 alpha 4) (+.f32 1 (*.f32 alpha alpha)))))
	0.7b	(+.f32 (.f32 1/2 (+.f32 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 PI.f32 (-.f32 1 (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 (.f32 (log.f32 alpha) PI.f32) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))))) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 PI.f32 (-.f32 1 (.f32 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))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 (log.f32 alpha) PI.f32))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.6b	(/.f32 (+.f32 alpha 1) (/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta))))))

Compiler

Compiled 3692 to 1735 computations (53% saved)

localize44.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
0.2b	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
0.2b	(/.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)

rewrite256.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`pow1_binary32` `add-exp-log_binary32`
16×	`add-cbrt-cube_binary32`
15×	`add-sqr-sqrt_binary32`
13×	`*-un-lft-identity_binary32`
10×	`add-cube-cbrt_binary32`

Counts

4 → 96

Calls

4 calls:

10.0ms	(/.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))))
10.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
8.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
6.0ms	(pow.f32 (*.f32 alpha alpha) PI.f32)

Compiler

Compiled 2875 to 1347 computations (53.1% saved)

series308.0ms (3%)

Error

0.0b

Counts

4 → 34

Calls

4 calls:

129.0ms	(/.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))))
41.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
37.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
21.0ms	(pow.f32 (*.f32 alpha alpha) PI.f32)

Compiler

Compiled 3216 to 2367 computations (26.4% saved)

simplify116.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

390×	`unswap-sqr_binary32`
377×	`associate-l_binary32`
362×	`times-frac_binary32`
321×	`associate-r_binary32`
251×	`associate-/r*_binary32`

Counts

130 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	279	3845
1	745	3461
2	4016	3433
3	5447	3433

prune190.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	117	8	125

Error

0.0b

Counts

125 → 8

Alt Table

Status	Error	Program
	0.5b	(/.f32 1 (/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))
▶	0.4b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (.f32 (.f32 (cbrt.f32 (pow.f32 alpha (.f32 2 PI.f32))) (cbrt.f32 (pow.f32 alpha (.f32 2 PI.f32)))) (cbrt.f32 (pow.f32 alpha (.f32 2 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 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 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 1 (.f32 alpha alpha))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (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 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 (log.f32 alpha) PI.f32))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.6b	(/.f32 (+.f32 alpha 1) (/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta))))))

Compiler

Compiled 3298 to 1541 computations (53.3% saved)

localize65.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.5b	(.f32 (cbrt.f32 (pow.f32 alpha (.f32 2 PI.f32))) (cbrt.f32 (pow.f32 alpha (*.f32 2 PI.f32))))
3.0b	(pow.f32 alpha (*.f32 2 PI.f32))
3.0b	(pow.f32 alpha (*.f32 2 PI.f32))
3.0b	(pow.f32 alpha (*.f32 2 PI.f32))

rewrite357.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

52×	`cbrt-prod_binary32`
43×	`add-sqr-sqrt_binary32`
29×	`unpow-prod-down_binary32`
19×	`add-cube-cbrt_binary32` `*-un-lft-identity_binary32`
16×	`unswap-sqr_binary32`

Counts

4 → 109

Calls

4 calls:

15.0ms	(.f32 (cbrt.f32 (pow.f32 alpha (.f32 2 PI.f32))) (cbrt.f32 (pow.f32 alpha (*.f32 2 PI.f32))))
2.0ms	(pow.f32 alpha (*.f32 2 PI.f32))
2.0ms	(pow.f32 alpha (*.f32 2 PI.f32))
2.0ms	(pow.f32 alpha (*.f32 2 PI.f32))

Compiler

Compiled 4785 to 3156 computations (34% saved)

series163.0ms (1.6%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

44.0ms	(.f32 (cbrt.f32 (pow.f32 alpha (.f32 2 PI.f32))) (cbrt.f32 (pow.f32 alpha (*.f32 2 PI.f32))))
28.0ms	(pow.f32 alpha (*.f32 2 PI.f32))
28.0ms	(pow.f32 alpha (*.f32 2 PI.f32))
26.0ms	(pow.f32 alpha (*.f32 2 PI.f32))

Compiler

Compiled 1574 to 1132 computations (28.1% saved)

simplify171.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

644×	`log-prod_binary32`
596×	`exp-prod_binary32`
403×	`log-pow_binary32`
330×	`sqr-pow_binary32` `*-commutative_binary32`
280×	`exp-sum_binary32`

Counts

121 → 104

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	111	2001
1	203	1962
2	476	1707
3	1216	1594
4	2641	1539
5	4181	1409
6	4824	1409
7	4807	1409

prune157.0ms (1.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	104	8	112

Error

0.0b

Counts

112 → 8

Alt Table

Status	Error	Program
▶	0.5b	(/.f32 1 (/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))
✓	0.4b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (.f32 (.f32 (cbrt.f32 (pow.f32 alpha (.f32 2 PI.f32))) (cbrt.f32 (pow.f32 alpha (.f32 2 PI.f32)))) (cbrt.f32 (pow.f32 alpha (.f32 2 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 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 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 1 (.f32 alpha alpha))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (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 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 (log.f32 alpha) PI.f32))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.6b	(/.f32 (+.f32 alpha 1) (/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta))))))

Compiler

Compiled 2368 to 1423 computations (39.9% saved)

localize58.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

rewrite552.0ms (5.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

189×	`times-frac_binary32`
105×	`add-exp-log_binary32`
77×	`add-sqr-sqrt_binary32`
74×	`add-cube-cbrt_binary32` `*-un-lft-identity_binary32`
61×	`add-cbrt-cube_binary32`

Counts

4 → 216

Calls

4 calls:

17.0ms	(/.f32 1 (/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))
13.0ms	(/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
6.0ms	(.f32 cosTheta (.f32 alpha alpha))
5.0ms	(*.f32 (log.f32 alpha) PI.f32)

Compiler

Compiled 9288 to 3956 computations (57.4% saved)

series373.0ms (3.6%)

Error

0.0b

Counts

4 → 35

Calls

4 calls:

138.0ms	(/.f32 1 (/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))
112.0ms	(/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
31.0ms	(.f32 cosTheta (.f32 alpha alpha))
22.0ms	(*.f32 (log.f32 alpha) PI.f32)

Compiler

Compiled 3436 to 2431 computations (29.2% saved)

simplify265.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

388×	`associate-/r*_binary32`
381×	`associate-/l*_binary32`
351×	`times-frac_binary32`
338×	`associate-l_binary32`
229×	`associate-/r/_binary32`

Counts

251 → 217

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	448	12139
1	1270	10938
2	4816	10933
3	4971	10933

prune280.0ms (2.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	217	8	225

Error

0.0b

Counts

225 → 8

Alt Table

Status	Error	Program
	0.5b	(/.f32 1 (/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))
	0.4b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (.f32 (.f32 (cbrt.f32 (pow.f32 alpha (.f32 2 PI.f32))) (cbrt.f32 (pow.f32 alpha (.f32 2 PI.f32)))) (cbrt.f32 (pow.f32 alpha (.f32 2 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 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 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))) (+.f32 1 (.f32 alpha alpha))))
	0.9b	(.f32 (.f32 (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta))))))) (cbrt.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 2 (.f32 (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 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 2 (.f32 (log.f32 alpha) PI.f32))) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta)))))
	0.6b	(/.f32 (+.f32 alpha 1) (/.f32 (.f32 2 (.f32 (log.f32 alpha) PI.f32)) (/.f32 (+.f32 alpha -1) (+.f32 1 (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta))))))

Compiler

Compiled 5261 to 2204 computations (58.1% saved)

regimes3.8s (36.7%)

Accuracy

Total 0.4b remaining (90.5%)

Threshold costs 0.4b (90.5%)

Compiler

Compiled 50232 to 31090 computations (38.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary32` `+-commutative_binary32`
1×	`1-exp_binary32` `sub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	37
1	22	37
2	23	37
3	21	37

end2.0ms (0%)

Compiler: Compiled 26 to 16 computations (38.5% saved)

sample2.0s (19.1%)

Algorithm

1×

intervals

Results

633.0ms	8000×	body	128	valid
191.0ms	8000×	pre	128	true

Compiler

Compiled 364 to 227 computations (37.6% saved)

Details

analyze150.0ms (1.5%)

sample49.0ms (0.5%)

simplify52.0ms (0.5%)

prune5.0ms (0.1%)

localize45.0ms (0.4%)

rewrite240.0ms (2.3%)

series288.0ms (2.8%)

simplify123.0ms (1.2%)

prune222.0ms (2.2%)

localize44.0ms (0.4%)

rewrite256.0ms (2.5%)

series308.0ms (3%)

simplify116.0ms (1.1%)

prune190.0ms (1.9%)

localize65.0ms (0.6%)

rewrite357.0ms (3.5%)

series163.0ms (1.6%)

simplify171.0ms (1.7%)

prune157.0ms (1.5%)

localize58.0ms (0.6%)

rewrite552.0ms (5.4%)

series373.0ms (3.6%)

simplify265.0ms (2.6%)

prune280.0ms (2.7%)

regimes3.8s (36.7%)

simplify3.0ms (0%)

end2.0ms (0%)

sample2.0s (19.1%)

Profiling