Details

analyze1.6s (3.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 42 to 30 computations (28.6% saved)

sample65.0ms (0.2%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
12.0ms	256×	pre	128	true

Compiler

Compiled 69 to 50 computations (27.5% saved)

simplify24.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

65×	`cancel-sign-sub-inv_binary32`
42×	`sub-neg_binary32`
41×	`div-sub_binary32`
32×	`distribute-rgt-neg-in_binary32`
29×	`distribute-rgt-in_binary32`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	30	26
2	41	26
3	53	26
4	62	26
5	73	26
6	93	26
7	121	26
8	143	26
9	160	26
10	199	26
11	215	26
12	303	26
13	290	26
14	316	26
15	311	26
16	312	26
17	271	26

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

13.3b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	13.3b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

Compiler

Compiled 44 to 30 computations (31.8% saved)

localize49.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f32 cos2phi (*.f32 alphax alphax))
0.2b	(/.f32 sin2phi (*.f32 alphay alphay))
0.3b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
14.9b	(log.f32 (-.f32 1 u0))

rewrite244.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

9.1b

Rules

66×	`*-un-lft-identity_binary32`
54×	`times-frac_binary32`
40×	`add-sqr-sqrt_binary32`
37×	`add-cube-cbrt_binary32`
20×	`distribute-rgt-neg-in_binary32` `distribute-lft-neg-in_binary32`

Counts

4 → 140

Calls

4 calls:

15.0ms	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
4.0ms	(/.f32 sin2phi (*.f32 alphay alphay))
4.0ms	(/.f32 cos2phi (*.f32 alphax alphax))
3.0ms	(log.f32 (-.f32 1 u0))

Compiler

Compiled 3127 to 1166 computations (62.7% saved)

series364.0ms (0.9%)

Error

0.4b

Counts

4 → 60

Calls

4 calls:

245.0ms	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
30.0ms	(/.f32 sin2phi (*.f32 alphay alphay))
30.0ms	(/.f32 cos2phi (*.f32 alphax alphax))
17.0ms	(log.f32 (-.f32 1 u0))

Compiler

Compiled 3369 to 2479 computations (26.4% saved)

simplify197.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

349×	`associate-/l/_binary32`
320×	`div-sub_binary32`
303×	`associate-/r/_binary32`
180×	`associate-/l*_binary32`
172×	`times-frac_binary32`

Counts

200 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	303	6320
1	699	6176
2	2218	6170
3	4653	6170
4	5125	6170

prune183.0ms (0.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	150	15	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	15	166

Error

0.2b

Counts

166 → 15

Alt Table

Status	Error	Program
	14.1b	(/.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (pow.f32 u0 3))) (log.f32 (+.f32 1 (+.f32 u0 (.f32 u0 u0)))))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	19.3b	(.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (-.f32 (/.f32 (.f32 cos2phi cos2phi) (pow.f32 alphax 4)) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	13.3b	(.f32 (.f32 (cbrt.f32 (log.f32 (-.f32 1 u0))) (cbrt.f32 (log.f32 (-.f32 1 u0)))) (/.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))
	14.5b	(/.f32 (neg.f32 (+.f32 (.f32 2 (log.f32 (cbrt.f32 (-.f32 1 u0)))) (log.f32 (cbrt.f32 (-.f32 1 u0))))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	13.3b	(.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (.f32 (.f32 alphay alphay) cos2phi) (.f32 sin2phi (.f32 alphax alphax)))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u0)))) (/.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax)))))
	14.1b	(/.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (.f32 u0 u0))) (log.f32 (+.f32 u0 1)))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	2.0b	(+.f32 (/.f32 u0 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) (+.f32 (+.f32 (.f32 1/2 (.f32 (/.f32 u0 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) u0)) (.f32 1/3 (/.f32 (pow.f32 u0 3) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))) (.f32 1/4 (/.f32 (pow.f32 u0 4) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))))
	13.3b	(.f32 (.f32 (/.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u0)))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (cbrt.f32 (log.f32 (-.f32 1 u0)))) (/.f32 (cbrt.f32 (log.f32 (-.f32 1 u0))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	13.3b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 1 (/.f32 alphay (/.f32 sin2phi alphay)))))
	4.1b	(/.f32 (neg.f32 (.f32 u0 (-.f32 -1 (.f32 1/2 u0)))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	13.3b	(.f32 (.f32 (cbrt.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (cbrt.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))) (cbrt.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	7.7b	(/.f32 u0 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))
	13.5b	(exp.f32 (log.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
▶	2.0b	(/.f32 (neg.f32 (-.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) u0)) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

Compiler

Compiled 3525 to 1577 computations (55.3% saved)

localize75.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f32 sin2phi (*.f32 alphay alphay))
0.3b	(/.f32 (neg.f32 (-.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) u0)) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
0.3b	(.f32 (.f32 u0 u0) (+.f32 1/2 (*.f32 1/3 u0)))
0.3b	(*.f32 1/3 u0)

rewrite390.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

89×	`*-un-lft-identity_binary32`
62×	`add-sqr-sqrt_binary32`
59×	`times-frac_binary32`
39×	`add-cube-cbrt_binary32`
25×	`distribute-rgt-neg-in_binary32` `distribute-lft-neg-in_binary32`

Counts

4 → 155

Calls

4 calls:

19.0ms	(/.f32 (neg.f32 (-.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) u0)) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
9.0ms	(/.f32 sin2phi (*.f32 alphay alphay))
7.0ms	(.f32 (.f32 u0 u0) (+.f32 1/2 (*.f32 1/3 u0)))
4.0ms	(*.f32 1/3 u0)

Compiler

Compiled 5888 to 2764 computations (53.1% saved)

series1.2s (2.9%)

Error

0.1b

Counts

4 → 69

Calls

4 calls:

937.0ms	(/.f32 (neg.f32 (-.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) u0)) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
37.0ms	(/.f32 sin2phi (*.f32 alphay alphay))
26.0ms	(.f32 (.f32 u0 u0) (+.f32 1/2 (*.f32 1/3 u0)))
16.0ms	(*.f32 1/3 u0)

Compiler

Compiled 11993 to 8918 computations (25.6% saved)

simplify279.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

500×	`times-frac_binary32`
454×	`associate-/l*_binary32`
406×	`associate-l_binary32`
268×	`associate-/r*_binary32`
131×	`associate-*l/_binary32`

Counts

224 → 190

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	507	19160
1	1498	18846
2	5180	18846

prune437.0ms (1.1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	179	11	190
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	185	20	205

Error

0.0b

Counts

205 → 20

Alt Table

Status	Error	Program
	14.1b	(/.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (pow.f32 u0 3))) (log.f32 (+.f32 1 (+.f32 u0 (.f32 u0 u0)))))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	19.3b	(.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (-.f32 (/.f32 (.f32 cos2phi cos2phi) (pow.f32 alphax 4)) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	13.3b	(.f32 (.f32 (cbrt.f32 (log.f32 (-.f32 1 u0))) (cbrt.f32 (log.f32 (-.f32 1 u0)))) (/.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))
	14.5b	(/.f32 (neg.f32 (+.f32 (.f32 2 (log.f32 (cbrt.f32 (-.f32 1 u0)))) (log.f32 (cbrt.f32 (-.f32 1 u0))))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u0)))) (/.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax)))))
▶	2.0b	(/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	2.2b	(.f32 (/.f32 -1 (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (/.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax))))))
	2.2b	(.f32 (sqrt.f32 (/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (sqrt.f32 (/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax))))))
	14.1b	(/.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (.f32 u0 u0))) (log.f32 (+.f32 u0 1)))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	13.3b	(.f32 (.f32 (/.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u0)))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (cbrt.f32 (log.f32 (-.f32 1 u0)))) (/.f32 (cbrt.f32 (log.f32 (-.f32 1 u0))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	2.3b	(.f32 (/.f32 -1 (.f32 (cbrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) (cbrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))) (/.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)) (cbrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	13.3b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 1 (/.f32 alphay (/.f32 sin2phi alphay)))))
	2.0b	(/.f32 (neg.f32 (-.f32 (.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0))))) (.f32 u0 u0))) (.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) (+.f32 u0 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 u0 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2)))))))
	3.7b	(exp.f32 (log.f32 (/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	13.3b	(.f32 (.f32 (cbrt.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (cbrt.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))) (cbrt.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	2.4b	(/.f32 (.f32 (cbrt.f32 (-.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) u0)) (cbrt.f32 (-.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) u0))) (/.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) (neg.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2))) u0))))))
	10.9b	(.f32 (/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (-.f32 (.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 cos2phi (.f32 alphax alphax))) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	2.2b	(.f32 (.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)))) (/.f32 (neg.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))
	2.0b	(.f32 (/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (.f32 (.f32 alphay alphay) cos2phi) (.f32 sin2phi (.f32 alphax alphax)))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
	2.3b	(.f32 (/.f32 (.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (/.f32 (neg.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))

Compiler

Compiled 8961 to 4767 computations (46.8% saved)

localize75.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))
0.2b	(/.f32 sin2phi (*.f32 alphay alphay))
0.3b	(/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
0.3b	(*.f32 1/3 u0)

rewrite411.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

58×	`*-un-lft-identity_binary32`
43×	`times-frac_binary32`
40×	`add-sqr-sqrt_binary32`
36×	`add-cube-cbrt_binary32`
15×	`add-exp-log_binary32` `add-cbrt-cube_binary32` `distribute-rgt-neg-in_binary32` `distribute-lft-neg-in_binary32`

Counts

4 → 134

Calls

4 calls:

22.0ms	(/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
6.0ms	(.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))
4.0ms	(/.f32 sin2phi (*.f32 alphay alphay))
4.0ms	(*.f32 1/3 u0)

Compiler

Compiled 5328 to 2673 computations (49.8% saved)

series1.1s (2.9%)

Error

0.0b

Counts

4 → 69

Calls

4 calls:

921.0ms	(/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
35.0ms	(/.f32 sin2phi (*.f32 alphay alphay))
24.0ms	(.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))
14.0ms	(*.f32 1/3 u0)

Compiler

Compiled 11999 to 8913 computations (25.7% saved)

simplify339.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

469×	`times-frac_binary32`
416×	`associate-/l*_binary32`
365×	`associate-l_binary32`
265×	`associate-/r*_binary32`
131×	`associate-*l/_binary32`

Counts

203 → 161

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	485	17648
1	1451	17319
2	4991	17319
3	4958	17319

prune407.0ms (1%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	19	19
Picked	0	1	1
Done	0	0	0
Total	161	20	181

Error

0.0b

Counts

181 → 20

Alt Table

Status	Error	Program
	14.1b	(/.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (pow.f32 u0 3))) (log.f32 (+.f32 1 (+.f32 u0 (.f32 u0 u0)))))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	19.3b	(.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (-.f32 (/.f32 (.f32 cos2phi cos2phi) (pow.f32 alphax 4)) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	13.3b	(.f32 (.f32 (cbrt.f32 (log.f32 (-.f32 1 u0))) (cbrt.f32 (log.f32 (-.f32 1 u0)))) (/.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))
	14.5b	(/.f32 (neg.f32 (+.f32 (.f32 2 (log.f32 (cbrt.f32 (-.f32 1 u0)))) (log.f32 (cbrt.f32 (-.f32 1 u0))))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u0)))) (/.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax)))))
✓	2.0b	(/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	2.2b	(.f32 (/.f32 -1 (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (/.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax))))))
	2.2b	(.f32 (sqrt.f32 (/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (sqrt.f32 (/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax))))))
	14.1b	(/.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (.f32 u0 u0))) (log.f32 (+.f32 u0 1)))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	13.3b	(.f32 (.f32 (/.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u0)))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (cbrt.f32 (log.f32 (-.f32 1 u0)))) (/.f32 (cbrt.f32 (log.f32 (-.f32 1 u0))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	2.3b	(.f32 (/.f32 -1 (.f32 (cbrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) (cbrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))) (/.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)) (cbrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	13.3b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 1 (/.f32 alphay (/.f32 sin2phi alphay)))))
▶	2.0b	(/.f32 (neg.f32 (-.f32 (.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0))))) (.f32 u0 u0))) (.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) (+.f32 u0 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 u0 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2)))))))
	3.7b	(exp.f32 (log.f32 (/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	13.3b	(.f32 (.f32 (cbrt.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (cbrt.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))) (cbrt.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	2.4b	(/.f32 (.f32 (cbrt.f32 (-.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) u0)) (cbrt.f32 (-.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) u0))) (/.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) (neg.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2))) u0))))))
	10.9b	(.f32 (/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (-.f32 (.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 cos2phi (.f32 alphax alphax))) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	2.2b	(.f32 (.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)))) (/.f32 (neg.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))
	2.0b	(.f32 (/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (.f32 (.f32 alphay alphay) cos2phi) (.f32 sin2phi (.f32 alphax alphax)))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
	2.3b	(.f32 (/.f32 (.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (/.f32 (neg.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))

Compiler

Compiled 8164 to 4301 computations (47.3% saved)

localize110.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f32 1/3 u0)
0.3b	(/.f32 (neg.f32 (-.f32 (.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0))))) (.f32 u0 u0))) (.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) (+.f32 u0 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 u0 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2)))))))
0.5b	(.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (*.f32 1/3 u0)))))
0.9b	(.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) (+.f32 u0 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 u0 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2))))))

rewrite974.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

24×	`add-sqr-sqrt_binary32`
22×	`*-un-lft-identity_binary32`
18×	`add-cube-cbrt_binary32`
16×	`frac-times_binary32`
15×	`pow1_binary32` `add-exp-log_binary32` `add-cbrt-cube_binary32`

Counts

4 → 142

Calls

4 calls:

30.0ms	(/.f32 (neg.f32 (-.f32 (.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0))))) (.f32 u0 u0))) (.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) (+.f32 u0 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 u0 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2)))))))
16.0ms	(.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) (+.f32 u0 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 u0 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2))))))
14.0ms	(.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (*.f32 1/3 u0)))))
4.0ms	(*.f32 1/3 u0)

Compiler

Compiled 12702 to 7296 computations (42.6% saved)

series6.1s (15.5%)

Error

0.0b

Counts

4 → 87

Calls

4 calls:

4.8s	(/.f32 (neg.f32 (-.f32 (.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0))))) (.f32 u0 u0))) (.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) (+.f32 u0 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 u0 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2)))))))
464.0ms	(.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) (+.f32 u0 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 u0 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2))))))
27.0ms	(.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (*.f32 1/3 u0)))))
24.0ms	(*.f32 1/3 u0)

Compiler

Compiled 60640 to 47016 computations (22.5% saved)

simplify927.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

380×	`+-commutative_binary32`
329×	`associate-+r+_binary32`
325×	`*-commutative_binary32`
141×	`unswap-sqr_binary32`
135×	`associate-/l*_binary32`

Counts

229 → 210

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1155	56677
1	3818	55756
2	4976	55755
3	4883	55755

prune1.4s (3.6%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	1	17	18
Picked	0	1	1
Done	0	1	1
Total	210	20	230

Error

0.0b

Counts

230 → 20

Alt Table

Status	Error	Program
	2.0b	(/.f32 (+.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) u0) (/.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) (/.f32 (neg.f32 (-.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 u0 (.f32 u0 (+.f32 1/2 (.f32 u0 1/3))))) u0)) (+.f32 u0 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 u0 (.f32 u0 (+.f32 1/2 (.f32 u0 1/3)))))))))
	14.1b	(/.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (pow.f32 u0 3))) (log.f32 (+.f32 1 (+.f32 u0 (.f32 u0 u0)))))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	19.3b	(.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (-.f32 (/.f32 (.f32 cos2phi cos2phi) (pow.f32 alphax 4)) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	13.3b	(.f32 (.f32 (cbrt.f32 (log.f32 (-.f32 1 u0))) (cbrt.f32 (log.f32 (-.f32 1 u0)))) (/.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))
	14.5b	(/.f32 (neg.f32 (+.f32 (.f32 2 (log.f32 (cbrt.f32 (-.f32 1 u0)))) (log.f32 (cbrt.f32 (-.f32 1 u0))))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u0)))) (/.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax)))))
	2.0b	(/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	2.2b	(.f32 (/.f32 -1 (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (/.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax))))))
	14.1b	(/.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (.f32 u0 u0))) (log.f32 (+.f32 u0 1)))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	13.3b	(.f32 (.f32 (/.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u0)))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (cbrt.f32 (log.f32 (-.f32 1 u0)))) (/.f32 (cbrt.f32 (log.f32 (-.f32 1 u0))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	2.3b	(.f32 (/.f32 -1 (.f32 (cbrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) (cbrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))) (/.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)) (cbrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	13.3b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 1 (/.f32 alphay (/.f32 sin2phi alphay)))))
	2.0b	(/.f32 (neg.f32 (-.f32 (.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0))))) (.f32 u0 u0))) (.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) (+.f32 u0 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 u0 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2)))))))
	3.7b	(exp.f32 (log.f32 (/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	13.3b	(.f32 (.f32 (cbrt.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (cbrt.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))) (cbrt.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	2.4b	(/.f32 (.f32 (cbrt.f32 (-.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) u0)) (cbrt.f32 (-.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (.f32 (.f32 u0 u0) (+.f32 1/2 (.f32 1/3 u0)))) u0))) (/.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) (neg.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2))) u0))))))
	10.9b	(.f32 (/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (-.f32 (.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 cos2phi (.f32 alphax alphax))) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	2.2b	(.f32 (.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)))) (/.f32 (neg.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))
	2.0b	(.f32 (/.f32 (neg.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (+.f32 (.f32 (.f32 alphay alphay) cos2phi) (.f32 sin2phi (.f32 alphax alphax)))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
	2.3b	(.f32 (/.f32 (.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0))) (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (/.f32 (neg.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 u0 4) -1/4) (+.f32 (.f32 u0 (.f32 u0 (+.f32 (.f32 1/3 u0) 1/2))) u0)))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))

Compiler

Compiled 28942 to 17779 computations (38.6% saved)

regimes19.3s (48.7%)

Accuracy

Total 0.6b remaining (82%)

Threshold costs 0.6b (82%)

Compiler

Compiled 288319 to 185093 computations (35.8% saved)

bsearch23.0ms (0.1%)

Compiler: Compiled 8 to 7 computations (12.5% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

27×	`distribute-rgt-neg-in_binary32`
24×	`cancel-sign-sub-inv_binary32`
18×	`+-commutative_binary32`
17×	`neg-mul-1_binary32` `neg-sub0_binary32` `sub-neg_binary32` `distribute-neg-in_binary32` `distribute-lft-neg-in_binary32`
15×	`*-commutative_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	87
1	66	87
2	91	87
3	122	85
4	172	85
5	204	85
6	217	85
7	220	85
8	211	85

end3.0ms (0%)

Compiler: Compiled 61 to 40 computations (34.4% saved)

sample3.4s (8.5%)

Algorithm

1×

intervals

Results

698.0ms	8000×	body	128	valid
349.0ms	8000×	pre	128	true

Compiler

Compiled 1099 to 709 computations (35.5% saved)

Iter	Nodes	Cost
0	16	26
1	30	26
2	41	26
3	53	26
4	62	26
5	73	26
6	93	26
7	121	26
8	143	26
9	160	26
10	199	26
11	215	26
12	303	26
13	290	26
14	316	26
15	311	26
16	312	26
17	271	26

Iter	Nodes	Cost
0	16	26
1	30	26
2	41	26
3	53	26
4	62	26
5	73	26
6	93	26
7	121	26
8	143	26
9	160	26
10	199	26
11	215	26
12	303	26
13	290	26
14	316	26
15	311	26
16	312	26
17	271	26

Details

analyze1.6s (3.9%)

sample65.0ms (0.2%)

simplify24.0ms (0.1%)

prune4.0ms (0%)

localize49.0ms (0.1%)

rewrite244.0ms (0.6%)

series364.0ms (0.9%)

simplify197.0ms (0.5%)

prune183.0ms (0.5%)

localize75.0ms (0.2%)

rewrite390.0ms (1%)

series1.2s (2.9%)

simplify279.0ms (0.7%)

prune437.0ms (1.1%)

localize75.0ms (0.2%)

rewrite411.0ms (1%)

series1.1s (2.9%)

simplify339.0ms (0.9%)

prune407.0ms (1%)

localize110.0ms (0.3%)

rewrite974.0ms (2.5%)

series6.1s (15.5%)

simplify927.0ms (2.3%)

prune1.4s (3.6%)

regimes19.3s (48.7%)

bsearch23.0ms (0.1%)

simplify8.0ms (0%)

end3.0ms (0%)

sample3.4s (8.5%)

Profiling

Iter	Nodes	Cost
0	16	26
1	30	26
2	41	26
3	53	26
4	62	26
5	73	26
6	93	26
7	121	26
8	143	26
9	160	26
10	199	26
11	215	26
12	303	26
13	290	26
14	316	26
15	311	26
16	312	26
17	271	26