Details

analyze536.0ms (5.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.1%	99.9%	0
0%	0.1%	99.9%	1
0%	0.1%	99.9%	2
0%	0.1%	99.9%	3
0%	0%	99.9%	4
0%	0%	99.9%	5
0%	0%	99.9%	6
0.1%	0%	99.9%	7
0.1%	0%	99.9%	8
0.1%	0%	99.9%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 51 to 37 computations (27.5% saved)

sample2.3s (25%)

Results

2.2s

8256×

body

128

valid

Compiler

Compiled 130 to 94 computations (27.7% saved)

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

743×	`sub-neg_binary32`
674×	`fma-neg_binary32`
386×	`associate--l-_binary32`
316×	`distribute-rgt-in_binary32`
286×	`unsub-neg_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	39
1	41	35
2	117	35
3	431	33
4	1755	33
5	4135	33
6	4966	33

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

13.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.4b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
	13.4b	(.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))

Status

Error

Program

▶

13.4b

(*.f32 (cos.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (*.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))

13.4b

(*.f32 (cos.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))

Compiler

Compiled 156 to 110 computations (29.5% saved)

localize51.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
✓	12.9b	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))

series34.0ms (0.4%)

Counts

4 → 72

Calls

4 calls:

19.0ms	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))
8.0ms	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
4.0ms	(.f32 (.f32 uy 2) (PI.f32))
2.0ms	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow1_binary32`
14×	`add-sqr-sqrt_binary32`
12×	`*-un-lft-identity_binary32`
11×	`add-cbrt-cube_binary32`
11×	`add-exp-log_binary32`

Counts

4 → 90

Calls

4 calls:

10.0ms	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
8.0ms	(.f32 (.f32 uy 2) (PI.f32))
4.0ms	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))
1.0ms	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))

simplify121.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

422×	`cancel-sign-sub-inv_binary32`
357×	`associate-+l+_binary32`
251×	`associate-l_binary32`
230×	`associate-r_binary32`
230×	`exp-prod_binary32`

Counts

162 → 180

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	4124
1	594	3285
2	2306	2943
3	4826	2931
4	4993	2931

prune239.0ms (2.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	173	7	180
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	175	7	182

Error

0.2b

Counts

182 → 7

Alt Table

Status	Error	Program
	13.4b	(.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (/.f32 (-.f32 1 (pow.f32 (fma.f32 maxCos ux (-.f32 1 ux)) 4)) (+.f32 1 (pow.f32 (sqrt.f32 (fma.f32 maxCos ux (-.f32 1 ux))) 4)))))
	2.2b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))
	13.4b	(.f32 (cos.f32 (expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
▶	0.3b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))
	0.3b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (+.f32 2 (.f32 ux (+.f32 maxCos -1))) (-.f32 ux (.f32 maxCos ux)))))
	0.3b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	7.7b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))

Compiler

Compiled 6201 to 3954 computations (36.2% saved)

localize88.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.2b	(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
✓	0.2b	(*.f32 maxCos (pow.f32 ux 2))
	0.3b	(.f32 (.f32 uy 2) (PI.f32))

series19.0ms (0.2%)

Counts

2 → 0

Calls

2 calls:

10.0ms	(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))
9.0ms	(*.f32 maxCos (pow.f32 ux 2))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary32`
20×	`unswap-sqr_binary32`
19×	`add-exp-log_binary32`
18×	`unpow-prod-down_binary32`
16×	`associate-r_binary32`

Counts

2 → 82

Calls

2 calls:

6.0ms	(*.f32 maxCos (pow.f32 ux 2))
5.0ms	(*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))

simplify107.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-def_binary32`
431×	`sqr-pow_binary32`
315×	`*-commutative_binary32`
281×	`distribute-lft-out_binary32`
276×	`log-prod_binary32`

Counts

82 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	1016
1	186	765
2	541	735
3	1035	681
4	1673	681
5	3450	681
6	4694	681
7	4974	681
8	4941	681

prune342.0ms (3.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	162	5	167
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	165	9	174

Error

0.1b

Counts

174 → 9

Alt Table

Status	Error	Program
	13.4b	(.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (/.f32 (-.f32 1 (pow.f32 (fma.f32 maxCos ux (-.f32 1 ux)) 4)) (+.f32 1 (pow.f32 (sqrt.f32 (fma.f32 maxCos ux (-.f32 1 ux))) 4)))))
	2.2b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))
	0.3b	(.f32 (cos.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))
▶	0.3b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	0.9b	(.f32 (log.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))
	0.5b	(.f32 (.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))
	0.4b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))
	7.7b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	0.4b	(.f32 (expm1.f32 (log1p.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))

Compiler

Compiled 7803 to 5391 computations (30.9% saved)

localize68.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.2b	(.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos))))
✓	0.2b	(.f32 maxCos (.f32 ux ux))
	0.3b	(.f32 (.f32 uy 2) (PI.f32))

series16.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(.f32 maxCos (.f32 ux ux))
7.0ms	(.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos))))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary32`
21×	`*-un-lft-identity_binary32`
19×	`add-cube-cbrt_binary32`
18×	`prod-diff_binary32`
13×	`distribute-lft-in_binary32`

Counts

2 → 71

Calls

2 calls:

8.0ms	(.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos))))
4.0ms	(.f32 maxCos (.f32 ux ux))

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Rules

348×	`fma-def_binary32`
292×	`fma-neg_binary32`
272×	`*-commutative_binary32`
261×	`exp-prod_binary32`
241×	`distribute-rgt-in_binary32`

Counts

119 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	2073
1	286	1426
2	907	1298
3	2395	1244
4	4648	1244
5	4826	1244

prune298.0ms (3.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	151	3	154
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	152	11	163

Error

0.1b

Counts

163 → 11

Alt Table

Status	Error	Program
	0.4b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))
	1.3b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (exp.f32 (+.f32 (log.f32 ux) (log.f32 (-.f32 2 (+.f32 ux (.f32 2 maxCos)))))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	0.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (+.f32 (.f32 (fma.f32 (.f32 (cbrt.f32 2) (cbrt.f32 2)) (cbrt.f32 2) (neg.f32 (.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos)))))) ux) (.f32 (fma.f32 (neg.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos)))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos))))) ux)) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	13.4b	(.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (/.f32 (-.f32 1 (pow.f32 (fma.f32 maxCos ux (-.f32 1 ux)) 4)) (+.f32 1 (pow.f32 (sqrt.f32 (fma.f32 maxCos ux (-.f32 1 ux))) 4)))))
	2.2b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))
	0.9b	(.f32 (log.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))
	0.5b	(.f32 (.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))
▶	0.3b	(.f32 (cos.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))
	7.7b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 (.f32 ux (sqrt.f32 (-.f32 2 (fma.f32 maxCos 2 ux)))) (sqrt.f32 (-.f32 2 (+.f32 ux (.f32 2 maxCos))))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	0.4b	(.f32 (expm1.f32 (log1p.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))

Compiler

Compiled 6654 to 4295 computations (35.5% saved)

localize105.0ms (1.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f32 maxCos (pow.f32 ux 2))
✓	0.2b	(log1p.f32 (.f32 2 (.f32 uy (PI.f32))))
✓	0.2b	(expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (PI.f32)))))
✓	0.3b	(*.f32 uy (PI.f32))

series34.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

29.0ms	(log1p.f32 (.f32 2 (.f32 uy (PI.f32))))
3.0ms	(expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (PI.f32)))))
2.0ms	(*.f32 uy (PI.f32))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary32`
5×	`*-un-lft-identity_binary32`
5×	`add-cube-cbrt_binary32`
5×	`add-cbrt-cube_binary32`
5×	`add-exp-log_binary32`

Counts

3 → 42

Calls

3 calls:

3.0ms	(*.f32 uy (PI.f32))
0.0ms	(log1p.f32 (.f32 2 (.f32 uy (PI.f32))))
0.0ms	(expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (PI.f32)))))

simplify110.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-neg_binary32`
447×	`associate-l_binary32`
401×	`associate-r_binary32`
340×	`unswap-sqr_binary32`
234×	`times-frac_binary32`

Counts

78 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	1005
1	260	904
2	861	900
3	3309	895
4	4944	895

prune396.0ms (4.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	135	11	146

Error

0.1b

Counts

146 → 11

Alt Table

Status	Error	Program
	0.4b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))
	1.3b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (exp.f32 (+.f32 (log.f32 ux) (log.f32 (-.f32 2 (+.f32 ux (.f32 2 maxCos)))))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	0.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (+.f32 (.f32 (fma.f32 (.f32 (cbrt.f32 2) (cbrt.f32 2)) (cbrt.f32 2) (neg.f32 (.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos)))))) ux) (.f32 (fma.f32 (neg.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos)))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos))))) ux)) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	13.4b	(.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (/.f32 (-.f32 1 (pow.f32 (fma.f32 maxCos ux (-.f32 1 ux)) 4)) (+.f32 1 (pow.f32 (sqrt.f32 (fma.f32 maxCos ux (-.f32 1 ux))) 4)))))
	2.2b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))
	0.9b	(.f32 (log.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))
	0.5b	(.f32 (.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))
✓	0.3b	(.f32 (cos.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))
	7.7b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 (.f32 ux (sqrt.f32 (-.f32 2 (fma.f32 maxCos 2 ux)))) (sqrt.f32 (-.f32 2 (+.f32 ux (.f32 2 maxCos))))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	0.4b	(.f32 (expm1.f32 (log1p.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))

Compiler

Compiled 6580 to 4549 computations (30.9% saved)

regimes3.7s (41.2%)

Accuracy

Total 0.2b remaining (73.3%)

Threshold costs 0.2b (73.3%)

Counts

210 → 1

Compiler

Compiled 88852 to 66410 computations (25.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary32`
9×	`+-commutative_binary32`
6×	`sub-neg_binary32`
6×	`neg-sub0_binary32`
5×	`neg-mul-1_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	47
1	42	47
2	54	45
3	73	45
4	81	45
5	84	45
6	81	45

end285.0ms (3.1%)

Compiler: Compiled 510 to 387 computations (24.1% saved)

Details

analyze536.0ms (5.9%)

sample2.3s (25%)

simplify49.0ms (0.5%)

prune5.0ms (0.1%)

localize51.0ms (0.6%)

series34.0ms (0.4%)

rewrite28.0ms (0.3%)

simplify121.0ms (1.3%)

prune239.0ms (2.6%)

localize88.0ms (1%)

series19.0ms (0.2%)

rewrite15.0ms (0.2%)

simplify107.0ms (1.2%)

prune342.0ms (3.8%)

localize68.0ms (0.8%)

series16.0ms (0.2%)

rewrite17.0ms (0.2%)

simplify91.0ms (1%)

prune298.0ms (3.3%)

localize105.0ms (1.2%)

series34.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify110.0ms (1.2%)

prune396.0ms (4.4%)

regimes3.7s (41.2%)

simplify4.0ms (0%)

end285.0ms (3.1%)

Profiling