Details

analyze5.3s (16.8%)

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%	0.1%	99.9%	4
0%	0.1%	99.9%	5
0%	0.1%	99.9%	6
0%	0.1%	99.9%	7
0%	0.1%	99.9%	8
0%	0.1%	99.9%	9
0%	0.1%	99.9%	10
0%	0.1%	99.9%	11
0%	0.1%	99.9%	12
0%	0.1%	99.9%	13
0%	0.1%	99.9%	14

Compiler

Compiled 51 to 37 computations (27.5% saved)

sample2.5s (7.8%)

Results

2.4s

8256×

body

128

valid

Compiler

Compiled 130 to 94 computations (27.7% saved)

simplify48.0ms (0.2%)

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

prune6.0ms (0%)

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

12.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	12.7b	(.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))))))
▶	12.7b	(.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

12.7b

(*.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))))))

▶

12.7b

(*.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)

localize58.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))
✓	0.2b	(.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)))
✓	0.4b	(.f32 (.f32 uy 2) (PI.f32))
✓	13.3b	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

series368.0ms (1.2%)

Counts

4 → 88

Calls

4 calls:

250.0ms	(.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)))
98.0ms	(sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))
16.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)
3.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite15.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary32`
12×	`pow1_binary32`
11×	`add-cbrt-cube_binary32`
11×	`add-exp-log_binary32`
9×	`associate-r_binary32`

Counts

4 → 69

Calls

4 calls:

5.0ms	(.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)))
4.0ms	(.f32 (.f32 uy 2) (PI.f32))
1.0ms	(sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))
0.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

simplify156.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-def_binary32`
555×	`associate-r_binary32`
512×	`associate-l_binary32`
240×	`times-frac_binary32`
207×	`associate-/l*_binary32`

Counts

157 → 211

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	515	10427
1	1674	9279
2	5422	9279

prune418.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	202	9	211
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	204	9	213

Error

0.1b

Counts

213 → 9

Alt Table

Status	Error	Program
	1.2b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (-.f32 (fma.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sqrt.f32 (.f32 ux (-.f32 2 ux)))) (.f32 (.f32 maxCos ux) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))))))
▶	0.3b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
	8.0b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	12.7b	(.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (*.f32 (cbrt.f32 (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))) (cbrt.f32 (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))))) (cbrt.f32 (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))))
	12.8b	(.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (log.f32 (exp.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))))
	12.7b	(log.f32 (exp.f32 (.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)))))
	2.0b	(-.f32 (.f32 (+.f32 (.f32 2/3 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 uy 4))) 1) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux)))))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))))) (+.f32 (.f32 2 (.f32 (.f32 uy uy) (pow.f32 (PI.f32) 2))) (.f32 4/45 (*.f32 (pow.f32 uy 6) (pow.f32 (PI.f32) 6))))))
	12.7b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (*.f32 (cbrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)) (cbrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))) (cbrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))))
	6.7b	(sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux)))))

Compiler

Compiled 13897 to 9162 computations (34.1% saved)

localize76.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 2 (.f32 maxCos ux))
✓	0.1b	(sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux)))))
✓	0.2b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
	0.4b	(.f32 (.f32 uy 2) (PI.f32))

series362.0ms (1.1%)

Counts

3 → 52

Calls

3 calls:

249.0ms

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

106.0ms

(sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (+.f32 (*.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux)) (*.f32 2 (*.f32 maxCos ux)))))

6.0ms

(*.f32 2 (*.f32 maxCos ux))

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary32`
11×	`pow1_binary32`
10×	`add-cbrt-cube_binary32`
10×	`add-exp-log_binary32`
8×	`*-un-lft-identity_binary32`

Counts

3 → 63

Calls

3 calls:

10.0ms

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

8.0ms

(sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (+.f32 (*.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux)) (*.f32 2 (*.f32 maxCos ux)))))

4.0ms

(*.f32 2 (*.f32 maxCos ux))

simplify154.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

593×	`associate-r_binary32`
585×	`fma-def_binary32`
505×	`associate-l_binary32`
240×	`times-frac_binary32`
207×	`associate-/l*_binary32`

Counts

115 → 178

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	515	9963
1	1694	8989
2	5585	8989

prune408.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	201	8	209
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	209	9	218

Error

0.0b

Counts

218 → 9

Alt Table

Status	Error	Program
	0.6b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux)))))))
	2.0b	(-.f32 (.f32 (+.f32 (.f32 2/3 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 uy 4))) 1) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (+.f32 (.f32 2 (.f32 (.f32 uy uy) (pow.f32 (PI.f32) 2))) (.f32 4/45 (*.f32 (pow.f32 uy 6) (pow.f32 (PI.f32) 6))))))
	1.4b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (log.f32 (exp.f32 (.f32 2 (*.f32 maxCos ux))))))))
	1.2b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (-.f32 (fma.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sqrt.f32 (.f32 ux (-.f32 2 ux)))) (.f32 (.f32 maxCos ux) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))))))
	0.6b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux)))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cos.f32 (.f32 2 (.f32 uy (PI.f32))))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))
	5.8b	(log.f32 (pow.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux)))))))
▶	0.5b	(.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))))

Compiler

Compiled 15833 to 9645 computations (39.1% saved)

localize108.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))
✓	0.3b	(.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32)))))
	0.4b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(*.f32 uy (PI.f32))

series768.0ms (2.4%)

Counts

3 → 56

Calls

3 calls:

436.0ms

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

329.0ms

(*.f32 (cbrt.f32 (cos.f32 (*.f32 (*.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (*.f32 (*.f32 uy 2) (PI.f32)))))

2.0ms

(*.f32 uy (PI.f32))

rewrite34.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`pow1_binary32`
23×	`add-sqr-sqrt_binary32`
19×	`add-exp-log_binary32`
16×	`cbrt-prod_binary32`
13×	`*-un-lft-identity_binary32`

Counts

3 → 88

Calls

3 calls:

12.0ms

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

9.0ms

(*.f32 (cbrt.f32 (cos.f32 (*.f32 (*.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (*.f32 (*.f32 uy 2) (PI.f32)))))

3.0ms

(*.f32 uy (PI.f32))

simplify183.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

621×	`associate-r_binary32`
538×	`associate-l_binary32`
527×	`fma-def_binary32`
174×	`*-commutative_binary32`
140×	`fma-neg_binary32`

Counts

144 → 184

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	482	10496
1	1393	7182
2	4920	7180
3	4967	7180

prune619.0ms (1.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	241	5	246
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	245	10	255

Error

0.0b

Counts

255 → 10

Alt Table

Status	Error	Program
▶	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))))
	2.0b	(-.f32 (.f32 (+.f32 (.f32 2/3 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 uy 4))) 1) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos (.f32 ux (fma.f32 maxCos maxCos 1))))))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos (.f32 ux (fma.f32 maxCos maxCos 1)))))) (+.f32 (.f32 2 (.f32 (.f32 uy uy) (pow.f32 (PI.f32) 2))) (.f32 4/45 (*.f32 (pow.f32 uy 6) (pow.f32 (PI.f32) 6))))))
	0.5b	(.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))
	0.6b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux)))))))
	1.2b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (-.f32 (fma.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sqrt.f32 (.f32 ux (-.f32 2 ux)))) (.f32 (.f32 maxCos ux) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))))))
	0.6b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux)))))))
	0.5b	(/.f32 (.f32 (cos.f32 (.f32 (.f32 (PI.f32) uy) 2)) (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 ux (.f32 (.f32 (fma.f32 2 maxCos (.f32 ux (fma.f32 maxCos maxCos 1))) (fma.f32 2 maxCos (.f32 ux (fma.f32 maxCos maxCos 1)))) ux))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 (PI.f32) uy) 2)) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos (.f32 ux (fma.f32 maxCos maxCos 1)))))))) (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 (PI.f32) uy) 2)) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos (.f32 ux (fma.f32 maxCos maxCos 1))))))))) (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 (PI.f32) uy) 2)) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos (*.f32 ux (fma.f32 maxCos maxCos 1)))))))))
	5.8b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 (.f32 (PI.f32) uy) 2)) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos (*.f32 ux (fma.f32 maxCos maxCos 1)))))))))
✓	0.5b	(.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))

Compiler

Compiled 18946 to 12032 computations (36.5% saved)

localize105.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))))
✓	0.3b	(/.f32 (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (+.f32 (.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))))))
	0.4b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.5b	(.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (+.f32 (.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))))

series8.8s (27.7%)

Counts

3 → 76

Calls

3 calls:

5.7s

(*.f32 (cos.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (*.f32 4 (*.f32 (fma.f32 maxCos (*.f32 ux ux) ux) (fma.f32 maxCos (*.f32 ux ux) ux))) (*.f32 (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))) (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux)))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux) (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux)))))))

3.1s

(/.f32 (sqrt.f32 (-.f32 (*.f32 4 (*.f32 (fma.f32 maxCos (*.f32 ux ux) ux) (fma.f32 maxCos (*.f32 ux ux) ux))) (*.f32 (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))) (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux)))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux) (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))))))

28.0ms

(*.f32 (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))) (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))))

rewrite88.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`sqrt-prod_binary32`
76×	`times-frac_binary32`
73×	`add-sqr-sqrt_binary32`
57×	`*-un-lft-identity_binary32`
57×	`add-cube-cbrt_binary32`

Counts

3 → 178

Calls

3 calls:

15.0ms

(*.f32 (cos.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (*.f32 4 (*.f32 (fma.f32 maxCos (*.f32 ux ux) ux) (fma.f32 maxCos (*.f32 ux ux) ux))) (*.f32 (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))) (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux)))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux) (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux)))))))

12.0ms

(*.f32 (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))) (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))))

8.0ms

(/.f32 (sqrt.f32 (-.f32 (*.f32 4 (*.f32 (fma.f32 maxCos (*.f32 ux ux) ux) (fma.f32 maxCos (*.f32 ux ux) ux))) (*.f32 (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))) (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux)))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux) (*.f32 ux (+.f32 (*.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))))))

simplify744.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1056×	`fma-def_binary32`
328×	`associate-*r/_binary32`
58×	`sqr-pow_binary32`
56×	`associate-/r*_binary32`
46×	`associate-/l*_binary32`

Counts

254 → 349

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2816	84928
1	5059	84928

prune2.8s (8.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	378	2	380
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	380	10	390

Error

0.0b

Counts

390 → 10

Alt Table

Status	Error	Program
✓	0.5b	(.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))
	0.9b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))) (cbrt.f32 (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))))) (/.f32 (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (fma.f32 2 maxCos (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cbrt.f32 (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (.f32 ux (fma.f32 2 maxCos (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (fma.f32 2 maxCos (.f32 (fma.f32 maxCos maxCos 1) ux))))))))))
	0.5b	(.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))
	0.6b	(.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (.f32 ux (fma.f32 2 maxCos (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (fma.f32 2 maxCos (.f32 (fma.f32 maxCos maxCos 1) ux))))))) (/.f32 1 (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (+.f32 (.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux)))))))
	0.6b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux)))))))
	1.2b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (-.f32 (fma.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sqrt.f32 (.f32 ux (-.f32 2 ux)))) (.f32 (.f32 maxCos ux) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))))))
	0.5b	(/.f32 (.f32 (cos.f32 (.f32 (.f32 (PI.f32) uy) 2)) (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 ux (.f32 (.f32 (fma.f32 2 maxCos (.f32 ux (fma.f32 maxCos maxCos 1))) (fma.f32 2 maxCos (.f32 ux (fma.f32 maxCos maxCos 1)))) ux))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 (PI.f32) uy) 2)) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos (.f32 ux (fma.f32 maxCos maxCos 1)))))))) (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 (PI.f32) uy) 2)) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos (.f32 ux (fma.f32 maxCos maxCos 1))))))))) (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 (PI.f32) uy) 2)) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos (*.f32 ux (fma.f32 maxCos maxCos 1)))))))))
	5.8b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 (.f32 (PI.f32) uy) 2)) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos (*.f32 ux (fma.f32 maxCos maxCos 1)))))))))
	2.0b	(-.f32 (.f32 (+.f32 (.f32 2/3 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 uy 4))) 1) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos (.f32 ux (fma.f32 maxCos maxCos 1))))))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos (.f32 ux (fma.f32 maxCos maxCos 1)))))) (+.f32 (.f32 2 (.f32 (.f32 uy uy) (pow.f32 (PI.f32) 2))) (.f32 4/45 (*.f32 (pow.f32 uy 6) (pow.f32 (PI.f32) 6))))))

Compiler

Compiled 120968 to 81034 computations (33% saved)

regimes7.3s (22.9%)

Accuracy

Total 0.2b remaining (78%)

Threshold costs 0.2b (78%)

Counts

338 → 1

Compiler

Compiled 207666 to 134135 computations (35.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary32`
10×	`+-commutative_binary32`
9×	`sub-neg_binary32`
8×	`neg-sub0_binary32`
8×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	47
1	35	47
2	43	47
3	64	47
4	83	47
5	95	47
6	102	47
7	104	47
8	102	47

end343.0ms (1.1%)

Compiler: Compiled 785 to 478 computations (39.1% saved)

Details

analyze5.3s (16.8%)

sample2.5s (7.8%)

simplify48.0ms (0.2%)

prune6.0ms (0%)

localize58.0ms (0.2%)

series368.0ms (1.2%)

rewrite15.0ms (0%)

simplify156.0ms (0.5%)

prune418.0ms (1.3%)

localize76.0ms (0.2%)

series362.0ms (1.1%)

rewrite28.0ms (0.1%)

simplify154.0ms (0.5%)

prune408.0ms (1.3%)

localize108.0ms (0.3%)

series768.0ms (2.4%)

rewrite34.0ms (0.1%)

simplify183.0ms (0.6%)

prune619.0ms (1.9%)

localize105.0ms (0.3%)

series8.8s (27.7%)

rewrite88.0ms (0.3%)

simplify744.0ms (2.3%)

prune2.8s (8.8%)

regimes7.3s (22.9%)

simplify4.0ms (0%)

end343.0ms (1.1%)

Profiling