Details

analyze666.0ms (3.9%)

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)

sample158.0ms (0.9%)

Algorithm

1×

intervals

Results

46.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true

Compiler

Compiled 82 to 60 computations (26.8% saved)

simplify48.0ms (0.3%)

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%)

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

13.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.0b	(.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))))))
▶	14.0b	(.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

14.0b

(*.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))))))

▶

14.0b

(*.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)

localize137.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.1b	(.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)))
✓	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	14.5b	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

series250.0ms (1.5%)

Counts

4 → 80

Calls

4 calls:

225.0ms	(.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)))
15.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)
7.0ms	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))
3.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 63

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	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))
0.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

simplify162.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

477×	`associate-l_binary32`
474×	`fma-neg_binary32`
411×	`associate-r_binary32`
313×	`fma-def_binary32`
258×	`*-commutative_binary32`

Counts

143 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	369	7663
1	1134	6796
2	4835	6794
3	5243	6794

prune397.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	165	8	173
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	166	9	175

Error

0.2b

Counts

175 → 9

Alt Table

Status	Error	Program
	14.0b	(.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))))))
▶	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))))))
	14.0b	(.f32 (cos.f32 (exp.f32 (log.f32 (.f32 2 (*.f32 uy (PI.f32)))))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
	2.4b	(-.f32 (.f32 (fma.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))))) (fma.f32 2 (.f32 (.f32 uy uy) (pow.f32 (PI.f32) 2)) (.f32 4/45 (*.f32 (pow.f32 uy 6) (pow.f32 (PI.f32) 6))))))
	7.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	2.4b	(-.f32 (+.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)))))) (.f32 2/3 (.f32 (.f32 (pow.f32 uy 4) (pow.f32 (PI.f32) 4)) (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))))))))) (+.f32 (.f32 4/45 (.f32 (.f32 (pow.f32 uy 6) (pow.f32 (PI.f32) 6)) (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)))))))) (.f32 2 (.f32 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 uy 2)) (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))))))))))
	14.0b	(.f32 (.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (cbrt.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)))
	0.9b	(-.f32 (+.f32 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos (pow.f32 ux 2))) (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))) (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))) (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos ux)) (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))))
	1.9b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 ux (-.f32 2 ux))))

Compiler

Compiled 10339 to 6782 computations (34.4% saved)

localize74.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)))))
	0.1b	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.1b	(.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))))))
	0.3b	(.f32 (.f32 uy 2) (PI.f32))

series355.0ms (2.1%)

Counts

2 → 52

Calls

2 calls:

256.0ms

(*.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))))))

99.0ms

(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)))))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary32`
7×	`sqrt-prod_binary32`
6×	`associate-r_binary32`
6×	`*-un-lft-identity_binary32`
6×	`add-cube-cbrt_binary32`

Counts

2 → 43

Calls

2 calls:

11.0ms

(*.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))))))

7.0ms

(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)))))

simplify152.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-def_binary32`
518×	`associate-r_binary32`
440×	`associate-l_binary32`
240×	`times-frac_binary32`
207×	`associate-/l*_binary32`

Counts

95 → 157

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	484	9759
1	1633	8827
2	5317	8827

prune456.0ms (2.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	205	8	213
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	212	10	222

Error

0.1b

Counts

222 → 10

Alt Table

Status	Error	Program
▶	0.3b	(.f32 (expm1.f32 (log1p.f32 (cos.f32 (.f32 2 (.f32 uy (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))))))
	0.5b	(/.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (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 (+.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 (+.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))))))
	1.8b	(.f32 (sqrt.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)))))) (sqrt.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)))))))
	0.4b	(.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 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 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 (.f32 8 (pow.f32 (fma.f32 maxCos (.f32 ux ux) ux) 3)) (pow.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) 3)))) (sqrt.f32 (+.f32 (.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux))) (+.f32 (.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux)))) (.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))))))))
	0.8b	(.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)))))))
	7.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	0.8b	(.f32 (log.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 uy (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))))))
	0.9b	(-.f32 (+.f32 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos (pow.f32 ux 2))) (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))) (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))) (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos ux)) (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))))
	1.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (exp.f32 (log.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))))))))

Compiler

Compiled 16138 to 9808 computations (39.2% saved)

localize85.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cos.f32 (.f32 2 (.f32 uy (PI.f32))))
✓	0.1b	(.f32 (expm1.f32 (log1p.f32 (cos.f32 (.f32 2 (.f32 uy (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))))))
✓	0.2b	(expm1.f32 (log1p.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32))))))
✓	0.3b	(*.f32 uy (PI.f32))

series291.0ms (1.7%)

Counts

4 → 68

Calls

4 calls:

281.0ms	(.f32 (expm1.f32 (log1p.f32 (cos.f32 (.f32 2 (.f32 uy (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))))))
4.0ms	(cos.f32 (.f32 2 (.f32 uy (PI.f32))))
3.0ms	(expm1.f32 (log1p.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32))))))
2.0ms	(*.f32 uy (PI.f32))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary32`
9×	`associate-r_binary32`
9×	`*-un-lft-identity_binary32`
9×	`add-cube-cbrt_binary32`
8×	`add-cbrt-cube_binary32`

Counts

4 → 67

Calls

4 calls:

10.0ms	(.f32 (expm1.f32 (log1p.f32 (cos.f32 (.f32 2 (.f32 uy (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))))))
3.0ms	(*.f32 uy (PI.f32))
2.0ms	(cos.f32 (.f32 2 (.f32 uy (PI.f32))))
0.0ms	(expm1.f32 (log1p.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32))))))

simplify162.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

483×	`fma-neg_binary32`
446×	`associate-r_binary32`
378×	`fma-def_binary32`
364×	`associate-l_binary32`
188×	`associate-+r+_binary32`

Counts

135 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	386	7260
1	1147	6501
2	4901	6499
3	5306	6499

prune390.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	159	10	169

Error

0.0b

Counts

169 → 10

Alt Table

Status	Error	Program
	0.5b	(/.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (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 (+.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 (+.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))))))
	1.8b	(.f32 (sqrt.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)))))) (sqrt.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)))))))
	0.5b	(/.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 (.f32 8 (pow.f32 (fma.f32 maxCos (.f32 ux ux) ux) 3)) (pow.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) 3)))) (sqrt.f32 (+.f32 (.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux))) (+.f32 (.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux)))) (.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))))))))
	0.8b	(.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)))))))
	7.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	0.8b	(.f32 (log.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 uy (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 (expm1.f32 (log1p.f32 (-.f32 (.f32 (cos.f32 (.f32 uy (PI.f32))) (cos.f32 (.f32 uy (PI.f32)))) (.f32 (sin.f32 (.f32 uy (PI.f32))) (sin.f32 (.f32 uy (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 (expm1.f32 (log1p.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 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 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos (pow.f32 ux 2))) (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))) (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))) (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos ux)) (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))))
	1.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (exp.f32 (log.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))))))))

Compiler

Compiled 11715 to 6903 computations (41.1% saved)

localize98.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(expm1.f32 (log1p.f32 (-.f32 (.f32 (cos.f32 (.f32 uy (PI.f32))) (cos.f32 (.f32 uy (PI.f32)))) (.f32 (sin.f32 (.f32 uy (PI.f32))) (sin.f32 (.f32 uy (PI.f32)))))))
✓	0.2b	(-.f32 (.f32 (cos.f32 (.f32 uy (PI.f32))) (cos.f32 (.f32 uy (PI.f32)))) (.f32 (sin.f32 (.f32 uy (PI.f32))) (sin.f32 (.f32 uy (PI.f32)))))
	0.3b	(*.f32 uy (PI.f32))
✓	0.5b	(.f32 (sin.f32 (.f32 uy (PI.f32))) (sin.f32 (*.f32 uy (PI.f32))))

series36.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

16.0ms

(-.f32 (*.f32 (cos.f32 (*.f32 uy (PI.f32))) (cos.f32 (*.f32 uy (PI.f32)))) (*.f32 (sin.f32 (*.f32 uy (PI.f32))) (sin.f32 (*.f32 uy (PI.f32)))))

12.0ms

(expm1.f32 (log1p.f32 (-.f32 (*.f32 (cos.f32 (*.f32 uy (PI.f32))) (cos.f32 (*.f32 uy (PI.f32)))) (*.f32 (sin.f32 (*.f32 uy (PI.f32))) (sin.f32 (*.f32 uy (PI.f32)))))))

8.0ms

(*.f32 (sin.f32 (*.f32 uy (PI.f32))) (sin.f32 (*.f32 uy (PI.f32))))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary32`
9×	`add-sqr-sqrt_binary32`
7×	`*-un-lft-identity_binary32`
7×	`add-cube-cbrt_binary32`
5×	`add-cbrt-cube_binary32`

Counts

3 → 62

Calls

3 calls:

6.0ms

(-.f32 (*.f32 (cos.f32 (*.f32 uy (PI.f32))) (cos.f32 (*.f32 uy (PI.f32)))) (*.f32 (sin.f32 (*.f32 uy (PI.f32))) (sin.f32 (*.f32 uy (PI.f32)))))

5.0ms

(*.f32 (sin.f32 (*.f32 uy (PI.f32))) (sin.f32 (*.f32 uy (PI.f32))))

0.0ms

(expm1.f32 (log1p.f32 (-.f32 (*.f32 (cos.f32 (*.f32 uy (PI.f32))) (cos.f32 (*.f32 uy (PI.f32)))) (*.f32 (sin.f32 (*.f32 uy (PI.f32))) (sin.f32 (*.f32 uy (PI.f32)))))))

simplify101.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-neg_binary32`
498×	`cancel-sign-sub-inv_binary32`
374×	`unswap-sqr_binary32`
361×	`fma-def_binary32`
189×	`*-commutative_binary32`

Counts

98 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	2123
1	331	1892
2	918	1846
3	2439	1831
4	4511	1831
5	4821	1831

prune519.0ms (3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	229	3	232
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	230	12	242

Error

0.0b

Counts

242 → 12

Alt Table

Status	Error	Program
	0.5b	(/.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (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 (+.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 (+.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))))))
	1.8b	(.f32 (sqrt.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)))))) (sqrt.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)))))))
	0.5b	(/.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 (.f32 8 (pow.f32 (fma.f32 maxCos (.f32 ux ux) ux) 3)) (pow.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) 3)))) (sqrt.f32 (+.f32 (.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux))) (+.f32 (.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux)))) (.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))))))))
	0.8b	(.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)))))))
	0.8b	(.f32 (log.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 uy (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 (expm1.f32 (log1p.f32 (-.f32 (.f32 (cos.f32 (.f32 uy (PI.f32))) (cos.f32 (.f32 uy (PI.f32)))) (.f32 (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 uy (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 uy (PI.f32))))) (.f32 (cbrt.f32 (sin.f32 (.f32 uy (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 uy (PI.f32)))))) (.f32 (cbrt.f32 (sin.f32 (.f32 uy (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 uy (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 (expm1.f32 (log1p.f32 (-.f32 (.f32 (cos.f32 (.f32 uy (PI.f32))) (cos.f32 (.f32 uy (PI.f32)))) (.f32 (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) uy)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) uy)) 2))) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) uy)) 2)))))) (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))))))
	1.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (exp.f32 (log.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))))))))
	7.6b	(.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 (-.f32 (.f32 (cos.f32 (.f32 uy (PI.f32))) (cos.f32 (.f32 (.f32 uy (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32))))) (.f32 (sin.f32 (.f32 uy (PI.f32))) (sin.f32 (.f32 uy (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 (expm1.f32 (log1p.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 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 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos (pow.f32 ux 2))) (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))) (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))) (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos ux)) (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))))

Compiler

Compiled 12603 to 4525 computations (64.1% saved)

regimes10.4s (60.5%)

Accuracy

Total 0.2b remaining (81%)

Threshold costs 0.2b (81%)

Counts

455 → 1

Compiler

Compiled 250346 to 154642 computations (38.2% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

15×	`*-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	26	55
1	38	55
2	46	55
3	67	55
4	86	55
5	98	55
6	105	55
7	107	55
8	105	55

end1.0ms (0%)

Compiler: Compiled 39 to 27 computations (30.8% saved)

sample2.1s (12.5%)

Algorithm

1×

intervals

Results

939.0ms	8000×	body	128	valid
282.0ms	8000×	pre	128	true

Compiler

Compiled 837 to 507 computations (39.4% saved)

Details

analyze666.0ms (3.9%)

sample158.0ms (0.9%)

simplify48.0ms (0.3%)

prune5.0ms (0%)

localize137.0ms (0.8%)

series250.0ms (1.5%)

rewrite16.0ms (0.1%)

simplify162.0ms (0.9%)

prune397.0ms (2.3%)

localize74.0ms (0.4%)

series355.0ms (2.1%)

rewrite22.0ms (0.1%)

simplify152.0ms (0.9%)

prune456.0ms (2.7%)

localize85.0ms (0.5%)

series291.0ms (1.7%)

rewrite20.0ms (0.1%)

simplify162.0ms (0.9%)

prune390.0ms (2.3%)

localize98.0ms (0.6%)

series36.0ms (0.2%)

rewrite14.0ms (0.1%)

simplify101.0ms (0.6%)

prune519.0ms (3%)

regimes10.4s (60.5%)

simplify5.0ms (0%)

end1.0ms (0%)

sample2.1s (12.5%)

Profiling