Details

analyze638.0ms (6.4%)

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)

sample2.1s (20.6%)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 102 to 74 computations (27.5% saved)

preprocess32.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

470×	`associate--r+_binary32`
333×	`distribute-neg-in_binary32`
293×	`associate-l_binary32`
285×	`associate-r_binary32`
247×	`cancel-sign-sub-inv_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	156
1	127	140
2	449	140
3	2073	132
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify20.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

674×	`fma-neg_binary32`
316×	`distribute-rgt-in_binary32`
280×	`unsub-neg_binary32`
279×	`distribute-lft-in_binary32`
275×	`distribute-neg-in_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	39
1	41	35
2	128	35
3	564	33
4	2968	33

Stop Event

1×	node limit

Counts

1 → 2

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

13.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.2b	(.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))))))
	13.3b	(.f32 (cos.f32 (.f32 uy (*.f32 2 (PI.f32)))) (sqrt.f32 (fma.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))

Status

Error

Program

▶

13.2b

(*.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))))))

13.3b

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

Compiler

Compiled 156 to 110 computations (29.5% saved)

localize49.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.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 (.f32 uy 2) (PI.f32))
✓	0.4b	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
✓	13.0b	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))

series201.0ms (2%)

Counts

4 → 92

Calls

24 calls:

31.0ms	(.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))))))	ux	0
20.0ms	(.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))))))	uy	inf
18.0ms	(.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))))))	uy	-inf
18.0ms	(.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))))))	maxCos	-inf
18.0ms	(.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))))))	maxCos	0

rewrite41.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

192×	`add-sqr-sqrt_binary32`
187×	`*-un-lft-identity_binary32`
187×	`pow1_binary32`
177×	`add-cbrt-cube_binary32`
177×	`add-exp-log_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	67
1	371	61
0	17	94

Stop Event

1×	saturated
1×	node limit

Counts

4 → 98

simplify114.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

410×	`fma-neg_binary32`
377×	`sub-neg_binary32`
318×	`fma-def_binary32`
269×	`associate-r_binary32`
250×	`associate-l_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	289	6589
1	1050	5816
2	4392	5810

Stop Event

1×	node limit

Counts

190 → 181

prune256.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	171	10	181
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	173	10	183

Error

0.2b

Counts

183 → 10

Alt Table

Status	Error	Program
	1.8b	(-.f32 (.f32 (+.f32 (.f32 (.f32 2/3 (pow.f32 (PI.f32) 4)) (pow.f32 uy 4)) 1) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)))))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (+.f32 (.f32 (.f32 2 (pow.f32 (PI.f32) 2)) (.f32 uy uy)) (.f32 4/45 (*.f32 (pow.f32 uy 6) (pow.f32 (PI.f32) 6))))))
	13.2b	(.f32 (cos.f32 (pow.f32 (cbrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
	1.8b	(-.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))))))))))
▶	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 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	1.0b	(-.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))))))
	13.2b	(log.f32 (pow.f32 (exp.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sqrt.f32 (-.f32 1 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2)))))
	7.7b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	12.7b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (-.f32 (fma.f32 ux ux (fma.f32 (.f32 2 maxCos) ux 1)) (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux))))))
	13.2b	(cbrt.f32 (.f32 (pow.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 1 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2)) 3/2)))
	1.0b	(fma.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos (.f32 (.f32 ux ux) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))))) (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (-.f32 (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 maxCos (.f32 ux (sqrt.f32 (/.f32 1 (*.f32 ux (-.f32 2 ux)))))))))

Compiler

Compiled 10524 to 7048 computations (33% saved)

localize69.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series233.0ms (2.3%)

Counts

3 → 64

Calls

18 calls:

32.0ms	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))	ux	0
18.0ms	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))	maxCos	-inf
18.0ms	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))	uy	-inf
18.0ms	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))	maxCos	inf
17.0ms	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))	maxCos	0

rewrite36.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

224×	`add-sqr-sqrt_binary32`
219×	`*-un-lft-identity_binary32`
219×	`pow1_binary32`
205×	`add-cbrt-cube_binary32`
205×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	88
1	441	88
0	21	92

Stop Event

1×	saturated
1×	node limit

Counts

3 → 54

simplify94.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-def_binary32`
414×	`associate-r_binary32`
301×	`associate-l_binary32`
230×	`times-frac_binary32`
202×	`associate--l+_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	426	7926
1	1601	7037

Stop Event

1×	node limit

Counts

118 → 153

prune414.0ms (4.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	157	12	169
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	167	12	179

Error

0.1b

Counts

179 → 12

Alt Table

Status	Error	Program
	0.8b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (pow.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))))) 3))
	1.0b	(.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 maxCos (.f32 ux (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))))))
	0.3b	(.f32 (cos.f32 (pow.f32 (sqrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 2)) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (pow.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) 2) (pow.f32 (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))) 2))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))))))
	0.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (pow.f32 (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 1/4) 2))
	1.4b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (pow.f32 (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2) 1/3))
	0.4b	(.f32 (-.f32 (exp.f32 (log1p.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) 1) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
▶	0.3b	(cbrt.f32 (.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	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)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))))
	0.3b	(.f32 (cos.f32 (expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	1.5b	(.f32 (pow.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) 2) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	0.4b	(.f32 (pow.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) 3) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))

Compiler

Compiled 13221 to 8431 computations (36.2% saved)

localize79.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))
✓	0.3b	(pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)
	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)

series819.0ms (8.2%)

Counts

3 → 68

Calls

18 calls:

166.0ms	(.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))	ux	0
138.0ms	(.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))	ux	-inf
132.0ms	(.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))	ux	inf
86.0ms	(.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))	maxCos	0
44.0ms	(.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))	uy	-inf

rewrite59.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

233×	`add-sqr-sqrt_binary32`
227×	`pow1_binary32`
225×	`*-un-lft-identity_binary32`
216×	`add-log-exp_binary32`
216×	`log1p-expm1-u_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	96
1	479	96
0	23	96

Stop Event

1×	saturated
1×	node limit

Counts

3 → 45

simplify226.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

459×	`*-commutative_binary32`
403×	`times-frac_binary32`
305×	`+-commutative_binary32`
286×	`fma-def_binary32`
250×	`associate-+r+_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1051	19289
1	3767	18809

Stop Event

1×	node limit

Counts

113 → 152

prune728.0ms (7.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	164	4	168
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	169	11	180

Error

0.0b

Counts

180 → 11

Alt Table

Status	Error	Program
	0.8b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (pow.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))))) 3))
	1.0b	(.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 maxCos (.f32 ux (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))))))
	0.3b	(cbrt.f32 (.f32 (pow.f32 (cos.f32 (pow.f32 (cbrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	0.3b	(.f32 (cos.f32 (pow.f32 (sqrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 2)) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
▶	0.3b	(cbrt.f32 (.f32 (log1p.f32 (expm1.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3))) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	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)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))))
	8.3b	(cbrt.f32 (.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (exp.f32 3/2) (+.f32 (log.f32 (+.f32 2 (.f32 -2 maxCos))) (log.f32 ux)))))
	0.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (pow.f32 (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 1/4) 2))
	1.4b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (pow.f32 (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2) 1/3))
	0.4b	(.f32 (-.f32 (exp.f32 (log1p.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) 1) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	0.4b	(cbrt.f32 (.f32 (-.f32 (exp.f32 (log1p.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3))) 1) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))

Compiler

Compiled 28369 to 20277 computations (28.5% saved)

localize90.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)
	0.3b	(.f32 (.f32 uy 2) (PI.f32))
	0.4b	(pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)
✓	0.7b	(expm1.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3))

series13.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

5.0ms	(expm1.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3))	uy	0
4.0ms	(expm1.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3))	uy	-inf
4.0ms	(expm1.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3))	uy	inf

rewrite41.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

798×	`log1p-expm1-u_binary32`
798×	`expm1-log1p-u_binary32`
96×	`add-sqr-sqrt_binary32`
92×	`pow1_binary32`
91×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	206	15
2	2230	15
0	10	15

Stop Event

1×	saturated
1×	node limit

Counts

1 → 20

simplify35.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

719×	`distribute-rgt-neg-in_binary32`
530×	`fma-neg_binary32`
471×	`*-commutative_binary32`
284×	`sub-neg_binary32`
249×	`distribute-lft-neg-in_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	258
1	114	248
2	351	244
3	1752	236
4	4344	230

Stop Event

1×	node limit

Counts

32 → 30

prune353.0ms (3.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	133	11	144

Error

0.0b

Counts

144 → 11

Alt Table

Status	Error	Program
	0.8b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (pow.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))))) 3))
	1.0b	(.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 maxCos (.f32 ux (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))))))
	0.3b	(cbrt.f32 (.f32 (pow.f32 (cos.f32 (pow.f32 (cbrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	0.3b	(.f32 (cos.f32 (pow.f32 (sqrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 2)) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
✓	0.3b	(cbrt.f32 (.f32 (log1p.f32 (expm1.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3))) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	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)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))))
	8.3b	(cbrt.f32 (.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (exp.f32 3/2) (+.f32 (log.f32 (+.f32 2 (.f32 -2 maxCos))) (log.f32 ux)))))
	0.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (pow.f32 (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 1/4) 2))
	1.4b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (pow.f32 (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2) 1/3))
	0.4b	(.f32 (-.f32 (exp.f32 (log1p.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) 1) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	0.4b	(cbrt.f32 (.f32 (-.f32 (exp.f32 (log1p.f32 (pow.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) 3))) 1) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))

Compiler

Compiled 11364 to 7844 computations (31% saved)

regimes3.0s (30.1%)

Accuracy

Total 0.2b remaining (71.6%)

Threshold costs 0.2b (71.6%)

Counts

170 → 1

Compiler

Compiled 81771 to 58737 computations (28.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary32`
2×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`neg-sub0_binary32`
1×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	51
1	34	51
2	38	51
3	40	51
4	41	51

Stop Event

1×

saturated

end254.0ms (2.6%)

Stop Event

1×

fuel

Compiler

Compiled 480 to 333 computations (30.6% saved)

Details

analyze638.0ms (6.4%)

sample2.1s (20.6%)

preprocess32.0ms (0.3%)

simplify20.0ms (0.2%)

prune5.0ms (0%)

localize49.0ms (0.5%)

series201.0ms (2%)

rewrite41.0ms (0.4%)

simplify114.0ms (1.1%)

prune256.0ms (2.6%)

localize69.0ms (0.7%)

series233.0ms (2.3%)

rewrite36.0ms (0.4%)

simplify94.0ms (0.9%)

prune414.0ms (4.2%)

localize79.0ms (0.8%)

series819.0ms (8.2%)

rewrite59.0ms (0.6%)

simplify226.0ms (2.3%)

prune728.0ms (7.3%)

localize90.0ms (0.9%)

series13.0ms (0.1%)

rewrite41.0ms (0.4%)

simplify35.0ms (0.4%)

prune353.0ms (3.6%)

regimes3.0s (30.1%)

simplify3.0ms (0%)

end254.0ms (2.6%)

Profiling