Details

analyze670.0ms (6.2%)

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)

sample2.2s (20.7%)

Results

2.2s

8256×

body

128

valid

Compiler

Compiled 102 to 74 computations (27.5% saved)

preprocess30.0ms (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)

simplify21.0ms (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

13.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.1b	(.f32 (sin.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))))))
	13.2b	(.f32 (sin.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

▶

13.1b

(*.f32 (sin.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))))))

13.2b

(*.f32 (sin.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)

localize47.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(.f32 (sin.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))))))
✓	0.4b	(.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))))

series182.0ms (1.7%)

Counts

4 → 92

Calls

24 calls:

29.0ms	(.f32 (sin.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
19.0ms	(.f32 (sin.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
18.0ms	(.f32 (sin.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
17.0ms	(.f32 (sin.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
16.0ms	(.f32 (sin.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

rewrite39.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

185×	`add-sqr-sqrt_binary32`
177×	`log1p-expm1-u_binary32`
177×	`expm1-log1p-u_binary32`
176×	`add-cbrt-cube_binary32`
172×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	67
1	373	61

Stop Event

1×	node limit

Counts

4 → 94

simplify110.0ms (1%)

Algorithm

1×	egg-herbie

Rules

497×	`fma-neg_binary32`
347×	`fma-def_binary32`
285×	`associate-r_binary32`
268×	`associate-l_binary32`
223×	`*-commutative_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	6612
1	1115	5692
2	4628	5688

Stop Event

1×	node limit

Counts

186 → 178

prune265.0ms (2.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	162	16	178
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	164	16	180

Error

0.2b

Counts

180 → 16

Alt Table

Status	Error	Program
	1.6b	(-.f32 (.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 (PI.f32) (.f32 2 uy)) (.f32 (.f32 4/15 (pow.f32 (PI.f32) 5)) (pow.f32 uy 5)))) (.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 4/3 (pow.f32 uy 3)) (pow.f32 (PI.f32) 3)) (.f32 (.f32 8/315 (pow.f32 uy 7)) (pow.f32 (PI.f32) 7)))))
▶	0.5b	(.f32 (sin.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))))))
	14.7b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (pow.f32 (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2) 3))))
	1.6b	(-.f32 (+.f32 (.f32 4/15 (.f32 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (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 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))))))))) (+.f32 (.f32 8/315 (.f32 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)) (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 4/3 (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 uy 3)) (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))))))))))
	13.2b	(pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 1 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))))) 3)
	13.3b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (/.f32 (+.f32 (pow.f32 (.f32 (-.f32 1 ux) (fma.f32 ux maxCos (-.f32 1 ux))) 3) (pow.f32 (.f32 maxCos (.f32 ux (fma.f32 ux maxCos (-.f32 1 ux)))) 3)) (+.f32 (.f32 (.f32 (-.f32 1 ux) (fma.f32 ux maxCos (-.f32 1 ux))) (.f32 (-.f32 1 ux) (fma.f32 ux maxCos (-.f32 1 ux)))) (-.f32 (.f32 (.f32 maxCos (.f32 ux (fma.f32 ux maxCos (-.f32 1 ux)))) (.f32 maxCos (.f32 ux (fma.f32 ux maxCos (-.f32 1 ux))))) (.f32 (.f32 (-.f32 1 ux) (fma.f32 ux maxCos (-.f32 1 ux))) (.f32 maxCos (.f32 ux (fma.f32 ux maxCos (-.f32 1 ux)))))))))))
	13.2b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (/.f32 (-.f32 1 (.f32 (neg.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2)) (neg.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2)))) (-.f32 1 (neg.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))))))
	5.6b	(.f32 2 (.f32 uy (.f32 (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))))))))
	1.2b	(fma.f32 (sin.f32 (.f32 (PI.f32) (.f32 2 uy))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 2 uy))) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (-.f32 (.f32 maxCos (.f32 ux ux)) (*.f32 maxCos ux))))
	0.7b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (neg.f32 (.f32 ux (+.f32 ux (.f32 2 maxCos)))))))
	2.3b	(fma.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 (PI.f32) (.f32 2 uy)) (.f32 (.f32 4/15 (pow.f32 (PI.f32) 5)) (pow.f32 uy 5))) (.f32 (.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 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) -4/3))
	7.7b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	13.2b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (/.f32 (+.f32 1 (pow.f32 (neg.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2)) 3)) (+.f32 1 (-.f32 (.f32 (neg.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2)) (neg.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))) (neg.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2)))))))
	1.0b	(-.f32 (fma.f32 (sin.f32 (.f32 (PI.f32) (.f32 2 uy))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 2 uy))) (+.f32 (.f32 (.f32 maxCos maxCos) (.f32 (pow.f32 ux 3) (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))))) (.f32 (.f32 ux ux) (.f32 maxCos (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))))))) (fma.f32 (sin.f32 (.f32 (PI.f32) (.f32 2 uy))) (.f32 ux (.f32 maxCos (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))))) (.f32 1/2 (+.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 2 uy))) (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 4)))) (.f32 (.f32 (.f32 ux (.f32 ux (.f32 maxCos maxCos))) (sin.f32 (.f32 (PI.f32) (.f32 2 uy)))) (+.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3)))))))))
	12.0b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (log.f32 (exp.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))))))
	13.2b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (log.f32 (exp.f32 (-.f32 1 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))))))

Compiler

Compiled 11018 to 7495 computations (32% saved)

localize83.0ms (0.8%)

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 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)))))
✓	0.2b	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(.f32 (sin.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))))))

series217.0ms (2%)

Counts

3 → 64

Calls

18 calls:

32.0ms	(.f32 (sin.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
17.0ms	(.f32 (sin.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
17.0ms	(.f32 (sin.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 (sin.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
16.0ms	(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

rewrite36.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

217×	`add-sqr-sqrt_binary32`
205×	`log1p-expm1-u_binary32`
205×	`expm1-log1p-u_binary32`
204×	`add-cbrt-cube_binary32`
200×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	88
1	441	88

Stop Event

1×	node limit

Counts

3 → 54

simplify126.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

600×	`fma-def_binary32`
437×	`associate-r_binary32`
319×	`associate-l_binary32`
230×	`times-frac_binary32`
202×	`associate--l+_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	437	7975
1	1639	7056

Stop Event

1×	node limit

Counts

118 → 153

prune360.0ms (3.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	156	14	170
Fresh	15	0	15
Picked	1	0	1
Done	0	0	0
Total	172	14	186

Error

0.0b

Counts

186 → 14

Alt Table

Status	Error	Program
	1.2b	(.f32 (sin.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))
	0.9b	(pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.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)
	0.7b	(.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 2 (.f32 uy (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))))))
	0.9b	(.f32 (pow.f32 (cbrt.f32 (sin.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))))))
	0.5b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (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))))))
	5.8b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (log.f32 (exp.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))))))))
	0.7b	(.f32 (sin.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))
▶	0.5b	(cbrt.f32 (.f32 (pow.f32 (sin.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)))
	1.3b	(pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.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))))))) 2)
	1.6b	(-.f32 (.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 (PI.f32) uy) (.f32 (pow.f32 uy 5) (.f32 (pow.f32 (PI.f32) 5) 4/15)))) (.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 (.f32 4/3 (pow.f32 uy 3)) (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 7) (.f32 (pow.f32 (PI.f32) 7) 8/315)))))
	1.3b	(.f32 (pow.f32 (sqrt.f32 (sin.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 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (cbrt.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)))
	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (cbrt.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))))) (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))))))))
	19.2b	(log.f32 (pow.f32 (exp.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.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)))))))

Compiler

Compiled 13510 to 8477 computations (37.3% saved)

localize79.0ms (0.7%)

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))
✓	0.3b	(.f32 (pow.f32 (sin.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))
✓	0.8b	(pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)

series713.0ms (6.6%)

Counts

3 → 68

Calls

18 calls:

144.0ms	(.f32 (pow.f32 (sin.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
132.0ms	(.f32 (pow.f32 (sin.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
108.0ms	(.f32 (pow.f32 (sin.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
72.0ms	(.f32 (pow.f32 (sin.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
40.0ms	(.f32 (pow.f32 (sin.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

rewrite38.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

226×	`add-sqr-sqrt_binary32`
216×	`log1p-expm1-u_binary32`
216×	`expm1-log1p-u_binary32`
213×	`add-cbrt-cube_binary32`
209×	`add-cube-cbrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	96
1	475	96

Stop Event

1×	node limit

Counts

3 → 45

simplify220.0ms (2%)

Algorithm

1×	egg-herbie

Rules

463×	`*-commutative_binary32`
403×	`times-frac_binary32`
290×	`+-commutative_binary32`
274×	`fma-def_binary32`
236×	`associate-+r+_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1045	19397
1	3732	18917

Stop Event

1×	node limit

Counts

113 → 153

prune674.0ms (6.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	168	2	170
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	172	12	184

Error

0.0b

Counts

184 → 12

Alt Table

Status	Error	Program
	1.2b	(.f32 (sin.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))
	0.9b	(pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.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)
	0.7b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 2 (.f32 uy (PI.f32)))) 2)) 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)))
	2.7b	(cbrt.f32 (.f32 (+.f32 (fma.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) (.f32 208/15 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)))) (.f32 -16 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (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)))
	0.9b	(.f32 (pow.f32 (cbrt.f32 (sin.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))))))
▶	0.5b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (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))))))
	5.8b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (log.f32 (exp.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))))))))
	1.3b	(pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.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))))))) 2)
	1.3b	(.f32 (pow.f32 (sqrt.f32 (sin.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 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (cbrt.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)))
	0.7b	(.f32 (sin.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))
	19.2b	(log.f32 (pow.f32 (exp.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.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)))))))

Compiler

Compiled 28670 to 20763 computations (27.6% saved)

localize110.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))
✓	0.4b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (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))))))

series174.0ms (1.6%)

Counts

4 → 68

Calls

18 calls:

30.0ms	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (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 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (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	inf
18.0ms	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (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 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (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 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (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

rewrite38.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

225×	`add-sqr-sqrt_binary32`
215×	`expm1-log1p-u_binary32`
214×	`log1p-expm1-u_binary32`
211×	`add-cbrt-cube_binary32`
207×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	68
1	462	68

Stop Event

1×	node limit

Counts

4 → 63

simplify96.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

479×	`fma-neg_binary32`
382×	`fma-def_binary32`
322×	`associate-r_binary32`
256×	`associate-l_binary32`
216×	`*-commutative_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	322	5597
1	1156	4888
2	4857	4888

Stop Event

1×	node limit

Counts

131 → 137

prune213.0ms (2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	137	12	149

Error

0.0b

Counts

149 → 12

Alt Table

Status	Error	Program
	1.2b	(.f32 (sin.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))
	0.9b	(pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.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)
	0.7b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 2 (.f32 uy (PI.f32)))) 2)) 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)))
	2.7b	(cbrt.f32 (.f32 (+.f32 (fma.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) (.f32 208/15 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)))) (.f32 -16 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (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)))
	0.9b	(.f32 (pow.f32 (cbrt.f32 (sin.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))))))
✓	0.5b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 uy (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))))))
	5.8b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (log.f32 (exp.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))))))))
	1.3b	(pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.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))))))) 2)
	1.3b	(.f32 (pow.f32 (sqrt.f32 (sin.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))))))
	0.8b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (pow.f32 (sqrt.f32 (.f32 uy (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))))))
	0.7b	(.f32 (sin.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))
	19.2b	(log.f32 (pow.f32 (exp.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.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)))))))

Compiler

Compiled 9494 to 5838 computations (38.5% saved)

regimes3.7s (34.7%)

Accuracy

Total 0.4b remaining (82.9%)

Threshold costs 0.4b (82.9%)

Counts

242 → 1

Compiler

Compiled 105573 to 75371 computations (28.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	63
1	35	63
2	39	63
3	41	63
4	42	63

Stop Event

1×

saturated

end261.0ms (2.4%)

Stop Event

1×

fuel

Compiler

Compiled 548 to 372 computations (32.1% saved)

Details

analyze670.0ms (6.2%)

sample2.2s (20.7%)

preprocess30.0ms (0.3%)

simplify21.0ms (0.2%)

prune5.0ms (0%)

localize47.0ms (0.4%)

series182.0ms (1.7%)

rewrite39.0ms (0.4%)

simplify110.0ms (1%)

prune265.0ms (2.5%)

localize83.0ms (0.8%)

series217.0ms (2%)

rewrite36.0ms (0.3%)

simplify126.0ms (1.2%)

prune360.0ms (3.3%)

localize79.0ms (0.7%)

series713.0ms (6.6%)

rewrite38.0ms (0.4%)

simplify220.0ms (2%)

prune674.0ms (6.3%)

localize110.0ms (1%)

series174.0ms (1.6%)

rewrite38.0ms (0.4%)

simplify96.0ms (0.9%)

prune213.0ms (2%)

regimes3.7s (34.7%)

simplify3.0ms (0%)

end261.0ms (2.4%)

Profiling