Details

analyze736.0ms (3.2%)

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)

sample172.0ms (0.7%)

Algorithm

1×

intervals

Results

37.0ms	256×	body	128	valid
11.0ms	256×	pre	128	true

Compiler

Compiled 82 to 60 computations (26.8% saved)

simplify51.0ms (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

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

13.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.7b	(.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))))))
▶	13.6b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))

Status

Error

Program

13.7b

(*.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))))))

▶

13.6b

(*.f32 (sin.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)

localize59.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.3b	(.f32 (sin.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)))
✓	14.3b	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

series258.0ms (1.1%)

Counts

4 → 80

Calls

4 calls:

234.0ms	(.f32 (sin.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)
5.0ms	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
3.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite15.0ms (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 (sin.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	(sin.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)

simplify143.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

494×	`associate-l_binary32`
437×	`associate-r_binary32`
366×	`fma-def_binary32`
185×	`associate-+r+_binary32`
156×	`times-frac_binary32`

Counts

143 → 172

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	381	7705
1	1177	6694
2	5029	6694

prune430.0ms (1.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	159	13	172
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	161	13	174

Error

0.3b

Counts

174 → 13

Alt Table

Status	Error	Program
	13.6b	(.f32 (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (cbrt.f32 (sin.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)))
	13.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (*.f32 (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))))
	5.3b	(-.f32 (+.f32 (.f32 1/2 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 6))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 5))))) (+.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)))) (+.f32 (.f32 (.f32 (sin.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 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 3))) (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 3)))) (+.f32 (.f32 1/2 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 4))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 3))))) (.f32 3/2 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 4))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 5)))))))))) (+.f32 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos ux)) (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))) (+.f32 (.f32 1/2 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 4))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 3))))) (+.f32 (.f32 1/2 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 3))))) (+.f32 (.f32 1/2 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 5))))) (+.f32 (.f32 3/2 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 5))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 5))))) (+.f32 (.f32 1/2 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))) (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2)))))) (.f32 1/2 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (*.f32 2 ux) (pow.f32 ux 2)) 3))))))))))))
	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 4/15 (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5))))) (.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 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) (.f32 8/315 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7))))))
	13.9b	(.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (sqrt.f32 (sin.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))))
	13.6b	(.f32 (sin.f32 (.f32 (.f32 (.f32 uy 2) (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
	3.4b	(-.f32 (.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 4/3 (.f32 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 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)))))))))
	13.8b	(.f32 (sin.f32 (exp.f32 (+.f32 (log.f32 (.f32 uy 2)) (log.f32 (PI.f32))))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
	13.9b	(.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sqrt.f32 (sin.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)))
	13.6b	(.f32 (.f32 (cbrt.f32 (.f32 (sin.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)))) (cbrt.f32 (.f32 (sin.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))))) (cbrt.f32 (.f32 (sin.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)))))
▶	0.5b	(.f32 (sin.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))))))
	7.4b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	1.8b	(fma.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))) (-.f32 (.f32 maxCos (.f32 ux ux)) (*.f32 maxCos ux))))

Compiler

Compiled 11215 to 7415 computations (33.9% saved)

localize79.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux)))
	0.1b	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.3b	(.f32 (sin.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))))))

series268.0ms (1.2%)

Counts

2 → 56

Calls

2 calls:

253.0ms

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

15.0ms

(+.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

9×	`add-sqr-sqrt_binary32`
6×	`associate-r_binary32`
5×	`*-un-lft-identity_binary32`
5×	`add-cube-cbrt_binary32`
4×	`sqrt-prod_binary32`

Counts

2 → 40

Calls

2 calls:

12.0ms

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

6.0ms

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

simplify153.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

452×	`associate-r_binary32`
410×	`associate-l_binary32`
362×	`fma-def_binary32`
184×	`associate-+r+_binary32`
156×	`times-frac_binary32`

Counts

96 → 126

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	354	7170
1	1152	6291
2	5040	6291

prune394.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	169	12	181
Fresh	12	0	12
Picked	1	0	1
Done	0	0	0
Total	182	12	194

Error

0.0b

Counts

194 → 12

Alt Table

Status	Error	Program
	2.8b	(exp.f32 (+.f32 (log.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (log.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))))))))
	0.6b	(/.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (pow.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) 3) (pow.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos 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))))))))
	0.5b	(.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy uy) uy) (.f32 (.f32 2 2) 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (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	(cbrt.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.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))))) (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)))))) (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))))))))
	1.2b	(.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (sqrt.f32 (sin.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)))))))
	0.8b	(.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))))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))) (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))))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))))) (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))))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))))
	0.8b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.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 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))))
▶	0.5b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))) (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 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (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 (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))))))) (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))))))
	0.7b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (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)))))))
	0.7b	(.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (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 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (cbrt.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 (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 (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 12739 to 7467 computations (41.4% saved)

localize87.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series305.0ms (1.3%)

Counts

4 → 56

Calls

4 calls:

283.0ms	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))) (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))))))
11.0ms	(*.f32 (PI.f32) uy)
7.0ms	(log1p.f32 (.f32 2 (.f32 (PI.f32) uy)))
3.0ms	(expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))

rewrite50.0ms (0.2%)

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 → 68

Calls

4 calls:

12.0ms	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))) (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 (PI.f32) uy)
0.0ms	(log1p.f32 (.f32 2 (.f32 (PI.f32) uy)))
0.0ms	(expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))

simplify171.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

622×	`fma-neg_binary32`
466×	`associate-r_binary32`
426×	`associate-l_binary32`
378×	`fma-def_binary32`
156×	`times-frac_binary32`

Counts

124 → 166

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	425	7319
1	1282	6527
2	4916	6527
3	5438	6527

prune324.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	168	10	178

Error

0.0b

Counts

178 → 10

Alt Table

Status	Error	Program
	2.8b	(exp.f32 (+.f32 (log.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (log.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))))))))
	0.6b	(/.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (pow.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) 3) (pow.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos 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))))))))
	1.2b	(.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (sqrt.f32 (sin.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)))))))
	0.8b	(.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))))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))) (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))))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))))) (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))))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))))
	0.8b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (.f32 (PI.f32) (.f32 (cbrt.f32 uy) (cbrt.f32 uy))) (cbrt.f32 uy)))))) (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))))))
	1.3b	(.f32 (sqrt.f32 (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))) (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))))))) (sqrt.f32 (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))) (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))))))))
	0.7b	(.f32 (sin.f32 (.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))) (sqrt.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))))) (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 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (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 (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))))))) (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))))))
	0.7b	(.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (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	(cbrt.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.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))))) (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)))))) (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 12355 to 7252 computations (41.3% saved)

localize120.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (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 (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)))))))
✓	0.3b	(/.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (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 (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))))))) (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))
✓	0.5b	(.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))))

series6.1s (26.5%)

Counts

3 → 92

Calls

3 calls:

5.7s

(/.f32 (*.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (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 (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))))))) (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))))))

393.0ms

(*.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (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 (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)))))))

25.0ms

(*.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))))

rewrite57.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary32`
14×	`*-un-lft-identity_binary32`
14×	`add-cube-cbrt_binary32`
12×	`add-cbrt-cube_binary32`
12×	`add-exp-log_binary32`

Counts

3 → 97

Calls

3 calls:

18.0ms

(/.f32 (*.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (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 (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))))))) (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))))))

12.0ms

(*.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))))

10.0ms

(*.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (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 (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)))))))

simplify540.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-def_binary32`
561×	`associate-+r+_binary32`
464×	`associate-r_binary32`
162×	`associate-*r/_binary32`
66×	`sqr-pow_binary32`

Counts

189 → 275

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1857	53961
1	5298	53961

prune1.8s (7.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	305	2	307
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	307	10	317

Error

Counts

317 → 10

Alt Table

Status	Error	Program
	2.8b	(exp.f32 (+.f32 (log.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (log.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))))))))
	0.6b	(/.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (pow.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) 3) (pow.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos 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 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (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 (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))))))) (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))))))) (cbrt.f32 (/.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (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 (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))))))) (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)))))))) (cbrt.f32 (/.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (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 (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))))))) (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))))))))
	0.7b	(.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (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 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux) (.f32 2 (.f32 maxCos 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)))))) (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	(cbrt.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.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))))) (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)))))) (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))))))))
	0.8b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (.f32 (PI.f32) (.f32 (cbrt.f32 uy) (cbrt.f32 uy))) (cbrt.f32 uy)))))) (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))))))
	1.3b	(.f32 (sqrt.f32 (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))) (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))))))) (sqrt.f32 (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))) (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))))))))
	0.7b	(.f32 (sin.f32 (.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))) (sqrt.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))))) (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 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (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 (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))))))) (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 80927 to 51594 computations (36.2% saved)

regimes8.1s (35.4%)

Accuracy

Total 0.4b remaining (84.5%)

Threshold costs 0.4b (84.5%)

Counts

342 → 1

Compiler

Compiled 256547 to 155132 computations (39.5% saved)

simplify4.0ms (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	21	47
1	33	47
2	41	47
3	62	47
4	81	47
5	93	47
6	100	47
7	102	47
8	100	47

end1.0ms (0%)

Compiler: Compiled 34 to 22 computations (35.3% saved)

sample2.5s (10.8%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
327.0ms	8000×	pre	128	true

Compiler

Compiled 950 to 530 computations (44.2% saved)

Details

analyze736.0ms (3.2%)

sample172.0ms (0.7%)

simplify51.0ms (0.2%)

prune5.0ms (0%)

localize59.0ms (0.3%)

series258.0ms (1.1%)

rewrite15.0ms (0.1%)

simplify143.0ms (0.6%)

prune430.0ms (1.9%)

localize79.0ms (0.3%)

series268.0ms (1.2%)

rewrite22.0ms (0.1%)

simplify153.0ms (0.7%)

prune394.0ms (1.7%)

localize87.0ms (0.4%)

series305.0ms (1.3%)

rewrite50.0ms (0.2%)

simplify171.0ms (0.7%)

prune324.0ms (1.4%)

localize120.0ms (0.5%)

series6.1s (26.5%)

rewrite57.0ms (0.2%)

simplify540.0ms (2.3%)

prune1.8s (7.9%)

regimes8.1s (35.4%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.5s (10.8%)

Profiling