Details

analyze722.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.1%	99.9%	0
0%	0.1%	99.9%	1
0%	0.1%	99.9%	2
0%	0.1%	99.9%	3
0%	0%	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)

sample3.8s (4.2%)

Results

3.7s

8256×

body

128

valid

Compiler

Compiled 130 to 94 computations (27.7% saved)

simplify48.0ms (0.1%)

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

14.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.2b	(.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))))))
▶	14.2b	(.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

14.2b

(*.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))))))

▶

14.2b

(*.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)

localize58.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(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)))
✓	14.8b	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

series267.0ms (0.3%)

Counts

4 → 80

Calls

4 calls:

242.0ms	(.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)
6.0ms	(.f32 (.f32 uy 2) (PI.f32))
4.0ms	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))

rewrite14.0ms (0%)

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)

simplify145.0ms (0.2%)

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

prune505.0ms (0.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	160	12	172
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	162	12	174

Error

0.3b

Counts

174 → 12

Alt Table

Status	Error	Program
	14.4b	(.f32 (sqrt.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)))) (sqrt.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)))))
	1.5b	(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))))
	14.2b	(.f32 (sin.f32 (.f32 (sqrt.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.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)))
	14.4b	(exp.f32 (log.f32 (.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) (sqrt.f32 (fma.f32 (fma.f32 maxCos ux (-.f32 1 ux)) (-.f32 ux (fma.f32 maxCos ux 1)) 1)))))
	14.3b	(.f32 (sin.f32 (exp.f32 (log.f32 (.f32 2 (*.f32 (PI.f32) uy))))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
	14.4b	(.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))))
	14.2b	(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)))))
	1.5b	(-.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))))))))))
	3.2b	(.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 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) -4/3)))
	14.2b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1))) 1)))
	7.0b	(-.f32 (fma.f32 1/2 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 6))) (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 5)))) (+.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (+.f32 (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))))) (+.f32 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (+.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 3))) (.f32 1/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 4)))))) (.f32 3/2 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 5))) (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 4)))))))) (fma.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos ux) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (+.f32 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (+.f32 (.f32 1/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 4)))) (.f32 1/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3)))))) (+.f32 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 5))) (+.f32 (.f32 1/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3)))) (.f32 3/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 5)))))) (.f32 (.f32 1/2 (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))))) (+.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sqrt.f32 (/.f32 1 (pow.f32 (*.f32 ux (-.f32 2 ux)) 3)))))))))
▶	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))))))

Compiler

Compiled 10991 to 7235 computations (34.2% saved)

localize128.0ms (0.1%)

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)))
	0.2b	(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))))))

series525.0ms (0.6%)

Counts

2 → 56

Calls

2 calls:

503.0ms

(*.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))))))

21.0ms

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

rewrite41.0ms (0%)

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:

25.0ms

(*.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))))))

9.0ms

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

simplify360.0ms (0.4%)

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

prune879.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	172	9	181
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	183	10	193

Error

0.0b

Counts

193 → 10

Alt Table

Status	Error	Program
	0.8b	(.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))))))
	1.3b	(.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (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))))))) (.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (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))))))))
	1.5b	(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))))
	1.0b	(.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 (PI.f32) uy))) (cbrt.f32 (.f32 2 (.f32 (PI.f32) uy)))) (cbrt.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))))))
	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)))))))
	0.7b	(.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (sqrt.f32 (PI.f32))) (sqrt.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))))))
	1.1b	(.f32 (sqrt.f32 (.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))))))) (sqrt.f32 (.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))))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 (cbrt.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)))))))
▶	0.6b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (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))))))
	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))))))))

Compiler

Compiled 12351 to 7243 computations (41.4% saved)

localize266.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (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)))))))
✓	0.3b	(*.f32 (PI.f32) uy)
✓	0.3b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (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))))))
✓	0.5b	(.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (+.f32 (.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))))

series11.3s (12.5%)

Counts

4 → 92

Calls

4 calls:

10.6s	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (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))))))
680.0ms	(.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (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)))))))
45.0ms	(.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (+.f32 (.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))))
16.0ms	(*.f32 (PI.f32) uy)

rewrite98.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`pow1_binary32`
25×	`add-cbrt-cube_binary32`
25×	`add-exp-log_binary32`
19×	`add-sqr-sqrt_binary32`
19×	`pow-prod-down_binary32`

Counts

4 → 128

Calls

4 calls:

21.0ms	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (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))))))
18.0ms	(.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (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)))))))
16.0ms	(.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (+.f32 (.f32 2 maxCos) (*.f32 (fma.f32 maxCos maxCos 1) ux))))
8.0ms	(*.f32 (PI.f32) uy)

simplify1.1s (1.2%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-def_binary32`
563×	`associate-+r+_binary32`
489×	`associate-r_binary32`
162×	`associate-*r/_binary32`
84×	`associate-l_binary32`

Counts

220 → 299

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1907	53780
1	5414	53780

prune5.2s (5.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	297	2	299
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	301	8	309

Error

0.0b

Counts

309 → 8

Alt Table

Status	Error	Program
	0.8b	(.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))))))
	1.5b	(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))))
	0.8b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) uy)))) (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))))))
	1.1b	(.f32 (sqrt.f32 (.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))))))) (sqrt.f32 (.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))))))))
	0.7b	(/.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (/.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 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (.f32 ux (fma.f32 2 maxCos (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (fma.f32 2 maxCos (*.f32 (fma.f32 maxCos maxCos 1) ux))))))))
	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)))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 (cbrt.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)))))))
▶	0.6b	(/.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))))))))

Compiler

Compiled 78862 to 51046 computations (35.3% saved)

localize204.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))
✓	0.4b	(/.f32 (.f32 (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	(pow.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))) 3)
✓	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))))

series44.6s (49.3%)

Counts

4 → 104

Calls

4 calls:

44.4s	(/.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))))))))
72.0ms	(.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))))
56.0ms	(pow.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))) 3)
48.0ms	(.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))))

rewrite108.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary32`
17×	`add-cbrt-cube_binary32`
17×	`add-exp-log_binary32`
17×	`pow1_binary32`
16×	`*-un-lft-identity_binary32`

Counts

4 → 121

Calls

4 calls:

41.0ms	(/.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))))))))
26.0ms	(.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	(pow.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))) 3)
8.0ms	(.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))))

simplify1.8s (2%)

Algorithm

1×	egg-herbie

Rules

1072×	`fma-def_binary32`
102×	`sqr-pow_binary32`
28×	`sub-neg_binary32`
23×	`cube-mult_binary32`
23×	`unpow3_binary32`

Counts

225 → 316

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3590	109015
1	5014	109015

prune7.9s (8.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	316	0	316
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	316	8	324

Error

0.0b

Counts

324 → 8

Alt Table

Status	Error	Program
	0.8b	(.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))))))
	1.5b	(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))))
	0.8b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) uy)))) (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))))))
	1.1b	(.f32 (sqrt.f32 (.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))))))) (sqrt.f32 (.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))))))))
	0.7b	(/.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (/.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 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (.f32 ux (fma.f32 2 maxCos (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (fma.f32 2 maxCos (*.f32 (fma.f32 maxCos maxCos 1) ux))))))))
	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)))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 (cbrt.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)))))))
✓	0.6b	(/.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))))))))

Compiler

Compiled 165130 to 115286 computations (30.2% saved)

regimes9.9s (10.9%)

Accuracy

Total 0.5b remaining (84.3%)

Threshold costs 0.5b (84.3%)

Counts

299 → 1

Compiler

Compiled 192346 to 119076 computations (38.1% saved)

simplify9.0ms (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	23	51
1	35	51
2	43	51
3	64	51
4	83	51
5	95	51
6	102	51
7	104	51
8	102	51

end465.0ms (0.5%)

Compiler: Compiled 584 to 347 computations (40.6% saved)

Details

analyze722.0ms (0.8%)

sample3.8s (4.2%)

simplify48.0ms (0.1%)

prune5.0ms (0%)

localize58.0ms (0.1%)

series267.0ms (0.3%)

rewrite14.0ms (0%)

simplify145.0ms (0.2%)

prune505.0ms (0.6%)

localize128.0ms (0.1%)

series525.0ms (0.6%)

rewrite41.0ms (0%)

simplify360.0ms (0.4%)

prune879.0ms (1%)

localize266.0ms (0.3%)

series11.3s (12.5%)

rewrite98.0ms (0.1%)

simplify1.1s (1.2%)

prune5.2s (5.8%)

localize204.0ms (0.2%)

series44.6s (49.3%)

rewrite108.0ms (0.1%)

simplify1.8s (2%)

prune7.9s (8.7%)

regimes9.9s (10.9%)

simplify9.0ms (0%)

end465.0ms (0.5%)

Profiling