Details

analyze1.1s (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)

sample141.0ms (0.5%)

Algorithm

1×

intervals

Results

64.0ms	256×	body	128	valid
35.0ms	256×	pre	128	true

Compiler

Compiled 82 to 60 computations (26.8% saved)

simplify71.0ms (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

12.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	12.6b	(.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))))))
▶	12.5b	(.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))

Status

Error

Program

12.6b

(*.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))))))

▶

12.5b

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

Compiler

Compiled 156 to 110 computations (29.5% saved)

localize57.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))
✓	0.1b	(.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
✓	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	13.1b	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

series436.0ms (1.5%)

Counts

4 → 88

Calls

4 calls:

318.0ms	(.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
98.0ms	(sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))
14.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)
5.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite14.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

5.0ms	(.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
4.0ms	(.f32 (.f32 uy 2) (PI.f32))
1.0ms	(sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))
0.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

simplify146.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-def_binary32`
555×	`associate-r_binary32`
512×	`associate-l_binary32`
240×	`times-frac_binary32`
207×	`associate-/l*_binary32`

Counts

157 → 211

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	515	10427
1	1674	9279
2	5422	9279

prune387.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	202	9	211
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	204	9	213

Error

0.2b

Counts

213 → 9

Alt Table

Status	Error	Program
▶	0.4b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
	12.5b	(.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))) (sqrt.f32 (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))))
	12.4b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))))
	0.8b	(.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)))) (fma.f32 (.f32 (.f32 maxCos maxCos) (pow.f32 ux 3)) (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (sqrt.f32 (.f32 ux (-.f32 2 ux))))) (fma.f32 (.f32 maxCos ux) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (.f32 1/2 (+.f32 (.f32 (.f32 maxCos (.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 maxCos maxCos)) (+.f32 (pow.f32 ux 4) (*.f32 ux ux))))))))
	12.5b	(.f32 (.f32 (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))) (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))))) (cbrt.f32 (.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))))
	8.0b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	2.6b	(-.f32 (.f32 (+.f32 (.f32 2/3 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 uy 4))) 1) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux)))))) (.f32 2 (.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 (*.f32 uy uy) (pow.f32 (PI.f32) 2)))))
	2.5b	(-.f32 (+.f32 (.f32 2/3 (.f32 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 uy 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)))))))) (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)))))))))
	5.6b	(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 14169 to 9354 computations (34% saved)

localize76.0ms (0.3%)

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 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos 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 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
	0.3b	(.f32 (.f32 uy 2) (PI.f32))

series342.0ms (1.2%)

Counts

3 → 64

Calls

3 calls:

240.0ms

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

98.0ms

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

3.0ms

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

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

13.0ms

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

8.0ms

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

3.0ms

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

simplify209.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

591×	`fma-def_binary32`
522×	`associate-r_binary32`
452×	`associate-l_binary32`
240×	`times-frac_binary32`
207×	`associate-/l*_binary32`

Counts

116 → 182

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	496	10081
1	1666	9118
2	5399	9118

prune929.0ms (3.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	203	10	213
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	211	11	222

Error

0.1b

Counts

222 → 11

Alt Table

Status	Error	Program
	0.4b	(.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.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 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))
	5.5b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))))
	0.9b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (.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 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))))
	2.9b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))
	12.5b	(.f32 (.f32 (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))) (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))))) (cbrt.f32 (.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (.f32 8 (pow.f32 (fma.f32 maxCos (.f32 ux ux) ux) 3)) (pow.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) 3))) (sqrt.f32 (fma.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))) (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (*.f32 ux ux) ux)))))))
	0.9b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.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)))))))
▶	0.4b	(.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
	0.9b	(.f32 (log.f32 (exp.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
	0.5b	(/.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))))))
	1.0b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (exp.f32 (log.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))))

Compiler

Compiled 16245 to 9879 computations (39.2% saved)

localize176.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
✓	0.3b	(.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))))
✓	0.3b	(*.f32 uy (PI.f32))
✓	0.5b	(.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (cbrt.f32 (.f32 2 (*.f32 uy (PI.f32)))))

series1.3s (4.6%)

Counts

4 → 68

Calls

4 calls:

620.0ms	(.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
620.0ms	(.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (cbrt.f32 (.f32 2 (*.f32 uy (PI.f32)))))
50.0ms	(.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))))
5.0ms	(*.f32 uy (PI.f32))

rewrite74.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary32`
23×	`add-sqr-sqrt_binary32`
17×	`associate-r_binary32`
15×	`add-exp-log_binary32`
15×	`pow1/3_binary32`

Counts

4 → 114

Calls

4 calls:

24.0ms	(.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
16.0ms	(.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))))
10.0ms	(.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (cbrt.f32 (.f32 2 (*.f32 uy (PI.f32)))))
5.0ms	(*.f32 uy (PI.f32))

simplify331.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

527×	`associate-l_binary32`
478×	`associate-r_binary32`
449×	`fma-neg_binary32`
325×	`fma-def_binary32`
156×	`times-frac_binary32`

Counts

182 → 197

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	428	8099
1	1267	7215
2	4947	7213
3	5317	7213

prune1.1s (3.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	239	2	241
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	242	10	252

Error

0.0b

Counts

252 → 10

Alt Table

Status	Error	Program
	0.9b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (.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 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))))
	2.9b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))
▶	0.4b	(.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (cbrt.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))))))) (cbrt.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
	12.5b	(.f32 (.f32 (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))) (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))))) (cbrt.f32 (.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (.f32 8 (pow.f32 (fma.f32 maxCos (.f32 ux ux) ux) 3)) (pow.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) 3))) (sqrt.f32 (fma.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))) (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (*.f32 ux ux) ux)))))))
	0.9b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.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)))))))
	0.9b	(.f32 (log.f32 (exp.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
	5.5b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))))
	0.5b	(/.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))))))
	0.4b	(.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))))) (cbrt.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (.f32 2 (.f32 uy (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 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))

Compiler

Compiled 17205 to 9698 computations (43.6% saved)

localize249.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f32 uy (PI.f32))
✓	0.4b	(.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (cbrt.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (cbrt.f32 (.f32 2 (*.f32 uy (PI.f32))))))))
✓	0.4b	(.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (cbrt.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))))))
✓	0.5b	(.f32 (cbrt.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (cbrt.f32 (.f32 2 (*.f32 uy (PI.f32))))))

series5.1s (18.1%)

Counts

3 → 36

Calls

3 calls:

1.7s

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

1.7s

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

1.7s

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

rewrite76.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary32`
26×	`cbrt-prod_binary32`
22×	`add-sqr-sqrt_binary32`
21×	`pow1/3_binary32`
19×	`add-exp-log_binary32`

Counts

3 → 97

Calls

3 calls:

24.0ms

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

20.0ms

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

14.0ms

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

simplify311.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

406×	`exp-prod_binary32`
389×	`*-commutative_binary32`
336×	`fma-def_binary32`
273×	`fma-neg_binary32`
222×	`sqr-pow_binary32`

Counts

133 → 151

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	173	4352
1	395	3633
2	1083	2819
3	2078	2604
4	4382	2514
5	4912	2514
6	4992	2514
7	4852	2514

prune1.4s (5.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	261	0	261
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	261	10	271

Error

0.0b

Counts

271 → 10

Alt Table

Status	Error	Program
	0.9b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (.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 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))))
	2.9b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))
✓	0.4b	(.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (cbrt.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))))))) (cbrt.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
	12.5b	(.f32 (.f32 (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))) (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))))) (cbrt.f32 (.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (.f32 8 (pow.f32 (fma.f32 maxCos (.f32 ux ux) ux) 3)) (pow.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) 3))) (sqrt.f32 (fma.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))) (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (*.f32 ux ux) ux)))))))
	0.9b	(.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.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)))))))
	0.9b	(.f32 (log.f32 (exp.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
	5.5b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))))
	0.5b	(/.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))))))
	0.4b	(.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))))) (cbrt.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (cbrt.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (.f32 2 (.f32 uy (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 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))

Compiler

Compiled 18059 to 9903 computations (45.2% saved)

regimes11.6s (40.7%)

Accuracy

Total 0.3b remaining (74.8%)

Threshold costs 0.3b (74.8%)

Counts

322 → 1

Compiler

Compiled 181148 to 121253 computations (33.1% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`*-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	25	71
1	38	71
2	46	71
3	67	71
4	86	71
5	98	71
6	105	71
7	107	71
8	105	71

end1.0ms (0%)

Compiler: Compiled 48 to 30 computations (37.5% saved)

sample2.7s (9.5%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
294.0ms	8000×	pre	128	true

Compiler

Compiled 754 to 475 computations (37% saved)

Details

analyze1.1s (4%)

sample141.0ms (0.5%)

simplify71.0ms (0.2%)

prune5.0ms (0%)

localize57.0ms (0.2%)

series436.0ms (1.5%)

rewrite14.0ms (0%)

simplify146.0ms (0.5%)

prune387.0ms (1.4%)

localize76.0ms (0.3%)

series342.0ms (1.2%)

rewrite28.0ms (0.1%)

simplify209.0ms (0.7%)

prune929.0ms (3.3%)

localize176.0ms (0.6%)

series1.3s (4.6%)

rewrite74.0ms (0.3%)

simplify331.0ms (1.2%)

prune1.1s (3.8%)

localize249.0ms (0.9%)

series5.1s (18.1%)

rewrite76.0ms (0.3%)

simplify311.0ms (1.1%)

prune1.4s (5.1%)

regimes11.6s (40.7%)

simplify5.0ms (0%)

end1.0ms (0%)

sample2.7s (9.5%)

Profiling