Details

analyze574.0ms (5.5%)

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)

sample2.3s (22.2%)

Results

2.2s

8256×

body

128

valid

Compiler

Compiled 130 to 94 computations (27.7% saved)

simplify52.0ms (0.5%)

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

14.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.2b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
	14.3b	(.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

▶

14.2b

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

14.3b

(*.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)

localize96.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.4b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
✓	13.8b	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))

series67.0ms (0.6%)

Counts

4 → 72

Calls

4 calls:

48.0ms	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))
13.0ms	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
3.0ms	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))
3.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow1_binary32`
14×	`add-sqr-sqrt_binary32`
12×	`*-un-lft-identity_binary32`
11×	`add-cbrt-cube_binary32`
11×	`add-exp-log_binary32`

Counts

4 → 90

Calls

4 calls:

12.0ms	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
4.0ms	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))
4.0ms	(.f32 (.f32 uy 2) (PI.f32))
1.0ms	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))

simplify113.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

422×	`cancel-sign-sub-inv_binary32`
357×	`associate-+l+_binary32`
251×	`associate-l_binary32`
230×	`associate-r_binary32`
230×	`exp-prod_binary32`

Counts

162 → 180

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	4124
1	594	3285
2	2306	2943
3	4826	2931
4	4993	2931

prune157.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	171	9	180
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	172	10	182

Error

0.3b

Counts

182 → 10

Alt Table

Status	Error	Program
	14.2b	(.f32 (cos.f32 (.f32 (.f32 (.f32 uy 2) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))
	14.3b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (log.f32 (exp.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))))
	14.2b	(.f32 (cos.f32 (expm1.f32 (log1p.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 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	14.3b	(.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)))
	0.4b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (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)))))))
	0.4b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (+.f32 2 (.f32 ux (+.f32 maxCos -1))) (-.f32 ux (.f32 maxCos ux)))))
	14.3b	(.f32 (.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (cbrt.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))))))
	7.0b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	13.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (exp.f32 (.f32 2 (log1p.f32 (*.f32 ux (+.f32 maxCos -1))))))))

Compiler

Compiled 6407 to 4100 computations (36% saved)

localize71.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.2b	(.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos))))
✓	0.2b	(.f32 maxCos (.f32 ux ux))
	0.4b	(.f32 (.f32 uy 2) (PI.f32))

series15.0ms (0.1%)

Counts

2 → 48

Calls

2 calls:

8.0ms	(.f32 maxCos (.f32 ux ux))
7.0ms	(.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos))))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary32`
21×	`*-un-lft-identity_binary32`
19×	`add-cube-cbrt_binary32`
18×	`prod-diff_binary32`
13×	`distribute-lft-in_binary32`

Counts

2 → 71

Calls

2 calls:

21.0ms	(.f32 maxCos (.f32 ux ux))
7.0ms	(.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos))))

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

348×	`fma-def_binary32`
292×	`fma-neg_binary32`
272×	`*-commutative_binary32`
261×	`exp-prod_binary32`
241×	`distribute-rgt-in_binary32`

Counts

119 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	2073
1	286	1426
2	907	1298
3	2395	1244
4	4648	1244
5	4826	1244

prune289.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	145	9	154
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	152	12	164

Error

0.1b

Counts

164 → 12

Alt Table

Status	Error	Program
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 (.f32 ux (+.f32 (sqrt.f32 (fma.f32 maxCos 2 ux)) (sqrt.f32 2))) (-.f32 (sqrt.f32 2) (sqrt.f32 (+.f32 ux (.f32 2 maxCos))))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	1.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (exp.f32 (log.f32 (.f32 ux (-.f32 2 (fma.f32 maxCos 2 ux))))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
▶	0.4b	(.f32 (log1p.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (+.f32 (.f32 (fma.f32 (sqrt.f32 2) (sqrt.f32 2) (neg.f32 (.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos)))))) ux) (.f32 (fma.f32 (neg.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos)))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos))))) ux)) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	0.9b	(.f32 (log.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	0.7b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (+.f32 (.f32 (fma.f32 (.f32 (cbrt.f32 2) (cbrt.f32 2)) (cbrt.f32 2) (neg.f32 (.f32 (cbrt.f32 (+.f32 ux (.f32 2 maxCos))) (.f32 (cbrt.f32 (+.f32 ux (.f32 2 maxCos))) (cbrt.f32 (+.f32 ux (.f32 2 maxCos))))))) ux) (.f32 (fma.f32 (neg.f32 (cbrt.f32 (+.f32 ux (.f32 2 maxCos)))) (.f32 (cbrt.f32 (+.f32 ux (.f32 2 maxCos))) (cbrt.f32 (+.f32 ux (.f32 2 maxCos)))) (.f32 (cbrt.f32 (+.f32 ux (.f32 2 maxCos))) (.f32 (cbrt.f32 (+.f32 ux (.f32 2 maxCos))) (cbrt.f32 (+.f32 ux (.f32 2 maxCos)))))) ux)) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	14.2b	(.f32 (cos.f32 (.f32 (.f32 (.f32 uy 2) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))
	0.4b	(.f32 (expm1.f32 (log1p.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	13.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (exp.f32 (.f32 2 (log1p.f32 (*.f32 ux (+.f32 maxCos -1))))))))
	0.5b	(.f32 (.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	14.2b	(.f32 (cos.f32 (expm1.f32 (log1p.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))))))

Compiler

Compiled 6770 to 4355 computations (35.7% saved)

localize81.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos))))
	0.2b	(.f32 maxCos (.f32 ux ux))
✓	0.4b	(*.f32 uy (PI.f32))
✓	0.6b	(expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))

series14.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

11.0ms	(expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))
2.0ms	(*.f32 uy (PI.f32))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary32`
4×	`*-un-lft-identity_binary32`
4×	`add-cube-cbrt_binary32`
4×	`add-cbrt-cube_binary32`
4×	`add-exp-log_binary32`

Counts

2 → 31

Calls

2 calls:

3.0ms	(*.f32 uy (PI.f32))
0.0ms	(expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

532×	`fma-neg_binary32`
455×	`unswap-sqr_binary32`
382×	`associate-l_binary32`
346×	`associate-r_binary32`
314×	`distribute-rgt-neg-in_binary32`

Counts

55 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	637
1	170	582
2	489	575
3	1807	561
4	4552	561
5	4895	561
6	4981	561

prune365.0ms (3.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	154	3	157
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	156	13	169

Error

0.1b

Counts

169 → 13

Alt Table

Status	Error	Program
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 (.f32 ux (+.f32 (sqrt.f32 (fma.f32 maxCos 2 ux)) (sqrt.f32 2))) (-.f32 (sqrt.f32 2) (sqrt.f32 (+.f32 ux (.f32 2 maxCos))))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	1.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (exp.f32 (log.f32 (.f32 ux (-.f32 2 (fma.f32 maxCos 2 ux))))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	0.7b	(.f32 (log1p.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (+.f32 (+.f32 (.f32 ux (fma.f32 (.f32 (cbrt.f32 2) (cbrt.f32 2)) (cbrt.f32 2) (neg.f32 (.f32 (+.f32 ux (.f32 2 maxCos)) 1)))) (.f32 ux (fma.f32 (neg.f32 (+.f32 ux (.f32 2 maxCos))) 1 (.f32 (+.f32 ux (.f32 2 maxCos)) 1)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (+.f32 (.f32 (fma.f32 (sqrt.f32 2) (sqrt.f32 2) (neg.f32 (.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos)))))) ux) (.f32 (fma.f32 (neg.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos)))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos))))) ux)) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	14.2b	(.f32 (cos.f32 (.f32 (.f32 (.f32 uy 2) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))
	0.4b	(.f32 (expm1.f32 (log1p.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	13.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (exp.f32 (.f32 2 (log1p.f32 (*.f32 ux (+.f32 maxCos -1))))))))
	1.0b	(.f32 (log1p.f32 (.f32 (.f32 (cbrt.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (cbrt.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32))))))) (cbrt.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
▶	0.4b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	0.5b	(.f32 (.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	0.9b	(.f32 (log.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	14.2b	(.f32 (cos.f32 (expm1.f32 (log1p.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))))))

Compiler

Compiled 7198 to 4590 computations (36.2% saved)

localize165.0ms (1.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos))))
	0.2b	(.f32 maxCos (.f32 ux ux))
	0.4b	(*.f32 uy (PI.f32))
	0.6b	(expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))

prune374.0ms (3.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	150	7	157
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	156	14	170

Error

0.1b

Counts

170 → 14

Alt Table

Status	Error	Program
	0.5b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))) (sqrt.f32 (+.f32 (.f32 (.f32 ux (sqrt.f32 (-.f32 2 (fma.f32 maxCos 2 ux)))) (sqrt.f32 (-.f32 2 (+.f32 ux (.f32 2 maxCos))))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	0.5b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 (.f32 uy (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32))))))))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	0.7b	(.f32 (log1p.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (+.f32 (+.f32 (.f32 ux (fma.f32 (.f32 (cbrt.f32 2) (cbrt.f32 2)) (cbrt.f32 2) (neg.f32 (.f32 (+.f32 ux (.f32 2 maxCos)) 1)))) (.f32 ux (fma.f32 (neg.f32 (+.f32 ux (.f32 2 maxCos))) 1 (.f32 (+.f32 ux (.f32 2 maxCos)) 1)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (+.f32 (.f32 (fma.f32 (sqrt.f32 2) (sqrt.f32 2) (neg.f32 (.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos)))))) ux) (.f32 (fma.f32 (neg.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos)))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (.f32 (sqrt.f32 (+.f32 ux (.f32 2 maxCos))) (sqrt.f32 (+.f32 ux (.f32 2 maxCos))))) ux)) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	1.1b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))) (sqrt.f32 (+.f32 (exp.f32 (log.f32 (.f32 ux (-.f32 2 (fma.f32 maxCos 2 ux))))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	14.2b	(.f32 (cos.f32 (expm1.f32 (log1p.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))))))
	1.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (exp.f32 (log.f32 (.f32 ux (-.f32 2 (fma.f32 maxCos 2 ux))))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	1.0b	(.f32 (log1p.f32 (.f32 (.f32 (cbrt.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (cbrt.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32))))))) (cbrt.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	0.5b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))) (sqrt.f32 (+.f32 (.f32 (.f32 ux (+.f32 (sqrt.f32 (fma.f32 maxCos 2 ux)) (sqrt.f32 2))) (-.f32 (sqrt.f32 2) (sqrt.f32 (+.f32 ux (.f32 2 maxCos))))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	1.0b	(.f32 (log1p.f32 (log.f32 (exp.f32 (.f32 (.f32 (cbrt.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) uy))))) (cbrt.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) uy)))))) (cbrt.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) uy))))))))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	0.9b	(.f32 (log.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	14.2b	(.f32 (cos.f32 (.f32 (.f32 (.f32 uy 2) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))
	0.5b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))) (sqrt.f32 (+.f32 (+.f32 (.f32 ux (fma.f32 (sqrt.f32 2) (sqrt.f32 2) (neg.f32 (.f32 (+.f32 ux (.f32 2 maxCos)) 1)))) (.f32 ux (fma.f32 (neg.f32 (+.f32 ux (.f32 2 maxCos))) 1 (.f32 (+.f32 ux (.f32 2 maxCos)) 1)))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	13.8b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))) (sqrt.f32 (+.f32 (log.f32 (exp.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))

Compiler

Compiled 7090 to 4597 computations (35.2% saved)

regimes5.1s (48.9%)

Accuracy

Total 0.2b remaining (73%)

Threshold costs 0.2b (73%)

Counts

304 → 1

Compiler

Compiled 131316 to 98141 computations (25.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary32`
10×	`+-commutative_binary32`
8×	`sub-neg_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	48
1	36	48
2	48	48
3	65	48
4	78	48
5	84	48
6	87	48
7	88	48
8	87	48

end349.0ms (3.3%)

Compiler: Compiled 686 to 513 computations (25.2% saved)

Details

analyze574.0ms (5.5%)

sample2.3s (22.2%)

simplify52.0ms (0.5%)

prune5.0ms (0%)

localize96.0ms (0.9%)

series67.0ms (0.6%)

rewrite25.0ms (0.2%)

simplify113.0ms (1.1%)

prune157.0ms (1.5%)

localize71.0ms (0.7%)

series15.0ms (0.1%)

rewrite32.0ms (0.3%)

simplify86.0ms (0.8%)

prune289.0ms (2.8%)

localize81.0ms (0.8%)

series14.0ms (0.1%)

rewrite4.0ms (0%)

simplify83.0ms (0.8%)

prune365.0ms (3.5%)

localize165.0ms (1.6%)

prune374.0ms (3.6%)

regimes5.1s (48.9%)

simplify4.0ms (0%)

end349.0ms (3.3%)

Profiling