Details

analyze1.1s (7.3%)

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)

sample91.0ms (0.6%)

Algorithm

1×

intervals

Results

46.0ms	256×	body	128	valid
14.0ms	256×	pre	128	true

Compiler

Compiled 82 to 60 computations (26.8% saved)

simplify73.0ms (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

prune10.0ms (0.1%)

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

12.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	12.7b	(.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))))))
	12.7b	(.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

▶

12.7b

(*.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))))))

12.7b

(*.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)

localize135.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.3b	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
✓	12.2b	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))

series50.0ms (0.3%)

Counts

4 → 72

Calls

4 calls:

27.0ms	(-.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)))
5.0ms	(.f32 (.f32 uy 2) (PI.f32))
4.0ms	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))

rewrite35.0ms (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:

16.0ms	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
6.0ms	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))
5.0ms	(.f32 (.f32 uy 2) (PI.f32))
2.0ms	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))

simplify150.0ms (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

prune229.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	168	12	180
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	170	12	182

Error

0.2b

Counts

182 → 12

Alt Table

Status	Error	Program
	12.7b	(.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))))))
	13.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (sqrt.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))) (pow.f32 (sqrt.f32 (fma.f32 maxCos ux (-.f32 1 ux))) 3)))))
	12.7b	(.f32 (log.f32 (exp.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))))))
	12.0b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (-.f32 (+.f32 (pow.f32 ux 2) (+.f32 1 (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (.f32 maxCos ux))))) (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (*.f32 2 ux))))))
	12.7b	(.f32 (expm1.f32 (log1p.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))))))
	12.7b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (/.f32 (-.f32 (pow.f32 1 3) (pow.f32 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))) 3)) (+.f32 (.f32 1 1) (+.f32 (.f32 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))) (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos)))) (.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos)))))))))
	13.8b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (pow.f32 (cbrt.f32 (fma.f32 maxCos ux (-.f32 1 ux))) 4) (*.f32 (cbrt.f32 (fma.f32 maxCos ux (-.f32 1 ux))) (cbrt.f32 (fma.f32 maxCos ux (-.f32 1 ux))))))))
	2.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))
	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)))))
	13.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (-.f32 1 (.f32 (-.f32 1 ux) (fma.f32 maxCos ux (-.f32 1 ux)))) (.f32 (.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)))))
	12.7b	(.f32 (cos.f32 (.f32 (.f32 (.f32 uy 2) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))

Compiler

Compiled 6707 to 4296 computations (35.9% saved)

localize72.0ms (0.5%)

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))
	0.3b	(.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))))

rewrite19.0ms (0.1%)

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:

8.0ms	(.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos))))
5.0ms	(.f32 maxCos (.f32 ux ux))

simplify93.0ms (0.6%)

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

prune449.0ms (3.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	146	8	154
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	155	11	166

Error

0.1b

Counts

166 → 11

Alt Table

Status	Error	Program
	0.4b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.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)))))
	12.7b	(.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))))))
	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 (+.f32 ux (.f32 2 maxCos)) 1))) ux) (.f32 (fma.f32 (neg.f32 (+.f32 ux (.f32 2 maxCos))) 1 (.f32 (+.f32 ux (.f32 2 maxCos)) 1)) ux)) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
	0.4b	(.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)))))
	13.2b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (log.f32 (pow.f32 (exp.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)))))
	12.7b	(.f32 (log.f32 (exp.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))))))
	13.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (-.f32 1 (.f32 (-.f32 1 ux) (fma.f32 maxCos ux (-.f32 1 ux)))) (.f32 (.f32 ux maxCos) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))
	0.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (log.f32 (exp.f32 (.f32 maxCos (.f32 ux ux)))) (-.f32 2 maxCos)))))

Compiler

Compiled 6634 to 4251 computations (35.9% saved)

localize192.0ms (1.3%)

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))
✓	0.3b	(*.f32 uy (PI.f32))
✓	0.6b	(expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))

series18.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

13.0ms	(expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))
5.0ms	(*.f32 uy (PI.f32))

rewrite8.0ms (0.1%)

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:

5.0ms	(*.f32 uy (PI.f32))
1.0ms	(expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))

simplify121.0ms (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

prune635.0ms (4.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	154	3	157
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	157	11	168

Error

0.1b

Counts

168 → 11

Alt Table

Status	Error	Program
	13.2b	(.f32 (log1p.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (+.f32 (log.f32 (pow.f32 (exp.f32 ux) (-.f32 2 (fma.f32 maxCos 2 ux)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
▶	0.4b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	12.7b	(.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))))))
	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 (+.f32 ux (.f32 2 maxCos)) 1))) ux) (.f32 (fma.f32 (neg.f32 (+.f32 ux (.f32 2 maxCos))) 1 (.f32 (+.f32 ux (.f32 2 maxCos)) 1)) ux)) (.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)))))
	12.7b	(.f32 (log.f32 (exp.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))))))
	13.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (-.f32 1 (.f32 (-.f32 1 ux) (fma.f32 maxCos ux (-.f32 1 ux)))) (.f32 (.f32 ux maxCos) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))
	0.9b	(.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)))))
	1.7b	(.f32 (log1p.f32 (exp.f32 (log.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)))))
	0.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (log.f32 (exp.f32 (.f32 maxCos (.f32 ux ux)))) (-.f32 2 maxCos)))))
	0.4b	(.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)))))

Compiler

Compiled 7078 to 4494 computations (36.5% saved)

localize157.0ms (1.1%)

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 (.f32 2 uy) (sqrt.f32 (PI.f32)))
✓	0.4b	(.f32 (.f32 (*.f32 2 uy) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))

series17.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

11.0ms	(.f32 (.f32 2 uy) (sqrt.f32 (PI.f32)))
5.0ms	(.f32 (.f32 (*.f32 2 uy) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary32`
16×	`add-exp-log_binary32`
16×	`pow1_binary32`
12×	`associate-r_binary32`
9×	`cbrt-unprod_binary32`

Counts

2 → 49

Calls

2 calls:

12.0ms	(.f32 (.f32 (*.f32 2 uy) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
8.0ms	(.f32 (.f32 2 uy) (sqrt.f32 (PI.f32)))

simplify111.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

443×	`distribute-rgt-in_binary32`
379×	`distribute-lft-in_binary32`
362×	`*-commutative_binary32`
247×	`associate-/l/_binary32`
231×	`associate-/l*_binary32`

Counts

73 → 68

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	72	858
1	170	772
2	681	772
3	952	772
4	1203	772
5	1721	772
6	4587	772
7	4940	772

prune623.0ms (4.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	168	11	179

Error

0.1b

Counts

179 → 11

Alt Table

Status	Error	Program
	13.2b	(.f32 (log1p.f32 (expm1.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (+.f32 (log.f32 (pow.f32 (exp.f32 ux) (-.f32 2 (fma.f32 maxCos 2 ux)))) (.f32 (.f32 maxCos (.f32 ux ux)) (-.f32 2 maxCos)))))
✓	0.4b	(.f32 (cos.f32 (.f32 (.f32 (.f32 2 uy) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (.f32 maxCos (*.f32 ux ux)) (-.f32 2 maxCos)))))
	12.7b	(.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))))))
	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 (+.f32 ux (.f32 2 maxCos)) 1))) ux) (.f32 (fma.f32 (neg.f32 (+.f32 ux (.f32 2 maxCos))) 1 (.f32 (+.f32 ux (.f32 2 maxCos)) 1)) ux)) (.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)))))
	12.7b	(.f32 (log.f32 (exp.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))))))
	13.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (-.f32 1 (.f32 (-.f32 1 ux) (fma.f32 maxCos ux (-.f32 1 ux)))) (.f32 (.f32 ux maxCos) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))
	0.9b	(.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)))))
	1.7b	(.f32 (log1p.f32 (exp.f32 (log.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)))))
	0.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 ux (-.f32 2 (+.f32 ux (.f32 2 maxCos)))) (.f32 (log.f32 (exp.f32 (.f32 maxCos (.f32 ux ux)))) (-.f32 2 maxCos)))))
	0.4b	(.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)))))

Compiler

Compiled 7314 to 4299 computations (41.2% saved)

regimes6.8s (46.7%)

Accuracy

Total 0.2b remaining (67.1%)

Threshold costs 0.2b (67.1%)

Counts

286 → 1

Compiler

Compiled 124650 to 91713 computations (26.4% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary32`
13×	`+-commutative_binary32`
10×	`sub-neg_binary32`
9×	`neg-sub0_binary32`
9×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	57
1	37	57
2	46	57
3	58	57
4	81	57
5	97	57
6	107	57
7	113	57
8	115	57
9	114	57

end1.0ms (0%)

Compiler: Compiled 40 to 31 computations (22.5% saved)

sample3.3s (22.9%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
321.0ms	8000×	pre	128	true

Compiler

Compiled 554 to 408 computations (26.4% saved)

Details

analyze1.1s (7.3%)

sample91.0ms (0.6%)

simplify73.0ms (0.5%)

prune10.0ms (0.1%)

localize135.0ms (0.9%)

series50.0ms (0.3%)

rewrite35.0ms (0.2%)

simplify150.0ms (1%)

prune229.0ms (1.6%)

localize72.0ms (0.5%)

series15.0ms (0.1%)

rewrite19.0ms (0.1%)

simplify93.0ms (0.6%)

prune449.0ms (3.1%)

localize192.0ms (1.3%)

series18.0ms (0.1%)

rewrite8.0ms (0.1%)

simplify121.0ms (0.8%)

prune635.0ms (4.4%)

localize157.0ms (1.1%)

series17.0ms (0.1%)

rewrite27.0ms (0.2%)

simplify111.0ms (0.8%)

prune623.0ms (4.3%)

regimes6.8s (46.7%)

simplify5.0ms (0%)

end1.0ms (0%)

sample3.3s (22.9%)

Profiling