Details

analyze375.0ms (4.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 37 to 28 computations (24.3% saved)

sample2.0s (23.9%)

Results

1.9s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 88 to 67 computations (23.9% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`sub-neg_binary32`
7×	`+-commutative_binary32`
6×	`fma-def_binary32`
4×	`*-commutative_binary32`
4×	`div-sub_binary32`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.4b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))

Compiler

Compiled 42 to 33 computations (21.4% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
✓	0.2b	(/.f32 u1 (-.f32 1 u1))
✓	0.2b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
✓	0.3b	(*.f32 314159265359/50000000000 u2)

series41.0ms (0.5%)

Counts

4 → 40

Calls

4 calls:

27.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
10.0ms	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
2.0ms	(/.f32 u1 (-.f32 1 u1))
2.0ms	(*.f32 314159265359/50000000000 u2)

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary32`
69×	`*-un-lft-identity_binary32`
56×	`times-frac_binary32`
50×	`sqrt-prod_binary32`
39×	`add-cube-cbrt_binary32`

Counts

4 → 148

Calls

4 calls:

11.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
5.0ms	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
5.0ms	(/.f32 u1 (-.f32 1 u1))
3.0ms	(*.f32 314159265359/50000000000 u2)

simplify118.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

595×	`associate-/r*_binary32`
481×	`fma-def_binary32`
401×	`times-frac_binary32`
261×	`associate-/l*_binary32`
204×	`fma-neg_binary32`

Counts

188 → 226

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	289	3681
1	635	3497
2	1868	3373
3	4856	3373
4	4924	3373

prune330.0ms (4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	215	11	226
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	216	11	227

Error

0.0b

Counts

227 → 11

Alt Table

Status	Error	Program
	0.5b	(.f32 (.f32 (sqrt.f32 (/.f32 1 (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (sqrt.f32 (/.f32 u1 (cbrt.f32 (-.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	0.5b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))))
	0.5b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (.f32 u1 u1)))) (sqrt.f32 (+.f32 u1 1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	2.3b	(-.f32 (+.f32 (.f32 9740909103402808085817682884085781839780052161/150000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 4) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (+.f32 (.f32 98696044010906577398881/5000000000000000000000 (.f32 (pow.f32 u2 2) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 961389193575684075633145058384385882649239799132134631991269883031841/11250000000000000000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 6) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))))
	0.5b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
	6.5b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
▶	0.4b	(.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	2.1b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2)))) (.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))))
	0.4b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (.f32 (cbrt.f32 u1) (cbrt.f32 u1)) 1)) (.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2))))

Compiler

Compiled 5285 to 3883 computations (26.5% saved)

localize38.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
✓	0.2b	(log1p.f32 (/.f32 u1 (-.f32 1 u1)))
✓	0.3b	(expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))
	0.3b	(*.f32 314159265359/50000000000 u2)

series32.0ms (0.4%)

Counts

3 → 44

Calls

3 calls:

26.0ms	(.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
3.0ms	(log1p.f32 (/.f32 u1 (-.f32 1 u1)))
2.0ms	(expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary32`
6×	`associate-l_binary32`
6×	`*-un-lft-identity_binary32`
6×	`add-cube-cbrt_binary32`
5×	`add-cbrt-cube_binary32`

Counts

3 → 46

Calls

3 calls:

4.0ms	(.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
0.0ms	(log1p.f32 (/.f32 u1 (-.f32 1 u1)))
0.0ms	(expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))

simplify85.0ms (1%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-neg_binary32`
451×	`fma-def_binary32`
337×	`associate-l_binary32`
293×	`associate-r_binary32`
254×	`associate-+l+_binary32`

Counts

90 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	1955
1	424	1792
2	1304	1668
3	4595	1668
4	5098	1668

prune173.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	141	10	151

Error

0.0b

Counts

151 → 10

Alt Table

Status	Error	Program
	0.5b	(.f32 (.f32 (sqrt.f32 (/.f32 1 (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (sqrt.f32 (/.f32 u1 (cbrt.f32 (-.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	0.5b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (.f32 u1 u1)))) (sqrt.f32 (+.f32 u1 1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	0.5b	(.f32 (.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (.f32 (cbrt.f32 u1) (cbrt.f32 u1)) 1)) (.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2))))
	6.5b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
▶	0.4b	(.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
	2.1b	(.f32 (sqrt.f32 (.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))))) (.f32 (.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (cos.f32 (.f32 314159265359/50000000000 u2))) (cos.f32 (.f32 314159265359/50000000000 u2)))))
	0.5b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))))

Compiler

Compiled 3476 to 2737 computations (21.3% saved)

localize49.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(log1p.f32 (/.f32 u1 (-.f32 1 u1)))
	0.3b	(expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))
✓	0.3b	(*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2))
✓	0.5b	(.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))

series21.0ms (0.3%)

Counts

2 → 8

Calls

2 calls:

12.0ms	(.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))
9.0ms	(*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`pow1_binary32`
38×	`pow-prod-down_binary32`
24×	`add-sqr-sqrt_binary32`
18×	`sqrt-pow1_binary32`
18×	`pow1/2_binary32`

Counts

2 → 81

Calls

2 calls:

12.0ms	(.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))
5.0ms	(*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2))

simplify88.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

792×	`unswap-sqr_binary32`
555×	`fma-def_binary32`
296×	`associate-*r/_binary32`
246×	`associate-*l/_binary32`
214×	`*-commutative_binary32`

Counts

89 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	73	617
1	141	567
2	425	543
3	654	543
4	961	543
5	1687	543
6	4034	543
7	4995	543
8	4982	543

prune316.0ms (3.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	200	4	204
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	202	12	214

Error

0.0b

Counts

214 → 12

Alt Table

Status	Error	Program
	1.3b	(.f32 (sqrt.f32 (exp.f32 (log.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
	2.1b	(.f32 (sqrt.f32 (.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	7.8b	(.f32 (sqrt.f32 u1) (cos.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
	0.5b	(.f32 (.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (.f32 (cbrt.f32 u1) (cbrt.f32 u1)) 1)) (.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2))))
	0.5b	(.f32 (sqrt.f32 (expm1.f32 (.f32 (sqrt.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))))) (cos.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
	6.5b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	1.6b	(.f32 (sqrt.f32 (expm1.f32 (fma.f32 (pow.f32 u1 3) 1/3 (fma.f32 (.f32 u1 u1) 1/2 (fma.f32 (pow.f32 u1 4) 1/4 u1))))) (cos.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
	0.5b	(.f32 (.f32 (sqrt.f32 (/.f32 1 (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (sqrt.f32 (/.f32 u1 (cbrt.f32 (-.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
▶	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))))) (.f32 (.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (cos.f32 (.f32 314159265359/50000000000 u2))) (cos.f32 (.f32 314159265359/50000000000 u2)))))
	0.5b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))))

Compiler

Compiled 5708 to 4238 computations (25.8% saved)

localize61.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))
	0.3b	(*.f32 314159265359/50000000000 u2)
✓	0.3b	(.f32 (.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))))
✓	0.5b	(*.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))))

series18.0ms (0.2%)

Counts

2 → 20

Calls

2 calls:

13.0ms

(*.f32 (*.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))))

4.0ms

(*.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`pow1_binary32`
33×	`add-sqr-sqrt_binary32`
31×	`pow-prod-up_binary32`
29×	`sqrt-pow1_binary32`
29×	`pow1/2_binary32`

Counts

2 → 104

Calls

2 calls:

10.0ms

(*.f32 (*.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))))

5.0ms

(*.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))))

simplify78.0ms (1%)

Algorithm

1×	egg-herbie

Rules

492×	`fma-neg_binary32`
382×	`associate-l_binary32`
315×	`associate-/r*_binary32`
293×	`associate-r_binary32`
272×	`fma-def_binary32`

Counts

124 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	1842
1	373	1454
2	1222	1396
3	4592	1396
4	4964	1396

prune612.0ms (7.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	314	2	316
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	315	13	328

Error

0.0b

Counts

328 → 13

Alt Table

Status	Error	Program
	1.3b	(.f32 (sqrt.f32 (exp.f32 (log.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
	2.1b	(.f32 (sqrt.f32 (.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	7.8b	(.f32 (sqrt.f32 u1) (cos.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
	0.5b	(.f32 (.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (.f32 (cbrt.f32 u1) (cbrt.f32 u1)) 1)) (.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2))))
	0.5b	(.f32 (sqrt.f32 (expm1.f32 (.f32 (sqrt.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))))) (cos.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
	6.5b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	0.3b	(cbrt.f32 (.f32 (sqrt.f32 (pow.f32 (/.f32 u1 (-.f32 1 u1)) 3)) (.f32 (.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (cos.f32 (.f32 314159265359/50000000000 u2))) (cos.f32 (.f32 314159265359/50000000000 u2)))))
	0.5b	(.f32 (.f32 (sqrt.f32 (/.f32 1 (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (sqrt.f32 (/.f32 u1 (cbrt.f32 (-.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
✓	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))))) (.f32 (.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (cos.f32 (.f32 314159265359/50000000000 u2))) (cos.f32 (.f32 314159265359/50000000000 u2)))))
	0.5b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))))
	1.0b	(cbrt.f32 (.f32 (.f32 (exp.f32 (log.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (expm1.f32 (log1p.f32 (/.f32 u1 (-.f32 1 u1)))))) (.f32 (.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (cos.f32 (.f32 314159265359/50000000000 u2))) (cos.f32 (*.f32 314159265359/50000000000 u2)))))

Compiler

Compiled 14248 to 11256 computations (21% saved)

regimes3.5s (42.2%)

Accuracy

Total 0.2b remaining (74.4%)

Threshold costs 0.2b (74.4%)

Counts

278 → 1

Compiler

Compiled 67499 to 53296 computations (21% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`
2×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`neg-sub0_binary32`
1×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	22	28
2	26	28
3	28	28
4	29	28
5	28	28

end235.0ms (2.8%)

Compiler: Compiled 411 to 328 computations (20.2% saved)

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

Details

analyze375.0ms (4.5%)

sample2.0s (23.9%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize27.0ms (0.3%)

series41.0ms (0.5%)

rewrite33.0ms (0.4%)

simplify118.0ms (1.4%)

prune330.0ms (4%)

localize38.0ms (0.5%)

series32.0ms (0.4%)

rewrite7.0ms (0.1%)

simplify85.0ms (1%)

prune173.0ms (2.1%)

localize49.0ms (0.6%)

series21.0ms (0.3%)

rewrite22.0ms (0.3%)

simplify88.0ms (1.1%)

prune316.0ms (3.8%)

localize61.0ms (0.7%)

series18.0ms (0.2%)

rewrite26.0ms (0.3%)

simplify78.0ms (1%)

prune612.0ms (7.4%)

regimes3.5s (42.2%)

simplify3.0ms (0%)

end235.0ms (2.8%)

Profiling

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17