Details

analyze385.0ms (3.3%)

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 (16.8%)

Results

1.9s	8256×	body	128	valid
1.0ms	4×	body	128	invalid

Compiler

Compiled 88 to 67 computations (23.9% saved)

simplify8.0ms (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

0.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.6b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2)))

Compiler

Compiled 42 to 33 computations (21.4% saved)

localize29.0ms (0.2%)

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))
✓	0.4b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2)))
✓	0.4b	(*.f32 314159265359/50000000000 u2)

series41.0ms (0.3%)

Counts

4 → 32

Calls

4 calls:

24.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2)))
13.0ms	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
2.0ms	(/.f32 u1 (-.f32 1 u1))
1.0ms	(*.f32 314159265359/50000000000 u2)

rewrite37.0ms (0.3%)

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:

10.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2)))
5.0ms	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
4.0ms	(/.f32 u1 (-.f32 1 u1))
3.0ms	(*.f32 314159265359/50000000000 u2)

simplify143.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

595×	`associate-/r*_binary32`
533×	`fma-def_binary32`
401×	`times-frac_binary32`
260×	`associate-/l*_binary32`
231×	`fma-neg_binary32`

Counts

180 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	286	3573
1	636	3380
2	1887	3262
3	4911	3262
4	4959	3262

prune274.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	211	11	222
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	212	11	223

Error

0.0b

Counts

223 → 11

Alt Table

Status	Error	Program
	0.7b	(.f32 (sqrt.f32 (/.f32 (/.f32 u1 (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1)))) (cbrt.f32 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
	1.3b	(.f32 (sqrt.f32 (exp.f32 (-.f32 (log.f32 u1) (log.f32 (-.f32 1 u1))))) (sin.f32 (.f32 314159265359/50000000000 u2)))
▶	0.6b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2)))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2)))))
	0.7b	(.f32 (.f32 (fabs.f32 (cbrt.f32 u1)) (sqrt.f32 (/.f32 (cbrt.f32 u1) (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
	0.8b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
	1.5b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (sin.f32 (.f32 314159265359/50000000000 u2)))) (.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (sin.f32 (*.f32 314159265359/50000000000 u2)))))
	1.4b	(-.f32 (+.f32 (.f32 314159265359/50000000000 (.f32 u2 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 3060196847853821555298148281676017575122444629042460390799/37500000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 5) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))) (+.f32 (.f32 302029322777818351566783844332719832329455959975176141755859165754785028165295919/3937500000000000000000000000000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 7) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 31006276680305942139213528068663279/750000000000000000000000000000000 (.f32 (pow.f32 u2 3) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (cbrt.f32 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
	0.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 (.f32 (sin.f32 (.f32 314159265359/50000000000 u2)) (sin.f32 (.f32 314159265359/50000000000 u2))) (sin.f32 (.f32 314159265359/50000000000 u2)))))
	1.8b	(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (exp.f32 (+.f32 (log.f32 314159265359/50000000000) (log.f32 u2)))))

Compiler

Compiled 5174 to 3787 computations (26.8% saved)

localize35.0ms (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))
✓	0.3b	(.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2))
✓	0.4b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))

series47.0ms (0.4%)

Counts

2 → 32

Calls

2 calls:

39.0ms

(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))

8.0ms

(*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`associate-l_binary32`
32×	`add-sqr-sqrt_binary32`
29×	`sqrt-prod_binary32`
25×	`*-un-lft-identity_binary32`
19×	`times-frac_binary32`

Counts

2 → 70

Calls

2 calls:

13.0ms

(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))

6.0ms

(*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))

simplify81.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

493×	`fma-neg_binary32`
367×	`*-commutative_binary32`
334×	`fma-def_binary32`
299×	`associate-/r*_binary32`
259×	`unswap-sqr_binary32`

Counts

102 → 130

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	203	2099
1	462	1958
2	1379	1848
3	3597	1840
4	4911	1840

prune360.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	237	5	242
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	243	10	253

Error

0.0b

Counts

253 → 10

Alt Table

Status	Error	Program
	0.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 (.f32 (sin.f32 (.f32 314159265359/50000000000 u2)) (sin.f32 (.f32 314159265359/50000000000 u2))) (sin.f32 (.f32 314159265359/50000000000 u2)))))
	0.9b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (sin.f32 (.f32 u2 314159265359/50000000000))) (cbrt.f32 (sin.f32 (.f32 u2 314159265359/50000000000))))) (cbrt.f32 (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2)))))
▶	0.5b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (*.f32 u2 u2) u2))))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (-.f32 1 (sqrt.f32 u1)))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2)))))
	0.7b	(.f32 (.f32 (fabs.f32 (cbrt.f32 u1)) (sqrt.f32 (/.f32 (cbrt.f32 u1) (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
	0.8b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
	1.4b	(-.f32 (+.f32 (.f32 314159265359/50000000000 (.f32 u2 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 3060196847853821555298148281676017575122444629042460390799/37500000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 5) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))) (+.f32 (.f32 302029322777818351566783844332719832329455959975176141755859165754785028165295919/3937500000000000000000000000000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 7) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 31006276680305942139213528068663279/750000000000000000000000000000000 (.f32 (pow.f32 u2 3) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))))
	0.6b	(.f32 (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (cbrt.f32 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
	0.7b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (pow.f32 u1 3)))) (sqrt.f32 (+.f32 1 (fma.f32 u1 u1 u1)))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2))))

Compiler

Compiled 6355 to 4912 computations (22.7% saved)

localize67.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (.f32 u2 u2) u2)))
✓	0.2b	(.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (*.f32 u2 u2) u2))
✓	0.3b	(.f32 (.f32 u2 u2) u2)
✓	0.4b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (*.f32 u2 u2) u2))))))

series83.0ms (0.7%)

Counts

4 → 56

Calls

4 calls:

44.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (*.f32 u2 u2) u2))))))
20.0ms	(.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (.f32 u2 u2) u2)))
15.0ms	(.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (*.f32 u2 u2) u2))
3.0ms	(.f32 (.f32 u2 u2) u2)

rewrite212.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

776×	`pow1_binary32`
359×	`pow-prod-down_binary32`
262×	`pow-plus_binary32`
262×	`pow-prod-up_binary32`
221×	`add-cbrt-cube_binary32`

Counts

4 → 325

Calls

4 calls:

81.0ms	(.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (.f32 u2 u2) u2)))
29.0ms	(.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (*.f32 u2 u2) u2))
15.0ms	(.f32 (.f32 u2 u2) u2)
13.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (.f32 (*.f32 u2 u2) u2))))))

simplify228.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

383×	`fma-def_binary32`
327×	`fma-neg_binary32`
303×	`associate-l_binary32`
299×	`associate-/r*_binary32`
292×	`associate-r_binary32`

Counts

381 → 245

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	298	5093
1	576	4319
2	1968	4195
3	4683	4175
4	4906	4175

prune402.0ms (3.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	240	5	245
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	245	10	255

Error

0.0b

Counts

255 → 10

Alt Table

Status	Error	Program
	0.8b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
	0.5b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (sqrt.f32 (.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000)) (sqrt.f32 (.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000))))))
▶	0.5b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (expm1.f32 (log1p.f32 (.f32 (pow.f32 u2 3) (.f32 314159265359/50000000000 (sqrt.f32 314159265359/50000000000)))))))))
	0.5b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sin.f32 (cbrt.f32 (*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000))) (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1))))))
	1.4b	(-.f32 (+.f32 (.f32 314159265359/50000000000 (.f32 u2 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 3060196847853821555298148281676017575122444629042460390799/37500000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 5) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))) (+.f32 (.f32 302029322777818351566783844332719832329455959975176141755859165754785028165295919/3937500000000000000000000000000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 7) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 31006276680305942139213528068663279/750000000000000000000000000000000 (.f32 (pow.f32 u2 3) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))))
	0.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 (.f32 (sin.f32 (.f32 314159265359/50000000000 u2)) (sin.f32 (.f32 314159265359/50000000000 u2))) (sin.f32 (.f32 314159265359/50000000000 u2)))))
	0.9b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (sin.f32 (.f32 u2 314159265359/50000000000))) (cbrt.f32 (sin.f32 (.f32 u2 314159265359/50000000000))))) (cbrt.f32 (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2)))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (.f32 (sin.f32 (cbrt.f32 (*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000))) (sqrt.f32 (/.f32 (cbrt.f32 u1) (cbrt.f32 (-.f32 1 u1))))))
	0.6b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 (pow.f32 1 3) (pow.f32 u1 3)))) (.f32 (sin.f32 (cbrt.f32 (*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000))) (sqrt.f32 (+.f32 1 (fma.f32 u1 u1 u1)))))
	0.7b	(.f32 (.f32 (fabs.f32 (cbrt.f32 u1)) (sqrt.f32 (/.f32 (cbrt.f32 u1) (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2)))

Compiler

Compiled 9756 to 7673 computations (21.4% saved)

localize70.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 u1 (-.f32 1 u1))
✓	0.2b	(.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (expm1.f32 (log1p.f32 (.f32 (pow.f32 u2 3) (*.f32 314159265359/50000000000 (sqrt.f32 314159265359/50000000000))))))
✓	0.2b	(.f32 (pow.f32 u2 3) (.f32 314159265359/50000000000 (sqrt.f32 314159265359/50000000000)))
✓	0.4b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (expm1.f32 (log1p.f32 (.f32 (pow.f32 u2 3) (.f32 314159265359/50000000000 (sqrt.f32 314159265359/50000000000)))))))))

series94.0ms (0.8%)

Counts

3 → 44

Calls

3 calls:

70.0ms

(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (expm1.f32 (log1p.f32 (*.f32 (pow.f32 u2 3) (*.f32 314159265359/50000000000 (sqrt.f32 314159265359/50000000000)))))))))

17.0ms

(*.f32 (*.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (expm1.f32 (log1p.f32 (*.f32 (pow.f32 u2 3) (*.f32 314159265359/50000000000 (sqrt.f32 314159265359/50000000000))))))

6.0ms

(*.f32 (pow.f32 u2 3) (*.f32 314159265359/50000000000 (sqrt.f32 314159265359/50000000000)))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`associate-l_binary32`
36×	`add-sqr-sqrt_binary32`
28×	`*-un-lft-identity_binary32`
27×	`add-exp-log_binary32`
26×	`sqrt-prod_binary32`

Counts

3 → 102

Calls

3 calls:

14.0ms

(*.f32 (*.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (expm1.f32 (log1p.f32 (*.f32 (pow.f32 u2 3) (*.f32 314159265359/50000000000 (sqrt.f32 314159265359/50000000000))))))

11.0ms

(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (expm1.f32 (log1p.f32 (*.f32 (pow.f32 u2 3) (*.f32 314159265359/50000000000 (sqrt.f32 314159265359/50000000000)))))))))

7.0ms

(*.f32 (pow.f32 u2 3) (*.f32 314159265359/50000000000 (sqrt.f32 314159265359/50000000000)))

simplify128.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

395×	`fma-def_binary32`
343×	`associate-l_binary32`
327×	`associate-r_binary32`
299×	`associate-/r*_binary32`
233×	`log-prod_binary32`

Counts

146 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	280	4630
1	613	3217
2	2156	3065
3	4624	3051
4	4950	3051

prune447.0ms (3.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	237	10	247

Error

0.0b

Counts

247 → 10

Alt Table

Status	Error	Program
✓	0.5b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (expm1.f32 (log1p.f32 (.f32 (pow.f32 u2 3) (.f32 314159265359/50000000000 (sqrt.f32 314159265359/50000000000)))))))))
	0.5b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sin.f32 (cbrt.f32 (*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000))) (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1))))))
	1.4b	(-.f32 (+.f32 (.f32 314159265359/50000000000 (.f32 u2 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 3060196847853821555298148281676017575122444629042460390799/37500000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 5) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))) (+.f32 (.f32 302029322777818351566783844332719832329455959975176141755859165754785028165295919/3937500000000000000000000000000000000000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 7) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 31006276680305942139213528068663279/750000000000000000000000000000000 (.f32 (pow.f32 u2 3) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))))
	0.7b	(.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 314159265359/50000000000)) (sqrt.f32 314159265359/50000000000)) (expm1.f32 (log1p.f32 (.f32 (pow.f32 u2 3) (*.f32 314159265359/50000000000 (sqrt.f32 314159265359/50000000000))))))))))
	0.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 (.f32 (sin.f32 (.f32 314159265359/50000000000 u2)) (sin.f32 (.f32 314159265359/50000000000 u2))) (sin.f32 (.f32 314159265359/50000000000 u2)))))
	0.9b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (sin.f32 (.f32 u2 314159265359/50000000000))) (cbrt.f32 (sin.f32 (.f32 u2 314159265359/50000000000))))) (cbrt.f32 (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2)))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (.f32 (sin.f32 (cbrt.f32 (*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000))) (sqrt.f32 (/.f32 (cbrt.f32 u1) (cbrt.f32 (-.f32 1 u1))))))
	0.6b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 (pow.f32 1 3) (pow.f32 u1 3)))) (.f32 (sin.f32 (cbrt.f32 (*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000))) (sqrt.f32 (+.f32 1 (fma.f32 u1 u1 u1)))))
	0.7b	(.f32 (.f32 (fabs.f32 (cbrt.f32 u1)) (sqrt.f32 (/.f32 (cbrt.f32 u1) (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
	0.5b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (sqrt.f32 (.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000)) (sqrt.f32 (.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000))))))

Compiler

Compiled 8632 to 7354 computations (14.8% saved)

regimes6.4s (53.9%)

Accuracy

Total 0.4b remaining (87.5%)

Threshold costs 0.4b (87.5%)

Counts

495 → 1

Compiler

Compiled 111861 to 90056 computations (19.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-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	18	52
1	27	52
2	31	52
3	33	52
4	34	52
5	33	52

end228.0ms (1.9%)

Compiler: Compiled 398 to 325 computations (18.3% 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

analyze385.0ms (3.3%)

sample2.0s (16.8%)

simplify8.0ms (0.1%)

prune2.0ms (0%)

localize29.0ms (0.2%)

series41.0ms (0.3%)

rewrite37.0ms (0.3%)

simplify143.0ms (1.2%)

prune274.0ms (2.3%)

localize35.0ms (0.3%)

series47.0ms (0.4%)

rewrite24.0ms (0.2%)

simplify81.0ms (0.7%)

prune360.0ms (3%)

localize67.0ms (0.6%)

series83.0ms (0.7%)

rewrite212.0ms (1.8%)

simplify228.0ms (1.9%)

prune402.0ms (3.4%)

localize70.0ms (0.6%)

series94.0ms (0.8%)

rewrite42.0ms (0.4%)

simplify128.0ms (1.1%)

prune447.0ms (3.8%)

regimes6.4s (53.9%)

simplify3.0ms (0%)

end228.0ms (1.9%)

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