Details

analyze398.0ms (2.1%)

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)

sample55.0ms (0.3%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true
0.0ms	1×	pre	128	false

Compiler

Compiled 54 to 42 computations (22.2% saved)

simplify16.0ms (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 (0.1%)

Local error

Found 4 expressions with local error:

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

series32.0ms (0.2%)

Counts

4 → 28

Calls

4 calls:

26.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2)))
2.0ms	(/.f32 u1 (-.f32 1 u1))
2.0ms	(sin.f32 (*.f32 314159265359/50000000000 u2))
1.0ms	(*.f32 314159265359/50000000000 u2)

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary32`
50×	`*-un-lft-identity_binary32`
37×	`times-frac_binary32`
30×	`associate-l_binary32`
29×	`add-cube-cbrt_binary32`

Counts

4 → 119

Calls

4 calls:

10.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2)))
4.0ms	(*.f32 314159265359/50000000000 u2)
4.0ms	(/.f32 u1 (-.f32 1 u1))
1.0ms	(sin.f32 (*.f32 314159265359/50000000000 u2))

simplify104.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-def_binary32`
448×	`associate-r_binary32`
378×	`associate-/r*_binary32`
357×	`times-frac_binary32`
261×	`fma-neg_binary32`

Counts

147 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	2754
1	569	2577
2	1673	2467
3	4686	2467
4	5037	2467

prune221.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	180	9	189
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	181	9	190

Error

0.1b

Counts

190 → 9

Alt Table

Status	Error	Program
▶	0.5b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.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)))))
	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 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)))))
	0.6b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 (pow.f32 1 3) (pow.f32 u1 3)))) (.f32 (sqrt.f32 (+.f32 (.f32 1 1) (+.f32 (.f32 u1 u1) (.f32 1 u1)))) (sin.f32 (.f32 314159265359/50000000000 u2))))
	3.4b	(-.f32 (.f32 314159265359/50000000000 (.f32 u2 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 31006276680305942139213528068663279/750000000000000000000000000000000 (.f32 (pow.f32 u2 3) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	0.8b	(.f32 (sqrt.f32 (/.f32 (.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 314159265359/50000000000 u2))))
	0.7b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
	0.8b	(.f32 (sqrt.f32 (.f32 (.f32 (/.f32 (cbrt.f32 u1) (sqrt.f32 (-.f32 1 u1))) (cbrt.f32 u1)) (/.f32 (cbrt.f32 u1) (sqrt.f32 (-.f32 1 u1))))) (sin.f32 (.f32 314159265359/50000000000 u2)))

Compiler

Compiled 4254 to 3106 computations (27% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series53.0ms (0.3%)

Counts

3 → 44

Calls

3 calls:

35.0ms

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

14.0ms

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

4.0ms

(sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary32`
28×	`associate-l_binary32`
26×	`sqrt-prod_binary32`
24×	`*-un-lft-identity_binary32`
19×	`times-frac_binary32`

Counts

3 → 80

Calls

3 calls:

11.0ms

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

7.0ms

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

3.0ms

(sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))

simplify92.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-neg_binary32`
426×	`fma-def_binary32`
352×	`*-commutative_binary32`
299×	`associate-/r*_binary32`
265×	`sub-neg_binary32`

Counts

124 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	2264
1	463	2106
2	1404	1994
3	3743	1994
4	4968	1994

prune260.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	199	10	209
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	207	11	218

Error

0.0b

Counts

218 → 11

Alt Table

Status	Error	Program
	4.5b	(.f32 (sqrt.f32 (fma.f32 u1 u1 u1)) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))
	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 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.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)))))
	0.9b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))) (cbrt.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))) (cbrt.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	1.2b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (sin.f32 (.f32 314159265359/50000000000 u2)))) (sqrt.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	0.9b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (sin.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (sin.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	0.7b	(.f32 (sqrt.f32 u1) (.f32 (sqrt.f32 (/.f32 1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	1.3b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))) (sqrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	0.6b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1)))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))))
▶	0.6b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))

Compiler

Compiled 5901 to 4681 computations (20.7% saved)

localize60.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series359.0ms (1.9%)

Counts

3 → 32

Calls

3 calls:

249.0ms

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

99.0ms

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

11.0ms

(/.f32 u1 (sqrt.f32 (-.f32 1 u1)))

rewrite63.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`sqrt-prod_binary32`
96×	`add-sqr-sqrt_binary32`
86×	`*-un-lft-identity_binary32`
83×	`times-frac_binary32`
72×	`associate-l_binary32`

Counts

3 → 168

Calls

3 calls:

23.0ms

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

13.0ms

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

7.0ms

(/.f32 u1 (sqrt.f32 (-.f32 1 u1)))

simplify167.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

568×	`times-frac_binary32`
565×	`fma-def_binary32`
383×	`associate-/l*_binary32`
351×	`fma-neg_binary32`
254×	`associate-r_binary32`

Counts

200 → 264

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	304	6788
1	675	4976
2	2108	4874
3	4851	4874
4	4979	4874

prune472.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	290	4	294
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	294	11	305

Error

0.0b

Counts

305 → 11

Alt Table

Status	Error	Program
	4.5b	(.f32 (sqrt.f32 (fma.f32 u1 u1 u1)) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))
	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 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.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)))))
	0.9b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))) (cbrt.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))) (cbrt.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	1.3b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))) (sqrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))))
▶	0.7b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (+.f32 1 (sqrt.f32 u1))))) (.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 (sqrt.f32 u1))))) (.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	0.8b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1))))) (.f32 (sin.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1))))))))
	0.7b	(.f32 (sqrt.f32 u1) (.f32 (sqrt.f32 (/.f32 1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	0.8b	(.f32 (sqrt.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
✓	0.6b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	1.2b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (exp.f32 (log.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1)))))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))))

Compiler

Compiled 11034 to 9045 computations (18% saved)

localize94.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (+.f32 1 (sqrt.f32 u1))))) (.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 (sqrt.f32 u1))))) (.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	0.3b	(.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))
✓	0.4b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 (sqrt.f32 u1))))) (.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))))
✓	0.5b	(/.f32 1 (sqrt.f32 (+.f32 1 (sqrt.f32 u1))))

series2.8s (14.7%)

Counts

3 → 25

Calls

3 calls:

1.4s

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

1.3s

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

95.0ms

(/.f32 1 (sqrt.f32 (+.f32 1 (sqrt.f32 u1))))

rewrite94.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

150×	`sqrt-prod_binary32`
92×	`*-un-lft-identity_binary32`
84×	`times-frac_binary32`
84×	`add-sqr-sqrt_binary32`
78×	`associate-l_binary32`

Counts

3 → 182

Calls

3 calls:

36.0ms

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

25.0ms

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

6.0ms

(/.f32 1 (sqrt.f32 (+.f32 1 (sqrt.f32 u1))))

simplify203.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

649×	`fma-neg_binary32`
549×	`times-frac_binary32`
425×	`associate-r_binary32`
366×	`fma-def_binary32`
319×	`associate-l_binary32`

Counts

207 → 257

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	9262
1	569	7251
2	1918	7075
3	3722	7073
4	5025	7073

prune634.0ms (3.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	354	1	355
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	355	11	366

Error

0.0b

Counts

366 → 11

Alt Table

Status	Error	Program
	4.5b	(.f32 (sqrt.f32 (fma.f32 u1 u1 u1)) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))
	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 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.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)))))
	0.9b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))) (cbrt.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))) (cbrt.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	3.5b	(.f32 (pow.f32 (/.f32 1 (.f32 (-.f32 1 (sqrt.f32 u1)) (.f32 (-.f32 1 u1) (+.f32 1 (sqrt.f32 u1))))) 1/4) (-.f32 (.f32 314159265359/50000000000 (.f32 (sqrt.f32 u1) u2)) (.f32 31006276680305942139213528068663279/750000000000000000000000000000000 (*.f32 (sqrt.f32 u1) (pow.f32 u2 3)))))
✓	0.7b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (+.f32 1 (sqrt.f32 u1))))) (.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 (sqrt.f32 u1))))) (.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	0.8b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1))))) (.f32 (sin.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1))))))))
	0.7b	(.f32 (sqrt.f32 u1) (.f32 (sqrt.f32 (/.f32 1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	0.8b	(.f32 (sqrt.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
✓	0.6b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	1.2b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (exp.f32 (log.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1)))))) (sin.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))))

Compiler

Compiled 16851 to 13326 computations (20.9% saved)

regimes9.3s (48.1%)

Accuracy

Total 0.5b remaining (85.7%)

Threshold costs 0.5b (85.7%)

Counts

473 → 1

Compiler

Compiled 124303 to 101243 computations (18.6% saved)

simplify5.0ms (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	13	24
1	20	24
2	24	24
3	26	24
4	27	24
5	26	24

end1.0ms (0%)

Compiler: Compiled 18 to 15 computations (16.7% saved)

sample3.7s (19%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
501.0ms	8000×	pre	128	true
0.0ms	3×	pre	128	false

Compiler

Compiled 423 to 350 computations (17.3% 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

analyze398.0ms (2.1%)

sample55.0ms (0.3%)

simplify16.0ms (0.1%)

prune2.0ms (0%)

localize29.0ms (0.1%)

series32.0ms (0.2%)

rewrite26.0ms (0.1%)

simplify104.0ms (0.5%)

prune221.0ms (1.1%)

localize43.0ms (0.2%)

series53.0ms (0.3%)

rewrite27.0ms (0.1%)

simplify92.0ms (0.5%)

prune260.0ms (1.3%)

localize60.0ms (0.3%)

series359.0ms (1.9%)

rewrite63.0ms (0.3%)

simplify167.0ms (0.9%)

prune472.0ms (2.4%)

localize94.0ms (0.5%)

series2.8s (14.7%)

rewrite94.0ms (0.5%)

simplify203.0ms (1.1%)

prune634.0ms (3.3%)

regimes9.3s (48.1%)

simplify5.0ms (0%)

end1.0ms (0%)

sample3.7s (19%)

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