Details

analyze445.0ms (1.9%)

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 (8.5%)

Results

2.0s	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 88 to 67 computations (23.9% saved)

simplify8.0ms (0%)

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

0.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.5b	(.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 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2)))
✓	0.4b	(*.f32 314159265359/50000000000 u2)

series31.0ms (0.1%)

Counts

4 → 28

Calls

4 calls:

25.0ms	(.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))
2.0ms	(*.f32 314159265359/50000000000 u2)

rewrite27.0ms (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 u1 (-.f32 1 u1))
3.0ms	(sin.f32 (*.f32 314159265359/50000000000 u2))
3.0ms	(*.f32 314159265359/50000000000 u2)

simplify103.0ms (0.4%)

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

prune229.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	179	10	189
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	180	10	190

Error

0.0b

Counts

190 → 10

Alt Table

Status	Error	Program
	0.7b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) (cbrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (sqrt.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sin.f32 (.f32 314159265359/50000000000 u2))))
▶	0.5b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))
	1.6b	(.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)))))
	0.9b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 314159265359/50000000000 u2)) (cbrt.f32 (.f32 314159265359/50000000000 u2))) (cbrt.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)))))
	1.5b	(-.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 (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))))
	0.5b	(.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))))
	0.7b	(.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)))))
	0.6b	(.f32 (sqrt.f32 (/.f32 1 (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (/.f32 u1 (cbrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 314159265359/50000000000 u2))))

Compiler

Compiled 4350 to 3192 computations (26.6% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series63.0ms (0.3%)

Counts

3 → 44

Calls

3 calls:

46.0ms

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

9.0ms

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

8.0ms

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

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 79

Calls

3 calls:

10.0ms

(*.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))

3.0ms

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

simplify113.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-neg_binary32`
421×	`fma-def_binary32`
377×	`*-commutative_binary32`
299×	`associate-/r*_binary32`
235×	`sub-neg_binary32`

Counts

123 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	2355
1	497	2167
2	1496	2057
3	3954	2049
4	4876	2049
5	4901	2049

prune281.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	211	6	217
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	218	9	227

Error

0.0b

Counts

227 → 9

Alt Table

Status	Error	Program
	0.6b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sin.f32 (*.f32 u2 314159265359/50000000000)) (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1))))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2)))))
	0.6b	(.f32 (sqrt.f32 (.f32 (.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) (cbrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))
	1.5b	(-.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)))))))
	0.9b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 314159265359/50000000000 u2)) (cbrt.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (.f32 314159265359/50000000000 u2)))))
▶	0.5b	(.f32 (sqrt.f32 (/.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1))) (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.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 (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 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2)))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))))
	0.6b	(.f32 (sqrt.f32 (/.f32 1 (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (/.f32 u1 (cbrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 314159265359/50000000000 u2))))

Compiler

Compiled 5583 to 4350 computations (22.1% saved)

localize46.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series59.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

41.0ms

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

15.0ms

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

2.0ms

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

rewrite254.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

1144×	`times-frac_binary32`
1083×	`sqrt-prod_binary32`
872×	`add-sqr-sqrt_binary32`
846×	`*-un-lft-identity_binary32`
462×	`add-cube-cbrt_binary32`

Counts

3 → 744

Calls

3 calls:

63.0ms

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

14.0ms

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

7.0ms

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

simplify626.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

557×	`fma-def_binary32`
406×	`associate-/l/_binary32`
374×	`associate-/r/_binary32`
230×	`*-commutative_binary32`
230×	`fma-neg_binary32`

Counts

780 → 878

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	665	26624
1	1356	23134
2	3036	22254
3	4720	21913
4	4939	21913

prune1.4s (5.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	911	2	913
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	913	9	922

Error

0.0b

Counts

922 → 9

Alt Table

Status	Error	Program
	0.6b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sin.f32 (*.f32 u2 314159265359/50000000000)) (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1))))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2)))))
	0.8b	(.f32 (sqrt.f32 (/.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (+.f32 1 (sqrt.f32 u1)))) (sqrt.f32 (+.f32 1 (sqrt.f32 u1))))) (.f32 (sqrt.f32 (/.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 (sqrt.f32 u1)))) (sqrt.f32 (-.f32 1 (sqrt.f32 u1))))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2)))))
	0.9b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 314159265359/50000000000 u2)) (cbrt.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (.f32 314159265359/50000000000 u2)))))
✓	0.5b	(.f32 (sqrt.f32 (/.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1))) (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))
	1.5b	(-.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)))))))
	2.8b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (fma.f32 u2 314159265359/50000000000 (.f32 -31006276680305942139213528068663279/750000000000000000000000000000000 (pow.f32 u2 3))))
▶	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 (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 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2)))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))))

Compiler

Compiled 32802 to 25055 computations (23.6% saved)

localize52.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series373.0ms (1.6%)

Counts

2 → 28

Calls

2 calls:

262.0ms

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

110.0ms

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

rewrite51.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`sqrt-prod_binary32`
72×	`associate-l_binary32`
65×	`add-sqr-sqrt_binary32`
56×	`times-frac_binary32`
55×	`*-un-lft-identity_binary32`

Counts

2 → 113

Calls

2 calls:

22.0ms

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

12.0ms

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

simplify136.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

496×	`fma-neg_binary32`
455×	`fma-def_binary32`
314×	`associate-/r*_binary32`
271×	`cancel-sign-sub-inv_binary32`
264×	`associate-r_binary32`

Counts

141 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	5175
1	581	4095
2	1880	3938
3	4574	3938
4	4972	3938

prune527.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	310	0	310
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	310	9	319

Error

0.0b

Counts

319 → 9

Alt Table

Status	Error	Program
	0.6b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sin.f32 (*.f32 u2 314159265359/50000000000)) (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1))))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2)))))
	0.8b	(.f32 (sqrt.f32 (/.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (+.f32 1 (sqrt.f32 u1)))) (sqrt.f32 (+.f32 1 (sqrt.f32 u1))))) (.f32 (sqrt.f32 (/.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 (sqrt.f32 u1)))) (sqrt.f32 (-.f32 1 (sqrt.f32 u1))))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2)))))
	0.9b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 314159265359/50000000000 u2)) (cbrt.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (.f32 314159265359/50000000000 u2)))))
✓	0.5b	(.f32 (sqrt.f32 (/.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1))) (sqrt.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))
	1.5b	(-.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)))))))
	2.8b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (fma.f32 u2 314159265359/50000000000 (.f32 -31006276680305942139213528068663279/750000000000000000000000000000000 (pow.f32 u2 3))))
✓	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 (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 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2)))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))))

Compiler

Compiled 10621 to 8601 computations (19% saved)

regimes16.9s (70.1%)

Accuracy

Total 0.4b remaining (84.5%)

Threshold costs 0.4b (84.5%)

Counts

982 → 1

Compiler

Compiled 263538 to 211867 computations (19.6% saved)

simplify4.0ms (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	16	29
1	23	29
2	27	29
3	29	29
4	30	29
5	29	29

end203.0ms (0.8%)

Compiler: Compiled 336 to 269 computations (19.9% 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

analyze445.0ms (1.9%)

sample2.0s (8.5%)

simplify8.0ms (0%)

prune2.0ms (0%)

localize29.0ms (0.1%)

series31.0ms (0.1%)

rewrite27.0ms (0.1%)

simplify103.0ms (0.4%)

prune229.0ms (1%)

localize37.0ms (0.2%)

series63.0ms (0.3%)

rewrite25.0ms (0.1%)

simplify113.0ms (0.5%)

prune281.0ms (1.2%)

localize46.0ms (0.2%)

series59.0ms (0.2%)

rewrite254.0ms (1.1%)

simplify626.0ms (2.6%)

prune1.4s (5.9%)

localize52.0ms (0.2%)

series373.0ms (1.6%)

rewrite51.0ms (0.2%)

simplify136.0ms (0.6%)

prune527.0ms (2.2%)

regimes16.9s (70.1%)

simplify4.0ms (0%)

end203.0ms (0.8%)

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