Details

analyze467.0ms (2.5%)

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)

sample2.1s (11.2%)

Results

2.1s	8256×	body	128	valid
1.0ms	3×	body	128	invalid

Compiler

Compiled 88 to 67 computations (23.9% saved)

simplify9.0ms (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)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series35.0ms (0.2%)

Counts

4 → 28

Calls

4 calls:

29.0ms	(.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:

11.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (.f32 314159265359/50000000000 u2)))
4.0ms	(/.f32 u1 (-.f32 1 u1))
3.0ms	(*.f32 314159265359/50000000000 u2)
1.0ms	(sin.f32 (*.f32 314159265359/50000000000 u2))

simplify118.0ms (0.6%)

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

prune235.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	178	11	189
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	179	11	190

Error

0.0b

Counts

190 → 11

Alt Table

Status	Error	Program
	1.2b	(.f32 (sqrt.f32 (exp.f32 (log.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (.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 314159265359/50000000000 u2))))
	0.5b	(.f32 (sqrt.f32 (/.f32 (/.f32 u1 (+.f32 1 (sqrt.f32 u1))) (-.f32 1 (sqrt.f32 u1)))) (sin.f32 (.f32 314159265359/50000000000 u2)))
	1.6b	(-.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)))))))
	0.8b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sin.f32 (.f32 314159265359/50000000000 u2))))
	0.5b	(.f32 (sqrt.f32 (.f32 (/.f32 (sqrt.f32 u1) (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1)))) (/.f32 (sqrt.f32 u1) (cbrt.f32 (-.f32 1 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))))
	0.6b	(.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))))
	0.5b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 314159265359/50000000000 314159265359/50000000000) 314159265359/50000000000) (.f32 (.f32 u2 u2) 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))))
	0.6b	(.f32 (sqrt.f32 (.f32 (/.f32 (sqrt.f32 u1) (+.f32 1 (sqrt.f32 u1))) (/.f32 (sqrt.f32 u1) (-.f32 1 (sqrt.f32 u1))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))

Compiler

Compiled 4354 to 3192 computations (26.7% saved)

localize46.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series52.0ms (0.3%)

Counts

3 → 44

Calls

3 calls:

33.0ms

(*.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))

5.0ms

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

rewrite29.0ms (0.2%)

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))))

8.0ms

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

2.0ms

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

simplify95.0ms (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

prune292.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	204	5	209
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	208	12	220

Error

0.0b

Counts

220 → 12

Alt Table

Status	Error	Program
	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 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	0.8b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sin.f32 (.f32 314159265359/50000000000 u2))))
	0.5b	(.f32 (sqrt.f32 (/.f32 (/.f32 u1 (+.f32 1 (sqrt.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))))
	1.2b	(.f32 (sqrt.f32 (exp.f32 (log.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (.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 314159265359/50000000000 u2))))
	0.5b	(.f32 (sqrt.f32 (.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1))) (/.f32 (sqrt.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 (sqrt.f32 (.f32 (/.f32 (sqrt.f32 u1) (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1)))) (/.f32 (sqrt.f32 u1) (cbrt.f32 (-.f32 1 u1))))) (sin.f32 (.f32 314159265359/50000000000 u2)))
	0.8b	(.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)))))
✓	0.5b	(.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))))
▶	0.5b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 314159265359/50000000000 314159265359/50000000000) 314159265359/50000000000) (.f32 (.f32 u2 u2) u2)))))
	1.6b	(-.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 (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)))))

Compiler

Compiled 5886 to 4649 computations (21% saved)

localize56.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 u2 u2) u2)
✓	0.3b	(.f32 (.f32 (.f32 314159265359/50000000000 314159265359/50000000000) 314159265359/50000000000) (.f32 (*.f32 u2 u2) u2))
✓	0.3b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 314159265359/50000000000 314159265359/50000000000) 314159265359/50000000000) (.f32 (.f32 u2 u2) u2)))))
✓	1.0b	(*.f32 314159265359/50000000000 314159265359/50000000000)

series49.0ms (0.3%)

Counts

4 → 44

Calls

4 calls:

43.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 314159265359/50000000000 314159265359/50000000000) 314159265359/50000000000) (.f32 (.f32 u2 u2) u2)))))
3.0ms	(.f32 (.f32 (.f32 314159265359/50000000000 314159265359/50000000000) 314159265359/50000000000) (.f32 (*.f32 u2 u2) u2))
3.0ms	(.f32 (.f32 u2 u2) u2)
0.0ms	(*.f32 314159265359/50000000000 314159265359/50000000000)

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`pow1_binary32`
57×	`pow-prod-down_binary32`
52×	`add-cbrt-cube_binary32`
49×	`add-exp-log_binary32`
47×	`pow-plus_binary32`

Counts

4 → 169

Calls

4 calls:

14.0ms	(.f32 (.f32 (.f32 314159265359/50000000000 314159265359/50000000000) 314159265359/50000000000) (.f32 (*.f32 u2 u2) u2))
13.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 314159265359/50000000000 314159265359/50000000000) 314159265359/50000000000) (.f32 (.f32 u2 u2) u2)))))
5.0ms	(.f32 (.f32 u2 u2) u2)
3.0ms	(*.f32 314159265359/50000000000 314159265359/50000000000)

simplify162.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

551×	`fma-neg_binary32`
399×	`*-commutative_binary32`
377×	`fma-def_binary32`
299×	`associate-/r*_binary32`
228×	`sub-neg_binary32`

Counts

213 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	257	3253
1	531	2924
2	1556	2757
3	4092	2718
4	4916	2718
5	4916	2718

prune313.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	205	2	207
Fresh	4	6	10
Picked	0	1	1
Done	1	0	1
Total	210	9	219

Error

0.0b

Counts

219 → 9

Alt Table

Status	Error	Program
▶	0.5b	(.f32 (sqrt.f32 (/.f32 (/.f32 u1 (+.f32 1 (sqrt.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))))
	0.9b	(.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 314159265359/50000000000 u2))))
	0.6b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sin.f32 (cbrt.f32 (*.f32 31006276680305942139213528068663279/125000000000000000000000000000000 (pow.f32 u2 3)))) (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1))))))
	1.6b	(-.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 (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 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	0.5b	(.f32 (sqrt.f32 (.f32 (/.f32 (sqrt.f32 u1) (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1)))) (/.f32 (sqrt.f32 u1) (cbrt.f32 (-.f32 1 u1))))) (sin.f32 (.f32 314159265359/50000000000 u2)))
	0.8b	(.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)))))
	0.6b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) (cbrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (sin.f32 (cbrt.f32 (.f32 31006276680305942139213528068663279/125000000000000000000000000000000 (pow.f32 u2 3)))) (sqrt.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))))))
✓	0.5b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 314159265359/50000000000 314159265359/50000000000) 314159265359/50000000000) (.f32 (.f32 u2 u2) u2)))))

Compiler

Compiled 6004 to 4321 computations (28% saved)

localize61.0ms (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))
✓	0.3b	(/.f32 (/.f32 u1 (+.f32 1 (sqrt.f32 u1))) (-.f32 1 (sqrt.f32 u1)))
✓	0.3b	(.f32 (sqrt.f32 (/.f32 (/.f32 u1 (+.f32 1 (sqrt.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))))
✓	0.4b	(/.f32 u1 (+.f32 1 (sqrt.f32 u1)))

series164.0ms (0.9%)

Counts

3 → 14

Calls

3 calls:

115.0ms

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

34.0ms

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

16.0ms

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

rewrite182.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

681×	`times-frac_binary32`
628×	`*-un-lft-identity_binary32`
603×	`add-sqr-sqrt_binary32`
388×	`sqrt-prod_binary32`
230×	`add-cube-cbrt_binary32`

Counts

3 → 496

Calls

3 calls:

51.0ms

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

12.0ms

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

4.0ms

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

simplify431.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

788×	`fma-def_binary32`
498×	`associate-*l/_binary32`
447×	`associate-/r/_binary32`
324×	`associate-*r/_binary32`
236×	`associate-/l/_binary32`

Counts

510 → 520

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	403	18321
1	875	15530
2	2326	15442
3	4597	15434
4	5165	15434

prune970.0ms (5.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	548	2	550
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	551	8	559

Error

0.0b

Counts

559 → 8

Alt Table

Status	Error	Program
	0.5b	(.f32 (sqrt.f32 (.f32 (/.f32 (sqrt.f32 u1) (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1)))) (/.f32 (sqrt.f32 u1) (cbrt.f32 (-.f32 1 u1))))) (sin.f32 (.f32 314159265359/50000000000 u2)))
	1.4b	(.f32 (sqrt.f32 (/.f32 (exp.f32 (-.f32 (log.f32 u1) (log1p.f32 (sqrt.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 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sin.f32 (cbrt.f32 (*.f32 31006276680305942139213528068663279/125000000000000000000000000000000 (pow.f32 u2 3)))) (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1))))))
	1.6b	(-.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 (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 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	0.6b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) (cbrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (sin.f32 (cbrt.f32 (.f32 31006276680305942139213528068663279/125000000000000000000000000000000 (pow.f32 u2 3)))) (sqrt.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))))))
✓	0.5b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 314159265359/50000000000 314159265359/50000000000) 314159265359/50000000000) (.f32 (.f32 u2 u2) u2)))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (+.f32 1 (sqrt.f32 u1)))) (/.f32 (sqrt.f32 u1) (sqrt.f32 (+.f32 1 (sqrt.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))))

Compiler

Compiled 20555 to 14375 computations (30.1% saved)

regimes12.7s (67.3%)

Accuracy

Total 0.4b remaining (82.6%)

Threshold costs 0.4b (82.6%)

Counts

776 → 1

Compiler

Compiled 213110 to 164399 computations (22.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`
2×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`*-lft-identity_binary32`
1×	`neg-sub0_binary32`

Iterations

Useful iterations: 0 (0.0ms)

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

end179.0ms (0.9%)

Compiler: Compiled 298 to 236 computations (20.8% 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

analyze467.0ms (2.5%)

sample2.1s (11.2%)

simplify9.0ms (0%)

prune2.0ms (0%)

localize31.0ms (0.2%)

series35.0ms (0.2%)

rewrite27.0ms (0.1%)

simplify118.0ms (0.6%)

prune235.0ms (1.2%)

localize46.0ms (0.2%)

series52.0ms (0.3%)

rewrite29.0ms (0.2%)

simplify95.0ms (0.5%)

prune292.0ms (1.5%)

localize56.0ms (0.3%)

series49.0ms (0.3%)

rewrite51.0ms (0.3%)

simplify162.0ms (0.9%)

prune313.0ms (1.7%)

localize61.0ms (0.3%)

series164.0ms (0.9%)

rewrite182.0ms (1%)

simplify431.0ms (2.3%)

prune970.0ms (5.1%)

regimes12.7s (67.3%)

simplify3.0ms (0%)

end179.0ms (0.9%)

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