Details

analyze260.0ms (5.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample39.0ms (0.8%)

Algorithm

1×

intervals

Results

26.0ms

256×

body

128

valid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify239.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

2682×	`fma-neg_binary64`
690×	`times-frac_binary64`
636×	`fma-def_binary64`
533×	`sub-neg_binary64`
432×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	25	19
2	45	17
3	65	17
4	78	17
5	89	17
6	129	17
7	180	17
8	288	17
9	497	17
10	671	17
11	811	17
12	976	17
13	1611	17
14	3407	17
15	3743	17
16	3727	17
17	3787	17
18	3819	17
19	3887	17
20	3898	17
21	4186	17
22	4220	17
23	4236	17
24	4236	17
25	4236	17
26	6212	17

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
▶	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 83 to 64 computations (22.9% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.1b	(fma.f64 6 x -6)
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series44.0ms (0.9%)

Counts

3 → 18

Calls

3 calls:

30.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
11.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
3.0ms	(fma.f64 6 x -6)

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 49

Calls

3 calls:

4.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
1.0ms	(fma.f64 6 x -6)
1.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))

simplify133.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

492×	`div-sub_binary64`
426×	`fma-neg_binary64`
384×	`*-commutative_binary64`
348×	`distribute-rgt-in_binary64`
336×	`distribute-lft-in_binary64`

Counts

67 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1136
1	110	1034
2	285	1034
3	751	1025
4	2413	1025
5	3154	1025
6	4752	1025
7	4942	1025

prune110.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	62	4	66

Error

Counts

66 → 4

Alt Table

Status	Error	Program
	1.5b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	1.0b	(cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	30.4b	(exp.f64 (log.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
▶	0.1b	(/.f64 (-.f64 (*.f64 6 x) 6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 1407 to 1016 computations (27.8% saved)

localize16.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.0b	(-.f64 (*.f64 6 x) 6)
✓	0.1b	(/.f64 (-.f64 (*.f64 6 x) 6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series36.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

33.0ms	(/.f64 (-.f64 (*.f64 6 x) 6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
3.0ms	(-.f64 (*.f64 6 x) 6)

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 52

Calls

2 calls:

10.0ms	(/.f64 (-.f64 (*.f64 6 x) 6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
6.0ms	(-.f64 (*.f64 6 x) 6)

simplify80.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-def_binary64`
764×	`distribute-rgt-in_binary64`
717×	`distribute-lft-in_binary64`
376×	`associate-/l*_binary64`
195×	`associate-/l/_binary64`

Counts

58 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	1085
1	217	990
2	543	984
3	1636	974
4	4975	974

prune159.0ms (3.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	105	4	109

Error

Counts

109 → 4

Alt Table

Status	Error	Program
	1.0b	(cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	30.4b	(exp.f64 (log.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.1b	(/.f64 (-.f64 (*.f64 6 x) 6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
▶	0.6b	(/.f64 (+.f64 (fma.f64 6 x (neg.f64 (.f64 (sqrt.f64 6) (sqrt.f64 6)))) (fma.f64 (neg.f64 (sqrt.f64 6)) (sqrt.f64 6) (.f64 (sqrt.f64 6) (sqrt.f64 6)))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 2417 to 1794 computations (25.8% saved)

localize35.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 6 x (neg.f64 (*.f64 (sqrt.f64 6) (sqrt.f64 6))))
✓	0.1b	(/.f64 (+.f64 (fma.f64 6 x (neg.f64 (.f64 (sqrt.f64 6) (sqrt.f64 6)))) (fma.f64 (neg.f64 (sqrt.f64 6)) (sqrt.f64 6) (.f64 (sqrt.f64 6) (sqrt.f64 6)))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	1.0b	(*.f64 (sqrt.f64 6) (sqrt.f64 6))
✓	61.9b	(fma.f64 (neg.f64 (sqrt.f64 6)) (sqrt.f64 6) (*.f64 (sqrt.f64 6) (sqrt.f64 6)))

series96.0ms (2%)

Counts

4 → 15

Calls

4 calls:

87.0ms	(/.f64 (+.f64 (fma.f64 6 x (neg.f64 (.f64 (sqrt.f64 6) (sqrt.f64 6)))) (fma.f64 (neg.f64 (sqrt.f64 6)) (sqrt.f64 6) (.f64 (sqrt.f64 6) (sqrt.f64 6)))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
8.0ms	(fma.f64 6 x (neg.f64 (*.f64 (sqrt.f64 6) (sqrt.f64 6))))
0.0ms	(fma.f64 (neg.f64 (sqrt.f64 6)) (sqrt.f64 6) (*.f64 (sqrt.f64 6) (sqrt.f64 6)))
0.0ms	(*.f64 (sqrt.f64 6) (sqrt.f64 6))

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
19×	`pow1_binary64`
18×	`sqrt-prod_binary64`

Counts

4 → 108

Calls

4 calls:

11.0ms	(*.f64 (sqrt.f64 6) (sqrt.f64 6))
7.0ms	(/.f64 (+.f64 (fma.f64 6 x (neg.f64 (.f64 (sqrt.f64 6) (sqrt.f64 6)))) (fma.f64 (neg.f64 (sqrt.f64 6)) (sqrt.f64 6) (.f64 (sqrt.f64 6) (sqrt.f64 6)))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
1.0ms	(fma.f64 (neg.f64 (sqrt.f64 6)) (sqrt.f64 6) (*.f64 (sqrt.f64 6) (sqrt.f64 6)))
1.0ms	(fma.f64 6 x (neg.f64 (*.f64 (sqrt.f64 6) (sqrt.f64 6))))

simplify140.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

781×	`distribute-rgt-in_binary64`
710×	`distribute-lft-in_binary64`
477×	`div-sub_binary64`
396×	`associate-l_binary64`
382×	`fma-def_binary64`

Counts

123 → 155

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	135	1591
1	241	1307
2	524	1301
3	1366	1280
4	4512	1276
5	5012	1276

prune481.0ms (9.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	214	4	218

Error

Counts

218 → 4

Alt Table

Status	Error	Program
▶	1.0b	(cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	30.4b	(exp.f64 (log.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.1b	(/.f64 (-.f64 (*.f64 6 x) 6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	0.6b	(/.f64 (+.f64 (fma.f64 6 x (neg.f64 (.f64 (sqrt.f64 6) (sqrt.f64 6)))) (fma.f64 (neg.f64 (sqrt.f64 6)) (sqrt.f64 6) (.f64 (sqrt.f64 6) (sqrt.f64 6)))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 7480 to 6450 computations (13.8% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	0.1b	(fma.f64 6 x -6)
	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	0.9b	(cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

series79.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

44.0ms

(*.f64 (*.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

34.0ms

(cbrt.f64 (*.f64 (*.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

rewrite62.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-cbrt-cube_binary64`
43×	`add-exp-log_binary64`
21×	`pow1_binary64`
18×	`cbrt-unprod_binary64`
18×	`prod-exp_binary64`

Counts

2 → 85

Calls

2 calls:

18.0ms

(*.f64 (*.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

14.0ms

(cbrt.f64 (*.f64 (*.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

simplify249.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-def_binary64`
445×	`associate-/l*_binary64`
259×	`associate-/l/_binary64`
238×	`times-frac_binary64`
210×	`fma-neg_binary64`

Counts

91 → 113

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	124	5494
1	245	2505
2	898	2400
3	2789	2388
4	3765	2076
5	4763	2003
6	4980	2003
7	4936	2003

prune577.0ms (11.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	263	4	267

Error

Counts

267 → 4

Alt Table

Status	Error	Program
✓	1.0b	(cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	30.4b	(exp.f64 (log.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.1b	(/.f64 (-.f64 (*.f64 6 x) 6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	0.6b	(/.f64 (+.f64 (fma.f64 6 x (neg.f64 (.f64 (sqrt.f64 6) (sqrt.f64 6)))) (fma.f64 (neg.f64 (sqrt.f64 6)) (sqrt.f64 6) (.f64 (sqrt.f64 6) (sqrt.f64 6)))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 12347 to 8775 computations (28.9% saved)

regimes503.0ms (10.3%)

Accuracy

Total 0.1b remaining (57.9%)

Threshold costs 0.1b (57.9%)

Counts

114 → 1

Compiler

Compiled 5616 to 4589 computations (18.3% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	39
1	27	39
2	31	39
3	34	39
4	35	39
5	34	39

end1.0ms (0%)

Compiler: Compiled 26 to 23 computations (11.5% saved)

sample1.4s (29.2%)

Algorithm

1×

intervals

Results

914.0ms	8000×	body	128	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 142 to 116 computations (18.3% saved)

Details

analyze260.0ms (5.3%)

sample39.0ms (0.8%)

simplify239.0ms (4.9%)

prune7.0ms (0.1%)

localize15.0ms (0.3%)

series44.0ms (0.9%)

rewrite10.0ms (0.2%)

simplify133.0ms (2.7%)

prune110.0ms (2.3%)

localize16.0ms (0.3%)

series36.0ms (0.7%)

rewrite22.0ms (0.5%)

simplify80.0ms (1.6%)

prune159.0ms (3.3%)

localize35.0ms (0.7%)

series96.0ms (2%)

rewrite34.0ms (0.7%)

simplify140.0ms (2.9%)

prune481.0ms (9.9%)

localize21.0ms (0.4%)

series79.0ms (1.6%)

rewrite62.0ms (1.3%)

simplify249.0ms (5.1%)

prune577.0ms (11.8%)

regimes503.0ms (10.3%)

simplify8.0ms (0.2%)

end1.0ms (0%)

sample1.4s (29.2%)

Profiling