Details

analyze3.0ms (0%)

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)

sample1.2s (0.8%)

Results

918.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 47 to 38 computations (19.1% saved)

simplify232.0ms (0.2%)

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

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 53 to 40 computations (24.5% saved)

localize7.0ms (0%)

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)
✓	0.4b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series23.0ms (0%)

Counts

3 → 18

Calls

3 calls:

16.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
5.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
2.0ms	(fma.f64 6 x -6)

rewrite5.0ms (0%)

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:

2.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
0.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
0.0ms	(fma.f64 6 x -6)

simplify97.0ms (0.1%)

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

prune58.0ms (0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	4	65

Error

0.0b

Counts

65 → 4

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	1.2b	(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)))))
▶	0.5b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	32.6b	6

Compiler

Compiled 1324 to 952 computations (28.1% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.0b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	0.1b	(fma.f64 6 x -6)
✓	0.4b	(/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6))

series28.0ms (0%)

Counts

2 → 6

Calls

2 calls:

16.0ms	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
12.0ms	(/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6))

rewrite15.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
2.0ms	(/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6))

simplify143.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

710×	`distribute-rgt-in_binary64`
694×	`distribute-lft-in_binary64`
455×	`div-sub_binary64`
283×	`associate-/l*_binary64`
276×	`+-commutative_binary64`

Counts

113 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	3414
1	179	3099
2	493	3072
3	1384	3057
4	3517	3057
5	4145	3057
6	5164	3057

prune149.0ms (0.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	169	5	174

Error

Counts

174 → 5

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
▶	1.2b	(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)))))
✓	0.5b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	32.6b	6
	1.4b	(/.f64 (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6)))) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6))))

Compiler

Compiled 4474 to 3355 computations (25% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.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))))
	0.1b	(fma.f64 6 x -6)
	0.4b	(/.f64 (fma.f64 6 x -6) (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)))))

series36.0ms (0%)

Counts

2 → 6

Calls

2 calls:

20.0ms

(*.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))))

16.0ms

(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)))))

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
14×	`add-cbrt-cube_binary64`

Counts

2 → 88

Calls

2 calls:

8.0ms

(*.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))))

7.0ms

(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)))))

simplify130.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

401×	`associate-/l/_binary64`
391×	`fma-def_binary64`
269×	`times-frac_binary64`
261×	`distribute-rgt-in_binary64`
259×	`distribute-lft-in_binary64`

Counts

94 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	4592
1	340	3466
2	1166	2921
3	3081	2618
4	4764	2618
5	5006	2618

prune322.0ms (0.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	287	0	287
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	287	5	292

Error

Counts

292 → 5

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	1.2b	(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)))))
✓	0.5b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	32.6b	6
▶	1.4b	(/.f64 (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6)))) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6))))

Compiler

Compiled 13986 to 9972 computations (28.7% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6)))) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6))))
✓	0.2b	(/.f64 (cbrt.f64 (fma.f64 6 x -6)) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6))))
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6)))
✓	1.0b	(cbrt.f64 (fma.f64 6 x -6))

series119.0ms (0.1%)

Counts

4 → 17

Calls

4 calls:

54.0ms	(/.f64 (cbrt.f64 (fma.f64 6 x -6)) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6))))
41.0ms	(/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6)))
18.0ms	(/.f64 (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6)))) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6))))
5.0ms	(cbrt.f64 (fma.f64 6 x -6))

rewrite7.1s (4.7%)

Algorithm

1×	rewrite-expression-head

Rules

37880×	`times-frac_binary64`
15911×	`*-un-lft-identity_binary64`
15911×	`add-sqr-sqrt_binary64`
15911×	`add-cube-cbrt_binary64`
14049×	`cbrt-prod_binary64`

Counts

4 → 10489

Calls

4 calls:

228.0ms	(/.f64 (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6)))) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6))))
11.0ms	(/.f64 (cbrt.f64 (fma.f64 6 x -6)) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6))))
4.0ms	(/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6)))
1.0ms	(cbrt.f64 (fma.f64 6 x -6))

simplify27.3s (18.2%)

Algorithm

1×	egg-herbie

Rules

4193×	`associate-/l/_binary64`
127×	`/-rgt-identity_binary64`
20×	`sub-neg_binary64`
8×	`fma-def_binary64`
5×	`sqr-pow_binary64`

Counts

10506 → 9447

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4665	1180758
1	9729	1180758

prune17.4s (11.6%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	9584	0	9584
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	9584	5	9589

Error

Counts

9589 → 5

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	1.2b	(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)))))
✓	0.5b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	32.6b	6
✓	1.4b	(/.f64 (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6)))) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 6 x -6))))

Compiler

Compiled 756175 to 589550 computations (22% saved)

regimes303.0ms (0.2%)

Accuracy

Total 0.2b remaining (89.4%)

Threshold costs 0.2b (89.4%)

Counts

139 → 1

Compiler

Compiled 8285 to 6548 computations (21% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	14	17
2	13	17

end1.6min (63.6%)

Compiler: Compiled 190 to 147 computations (22.6% saved)

Details

analyze3.0ms (0%)

sample1.2s (0.8%)

simplify232.0ms (0.2%)

prune3.0ms (0%)

localize7.0ms (0%)

series23.0ms (0%)

rewrite5.0ms (0%)

simplify97.0ms (0.1%)

prune58.0ms (0%)

localize9.0ms (0%)

series28.0ms (0%)

rewrite15.0ms (0%)

simplify143.0ms (0.1%)

prune149.0ms (0.1%)

localize11.0ms (0%)

series36.0ms (0%)

rewrite28.0ms (0%)

simplify130.0ms (0.1%)

prune322.0ms (0.2%)

localize15.0ms (0%)

series119.0ms (0.1%)

rewrite7.1s (4.7%)

simplify27.3s (18.2%)

prune17.4s (11.6%)

regimes303.0ms (0.2%)

simplify2.0ms (0%)

end1.6min (63.6%)

Profiling