Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	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)

sample964.0ms (39.6%)

Infinites

0% of outputs are infinite.

Results

692.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 47 to 38 computations (19.1% saved)

simplify233.0ms (9.5%)

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

prune4.0ms (0.2%)

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

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 53 to 40 computations (24.5% saved)

localize9.0ms (0.4%)

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)
✓	0.8b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series22.0ms (0.9%)

Counts

3 → 18

Calls

3 calls:

13.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
6.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
2.0ms	(fma.f64 6 x -6)

rewrite5.0ms (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:

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)

simplify90.0ms (3.7%)

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

prune63.0ms (2.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	58	6	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	6	65

Error

0.0b

Counts

65 → 6

Alt Table

Status	Error	Program
	1.0b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	33.1b	6
▶	0.8b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
	1.0b	(/.f64 (fma.f64 6 x -6) (*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	0.9b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	33.5b	(*.f64 (sqrt.f64 (fma.f64 6 x -6)) (/.f64 (sqrt.f64 (fma.f64 6 x -6)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

Compiler

Compiled 1373 to 994 computations (27.6% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) x)
✓	0.1b	(fma.f64 -6 x 6)
✓	0.8b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))

series26.0ms (1.1%)

Counts

3 → 17

Calls

3 calls:

19.0ms	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
5.0ms	(fma.f64 4 (sqrt.f64 x) x)
2.0ms	(fma.f64 -6 x 6)

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

3 → 59

Calls

3 calls:

4.0ms	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
0.0ms	(fma.f64 -6 x 6)
0.0ms	(fma.f64 4 (sqrt.f64 x) x)

simplify106.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

506×	`times-frac_binary64`
445×	`distribute-rgt-in_binary64`
428×	`distribute-lft-in_binary64`
337×	`associate-/l*_binary64`
242×	`fma-def_binary64`

Counts

76 → 69

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	1396
1	166	1291
2	388	1291
3	1085	1289
4	4582	1289
5	4984	1289
6	4940	1289

prune59.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Error

Counts

75 → 7

Alt Table

Status	Error	Program
	1.0b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	33.1b	6
	32.0b	(*.f64 (sqrt.f64 (fma.f64 -6 x 6)) (/.f64 (sqrt.f64 (fma.f64 -6 x 6)) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x))))
✓	0.8b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
	1.0b	(/.f64 (fma.f64 6 x -6) (*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
▶	0.9b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	33.5b	(*.f64 (sqrt.f64 (fma.f64 6 x -6)) (/.f64 (sqrt.f64 (fma.f64 6 x -6)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

Compiler

Compiled 1611 to 1159 computations (28.1% saved)

localize10.0ms (0.4%)

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 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	0.1b	(fma.f64 6 x -6)
✓	0.9b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

series30.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

17.0ms	(/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
13.0ms	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

rewrite12.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

2 → 71

Calls

2 calls:

6.0ms	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
2.0ms	(/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

simplify113.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

780×	`distribute-rgt-in_binary64`
765×	`distribute-lft-in_binary64`
466×	`fma-neg_binary64`
286×	`fma-def_binary64`
279×	`div-sub_binary64`

Counts

77 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	1535
1	136	1358
2	379	1358
3	1052	1339
4	2953	1339
5	3780	1339
6	4677	1339
7	4954	1339

prune125.0ms (5.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	139	7	146

Error

Counts

146 → 7

Alt Table

Status	Error	Program
▶	1.0b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	33.1b	6
	32.0b	(*.f64 (sqrt.f64 (fma.f64 -6 x 6)) (/.f64 (sqrt.f64 (fma.f64 -6 x 6)) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x))))
✓	0.8b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
	1.0b	(/.f64 (fma.f64 6 x -6) (*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.9b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	33.5b	(*.f64 (sqrt.f64 (fma.f64 6 x -6)) (/.f64 (sqrt.f64 (fma.f64 6 x -6)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

Compiler

Compiled 3209 to 2382 computations (25.8% saved)

localize9.0ms (0.4%)

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)
✓	0.9b	(/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6))

series24.0ms (1%)

Counts

2 → 6

Calls

2 calls:

13.0ms	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
11.0ms	(/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6))

rewrite15.0ms (0.6%)

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))

simplify144.0ms (5.9%)

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

prune142.0ms (5.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	170	7	177

Error

Counts

177 → 7

Alt Table

Status	Error	Program
✓	1.0b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	33.1b	6
	32.0b	(*.f64 (sqrt.f64 (fma.f64 -6 x 6)) (/.f64 (sqrt.f64 (fma.f64 -6 x 6)) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x))))
✓	0.8b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
	1.0b	(/.f64 (fma.f64 6 x -6) (*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.9b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	33.5b	(*.f64 (sqrt.f64 (fma.f64 6 x -6)) (/.f64 (sqrt.f64 (fma.f64 6 x -6)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

Compiler

Compiled 4398 to 3300 computations (25% saved)

regimes91.0ms (3.7%)

Accuracy

Total 0.2b remaining (93.1%)

Threshold costs 0.2b (93.1%)

Counts

41 → 1

Compiler

Compiled 1603 to 1260 computations (21.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	13	17
2	17	17
3	19	17
4	20	17
5	20	17

end121.0ms (5%)

Compiler: Compiled 134 to 105 computations (21.6% saved)

Details

analyze2.0ms (0.1%)

sample964.0ms (39.6%)

simplify233.0ms (9.5%)

prune4.0ms (0.2%)

localize9.0ms (0.4%)

series22.0ms (0.9%)

rewrite5.0ms (0.2%)

simplify90.0ms (3.7%)

prune63.0ms (2.6%)

localize8.0ms (0.3%)

series26.0ms (1.1%)

rewrite7.0ms (0.3%)

simplify106.0ms (4.3%)

prune59.0ms (2.4%)

localize10.0ms (0.4%)

series30.0ms (1.2%)

rewrite12.0ms (0.5%)

simplify113.0ms (4.7%)

prune125.0ms (5.1%)

localize9.0ms (0.4%)

series24.0ms (1%)

rewrite15.0ms (0.6%)

simplify144.0ms (5.9%)

prune142.0ms (5.8%)

regimes91.0ms (3.7%)

simplify3.0ms (0.1%)

end121.0ms (5%)

Profiling