Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify84.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	38	7
1	72	7
2	167	6
3	354	6
4	646	6
5	921	6
6	1060	6
7	1331	6
8	1792	6
9	1860	6
10	1861	6
11	1861	6

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 16.1b

Counts

2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
4.5b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.9b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

1.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series258.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
31.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
65.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
142.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify104.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	244	408
1	754	361
2	3433	358
3	5002	356

prune201.0ms

Filtered

71 candidates to 59 candidates (16.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	68	5	73

Merged error: 0.0b

Counts

73 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

15.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.9b	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ y (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ y (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series424.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
109.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
112.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
90.0ms	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ y (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify75.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	194	563
1	578	504
2	2319	479
3	5002	461

prune433.0ms

Filtered

61 candidates to 56 candidates (8.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	61	5	66

Merged error: 0.0b

Counts

66 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

15.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.9b	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (expm1 (log1p (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))))) (/ y (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (expm1 (log1p (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))))) (/ y (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

115.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
111.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
113.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
812.0ms	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (expm1 (log1p (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))))) (/ y (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify80.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	209	591
1	641	527
2	2609	501
3	5001	480

prune265.0ms

Filtered

61 candidates to 57 candidates (6.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	61	5	66

Merged error: 0.0b

Counts

66 → 5

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma (/ 0.07512208616047561 z) y (fma y 0.0692910599291889 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (/ 0.07512208616047561 z) y (fma y 0.0692910599291889 x))

series39.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(fma (/ 0.07512208616047561 z) y (fma y 0.0692910599291889 x))

simplify52.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	36	62
1	78	52
2	285	52
3	1849	52
4	5002	52

prune24.0ms

Filtered

13 candidates to 10 candidates (23.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	13	5	18

Merged error: 0.0b

Counts

18 → 5

regimes222.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.3b

bsearch92.0ms

Steps

Iters	Range		Point
4	56013586448040.74	93988328089074.5	56831241125707.26
9	-1.0950129536022494e+80	-1.097976324901487e+74	-1.1089666868347514e+74

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	9
1	28	9

end0.0ms

sample512.0ms

Algorithm

intervals

Results

341.0ms

8000×

body

valid