Details

sample25.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify83.0ms

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 (100.0%)

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: 18.1b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
4.8b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
18.1b	(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)

series239.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
25.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
61.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
134.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify106.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	245	408
1	760	361
2	3482	358
3	5001	356

prune231.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	66	5	71
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	67	6	73

Merged error: 0b

Counts

73 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z 6.012459259764103 (fma z z 3.350343815022304))
0.0b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
4.8b	(/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))
18.1b	(fma (/ y (fma z 6.012459259764103 (fma z 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 (fma z z 3.350343815022304))
1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.0ms	(/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))
1.0ms	(fma (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series256.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(fma z 6.012459259764103 (fma z z 3.350343815022304))
26.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
67.0ms	(/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))
140.0ms	(fma (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify109.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	243	404
1	794	360
2	3558	357
3	5002	355

prune206.0ms

Filtered

71 candidates to 57 candidates (80.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Merged error: 0b

Counts

77 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
0.6b	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
4.7b	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
18.1b	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `fma-udef` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 91

Calls

4 calls:

1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.0ms	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
7.0ms	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
1.0ms	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series257.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
40.0ms	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
58.0ms	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
134.0ms	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify51.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	364	632
1	1472	543
2	5001	514

prune238.0ms

Filtered

103 candidates to 68 candidates (66.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	103	6	109

Merged error: 0b

Counts

109 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

4.8b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
18.1b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
18.1b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
18.1b	(fma (/ y (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

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:

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

series459.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
133.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
130.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
134.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify98.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	209	520
1	674	461
2	2867	456
3	5001	450

prune268.0ms

Filtered

71 candidates to 62 candidates (87.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	71	6	77

Merged error: 0b

Counts

77 → 6

regimes238.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 17.3b

bsearch148.0ms

Steps

Iters	Range		Point
9	23682.176306478614	1721105950.3263278	170937625.80251658
8	-13078662382.933744	-3672304.856414551	-656707439.4289438

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	13
1	40	13

end0.0ms

sample576.0ms

Algorithm

intervals

Results

406.0ms

8000×

body

valid