Details

sample25.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify85.0ms

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: 15.8b

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)
5.0b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(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)

series236.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
28.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
57.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
132.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify101.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (94.0ms)

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

prune225.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	69	4	73

Merged error: 0.0b

Counts

73 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

15.2b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.2b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.2b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(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)

series418.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
114.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
108.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
87.0ms	(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)

simplify74.0ms

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

prune271.0ms

Filtered

61 candidates to 56 candidates (91.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	60	5	65

Merged error: 0b

Counts

65 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

5.0b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
15.7b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
15.7b	(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:

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)

series467.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
136.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
132.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
136.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify93.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (85.0ms)

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

prune285.0ms

Filtered

71 candidates to 62 candidates (87.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	71	5	76

Merged error: 0b

Counts

76 → 5

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)
3.6b	(* y (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
17.1b	(/ (* y (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
4×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 65

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 (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
5.0ms	(/ (* y (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (fma (+ z 6.012459259764103) z 3.350343815022304))

series209.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
30.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
47.0ms	(* y (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
113.0ms	(/ (* y (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify40.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	258	452
1	1168	371
2	5001	369

prune189.0ms

Filtered

77 candidates to 57 candidates (74.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	77	5	82

Merged error: 0b

Counts

82 → 5

regimes161.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.2b

bsearch131.0ms

Steps

Iters	Range		Point
8	118875297.13418089	155178070842.29883	465380250.59235376
9	-39495616121.36297	-27949.393755151574	-1222349140.8800933

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	10
1	31	10

end0.0ms

sample515.0ms

Algorithm

intervals

Results

340.0ms

8000×

body

valid