Details

sample26.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify87.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

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: 16.4b

Counts

2 → 2

localize13.0ms

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)
2.4b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
17.0b	(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)

series245.0ms

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)
59.0ms	(/ 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)

simplify105.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (98.0ms)

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

prune251.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	66	7	73

Merged error: 0b

Counts

73 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
0.8b	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y))
2.2b	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
17.0b	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
17×	`add-exp-log`
16×	`associate-/r*`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `fma-udef`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

4 → 127

Calls

4 calls:

1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
6.0ms	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y))
3.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
1.0ms	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series198.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
41.0ms	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y))
44.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
87.0ms	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify64.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	475	1087
1	1998	960
2	5002	880

prune305.0ms

Filtered

139 candidates to 83 candidates (59.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	140	6	146

Merged error: 0b

Counts

146 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) x)
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
2.2b	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
20.5b	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
91×	`*-un-lft-identity`
89×	`add-sqr-sqrt` `add-cube-cbrt`
44×	`fma-def`
16×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
6×	`associate-/l*` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `fma-udef` `distribute-lft-out`

Counts

4 → 169

Calls

4 calls:

17.0ms	(+ (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) x)
1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
6.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y))

series235.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) x)
30.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
38.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
76.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y))

simplify63.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	511	1353
1	1893	1274
2	5001	1271

prune569.0ms

Filtered

181 candidates to 157 candidates (86.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	181	6	187

Merged error: 0b

Counts

187 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b	(fma (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x)
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
15.8b	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

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:

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

series228.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
107.0ms	(fma (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x)
25.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
72.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify81.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	214	483
1	583	428
2	2886	425
3	5001	420

prune196.0ms

Filtered

71 candidates to 58 candidates (81.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	71	6	77

Merged error: 0b

Counts

77 → 6

regimes169.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.0b

bsearch119.0ms

Steps

Iters	Range		Point
9	1.8094954886202674e-05	719.5386143167987	706.9288753704659
6	-4.96210287426386e+63	-3.5144341349313177e+62	-4.473702690008259e+63

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	9
1	28	9

end0.0ms

sample494.0ms

Algorithm

intervals

Results

329.0ms

8000×

body

valid