Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

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

prune8.0ms

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: 16.1b

Counts

2 → 2

localize16.0ms

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)
3.6b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
16.8b	(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)

series235.0ms

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)
62.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
130.0ms	(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

prune256.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	68	5	73

Merged error: 0b

Counts

73 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z 6.012459259764103 (fma z z 3.350343815022304))
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.6b	(/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))
16.8b	(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)

series444.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(fma z 6.012459259764103 (fma z z 3.350343815022304))
25.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
257.0ms	(/ 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)

simplify103.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (97.0ms)

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

prune240.0ms

Filtered

71 candidates to 57 candidates (80.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	71	5	76

Merged error: 0b

Counts

76 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
0.5b	(/ 1 (/ (fma z 6.012459259764103 (fma z z 3.350343815022304)) y))
3.3b	(/ (fma z 6.012459259764103 (fma z z 3.350343815022304)) y)
16.8b	(fma (/ 1 (/ (fma z 6.012459259764103 (fma z z 3.350343815022304)) y)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite14.0ms

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

series206.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
44.0ms	(/ 1 (/ (fma z 6.012459259764103 (fma z z 3.350343815022304)) y))
46.0ms	(/ (fma z 6.012459259764103 (fma z z 3.350343815022304)) y)
88.0ms	(fma (/ 1 (/ (fma z 6.012459259764103 (fma z z 3.350343815022304)) y)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify57.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	475	1087
1	2001	960
2	5002	880

prune361.0ms

Filtered

139 candidates to 86 candidates (61.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	139	5	144

Merged error: 0b

Counts

144 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

16.8b	(fma (* (* (cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))) (cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))) (cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
17.8b	(cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))
17.8b	(cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))
17.8b	(cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`times-frac`
25×	`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×	`cbrt-div` `pow1/3` `div-inv`
1×	`fma-udef`

Counts

4 → 82

Calls

4 calls:

1.0ms	(fma (* (* (cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))) (cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))) (cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
2.0ms	(cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))
2.0ms	(cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))
2.0ms	(cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))

series703.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(fma (* (* (cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))) (cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))) (cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
183.0ms	(cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))
179.0ms	(cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))
180.0ms	(cbrt (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))))

simplify77.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	281	1164
1	740	1096
2	2702	1012
3	5001	964

prune445.0ms

Filtered

94 candidates to 84 candidates (89.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	94	5	99

Merged error: 0b

Counts

99 → 5

regimes215.0ms

Accuracy

98.7% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.1b

bsearch128.0ms

Steps

Iters	Range		Point
9	83.6778071934239	10451050.785873119	9202216.68121223
8	-1.1406388206438882e+35	-2.7167357396098293e+32	-2.7443029454137152e+32

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	13
1	40	13

end0.0ms

sample479.0ms

Algorithm

intervals

Results

306.0ms

8000×

body

valid