Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify88.0ms

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: 16.9b

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)
5.3b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
16.2b	(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)

series242.0ms

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)
63.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
135.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify112.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (100.0ms)

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

prune254.0ms

Filtered

71 candidates to 59 candidates (83.1%)

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: 0b

Counts

73 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
15.7b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
16.2b	(fma (* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
58×	`times-frac`
38×	`*-un-lft-identity`
35×	`sqrt-prod`
32×	`add-cube-cbrt`
26×	`add-exp-log`
22×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
8×	`pow1` `div-exp` `prod-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef`

Counts

4 → 125

Calls

4 calls:

22.0ms	(* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
2.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (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:

48.0ms	(* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
56.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
51.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
89.0ms	(fma (* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify74.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	569	1489
1	2571	1300
2	5001	1177

prune429.0ms

Filtered

137 candidates to 91 candidates (66.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	137	5	142

Merged error: 0b

Counts

142 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

14.2b	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
14.2b	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
14.2b	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
16.2b	(fma (* (* (cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304))) (cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))) (cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

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:

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

series719.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
188.0ms	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
186.0ms	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
158.0ms	(fma (* (* (cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304))) (cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))) (cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify87.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	281	1164
1	735	1096
2	2695	1012
3	5003	964

prune637.0ms

Filtered

94 candidates to 83 candidates (88.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

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

Merged error: 0b

Counts

99 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 0.0692910599291889) 0.4917317610505968)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.8b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.7b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `fma-def` `frac-2neg` `distribute-lft-in` `clear-num` `sum-log` `div-inv` `associate-/l*`

Counts

4 → 87

Calls

4 calls:

4.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
16.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series279.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
66.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
52.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
125.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify76.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	505	679
1	2301	571
2	5003	552

prune291.0ms

Filtered

99 candidates to 78 candidates (78.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	99	5	104

Merged error: 0b

Counts

104 → 5

regimes193.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.6b

bsearch136.0ms

Steps

Iters	Range		Point
8	1.9936437952865932e-05	0.09117784756913819	0.08969441358922764
8	-4.2197574811023237e+18	-113800757124221.17	-115891591468242.34

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	13
1	40	13

end0.0ms

sample491.0ms

Algorithm

intervals

Results

317.0ms

8000×

body

valid