Details

sample23.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify84.0ms

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

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.1b

localize12.0ms

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)
3.4b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.0b	(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:

0.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
5.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(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:

18.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
30.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
56.0ms	(/ 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)

simplify103.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (96.0ms)

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

prune269.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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)
3.4b	(/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))
15.0b	(fma (/ y (fma z 6.012459259764103 (fma z 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:

0.0ms	(fma z 6.012459259764103 (fma z z 3.350343815022304))
0.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
5.0ms	(/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))
0.0ms	(fma (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series249.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(fma z 6.012459259764103 (fma z z 3.350343815022304))
24.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
69.0ms	(/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))
133.0ms	(fma (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify114.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (100.0ms)

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

prune269.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

3.4b	(/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))
14.1b	(sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
14.1b	(sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
15.0b	(fma (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))) (* (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))) x)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 69

Calls

4 calls:

5.0ms	(/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))
1.0ms	(sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
2.0ms	(sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
0.0ms	(fma (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))) (* (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))) x)

series583.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))
289.0ms	(sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
88.0ms	(sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
142.0ms	(fma (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))) (* (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))) x)

simplify149.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	316	596
1	1049	537
2	4861	516
3	5001	516

prune331.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

14.5b	(cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304)))
14.5b	(cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304)))
14.5b	(cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304)))
15.0b	(fma (* (/ (* (cbrt y) (cbrt y)) (* (cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304))) (cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304))))) (/ (cbrt y) (cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304))))) (* (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))) x)

rewrite4.0ms

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 (fma z z 3.350343815022304)))
1.0ms	(cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304)))
1.0ms	(cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304)))
0.0ms	(fma (* (/ (* (cbrt y) (cbrt y)) (* (cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304))) (cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304))))) (/ (cbrt y) (cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304))))) (* (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))) x)

series486.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304)))
112.0ms	(cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304)))
109.0ms	(cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304)))
155.0ms	(fma (* (/ (* (cbrt y) (cbrt y)) (* (cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304))) (cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304))))) (/ (cbrt y) (cbrt (fma z 6.012459259764103 (fma z z 3.350343815022304))))) (* (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))) x)

simplify74.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	203	675
1	624	580
2	2454	553
3	5002	542

prune356.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes128.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.6b

bsearch110.0ms

Steps

Iters	Range		Point
5	71269444.69622602	197909896.62939358	147550388.83208096
8	-2.0260175217475176e+30	-8.115669647949308e+25	-8.335532760039213e+25

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	10
1	30	10

end0.0ms

sample538.0ms

Algorithm

intervals

Results

304.0ms

8000×

body

valid