Details

sample24.0ms

Algorithm

intervals

Results

12.0ms

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: 15.4b

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)
3.1b	(/ 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)

rewrite4.0ms

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)
2.0ms	(/ 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)

series246.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
30.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
63.0ms	(/ 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)

simplify102.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (95.0ms)

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

prune259.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

14.7b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.7b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.7b	(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)

rewrite3.0ms

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:

0.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(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)

series422.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
109.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
109.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
88.0ms	(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)

simplify73.0ms

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

prune304.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))
14.2b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.2b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(fma (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 217

Calls

4 calls:

11.0ms	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))
1.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series317.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))
52.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
58.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
139.0ms	(fma (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify86.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	714	3355
1	2634	2956
2	5001	2888

prune740.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

14.2b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.2b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.2b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(fma (/ (/ 1 (sqrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (/ y (sqrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

4 → 55

Calls

4 calls:

1.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (/ (/ 1 (sqrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (/ y (sqrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series243.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
53.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
50.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
87.0ms	(fma (/ (/ 1 (sqrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (/ y (sqrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify50.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	164	517
1	440	470
2	1715	453
3	5001	448

prune280.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes143.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch149.0ms

Steps

Iters	Range		Point
10	3273232.3860693905	3.06018844003218e+16	55515817.475789115
10	-212885859736577.44	-238.82950093874626	-132404126.90153868

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	10
1	31	10

end0.0ms

sample484.0ms

Algorithm

intervals

Results

318.0ms

8000×

body

valid