Details

sample24.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify110.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.4b

localize18.0ms

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)
4.3b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
17.1b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite8.0ms

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)

series252.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
27.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
65.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
139.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify119.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (112.0ms)

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

prune282.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

14.6b	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
14.6b	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
14.6b	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
17.1b	(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)

series743.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
197.0ms	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
192.0ms	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
163.0ms	(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)

simplify89.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (76.0ms)

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

prune475.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

14.6b	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
17.1b	(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)
17.1b	(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)
17.1b	(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)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

13×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 54

Calls

4 calls:

3.0ms	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
0.0ms	(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)
0.0ms	(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)
4.0ms	(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)

series682.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(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)
168.0ms	(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)
159.0ms	(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)

simplify88.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	281	1044
1	735	920
2	2695	868
3	5003	836

prune419.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.7b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.8b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

21.0ms	(* (+ z 6.012459259764103) z)
27.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
51.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
48.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series306.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (+ z 6.012459259764103) z)
72.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
54.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
127.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify81.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	549	703
1	2591	599
2	5001	580

prune367.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes214.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.8b

bsearch106.0ms

Steps

Iters	Range		Point
5	3390.167536312335	7732.291311132395	7653.416994905711
8	-2.0822744224856455e+29	-2.1521170067023927e+26	-2.1821084219369114e+26

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	9
1	28	9

end0.0ms

sample569.0ms

Algorithm

intervals

Results

340.0ms

8000×

body

valid