Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.9b

localize13.0ms

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)
5.5b	(/ 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)

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)

series248.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
26.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
63.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
138.0ms	(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

prune275.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
0.3b	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
5.4b	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
16.8b	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `fma-udef` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 91

Calls

4 calls:

0.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
2.0ms	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
8.0ms	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
0.0ms	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series270.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
38.0ms	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
64.0ms	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
141.0ms	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify54.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	364	632
1	1472	543
2	5001	514

prune299.0ms

Filtered

103 candidates to 67 candidates (65.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

14.4b	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
14.4b	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
14.4b	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
16.8b	(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)

rewrite7.0ms

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	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
1.0ms	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
2.0ms	(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)

series730.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
190.0ms	(cbrt (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))
189.0ms	(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)

simplify80.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (67.0ms)

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

prune468.0ms

Filtered

94 candidates to 82 candidates (87.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.6b	(* 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))

rewrite62.0ms

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:

10.0ms	(* (+ z 6.012459259764103) z)
11.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
21.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
17.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series303.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (+ z 6.012459259764103) z)
69.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
53.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
131.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify75.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (65.0ms)

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

prune332.0ms

Filtered

108 candidates to 86 candidates (79.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes147.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.2b

bsearch116.0ms

Steps

Iters	Range		Point
8	927621.7061119184	6212637483.285134	698981194.6084762
6	-5.517392773027729e+49	-6.984729234488143e+48	-1.6182939126081175e+49

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	11
1	38	11
2	38	11

end0.0ms

sample494.0ms

Algorithm

intervals

Results

323.0ms

8000×

body

valid