Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify82.0ms

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: 13.9b

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)
2.6b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
13.8b	(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)

series239.0ms

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)
61.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
133.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify100.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (94.0ms)

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

prune274.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

13.3b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
13.3b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
13.3b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
13.8b	(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)

series407.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
105.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
109.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
86.0ms	(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 (65.0ms)

Iter	Nodes	Cost
0	194	563
1	578	504
2	2319	479
3	5002	461

prune315.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
1.4b	(* (* (cbrt y) (cbrt y)) (/ (cbrt y) (fma (+ z 6.012459259764103) z 3.350343815022304)))
1.5b	(/ (cbrt y) (fma (+ z 6.012459259764103) z 3.350343815022304))
13.8b	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `times-frac`
33×	`add-cube-cbrt` `*-un-lft-identity`
25×	`cbrt-prod`
22×	`associate-r`
18×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/r*` `unswap-sqr`
2×	`div-inv`
1×	`frac-2neg` `pow1/3` `associate-r/` `associate-l` `clear-num` `-commutative` `fma-udef`

Counts

4 → 111

Calls

4 calls:

0.0ms	(cbrt y)
18.0ms	(* (* (cbrt y) (cbrt y)) (/ (cbrt y) (fma (+ z 6.012459259764103) z 3.350343815022304)))
3.0ms	(/ (cbrt y) (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series516.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt y)
77.0ms	(* (* (cbrt y) (cbrt y)) (/ (cbrt y) (fma (+ z 6.012459259764103) z 3.350343815022304)))
108.0ms	(/ (cbrt y) (fma (+ z 6.012459259764103) z 3.350343815022304))
154.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify71.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	525	1133
1	2545	969
2	5002	931

prune527.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

13.3b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
13.3b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
13.3b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
13.8b	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (expm1 (log1p (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)) (expm1 (log1p (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)

series1.1s

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
111.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
109.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
820.0ms	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (expm1 (log1p (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)

simplify85.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	209	591
1	641	527
2	2609	501
3	5001	480

prune340.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes192.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 17.1b

bsearch125.0ms

Steps

Iters	Range		Point
8	34603714037.68664	1348841620748990.5	35623158844.36978
7	-537794128203271.2	-8723610261783.773	-69321189749152.56

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	10
1	31	10

end0.0ms

sample511.0ms

Algorithm

intervals

Results

343.0ms

8000×

body

valid