Details

sample25.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify76.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	10
1	64	10
2	143	10
3	288	10
4	443	10
5	563	10
6	648	10
7	817	10
8	1060	10
9	1066	10
10	1066	10

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 21.5b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.8b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.5b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

15.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
11.0ms	(* 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))

series513.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
71.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
63.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
140.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify88.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	534	840
1	2452	738
2	5003	738

prune263.0ms

Filtered

91 candidates to 65 candidates (71.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	6	92

Merged error: 0.0b

Counts

92 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.1b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.1b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/r/`
3×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `associate-/l/`
1×	`+-commutative` `frac-2neg` `associate-*r/` `clear-num` `sum-log`

Counts

4 → 96

Calls

4 calls:

4.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
17.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series515.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
74.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
138.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
74.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify84.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	554	1187
1	2427	1075
2	5001	1075

prune293.0ms

Filtered

108 candidates to 80 candidates (74.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	107	7	114

Merged error: 0.0b

Counts

114 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

14.0b	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
15.0b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.0b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.0b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
28×	`times-frac`
25×	`add-exp-log`
24×	`associate-r`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`cbrt-prod` `cbrt-div`
18×	`add-cbrt-cube`
15×	`associate-l`
10×	`flip3-+` `associate-/r/` `flip-+`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `unswap-sqr`
5×	`frac-times`
4×	`add-log-exp`
3×	`pow1/3` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 108

Calls

4 calls:

41.0ms	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
6.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
6.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
10.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series515.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
122.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
126.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
125.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify113.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	678	2226
1	3161	1944
2	5003	1833

prune493.0ms

Filtered

120 candidates to 101 candidates (84.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	120	7	127

Merged error: 0.0b

Counts

127 → 7

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y)))
0.0b	(+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y))
0.2b	(* 0.07512208616047561 (/ y z))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`-un-lft-identity` `associate-r*`
11×	`add-cube-cbrt`
10×	`times-frac` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`sum-log`
3×	`associate-l`
2×	`+-commutative` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`cbrt-undiv` `associate-+r+` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `distribute-lft-out`

Counts

3 → 57

Calls

3 calls:

12.0ms	(+ x (+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y)))
6.0ms	(+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y))
7.0ms	(* 0.07512208616047561 (/ y z))

series111.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ x (+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y)))
43.0ms	(+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y))
23.0ms	(* 0.07512208616047561 (/ y z))

simplify52.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	312	347
1	1297	326
2	5001	326

prune120.0ms

Filtered

66 candidates to 45 candidates (68.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	66	7	73

Merged error: 0.0b

Counts

73 → 7

regimes296.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.6b

bsearch204.0ms

Steps

Iters	Range		Point
10	1.9435667087631803	18857861456050.914	680550425.79129
10	-5.739400436815266e+25	-15263713579044.31	-96048976883392.06

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	15
1	46	15

end0.0ms

sample541.0ms

Algorithm

intervals

Results

365.0ms

8000×

body

valid