Details

sample26.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify66.0ms

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: 17.7b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.0b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.6b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
17.1b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite41.0ms

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×	`associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `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 → 88

Calls

4 calls:

7.0ms	(* (+ z 6.012459259764103) z)
7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
16.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series282.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (+ z 6.012459259764103) z)
65.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
50.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
122.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify71.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	525	728
1	2508	623
2	5001	623

prune228.0ms

Filtered

100 candidates to 68 candidates (68.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	4	101

Merged error: 0b

Counts

101 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.0b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.1b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.4b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `associate-l`
5×	`flip3-+` `flip-+`
4×	`associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l/`
1×	`frac-2neg` `associate-*r/` `clear-num` `distribute-lft-out`

Counts

4 → 106

Calls

4 calls:

6.0ms	(* (+ z 6.012459259764103) z)
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))

series295.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (+ z 6.012459259764103) z)
64.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
119.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
67.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify74.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	545	1085
1	2456	970
2	5001	970

prune265.0ms

Filtered

118 candidates to 85 candidates (72.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Merged error: 0b

Counts

122 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.0b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.4b	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
15.4b	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
64×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
60×	`add-cube-cbrt`
18×	`associate-/r*`
15×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r/`
8×	`pow1` `flip3-+` `flip-+`
7×	`associate-l`
6×	`associate-r` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`distribute-lft-out`

Counts

4 → 150

Calls

4 calls:

6.0ms	(* (+ z 6.012459259764103) z)
7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
15.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
14.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

series292.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (+ z 6.012459259764103) z)
62.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
122.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
64.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

simplify101.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	733	2059
1	3325	1939
2	5001	1937

prune398.0ms

Filtered

162 candidates to 126 candidates (77.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	162	4	166

Merged error: 0b

Counts

166 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ z 6.012459259764103)) z)
0.7b	(* (cbrt (+ z 6.012459259764103)) (cbrt (+ z 6.012459259764103)))
3.6b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
17.1b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (* (cbrt (+ z 6.012459259764103)) (cbrt (+ z 6.012459259764103))) (* (cbrt (+ z 6.012459259764103)) z)) 3.350343815022304))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
29×	`cbrt-prod`
19×	`add-cube-cbrt`
17×	`associate-l`
15×	`pow1` `add-exp-log`
14×	`cbrt-div`
13×	`associate-r`
12×	`add-cbrt-cube`
10×	`flip3-+` `flip-+`
9×	`swap-sqr`
7×	`distribute-lft-out` `unswap-sqr`
6×	`pow1/3` `associate-*r/`
4×	`frac-times` `pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `associate-/r` `-commutative`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`pow2` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-plus` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 125

Calls

4 calls:

7.0ms	(* (cbrt (+ z 6.012459259764103)) z)
10.0ms	(* (cbrt (+ z 6.012459259764103)) (cbrt (+ z 6.012459259764103)))
10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
28.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (* (cbrt (+ z 6.012459259764103)) (cbrt (+ z 6.012459259764103))) (* (cbrt (+ z 6.012459259764103)) z)) 3.350343815022304))

series419.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (cbrt (+ z 6.012459259764103)) z)
104.0ms	(* (cbrt (+ z 6.012459259764103)) (cbrt (+ z 6.012459259764103)))
51.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
123.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (* (cbrt (+ z 6.012459259764103)) (cbrt (+ z 6.012459259764103))) (* (cbrt (+ z 6.012459259764103)) z)) 3.350343815022304))

simplify93.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	726	1386
1	3074	1224
2	5002	1177

prune369.0ms

Filtered

137 candidates to 92 candidates (67.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	137	4	141

Merged error: 0b

Counts

141 → 4

regimes140.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.0b

bsearch166.0ms

Steps

Iters	Range		Point
9	573.0632436401448	118875297.13418089	315594.62982369476
9	-39495616121.36297	-27949.393755151574	-962988.3809334021

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	26
1	57	26

end0.0ms

sample486.0ms

Algorithm

intervals

Results

323.0ms

8000×

body

valid