Details

sample25.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify72.0ms

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: 21.4b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.8b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.6b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

253×	`*-un-lft-identity`
119×	`distribute-lft-out`
100×	`associate-l`
96×	`times-frac`
68×	`add-sqr-sqrt`
62×	`associate-r`
48×	`add-cube-cbrt`
16×	`associate-/l*`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `*-commutative` `unswap-sqr`
6×	`associate-/r*`
5×	`flip3-+` `flip-+`
4×	`associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`pow-prod-down`
2×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-/r/` `associate-/l/`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 207

Calls

4 calls:

6.0ms	(* (+ z 6.012459259764103) z)
13.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
21.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
32.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series306.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (+ z 6.012459259764103) z)
68.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
58.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
133.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify106.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	643	2269
1	3021	2162
2	5001	2162

prune319.0ms

Filtered

219 candidates to 104 candidates (47.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	214	5	219
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	215	5	220

Merged error: 0b

Counts

220 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
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)))
16.1b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

309×	`*-un-lft-identity`
157×	`distribute-lft-out`
105×	`associate-l`
85×	`times-frac`
54×	`associate-r`
49×	`add-sqr-sqrt`
40×	`add-cube-cbrt`
19×	`associate-/l*`
18×	`associate-*r/`
15×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
10×	`pow1`
6×	`flip3-+` `un-div-inv` `flip-+`
4×	`associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `clear-num` `*-commutative`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 204

Calls

4 calls:

6.0ms	(* (+ z 6.012459259764103) z)
13.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
38.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
27.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series321.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (+ z 6.012459259764103) z)
70.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
127.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
72.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify97.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	576	1716
1	2628	1606
2	5002	1606

prune280.0ms

Filtered

216 candidates to 93 candidates (43.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	213	3	216
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	216	5	221

Merged error: 0b

Counts

221 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

8.6b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
15.4b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.4b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.5b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

953×	`*-un-lft-identity`
448×	`distribute-lft-out`
354×	`sqrt-prod`
351×	`associate-/r*`
315×	`frac-times`
293×	`associate-l`
218×	`add-sqr-sqrt`
190×	`associate-/l*`
186×	`add-cube-cbrt`
165×	`times-frac`
69×	`associate-r`
40×	`clear-num`
39×	`frac-2neg`
34×	`associate-/l/`
22×	`flip3-+` `flip-+`
21×	`associate-*r/`
18×	`add-exp-log` `add-cbrt-cube`
15×	`associate-*l/`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`associate-/r/` `un-div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 616

Calls

4 calls:

92.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
10.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
10.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
29.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
52.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
58.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
136.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify157.0ms

Algorithm

egg-herbie

Counts

628 → 628

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	1518	9979
1	5001	9271

prune709.0ms

Filtered

628 candidates to 194 candidates (30.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	628	0	628
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	628	5	633

Merged error: 0b

Counts

633 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
0.3b	(* (* y (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
16.1b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
16.1b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

1402×	`*-un-lft-identity`
730×	`distribute-lft-out`
702×	`sqrt-div`
504×	`associate-l`
378×	`associate-*r/`
324×	`frac-times`
287×	`associate-/l*`
246×	`associate-/r*`
219×	`times-frac`
214×	`add-sqr-sqrt`
162×	`sqrt-prod`
160×	`add-cube-cbrt`
153×	`associate-r`
82×	`associate-/l/`
46×	`flip3-+` `flip-+`
41×	`frac-2neg` `clear-num`
27×	`unswap-sqr`
18×	`associate-*l/`
15×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`associate-/r/`
5×	`div-inv`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`*-commutative`
2×	`cbrt-undiv` `div-exp`

Counts

4 → 727

Calls

4 calls:

40.0ms	(* y (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
132.0ms	(* (* y (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
28.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
32.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series497.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(* y (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
134.0ms	(* (* y (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
71.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
66.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify251.0ms

Algorithm

egg-herbie

Counts

739 → 739

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	1245	14321
1	4496	13541
2	5001	13115

prune1.0s

Filtered

739 candidates to 200 candidates (27.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	738	1	739
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	739	5	744

Merged error: 0b

Counts

744 → 5

regimes143.0ms

Accuracy

99.5% (0.1b remaining)

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

bsearch161.0ms

Steps

Iters	Range		Point
8	1450.1527464788446	55266295.648746796	624836.2270522026
9	-3.532745445146559e+20	-21436759175312.676	-35030970911263.484

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	30
1	56	30

end0.0ms

sample503.0ms

Algorithm

intervals

Results

328.0ms

8000×

body

valid