Details

sample23.0ms

Algorithm

intervals

Results

10.0ms

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 (100.0%)

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

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.6b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.7b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 200

Calls

4 calls:

10.0ms	(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
10.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
23.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
33.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series289.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
74.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
57.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
132.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify100.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	601	2277
1	2767	2168
2	5001	2168

prune317.0ms

Filtered

212 candidates to 99 candidates (53.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	208	4	212
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	209	4	213

Merged error: 0.0b

Counts

213 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (+ 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)))
15.6b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

312×	`*-un-lft-identity`
160×	`distribute-lft-out`
103×	`associate-l`
85×	`times-frac`
51×	`associate-r`
45×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
19×	`associate-/l*`
18×	`associate-*r/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
8×	`pow1`
6×	`flip3-+` `un-div-inv` `flip-+` `add-log-exp`
4×	`associate-/r/` `associate-/l/`
3×	`prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `sum-log`

Counts

4 → 197

Calls

4 calls:

10.0ms	(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
10.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
39.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
31.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series298.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
72.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
134.0ms	(* y (/ (+ (* (+ (* 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))

simplify83.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	534	1724
1	2374	1612
2	5003	1612

prune261.0ms

Filtered

209 candidates to 87 candidates (58.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	207	2	209
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	209	4	213

Merged error: 0.0b

Counts

213 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 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))))
15.6b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.6b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite315.0ms

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:

44.0ms	(* y (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
133.0ms	(* (* 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))
28.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series506.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(* y (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
135.0ms	(* (* 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))))
73.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
78.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify253.0ms

Algorithm

egg-herbie

Counts

739 → 739

Iterations

Useful iterations: 2 (94.0ms)

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

prune837.0ms

Filtered

739 candidates to 199 candidates (73.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	739	0	739
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	739	4	743

Merged error: 0.0b

Counts

743 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.3b	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
15.7b	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

718×	`*-un-lft-identity`
354×	`times-frac`
346×	`distribute-lft-out`
210×	`associate-l`
130×	`add-sqr-sqrt`
128×	`add-cube-cbrt`
62×	`associate-/r*`
28×	`associate-/r/`
15×	`associate-/l*`
13×	`add-exp-log` `add-cbrt-cube`
9×	`flip3-+` `flip-+`
6×	`pow1` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`frac-2neg` `associate-r` `clear-num`
2×	`associate-*l/`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 334

Calls

4 calls:

10.0ms	(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
13.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
36.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
29.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

series297.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
66.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
134.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
72.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

simplify120.0ms

Algorithm

egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	690	4151
1	3073	4032
2	5001	4030

prune602.0ms

Filtered

346 candidates to 128 candidates (63.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	345	1	346
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	345	5	350

Merged error: 0b

Counts

350 → 5

regimes136.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch90.0ms

Steps

Iters	Range		Point
4	56013586448040.74	93988328089074.5	56831241125707.26
6	-9.364925312448983e+44	-1.0208429830464386e+44	-1.6610773661727467e+44

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	19
1	53	19

end0.0ms

sample501.0ms

Algorithm

intervals

Results

330.0ms

8000×

body

valid