Details

sample25.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 20.7b

Counts

2 → 1

localize13.0ms

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)
3.1b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.9b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite50.0ms

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:

16.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
15.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series413.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
60.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
52.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
116.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify73.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (15.0ms)

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

prune210.0ms

Filtered

91 candidates to 65 candidates (71.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	4	92

Merged error: 0b

Counts

92 → 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)
0.2b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
14.4b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite50.0ms

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:

7.0ms	(+ (* (+ 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)))
17.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series258.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
62.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
115.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
62.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify68.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	504	1086
1	2201	967
2	5001	967

prune238.0ms

Filtered

108 candidates to 80 candidates (74.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	108	4	112

Merged error: 0b

Counts

112 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

10.7b	(* (/ 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))))
14.2b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.2b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.2b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite64.0ms

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))
6.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series432.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (/ 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))))
110.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
101.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
102.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify87.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (67.0ms)

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

prune429.0ms

Filtered

120 candidates to 102 candidates (85.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	120	4	124

Merged error: 0b

Counts

124 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(* (cbrt z) (cbrt z))
3.1b	(* y (+ (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) (* (cbrt z) (cbrt z))) (cbrt z)) 0.279195317918525))
19.9b	(/ (* y (+ (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) (* (cbrt z) (cbrt z))) (cbrt z)) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`cbrt-prod`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `add-exp-log`
11×	`add-cbrt-cube`
9×	`associate-r` `associate-l`
7×	`pow1/3`
6×	`swap-sqr`
5×	`unswap-sqr`
4×	`associate-*r/` `add-log-exp`
3×	`flip3-+` `times-frac` `pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod` `flip-+`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `pow-sqr` `*-commutative` `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 → 98

Calls

4 calls:

1.0ms	(cbrt z)
11.0ms	(* (cbrt z) (cbrt z))
16.0ms	(* y (+ (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) (* (cbrt z) (cbrt z))) (cbrt z)) 0.279195317918525))
23.0ms	(/ (* y (+ (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) (* (cbrt z) (cbrt z))) (cbrt z)) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series610.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt z)
202.0ms	(* (cbrt z) (cbrt z))
86.0ms	(* y (+ (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) (* (cbrt z) (cbrt z))) (cbrt z)) 0.279195317918525))
149.0ms	(/ (* y (+ (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) (* (cbrt z) (cbrt z))) (cbrt z)) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify80.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	477	1056
1	2402	869
2	5001	822

prune294.0ms

Filtered

110 candidates to 83 candidates (75.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	110	4	114

Merged error: 0b

Counts

114 → 4

regimes127.0ms

Accuracy

99% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.1b

bsearch156.0ms

Steps

Iters	Range		Point
9	1.70242804785995e-07	1.2368608357549227	1.2145866554018125
9	-169909034969.6844	-225.5047040817839	-4234907.129887061

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	20
1	50	20

end0.0ms

sample588.0ms

Algorithm

intervals

Results

413.0ms

8000×

body

valid