Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

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

localize18.0ms

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)
4.1b	(* 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))

rewrite44.0ms

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:

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

series434.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
65.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
55.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
121.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify71.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (15.0ms)

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

prune226.0ms

Filtered

91 candidates to 65 candidates (71.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	5	92

Merged error: 0.0b

Counts

92 → 5

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)
0.1b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.8b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite44.0ms

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:

3.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
16.0ms	(* 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))

series456.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
67.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
122.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
68.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify77.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (15.0ms)

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

prune256.0ms

Filtered

108 candidates to 81 candidates (75.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	108	5	113

Merged error: 0.0b

Counts

113 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))))
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)))
15.9b	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

23.0ms	(+ x (/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))))
6.0ms	(* (+ (* 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))

series449.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(+ x (/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))))
67.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
121.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
66.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

simplify96.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	740	2166
1	3239	2054
2	5001	2052

prune398.0ms

Filtered

153 candidates to 123 candidates (80.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	152	6	158

Merged error: 0.0b

Counts

158 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ y (+ (- 14.431876219268938 (* 15.646356830292035 (/ 1 z))) (/ (/ 101.23733352003816 z) z))))
0.1b	(/ (/ 101.23733352003816 z) z)
0.2b	(* 15.646356830292035 (/ 1 z))
2.6b	(/ y (+ (- 14.431876219268938 (* 15.646356830292035 (/ 1 z))) (/ (/ 101.23733352003816 z) z)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

98×	`times-frac`
74×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
20×	`add-exp-log`
16×	`add-cbrt-cube` `associate-/l*`
13×	`associate-r`
7×	`associate-/r*` `div-inv`
6×	`pow1` `div-exp` `add-log-exp`
5×	`cbrt-undiv` `distribute-lft-out`
4×	`prod-exp` `associate-/r/`
3×	`associate-l` `unswap-sqr`
2×	`frac-2neg` `flip3-+` `frac-add` `clear-num` `cbrt-unprod` `flip-+`
1×	`+-commutative` `rec-exp` `flip3--` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `flip--` `associate-/l/`

Counts

4 → 153

Calls

4 calls:

24.0ms	(+ x (/ y (+ (- 14.431876219268938 (* 15.646356830292035 (/ 1 z))) (/ (/ 101.23733352003816 z) z))))
7.0ms	(/ (/ 101.23733352003816 z) z)
7.0ms	(* 15.646356830292035 (/ 1 z))
15.0ms	(/ y (+ (- 14.431876219268938 (* 15.646356830292035 (/ 1 z))) (/ (/ 101.23733352003816 z) z)))

series189.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ x (/ y (+ (- 14.431876219268938 (* 15.646356830292035 (/ 1 z))) (/ (/ 101.23733352003816 z) z))))
24.0ms	(/ (/ 101.23733352003816 z) z)
21.0ms	(* 15.646356830292035 (/ 1 z))
71.0ms	(/ y (+ (- 14.431876219268938 (* 15.646356830292035 (/ 1 z))) (/ (/ 101.23733352003816 z) z)))

simplify76.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	757	1180
1	2997	1093
2	5001	1074

prune313.0ms

Filtered

165 candidates to 115 candidates (69.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	165	6	171

Merged error: 0b

Counts

171 → 6

regimes144.0ms

Accuracy

99.3% (0.1b remaining)

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

bsearch123.0ms

Steps

Iters	Range		Point
9	1.8094954886202674e-05	719.5386143167987	706.9288753704659
6	-4.96210287426386e+63	-3.5144341349313177e+62	-4.473702690008259e+63

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	15
1	46	15

end0.0ms

sample502.0ms

Algorithm

intervals

Results

334.0ms

8000×

body

valid