Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify67.0ms

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: 20.4b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 0.0692910599291889) 0.4917317610505968)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.8b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.7b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
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` `associate-/l*`

Counts

4 → 78

Calls

4 calls:

8.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
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))

series282.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
63.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
59.0ms	(* 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))

simplify72.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	479	705
1	2236	601
2	5002	601

prune248.0ms

Filtered

90 candidates to 63 candidates (70.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	3	91

Merged error: 0.0b

Counts

91 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 0.0692910599291889) 0.4917317610505968)
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)))
16.4b	(/ (+ (* (+ (* 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:

4.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
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)))
14.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series295.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
67.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
123.0ms	(* 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))

simplify68.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	499	1062
1	2187	948
2	5002	948

prune298.0ms

Filtered

108 candidates to 80 candidates (74.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	108	3	111

Merged error: 0.0b

Counts

111 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 0.0692910599291889) 0.4917317610505968)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.4b	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
16.4b	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
60×	`add-sqr-sqrt`
58×	`add-cube-cbrt` `*-un-lft-identity`
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` `unswap-sqr`

Counts

4 → 140

Calls

4 calls:

4.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
18.0ms	(/ 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))

series296.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
70.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
124.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
68.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

simplify91.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	685	2031
1	3036	1917
2	5002	1915

prune479.0ms

Filtered

152 candidates to 122 candidates (80.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	152	3	155

Merged error: 0.0b

Counts

155 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 0.40462203869992125 (/ 1 (pow z 2)))
0.3b	(* 0.07512208616047561 (/ 1 z))
0.6b	(/ 1 (pow z 2))
4.1b	(* y (- (+ (* 0.07512208616047561 (/ 1 z)) 0.0692910599291889) (* 0.40462203869992125 (/ 1 (pow z 2)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
67×	`times-frac`
52×	`*-un-lft-identity`
47×	`add-cube-cbrt`
44×	`add-exp-log` `associate-r`
23×	`unpow-prod-down`
18×	`add-cbrt-cube`
15×	`prod-exp`
14×	`div-exp`
13×	`unswap-sqr`
10×	`pow1` `associate-*r/`
9×	`associate-l` `unpow2` `sqr-pow`
8×	`associate-/r*`
7×	`rec-exp` `1-exp`
6×	`pow-to-exp` `pow-exp`
5×	`cbrt-unprod`
4×	`un-div-inv` `frac-sub` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `-commutative` `div-inv` `associate-/l`
2×	`sub-neg` `flip3-+` `associate--l+` `flip-+`
1×	`flip3--` `pow-flip` `frac-2neg` `clear-num` `flip--` `inv-pow`

Counts

4 → 186

Calls

4 calls:

11.0ms	(* 0.40462203869992125 (/ 1 (pow z 2)))
7.0ms	(* 0.07512208616047561 (/ 1 z))
5.0ms	(/ 1 (pow z 2))
11.0ms	(* y (- (+ (* 0.07512208616047561 (/ 1 z)) 0.0692910599291889) (* 0.40462203869992125 (/ 1 (pow z 2)))))

series123.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* 0.40462203869992125 (/ 1 (pow z 2)))
16.0ms	(* 0.07512208616047561 (/ 1 z))
16.0ms	(/ 1 (pow z 2))
59.0ms	(* y (- (+ (* 0.07512208616047561 (/ 1 z)) 0.0692910599291889) (* 0.40462203869992125 (/ 1 (pow z 2)))))

simplify86.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	685	1077
1	3187	880
2	5002	798

prune393.0ms

Filtered

198 candidates to 106 candidates (53.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	198	3	201

Merged error: 0.0b

Counts

201 → 3

regimes112.0ms

Accuracy

99.1% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.0b

bsearch153.0ms

Steps

Iters	Range		Point
8	1.9936437952865932e-05	0.09117784756913819	0.08969441358922764
9	-3.925732954088894e+24	-4.2197574811023237e+18	-3.8789965973328694e+24

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	19
1	56	19

end0.0ms

sample697.0ms

Algorithm

intervals

Results

528.0ms

8000×

body

valid