Details

sample36.0ms

Algorithm

intervals

Results

23.0ms

256×

body

valid

simplify65.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize14.0ms

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)
3.8b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.5b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite65.0ms

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:

17.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
10.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
20.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
17.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series419.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
62.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
50.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
119.0ms	(/ (* 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 (14.0ms)

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

prune241.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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)))
15.1b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite76.0ms

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))))
10.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
37.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
23.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series434.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
63.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
116.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
64.0ms	(/ (+ (* (+ (* 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

prune297.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

6.3b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
14.5b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.5b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.6b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`times-frac`
47×	`add-cube-cbrt` `*-un-lft-identity`
42×	`sqrt-prod`
24×	`associate-r` `associate-l`
18×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 150

Calls

4 calls:

71.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
7.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
7.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
25.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
46.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
49.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
115.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify86.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	720	2535
1	3084	2327
2	5002	2242

prune501.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y)))
0.0b	(+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y))
0.2b	(* 0.07512208616047561 (/ y z))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`-un-lft-identity` `associate-r*`
11×	`add-cube-cbrt`
10×	`times-frac` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`sum-log`
3×	`associate-l`
2×	`+-commutative` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`cbrt-undiv` `associate-+r+` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `distribute-lft-out`

Counts

3 → 57

Calls

3 calls:

14.0ms	(+ x (+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y)))
4.0ms	(+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y))
7.0ms	(* 0.07512208616047561 (/ y z))

series90.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ x (+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y)))
36.0ms	(+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y))
18.0ms	(* 0.07512208616047561 (/ y z))

simplify42.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	312	347
1	1297	326
2	5001	326

prune121.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes194.0ms

Accuracy

99.3% (0.1b remaining)

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

bsearch195.0ms

Steps

Iters	Range		Point
10	1.9435667087631803	18857861456050.914	680550425.79129
10	-5.739400436815266e+25	-15263713579044.31	-96048976883392.06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	16
1	53	16
2	53	16

end0.0ms

sample903.0ms

Algorithm

intervals

Results

732.0ms

8000×

body

valid