Details

sample24.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify72.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.7b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.8b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
9×	`associate-r`
5×	`flip3-+` `flip-+`
4×	`associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `-commutative` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `associate-/l/`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 88

Calls

4 calls:

22.0ms	(* (+ z 6.012459259764103) z)
27.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
51.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
48.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series306.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (+ z 6.012459259764103) z)
61.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
53.0ms	(* 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))

simplify78.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	525	728
1	2508	623
2	5001	623

prune286.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
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)))
16.8b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `associate-l`
5×	`flip3-+` `flip-+`
4×	`associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l/`
1×	`frac-2neg` `associate-*r/` `clear-num` `distribute-lft-out`

Counts

4 → 106

Calls

4 calls:

21.0ms	(* (+ z 6.012459259764103) z)
28.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
81.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
57.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series292.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (+ z 6.012459259764103) z)
65.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
119.0ms	(* 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))

simplify81.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	545	1085
1	2456	970
2	5001	970

prune334.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

7.7b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
16.1b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
16.1b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
16.2b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite242.0ms

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:

143.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
16.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
16.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
59.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (/ 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))
119.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify100.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	720	2533
1	3090	2327
2	5002	2242

prune543.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

15.2b	(* (* (* (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))) y) (/ (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
16.7b	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
16.7b	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
16.7b	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

rewrite563.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-div`
28×	`associate-*l/`
25×	`add-exp-log`
24×	`associate-r`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`cbrt-prod` `times-frac` `add-cbrt-cube`
16×	`frac-times` `flip3-+` `flip-+`
13×	`pow1`
12×	`prod-exp` `cbrt-unprod`
6×	`pow-prod-down`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow1/3` `div-exp`
2×	`associate-/r/`
1×	`associate-l` `*-commutative` `div-inv`

Counts

4 → 104

Calls

4 calls:

520.0ms	(* (* (* (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))) y) (/ (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
12.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
12.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
13.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

series516.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (* (* (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))) y) (/ (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
148.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
150.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
148.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

simplify119.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	792	2610
1	3467	2320
2	5001	2204

prune480.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes140.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.8b

bsearch130.0ms

Steps

Iters	Range		Point
5	3390.167536312335	7732.291311132395	7653.416994905711
8	-7.337636233897625e+33	-2.0822744224856455e+29	-2.1290038037395552e+29

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	25
1	55	25

end0.0ms

sample553.0ms

Algorithm

intervals

Results

327.0ms

8000×

body

valid