Details

sample23.0ms

Algorithm

intervals

Results

10.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.8b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.6b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite62.0ms

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:

9.0ms	(* (+ z 6.012459259764103) z)
10.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
23.0ms	(* 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))

series287.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (+ z 6.012459259764103) z)
66.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
54.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
122.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify71.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (15.0ms)

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

prune271.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
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)))
15.4b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite85.0ms

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:

10.0ms	(* (+ z 6.012459259764103) z)
11.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
37.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
22.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series294.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (+ z 6.012459259764103) z)
65.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
123.0ms	(* 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))

simplify75.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (16.0ms)

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

prune325.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

7.8b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
14.6b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite120.0ms

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:

73.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
26.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
8.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
8.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series362.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
124.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
56.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
50.0ms	(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	2533
1	3090	2327
2	5002	2242

prune532.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.6b	(* (/ (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (sqrt (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

495×	`times-frac`
411×	`sqrt-prod`
389×	`add-sqr-sqrt`
222×	`associate-l`
216×	`add-cube-cbrt` `*-un-lft-identity`
40×	`unswap-sqr`
33×	`associate-r`
32×	`sqrt-div`
25×	`add-exp-log` `add-cbrt-cube`
22×	`associate-/r/`
14×	`flip3-+` `flip-+`
11×	`div-inv`
9×	`pow1` `cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 364

Calls

4 calls:

8.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
8.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
8.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
228.0ms	(* (/ (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (sqrt (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
50.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
55.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
125.0ms	(* (/ (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (sqrt (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))))

simplify109.0ms

Algorithm

egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1259	9230
1	5001	8399

prune1.4s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes133.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.0b

bsearch180.0ms

Steps

Iters	Range		Point
9	89650.56729712563	167712351607.73917	405500.71364467713
10	-1.3796619314999023e+25	-146662999352.95746	-199552179246.0691

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	32
1	57	32

end0.0ms

sample506.0ms

Algorithm

intervals

Results

335.0ms

8000×

body

valid