Details

sample79.0ms

Algorithm

intervals

Results

33.0ms	99×	body	2560	valid
17.0ms	76×	body	1280	valid
7.0ms	45×	body	640	valid
7.0ms	258×	body	80	nan
3.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	4×	body	80	valid

simplify97.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	42	7
2	77	7
3	146	7
4	242	7
5	417	7
6	2789	7
7	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (* 5.0 (* v v)))
0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.3b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp`
4×	`associate-/r*` `difference-of-squares`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

3.0ms	(- 1.0 (* 5.0 (* v v)))
7.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series177.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- 1.0 (* 5.0 (* v v)))
86.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
30.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	355	664
1	1356	609
2	5001	605

prune186.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

9.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
133.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
141.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
135.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify83.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	117	1278
1	417	1112
2	2698	1044
3	5001	1031

prune178.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (sqrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (pow (sqrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
46×	`sqrt-prod`
32×	`cbrt-prod`
24×	`associate-r` `unswap-sqr`
18×	`unpow-prod-down` `cube-prod`
17×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `associate-l`
6×	`add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp` `sqr-pow`
3×	`pow1/3` `prod-exp`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

12.0ms	(* (sqrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (pow (sqrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

series573.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (sqrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (pow (sqrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3))
139.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
132.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
137.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify47.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	230	2519
1	811	1959
2	5001	1840

prune250.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

series546.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
134.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
138.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
134.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify50.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 4 (43.0ms)

Iter	Nodes	Cost
0	58	672
1	123	604
2	307	596
3	1028	596
4	5001	592

prune214.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

regimes63.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	3067×	body	2560	valid
567.0ms	2513×	body	1280	valid
216.0ms	7877×	body	80	nan
200.0ms	1227×	body	640	valid
73.0ms	613×	body	320	valid
32.0ms	370×	body	160	valid
10.0ms	210×	body	80	valid