Details

Time bar (total: 15.0s)

sample146.0ms

Algorithm
intervals
Results
54.0ms88×body2560valid
33.0ms80×body1280valid
14.0ms247×body80nan
14.0ms45×body640valid
5.0ms23×body320valid
2.0ms14×body160valid
0.0ms6×body80valid

simplify689.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
12014
24314
38414
415514
525214
693414
done500014

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize13.0ms

Local error

Found 2 expressions with local error:

0.2b
(* 5.0 (* v v))
0.7b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
4×add-sqr-sqrt
3×add-cube-cbrt *-un-lft-identity associate-*l* pow-prod-down prod-exp cbrt-unprod
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×acos-asin associate-*r* *-commutative unswap-sqr
Counts
2 → 31
Calls
2 calls:
17.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series45.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(* 5.0 (* v v))
5.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify767.0ms

Counts
37 → 37
Iterations

Useful iterations: 2 (141.0ms)

IterNodesCost
057413
1130410
2555352
done5001352

prune142.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.2b
(* 5.0 (* v v))
0.8b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
47×*-un-lft-identity
45×add-cube-cbrt
39×prod-diff
37×times-frac
13×fma-neg
8×pow1 add-exp-log add-cbrt-cube
5×add-log-exp
4×div-inv
3×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
2×asin-acos difference-of-squares
1×sub-neg flip3-- diff-log associate-*r* *-commutative flip-- distribute-lft-out-- associate--r- unswap-sqr
Counts
3 → 101
Calls
3 calls:
48.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
36.0ms
(* 5.0 (* v v))
2.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series111.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
57.0ms
(* 5.0 (* v v))
9.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.6s

Counts
110 → 110
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01655338
13663388
213652629
done50001956

prune385.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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×expm1-log1p-u add-cbrt-cube log1p-expm1-u 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 → 81
Calls
4 calls:
2.0ms
(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
2.0ms
(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
2.0ms
(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
23.0ms
(* (cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series857.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
224.0ms
(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
181.0ms
(cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
249.0ms
(* (cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify1.3s

Counts
93 → 93
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0652636
11422441
25871957
done50001895

prune438.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize43.0ms

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))))

rewrite25.0ms

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×expm1-log1p-u add-cbrt-cube log1p-expm1-u 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 → 81
Calls
4 calls:
18.0ms
(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
2.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
2.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
2.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

series790.0ms

Counts
4 → 12
Calls
4 calls:
231.0ms
(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
188.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
189.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
182.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify1.3s

Counts
93 → 93
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0652636
11422441
26021957
done50001895

prune339.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

regimes221.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.6b and baseline of 0.6b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
01318
11418
done1418

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.3s3005×body2560valid
1.3s2497×body1280valid
732.0ms7899×body80nan
466.0ms1279×body640valid
169.0ms594×body320valid
71.0ms193×body80valid
66.0ms432×body160valid