Details

Time bar (total: 15.3s)

sample79.0ms

Algorithm
intervals
Results
34.0ms102×body2560valid
16.0ms72×body1280valid
6.0ms232×body80nan
5.0ms34×body640valid
3.0ms22×body320valid
1.0ms17×body160valid
0.0ms9×body80valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0914
11914
24114
38114
415014
524214
638114
7128214
done500014

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.1b
(* 5.0 (* v v))
0.9b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×times-frac
10×add-exp-log add-cbrt-cube
8×pow1
4×associate-/r* difference-of-squares
3×associate-*l* pow-prod-down prod-exp cbrt-unprod associate-/l* add-log-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv acos-asin frac-2neg div-sub div-exp associate-*r* clear-num *-commutative div-inv unswap-sqr
Counts
3 → 63
Calls
3 calls:
10.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
10.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series107.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
24.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify418.0ms

Counts
72 → 72
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
01391198
13341166
212051054
done50011054

prune148.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* v v) (pow v 4))
0.0b
(* 4.0 (+ (* v v) (pow v 4)))
0.9b
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
2×flip3-+ associate-*r/ flip-+
1×+-commutative distribute-rgt-in acos-asin distribute-lft-in pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
3 → 41
Calls
3 calls:
5.0ms
(+ (* v v) (pow v 4))
17.0ms
(* 4.0 (+ (* v v) (pow v 4)))
0.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

series166.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(+ (* v v) (pow v 4))
89.0ms
(* 4.0 (+ (* v v) (pow v 4)))
6.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

simplify3.4s

Counts
50 → 50
Iterations

Useful iterations: 3 (439.0ms)

IterNodesCost
075668
1198640
2837546
33808542
done5000542

prune106.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ PI 2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
0.0b
(+ (* v v) (pow v 4))
0.0b
(* 4.0 (+ (* v v) (pow v 4)))
1.0b
(asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
8×*-un-lft-identity add-log-exp
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
3×associate-*r* associate-*l*
2×asin-acos flip3-+ associate-*r/ flip-+ difference-of-squares
1×+-commutative distribute-rgt-in sub-neg flip3-- distribute-lft-in times-frac diff-log pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 57
Calls
4 calls:
10.0ms
(- (/ PI 2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
4.0ms
(+ (* v v) (pow v 4))
17.0ms
(* 4.0 (+ (* v v) (pow v 4)))
0.0ms
(asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

series203.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (/ PI 2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
72.0ms
(+ (* v v) (pow v 4))
92.0ms
(* 4.0 (+ (* v v) (pow v 4)))
4.0ms
(asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

simplify4.0s

Counts
69 → 69
Iterations

Useful iterations: 3 (513.0ms)

IterNodesCost
01071152
12711074
21021972
34680964
done5000964

prune162.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.9b

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))))

rewrite9.0ms

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:
6.0ms
(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.0ms
(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))))

series556.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
134.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
130.0ms
(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))))

simplify1.3s

Counts
85 → 85
Iterations

Useful iterations: 3 (231.0ms)

IterNodesCost
0612476
11202285
23991827
317951757
done50011757

prune152.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

regimes130.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01416
11616
done1616

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.0s3029×body2560valid
554.0ms2481×body1280valid
215.0ms8132×body80nan
208.0ms1277×body640valid
72.0ms621×body320valid
29.0ms364×body160valid
11.0ms228×body80valid