Details

Time bar (total: 15.3s)

sample80.0ms

Algorithm
intervals
Results
33.0ms102×body2560valid
16.0ms72×body1280valid
8.0ms34×body640valid
7.0ms232×body80nan
3.0ms22×body320valid
1.0ms17×body160valid
0.0ms9×body80valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0914
11914
24114
38114
415014
523514
631214
746114
8119314
done500014

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize11.0ms

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)))

rewrite19.0ms

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))
6.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series110.0ms

Counts
3 → 9
Calls
3 calls:
82.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.6s

Counts
72 → 72
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01391198
13321158
29881054
336461052
done50001050

prune155.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize11.0ms

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:
4.0ms
(+ (* v v) (pow v 4))
18.0ms
(* 4.0 (+ (* v v) (pow v 4)))
1.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

series166.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(+ (* v v) (pow v 4))
92.0ms
(* 4.0 (+ (* v v) (pow v 4)))
4.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

simplify2.1s

Counts
50 → 50
Iterations

Useful iterations: 3 (534.0ms)

IterNodesCost
075668
1196626
2619546
32898542
done5001542

prune107.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize11.0ms

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))

rewrite38.0ms

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)))
5.0ms
(+ (* v v) (pow v 4))
21.0ms
(* 4.0 (+ (* v v) (pow v 4)))
0.0ms
(asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

series194.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (/ PI 2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
69.0ms
(+ (* v v) (pow v 4))
89.0ms
(* 4.0 (+ (* v v) (pow v 4)))
4.0ms
(asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

simplify2.2s

Counts
69 → 69
Iterations

Useful iterations: 3 (589.0ms)

IterNodesCost
01071152
12691060
2766972
33142964
done5000964

prune159.0ms

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))))

series542.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
129.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
127.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
131.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify3.2s

Counts
85 → 85
Iterations

Useful iterations: 4 (1.1s)

IterNodesCost
0612476
11172281
23131827
311381757
438311737
done50011737

prune154.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

regimes126.0ms

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

sample2.4s

Algorithm
intervals
Results
1.0s3029×body2560valid
558.0ms2481×body1280valid
229.0ms8132×body80nan
207.0ms1277×body640valid
74.0ms621×body320valid
29.0ms364×body160valid
11.0ms228×body80valid