Details

Time bar (total: 16.0s)

sample78.0ms

Algorithm
intervals
Results
31.0ms94×body2560valid
20.0ms90×body1280valid
6.0ms40×body640valid
6.0ms234×body80nan
2.0ms16×body320valid
0.0ms6×body160valid
0.0ms10×body80valid

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0914
11914
24114
38114
415014
524014
637214
7108314
done500114

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

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))
0.4b
(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)))

series114.0ms

Counts
3 → 9
Calls
3 calls:
83.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
27.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify821.0ms

Counts
72 → 72
Iterations

Useful iterations: done (819.0ms)

IterNodesCost
01391198
13321158
210521054
done50021052

prune154.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 4.0 (+ (* v v) (pow v 4)))
0.0b
(+ (* v v) (pow v 4))
0.4b
(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:
18.0ms
(* 4.0 (+ (* v v) (pow v 4)))
5.0ms
(+ (* v v) (pow v 4))
0.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

series164.0ms

Counts
3 → 9
Calls
3 calls:
90.0ms
(* 4.0 (+ (* v v) (pow v 4)))
69.0ms
(+ (* v v) (pow v 4))
4.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

simplify2.9s

Counts
50 → 50
Iterations

Useful iterations: 3 (900.0ms)

IterNodesCost
075668
1196626
2727546
34065542
done5000542

prune106.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ PI 2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
0.0b
(* 4.0 (+ (* v v) (pow v 4)))
0.0b
(+ (* v v) (pow v 4))
0.4b
(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:
11.0ms
(- (/ PI 2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
21.0ms
(* 4.0 (+ (* v v) (pow v 4)))
5.0ms
(+ (* v v) (pow v 4))
0.0ms
(asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

series197.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (/ PI 2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
91.0ms
(* 4.0 (+ (* v v) (pow v 4)))
71.0ms
(+ (* v v) (pow v 4))
4.0ms
(asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

simplify3.4s

Counts
69 → 69
Iterations

Useful iterations: 3 (950.0ms)

IterNodesCost
01071152
12691060
2889972
34804964
done5000964

prune164.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (- (pow (/ PI 2) 3) (pow (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)) 3)) (+ (* (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)) (+ (/ PI 2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))) (* (/ PI 4) PI)))
1.0b
(pow (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)) 3)
1.0b
(pow (/ PI 2) 3)
1.4b
(+ (/ PI 2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
244×add-sqr-sqrt
149×times-frac
102×*-un-lft-identity
96×difference-of-squares
88×unpow-prod-down cube-prod
60×add-cube-cbrt
42×sqr-pow
33×associate-/l*
20×distribute-lft-out--
10×add-exp-log add-cbrt-cube
6×pow1 pow-unpow add-log-exp
4×difference-cubes associate-/r/
3×flip3-+ pow-exp associate-/r* flip-+ div-inv rem-cube-cbrt
2×cbrt-undiv cube-mult pow-to-exp pow-pow unpow3 associate-*r/ div-exp associate-*l/ frac-add associate-/l/
1×+-commutative cube-div associate-+r- asin-acos flip3-- frac-2neg div-sub clear-num sum-log flip-- distribute-lft-out
Counts
4 → 236
Calls
4 calls:
131.0ms
(/ (- (pow (/ PI 2) 3) (pow (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)) 3)) (+ (* (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)) (+ (/ PI 2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))) (* (/ PI 4) PI)))
1.0ms
(pow (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)) 3)
4.0ms
(pow (/ PI 2) 3)
9.0ms
(+ (/ PI 2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))

series518.0ms

Counts
4 → 10
Calls
4 calls:
439.0ms
(/ (- (pow (/ PI 2) 3) (pow (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)) 3)) (+ (* (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)) (+ (/ PI 2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))) (* (/ PI 4) PI)))
47.0ms
(pow (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)) 3)
0.0ms
(pow (/ PI 2) 3)
32.0ms
(+ (/ PI 2) (asin (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))

simplify1.3s

Counts
246 → 246
Iterations

Useful iterations: 2 (477.0ms)

IterNodesCost
034516848
189716290
2344215917
done500015917

prune911.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

regimes44.0ms

Accuracy

0% (0.0b remaining)

Error of 0.8b against oracle of 0.7b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02858
13658
done3658

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s3042×body2560valid
584.0ms2524×body1280valid
223.0ms8044×body80nan
197.0ms1176×body640valid
75.0ms615×body320valid
36.0ms425×body160valid
11.0ms218×body80valid