Details

Time bar (total: 11.2s)

sample81.0ms

Algorithm
intervals
Results
31.0ms94×body2560valid
20.0ms90×body1280valid
6.0ms40×body640valid
6.0ms234×body80nan
2.0ms16×body320valid
1.0ms10×body80valid
0.0ms6×body160valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0914
12014
24214
38814
415914
525614
640114
7113914
done500014

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×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u 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 → 69
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)))

series117.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
29.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify842.0ms

Counts
78 → 78
Iterations

Useful iterations: done (839.0ms)

IterNodesCost
01451268
13451223
211071120
done50001118

prune186.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 4.0 (fma v v (pow v 4)))
0.4b
(acos (- (* 4.0 (fma v v (pow v 4))) 1.0))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
4×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×associate-*r* associate-*l*
2×expm1-log1p-u fma-udef log1p-expm1-u add-log-exp
1×distribute-rgt-in acos-asin distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
2 → 32
Calls
2 calls:
3.0ms
(* 4.0 (fma v v (pow v 4)))
1.0ms
(acos (- (* 4.0 (fma v v (pow v 4))) 1.0))

series106.0ms

Counts
2 → 6
Calls
2 calls:
103.0ms
(* 4.0 (fma v v (pow v 4)))
3.0ms
(acos (- (* 4.0 (fma v v (pow v 4))) 1.0))

simplify1.1s

Counts
38 → 38
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
059471
1107459
2350399
31715399
done5001399

prune274.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0)))
0.0b
(* 4.0 (fma v v (pow v 4)))
0.4b
(asin (- (* 4.0 (fma v v (pow v 4))) 1.0))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
53×add-sqr-sqrt
48×*-un-lft-identity
46×add-cube-cbrt
39×prod-diff
37×times-frac
13×fma-neg
5×pow1 add-exp-log add-cbrt-cube add-log-exp
4×div-inv
3×expm1-log1p-u associate-*r* associate-*l* log1p-expm1-u
2×asin-acos fma-udef difference-of-squares
1×distribute-rgt-in sub-neg flip3-- distribute-lft-in diff-log pow-prod-down prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- associate--r- unswap-sqr
Counts
3 → 102
Calls
3 calls:
14.0ms
(- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0)))
3.0ms
(* 4.0 (fma v v (pow v 4)))
0.0ms
(asin (- (* 4.0 (fma v v (pow v 4))) 1.0))

series135.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0)))
100.0ms
(* 4.0 (fma v v (pow v 4)))
6.0ms
(asin (- (* 4.0 (fma v v (pow v 4))) 1.0))

simplify737.0ms

Counts
111 → 111
Iterations

Useful iterations: done (732.0ms)

IterNodesCost
01664565
13222966
29312322
done50002209

prune212.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0)))) (cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0)))))
1.0b
(cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0))))
1.0b
(cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0))))
1.0b
(cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
50×cbrt-prod
35×*-un-lft-identity
18×cbrt-div
15×add-cube-cbrt
14×difference-of-squares
11×pow1 swap-sqr
9×flip3-- pow1/3 associate-*r* associate-*l* flip-- distribute-lft-out--
7×times-frac
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 115
Calls
4 calls:
55.0ms
(* (cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0)))) (cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0)))))
9.0ms
(cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0))))
7.0ms
(cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0))))
7.0ms
(cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0))))

series844.0ms

Counts
4 → 12
Calls
4 calls:
248.0ms
(* (cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0)))) (cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0)))))
200.0ms
(cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0))))
198.0ms
(cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0))))
198.0ms
(cbrt (- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0))))

simplify1.5s

Counts
127 → 127
Iterations

Useful iterations: 3 (483.0ms)

IterNodesCost
01134526
12084240
25624014
323283570
done50013570

prune346.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

regimes42.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01315
11415
done1415

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.0s3042×body2560valid
561.0ms2524×body1280valid
218.0ms8044×body80nan
190.0ms1176×body640valid
72.0ms615×body320valid
35.0ms425×body160valid
10.0ms218×body80valid