Details

Time bar (total: 13.9s)

sample78.0ms

Algorithm
intervals
Results
34.0ms102×body2560valid
16.0ms72×body1280valid
7.0ms232×body80nan
6.0ms34×body640valid
3.0ms22×body320valid
1.0ms17×body160valid
0.0ms9×body80valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0914
12014
24214
38814
415914
525014
633914
749914
8123814
done500014

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize8.0ms

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×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)))

series111.0ms

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)))

simplify1.8s

Counts
78 → 78
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01451268
13451223
210431120
339291118
done50001116

prune176.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

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:
6.0ms
(* 4.0 (fma v v (pow v 4)))
0.0ms
(acos (- (* 4.0 (fma v v (pow v 4))) 1.0))

series105.0ms

Counts
2 → 6
Calls
2 calls:
102.0ms
(* 4.0 (fma v v (pow v 4)))
3.0ms
(acos (- (* 4.0 (fma v v (pow v 4))) 1.0))

simplify1.2s

Counts
38 → 38
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
059471
1107459
2273399
3978399
done5000399

prune87.0ms

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

rewrite21.0ms

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:
13.0ms
(- (/ 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))

series141.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(- (/ PI 2) (asin (- (* 4.0 (fma v v (pow v 4))) 1.0)))
109.0ms
(* 4.0 (fma v v (pow v 4)))
3.0ms
(asin (- (* 4.0 (fma v v (pow v 4))) 1.0))

simplify1.3s

Counts
111 → 111
Iterations

Useful iterations: 3 (520.0ms)

IterNodesCost
01664565
13222966
27962322
327492207
done50002207

prune227.0ms

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×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:
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))))

series561.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
136.0ms
(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))))
134.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify3.3s

Counts
93 → 93
Iterations

Useful iterations: 4 (1.4s)

IterNodesCost
0652636
11222441
23211957
311651887
439161867
done50001867

prune178.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

regimes134.0ms

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
01315
11415
done1415

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s3029×body2560valid
568.0ms2481×body1280valid
228.0ms8132×body80nan
218.0ms1277×body640valid
73.0ms621×body320valid
30.0ms364×body160valid
11.0ms228×body80valid