Details

Time bar (total: 12.9s)

sample82.0ms

Algorithm
intervals
Results
32.0ms98×body2560valid
17.0ms78×body1280valid
10.0ms272×body80nan
7.0ms41×body640valid
2.0ms19×body320valid
1.0ms16×body160valid
0.0ms4×body80valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0914
11914
24114
38114
415014
524014
637214
7108314
done500114

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b
(* 5.0 (* v v))
0.5b
(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))
7.0ms
(* 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))
24.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify823.0ms

Counts
72 → 72
Iterations

Useful iterations: done (820.0ms)

IterNodesCost
01391198
13321158
210521054
done50021052

prune157.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- 1.0 (* 5.0 (* v v))))
0.2b
(* 5.0 (* v v))
0.2b
(* 5.0 (* v v))
0.5b
(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*l* pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×sqrt-prod
2×sqrt-div associate-*r* *-commutative unswap-sqr
1×acos-asin rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 61
Calls
4 calls:
2.0ms
(sqrt (- 1.0 (* 5.0 (* v v))))
6.0ms
(* 5.0 (* v v))
9.0ms
(* 5.0 (* v v))
1.0ms
(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

series132.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(sqrt (- 1.0 (* 5.0 (* v v))))
25.0ms
(* 5.0 (* v v))
25.0ms
(* 5.0 (* v v))
4.0ms
(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

simplify1.5s

Counts
73 → 73
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
0110931
1246747
2740681
33733681
done5001681

prune166.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

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)))
0.5b
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

rewrite26.0ms

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:
7.0ms
(+ (* 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))

series162.0ms

Counts
3 → 9
Calls
3 calls:
69.0ms
(+ (* v v) (pow v 4))
89.0ms
(* 4.0 (+ (* v v) (pow v 4)))
4.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

simplify3.1s

Counts
50 → 50
Iterations

Useful iterations: 3 (859.0ms)

IterNodesCost
075668
1196626
2724546
34114542
done5001542

prune111.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))
1.0b
(sqrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
1.0b
(sqrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
1.0b
(* (sqrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))) (sqrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 acos-asin pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 83
Calls
4 calls:
0.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))
1.0ms
(sqrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
1.0ms
(sqrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
7.0ms
(* (sqrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))) (sqrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))))

series52.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))
20.0ms
(sqrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
23.0ms
(sqrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
5.0ms
(* (sqrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))) (sqrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))))

simplify1.5s

Counts
95 → 95
Iterations

Useful iterations: 3 (319.0ms)

IterNodesCost
0722344
11241615
23431445
317711376
done50001376

prune151.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

regimes38.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01124
11324
done1324

end0.0ms

sample2.4s

Algorithm
intervals
Results
997.0ms2937×body2560valid
571.0ms2545×body1280valid
227.0ms8079×body80nan
204.0ms1240×body640valid
77.0ms648×body320valid
34.0ms414×body160valid
11.0ms216×body80valid