Details

Time bar (total: 13.4s)

sample81.0ms

Algorithm
intervals
Results
32.0ms98×body2560valid
20.0ms78×body1280valid
7.0ms272×body80nan
7.0ms41×body640valid
2.0ms19×body320valid
1.0ms16×body160valid
0.0ms4×body80valid

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0914
11914
24114
38114
415014
523514
631214
746114
8119414
done500014

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize8.0ms

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)))

rewrite24.0ms

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:
16.0ms
(/ (- 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)))

series107.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(/ (- 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)))

simplify1.7s

Counts
72 → 72
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01391198
13321158
29881054
336471052
done50001050

prune153.0ms

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))))

rewrite17.0ms

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))
6.0ms
(* 5.0 (* v v))
0.0ms
(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

series131.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(sqrt (- 1.0 (* 5.0 (* v v))))
27.0ms
(* 5.0 (* v v))
24.0ms
(* 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))))

simplify1.4s

Counts
73 → 73
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
0110931
1246747
2713681
33102681
done5000681

prune168.0ms

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))

rewrite23.0ms

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:
5.0ms
(+ (* 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))

series160.0ms

Counts
3 → 9
Calls
3 calls:
68.0ms
(+ (* v v) (pow v 4))
87.0ms
(* 4.0 (+ (* v v) (pow v 4)))
4.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

simplify2.2s

Counts
50 → 50
Iterations

Useful iterations: 3 (648.0ms)

IterNodesCost
075668
1196626
2619546
32915542
done5001542

prune105.0ms

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))))

rewrite10.0ms

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))))

series44.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))
18.0ms
(sqrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
18.0ms
(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: 4 (394.0ms)

IterNodesCost
0722344
11241615
22651445
36421376
414561328
done50001328

prune142.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes44.0ms

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

sample2.3s

Algorithm
intervals
Results
986.0ms2937×body2560valid
564.0ms2545×body1280valid
224.0ms8079×body80nan
198.0ms1240×body640valid
76.0ms648×body320valid
36.0ms414×body160valid
10.0ms216×body80valid