Details

Time bar (total: 15.8s)

sample82.0ms

Algorithm
intervals
Results
31.0ms96×body2560valid
18.0ms81×body1280valid
10.0ms238×body80nan
5.0ms34×body640valid
2.0ms21×body320valid
1.0ms18×body160valid
0.0ms6×body80valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11914
24214
37714
414614
522214
629714
743614
8104314
done500014

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

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))
0.6b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite42.0ms

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:
23.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
16.0ms
(* 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:
83.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
30.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify2.0s

Counts
72 → 72
Iterations

Useful iterations: 3 (603.0ms)

IterNodesCost
01391198
13221158
29591054
329951052
done50001052

prune147.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))
0.0b
(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
0.2b
(* 5.0 (* v v))
0.6b
(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
82×add-sqr-sqrt
65×add-cube-cbrt *-un-lft-identity
22×add-exp-log
21×associate-/r*
16×add-cbrt-cube difference-of-squares
11×associate-/r/
10×pow1
8×div-exp
7×associate-/l*
6×flip3-- flip-- div-inv
4×cbrt-undiv add-log-exp
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×rec-exp frac-2neg 1-exp clear-num associate-/l/
1×acos-asin pow-flip div-sub associate-*r* *-commutative inv-pow unswap-sqr
Counts
4 → 159
Calls
4 calls:
24.0ms
(/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))
22.0ms
(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
18.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

series190.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))
80.0ms
(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
26.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

simplify1.0s

Counts
171 → 171
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02823944
16493618
216303277
done50013237

prune295.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

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)))
0.6b
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

rewrite50.0ms

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:
10.0ms
(+ (* v v) (pow v 4))
37.0ms
(* 4.0 (+ (* v v) (pow v 4)))
1.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

series167.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(+ (* v v) (pow v 4))
91.0ms
(* 4.0 (+ (* v v) (pow v 4)))
5.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

simplify1.4s

Counts
50 → 50
Iterations

Useful iterations: 3 (514.0ms)

IterNodesCost
075668
1192626
2628546
32599542
done5000542

prune113.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.6b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

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×add-cbrt-cube 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 → 73
Calls
4 calls:
11.0ms
(* (cbrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))) (cbrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))))
1.0ms
(cbrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
1.0ms
(cbrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
1.0ms
(cbrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))

series597.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(* (cbrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))) (cbrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))))
138.0ms
(cbrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
144.0ms
(cbrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))
144.0ms
(cbrt (acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0)))

simplify3.7s

Counts
85 → 85
Iterations

Useful iterations: done (3.7s)

IterNodesCost
0622196
11141997
23061603
310341541
445241523
done50001458

prune168.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes38.0ms

Accuracy

0% (0.0b 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
01116
11416
done1416

end0.0ms

sample2.4s

Algorithm
intervals
Results
997.0ms3000×body2560valid
549.0ms2486×body1280valid
212.0ms7918×body80nan
200.0ms1230×body640valid
77.0ms654×body320valid
34.0ms412×body160valid
10.0ms218×body80valid