Details

Time bar (total: 14.7s)

sample81.0ms

Algorithm
intervals
Results
32.0ms97×body2560valid
20.0ms80×body1280valid
7.0ms42×body640valid
6.0ms228×body80nan
2.0ms19×body320valid
1.0ms11×body160valid
0.0ms7×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: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b
(- 1.0 (* 5.0 (* v v)))
0.2b
(* 5.0 (* v v))
0.3b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
12×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
6×add-log-exp
4×associate-/r* difference-of-squares
3×flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod associate-/l*
2×associate-/r/ associate-/l/
1×cbrt-undiv acos-asin sub-neg frac-2neg diff-log div-sub div-exp associate-*r* clear-num *-commutative div-inv unswap-sqr
Counts
4 → 75
Calls
4 calls:
22.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms
(- 1.0 (* 5.0 (* v v)))
16.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series168.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
56.0ms
(- 1.0 (* 5.0 (* v v)))
28.0ms
(* 5.0 (* v v))
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.5s

Counts
87 → 87
Iterations

Useful iterations: 3 (675.0ms)

IterNodesCost
01461376
13411319
210351207
334601205
done50001205

prune182.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* 5.0 (pow v 2)) 3)
0.2b
(* 5.0 (pow v 2))
0.3b
(acos (/ (- 1.0 (cbrt (pow (* 5.0 (pow v 2)) 3))) (- (* v v) 1.0)))
22.3b
(cbrt (pow (* 5.0 (pow v 2)) 3))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
15×add-exp-log add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity add-cbrt-cube
8×cbrt-prod associate-*r*
6×unpow-prod-down pow-exp prod-exp
5×pow1
4×add-log-exp unswap-sqr sqr-pow
3×pow-to-exp pow-unpow associate-*l*
2×cube-mult unpow3 cube-prod cbrt-unprod unpow2 rem-cube-cbrt
1×acos-asin pow-pow pow1/3 *-commutative rem-cbrt-cube
Counts
4 → 75
Calls
4 calls:
7.0ms
(pow (* 5.0 (pow v 2)) 3)
11.0ms
(* 5.0 (pow v 2))
1.0ms
(acos (/ (- 1.0 (cbrt (pow (* 5.0 (pow v 2)) 3))) (- (* v v) 1.0)))
3.0ms
(cbrt (pow (* 5.0 (pow v 2)) 3))

series110.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(pow (* 5.0 (pow v 2)) 3)
25.0ms
(* 5.0 (pow v 2))
4.0ms
(acos (/ (- 1.0 (cbrt (pow (* 5.0 (pow v 2)) 3))) (- (* v v) 1.0)))
29.0ms
(cbrt (pow (* 5.0 (pow v 2)) 3))

simplify2.8s

Counts
87 → 87
Iterations

Useful iterations: done (2.8s)

IterNodesCost
0111933
1201744
2542685
33610685
done5000682

prune207.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 5.0 (pow v 2))
0.3b
(acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))
1.0b
(cbrt (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3))
1.0b
(pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×cbrt-prod
10×add-exp-log unpow-prod-down
8×associate-*r*
7×add-cbrt-cube
6×cube-prod
5×pow1
4×add-log-exp unswap-sqr sqr-pow
3×pow-unpow associate-*l* prod-exp
2×cube-mult pow-to-exp unpow3 pow-exp unpow2
1×acos-asin pow-pow pow1/3 *-commutative rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 79
Calls
4 calls:
11.0ms
(* 5.0 (pow v 2))
1.0ms
(acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))
2.0ms
(cbrt (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3))
3.0ms
(pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)

series80.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 5.0 (pow v 2))
4.0ms
(acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))
4.0ms
(cbrt (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3))
46.0ms
(pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)

simplify1.8s

Counts
91 → 91
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01041726
12051508
25041304
326841296
done50001293

prune170.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))))
1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))))
1.0b
(cbrt (pow (* (sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))))) 3))
1.0b
(pow (* (sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))))) 3)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
22×pow1
14×pow-pow
10×add-sqr-sqrt sqrt-pow1 pow1/2
8×cbrt-prod add-cube-cbrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
6×sqrt-prod
5×pow-prod-up
4×add-log-exp
3×pow-unpow pow-prod-down pow-sqr
2×cube-mult unpow-prod-down rem-sqrt-square unpow3 cube-prod pow-exp rem-cube-cbrt sqr-pow
1×pow2 pow-to-exp pow-plus pow1/3 sqrt-unprod prod-exp sqrt-pow2 rem-cbrt-cube cbrt-unprod
Counts
4 → 78
Calls
4 calls:
1.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))))
1.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))))
3.0ms
(cbrt (pow (* (sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))))) 3))
9.0ms
(pow (* (sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))))) 3)

series91.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))))
18.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))))
5.0ms
(cbrt (pow (* (sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))))) 3))
48.0ms
(pow (* (sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))))) 3)

simplify1.6s

Counts
90 → 90
Iterations

Useful iterations: 3 (215.0ms)

IterNodesCost
0832483
11381423
22851330
310911320
done50011320

prune169.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

regimes75.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01534
11634
done1634

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s3003×body2560valid
562.0ms2497×body1280valid
221.0ms7874×body80nan
198.0ms1227×body640valid
77.0ms655×body320valid
36.0ms413×body160valid
10.0ms205×body80valid