Details

Time bar (total: 25.6s)

sample148.0ms

Algorithm
intervals
Results
53.0ms87×body2560valid
41.0ms97×body1280valid
16.0ms262×body80nan
11.0ms36×body640valid
4.0ms20×body320valid
2.0ms10×body160valid
1.0ms6×body80valid

simplify5.1s

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: 0.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b
(* 5.0 (* v v))
0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
4×add-sqr-sqrt
3×add-cube-cbrt *-un-lft-identity associate-*l* pow-prod-down prod-exp cbrt-unprod
2×add-log-exp
1×acos-asin associate-*r* *-commutative unswap-sqr
Counts
2 → 27
Calls
2 calls:
20.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series46.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(* 5.0 (* v v))
5.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify3.6s

Counts
33 → 33
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
053371
1105368
2262310
3554310
4875310
52155310
done5000310

prune94.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite20.0ms

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:
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
14.0ms
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series62.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
29.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
20.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
9.0ms
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify3.1s

Counts
95 → 95
Iterations

Useful iterations: done (3.1s)

IterNodesCost
0712646
11141855
22531657
34851576
49861520
done50001475

prune235.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b
(* (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3))
1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
75×sqrt-prod
63×add-sqr-sqrt
24×associate-*r* unswap-sqr
18×unpow-prod-down cube-prod
16×add-cube-cbrt *-un-lft-identity
9×add-exp-log associate-*l*
7×pow1
6×add-cbrt-cube
4×add-log-exp sqr-pow
3×prod-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×acos-asin cube-mult pow-to-exp unpow3 pow-exp *-commutative pow-prod-up cbrt-unprod
Counts
4 → 104
Calls
4 calls:
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
35.0ms
(* (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3))
1.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

series59.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
9.0ms
(* (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3))
20.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
21.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify3.7s

Counts
116 → 116
Iterations

Useful iterations: 3 (952.0ms)

IterNodesCost
0994435
12004070
25032764
327822634
done50012634

prune398.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
162×sqrt-prod
157×add-sqr-sqrt
112×cbrt-prod
78×unpow-prod-down cube-prod
72×unswap-sqr
28×add-cube-cbrt *-un-lft-identity
27×associate-*r*
24×associate-*l*
20×sqr-pow
9×add-exp-log
6×pow1
5×add-cbrt-cube
4×add-log-exp
3×cube-mult unpow3 prod-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow-to-exp pow1/3 pow-exp *-commutative rem-cbrt-cube cbrt-unprod
Counts
4 → 194
Calls
4 calls:
73.0ms
(* (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3) (cbrt (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3)))
2.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
2.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
5.0ms
(cbrt (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3))

series250.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3) (cbrt (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3)))
25.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
26.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
188.0ms
(cbrt (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3))

simplify1.9s

Counts
206 → 206
Iterations

Useful iterations: done (1.9s)

IterNodesCost
013310292
12598889
28476558
done50006442

prune507.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes120.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11014
done1014

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.4s3086×body2560valid
1.3s2446×body1280valid
1.0s7995×body80nan
545.0ms1234×body640valid
167.0ms604×body320valid
65.0ms423×body160valid
18.0ms207×body80valid