Details

Time bar (total: 19.8s)

sample195.0ms

Algorithm
intervals
Results
90.0ms95×body2560valid
33.0ms75×body1280valid
18.0ms283×body80nan
18.0ms49×body640valid
5.0ms20×body320valid
2.0ms10×body160valid
1.0ms7×body80valid

simplify759.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11914
24214
37714
414614
523314
690114
done500014

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (* 5.0 (* v v)))
0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b
(* 5.0 (* v v))
0.7b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite93.0ms

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:
10.0ms
(- 1.0 (* 5.0 (* v v)))
45.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
31.0ms
(* 5.0 (* v v))
2.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(- 1.0 (* 5.0 (* v v)))
145.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
54.0ms
(* 5.0 (* v v))
8.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify2.1s

Counts
87 → 87
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01461376
13961329
220771209
done50001205

prune532.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.2b
(* 5.0 (* v v))
0.7b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
13×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
6×add-log-exp difference-of-squares
4×associate-/r*
3×flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod associate-/l*
2×asin-acos associate-/r/ associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp associate-*r* clear-num *-commutative div-inv distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 79
Calls
4 calls:
53.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
36.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
34.0ms
(* 5.0 (* v v))
2.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
61.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
48.0ms
(* 5.0 (* v v))
8.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify2.0s

Counts
91 → 91
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01711732
14521674
221661530
done50001528

prune629.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 5.0 (* v v))
0.2b
(* 5.0 (* v v))
0.2b
(* 5.0 (* v v))
0.7b
(asin (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (* (+ (* 1.0 1.0) (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0))) (- (* v v) 1.0))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1 add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×associate-*l* pow-prod-down prod-exp cbrt-unprod
7×add-cube-cbrt *-un-lft-identity
4×add-log-exp
3×associate-*r* *-commutative unswap-sqr
1×asin-acos
Counts
4 → 65
Calls
4 calls:
35.0ms
(* 5.0 (* v v))
37.0ms
(* 5.0 (* v v))
36.0ms
(* 5.0 (* v v))
7.0ms
(asin (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (* (+ (* 1.0 1.0) (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0))) (- (* v v) 1.0))))

series184.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* 5.0 (* v v))
53.0ms
(* 5.0 (* v v))
50.0ms
(* 5.0 (* v v))
20.0ms
(asin (/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (* (+ (* 1.0 1.0) (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0))) (- (* v v) 1.0))))

simplify1.9s

Counts
77 → 77
Iterations

Useful iterations: 2 (276.0ms)

IterNodesCost
072979
1194946
21049808
done5000808

prune551.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b
(sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b
(sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b
(* (sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
46×sqrt-prod
32×*-un-lft-identity
21×pow1
16×sqrt-div
14×add-cube-cbrt
13×swap-sqr
12×difference-of-squares
10×sqrt-pow1 pow1/2
9×associate-*r* associate-*l*
8×flip3-- flip-- distribute-lft-out--
6×add-exp-log times-frac add-cbrt-cube
5×pow-prod-up
4×frac-times add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 asin-acos pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 112
Calls
4 calls:
2.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
42.0ms
(sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
40.0ms
(sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
201.0ms
(* (sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
107.0ms
(sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
118.0ms
(sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
65.0ms
(* (sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))

simplify1.7s

Counts
124 → 124
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01245023
12563666
29683399
done50003306

prune626.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

regimes303.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify16.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02140
12640
done2640

end0.0ms

sample6.6s

Algorithm
intervals
Results
2.4s2972×body2560valid
1.6s2584×body1280valid
1.2s8122×body80nan
560.0ms1266×body640valid
202.0ms589×body320valid
73.0ms416×body160valid
17.0ms173×body80valid