Details

Time bar (total: 21.9s)

sample278.0ms

Algorithm
intervals
Results
127.0ms96×body2560valid
69.0ms84×body1280valid
28.0ms245×body80nan
21.0ms35×body640valid
10.0ms23×body320valid
3.0ms11×body160valid
1.0ms7×body80valid

simplify1.6s

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize28.0ms

Local error

Found 3 expressions with local error:

0.7b
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
0.2b
(* 5 (* v v))
0.0b
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
18×times-frac
15×add-cube-cbrt
10×add-cbrt-cube add-exp-log
8×pow1 difference-of-squares
6×associate-/r*
4×difference-of-sqr-1
3×associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 associate-/l* add-log-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×acos-asin cbrt-undiv clear-num frac-2neg div-sub div-exp associate-*r* *-commutative div-inv unswap-sqr
Counts
3 → 74
Calls
3 calls:
Slowest
24.0ms
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
13.0ms
(* 5 (* v v))
2.0ms
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series129.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
74.0ms
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
50.0ms
(* 5 (* v v))
6.0ms
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify1.5s

Counts
83 → 83

prune598.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.8b
(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
0.2b
(* 5 (* v v))
0.0b
(- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
0.0b
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
19×times-frac
16×add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×difference-of-squares
9×pow1
6×associate-/r* add-log-exp
4×difference-of-sqr-1 insert-posit16
3×flip3-- associate-*l* pow-prod-down prod-exp cbrt-unprod flip-- associate-/l*
2×asin-acos associate-/r/ associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp associate-*r* *-commutative div-inv distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 91
Calls
4 calls:
Slowest
20.0ms
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
13.0ms
(- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
13.0ms
(* 5 (* v v))
2.0ms
(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series190.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
92.0ms
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
47.0ms
(* 5 (* v v))
45.0ms
(- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
6.0ms
(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify2.1s

Counts
103 → 103

prune985.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (+ (* 4 (+ (* v v) (* (* v v) (* v v)))) -1))
0.1b
(* (* v v) (* v v))
0.0b
(* 4 (+ (* v v) (* (* v v) (* v v))))
0.0b
(+ (* v v) (* (* v v) (* v v)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
117×pow1
36×pow-prod-up
24×pow-prod-down
22×pow-sqr
18×pow-plus add-cbrt-cube add-exp-log
13×pow2
9×prod-exp cbrt-unprod
8×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt add-log-exp
5×associate-*r*
4×associate-*l* insert-posit16
2×flip3-+ distribute-rgt1-in associate-*r/ *-commutative flip-+ unswap-sqr
1×distribute-rgt-in acos-asin +-commutative sum-log distribute-lft-in swap-sqr
Counts
4 → 110
Calls
4 calls:
Slowest
46.0ms
(* (* v v) (* v v))
38.0ms
(* 4 (+ (* v v) (* (* v v) (* v v))))
18.0ms
(+ (* v v) (* (* v v) (* v v)))
4.0ms
(acos (+ (* 4 (+ (* v v) (* (* v v) (* v v)))) -1))

series329.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(* 4 (+ (* v v) (* (* v v) (* v v))))
119.0ms
(+ (* v v) (* (* v v) (* v v)))
62.0ms
(* (* v v) (* v v))
7.0ms
(acos (+ (* 4 (+ (* v v) (* (* v v) (* v v)))) -1))

simplify1.6s

Counts
122 → 122

prune986.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize51.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (* (* (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))))
1.0b
(* (* (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))
0.8b
(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
0.8b
(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

rewrite273.0ms

Algorithm
rewrite-expression-head
Rules
56×frac-times
54×flip3-- flip--
28×associate-*l/
26×cbrt-div
23×pow1
16×associate-*r/
11×add-sqr-sqrt
9×add-cbrt-cube add-exp-log
7×*-un-lft-identity
6×pow-plus associate-*r* pow-prod-up
5×add-cube-cbrt
4×asin-acos insert-posit16 add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod
2×pow2 sub-neg pow3 pow-sqr associate--r- difference-of-squares
1×cbrt-prod times-frac pow1/3 associate-*l* *-commutative rem-cbrt-cube distribute-lft-out-- unswap-sqr
Counts
4 → 119
Calls
4 calls:
Slowest
143.0ms
(* (* (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))
121.0ms
(cbrt (* (* (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))))
3.0ms
(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
2.0ms
(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series206.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(* (* (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))
60.0ms
(cbrt (* (* (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))))
3.0ms
(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
3.0ms
(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify973.0ms

Counts
131 → 131

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

regimes146.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.5b and baseline of 0.7b

bsearch2.0ms

end0.0ms

sample8.1s

Algorithm
intervals
Results
3.4s2997×body2560valid
2.5s2520×body1280valid
842.0ms8216×body80nan
710.0ms1225×body640valid
259.0ms629×body320valid
109.0ms416×body160valid
29.0ms213×body80valid