Details

Time bar (total: 18.8s)

sample130.0ms

Algorithm
intervals
Results
49.0ms86×body2560valid
33.0ms85×body1280valid
12.0ms240×body80nan
12.0ms44×body640valid
4.0ms19×body320valid
2.0ms13×body160valid
1.0ms9×body80valid

simplify1.6s

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize50.0ms

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

rewrite83.0ms

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:
47.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
32.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series162.0ms

Counts
3 → 9
Calls
3 calls:
113.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
44.0ms
(* 5.0 (* v v))
5.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify616.0ms

Counts
72 → 72

prune241.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0)))
0.2b
(* 5.0 (* v v))
0.2b
(* 5.0 (* v v))
0.4b
(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
32×associate-*r*
28×times-frac
23×add-cube-cbrt *-un-lft-identity
20×sqrt-prod
19×add-exp-log add-cbrt-cube
16×pow1
12×associate-*l*
8×prod-exp cbrt-unprod unswap-sqr
7×pow-prod-down
6×difference-of-squares
4×sqrt-div add-log-exp
3×flip3-- *-commutative flip--
2×frac-times associate-*l/ associate-/r/
1×cbrt-undiv acos-asin associate-*r/ div-exp div-inv
Counts
4 → 106
Calls
4 calls:
92.0ms
(* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0)))
31.0ms
(* 5.0 (* v v))
27.0ms
(* 5.0 (* v v))
1.0ms
(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

series236.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0)))
54.0ms
(* 5.0 (* v v))
35.0ms
(* 5.0 (* v v))
9.0ms
(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

simplify933.0ms

Counts
118 → 118

prune366.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize18.0ms

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)))))

rewrite19.0ms

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))))
13.0ms
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series67.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
23.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
34.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
5.0ms
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify6.5s

Counts
95 → 95

prune239.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
48×cbrt-prod
35×sqrt-prod
23×add-cube-cbrt *-un-lft-identity
22×unpow-prod-down cube-prod
21×associate-*l*
14×unswap-sqr
9×pow1
7×add-exp-log
6×associate-*r* add-cbrt-cube
5×sqr-pow
4×add-log-exp
3×cube-mult pow-unpow pow-pow unpow3
2×sqrt-pow1 pow1/2
1×pow-to-exp rem-sqrt-square pow1/3 pow-prod-down pow-exp prod-exp *-commutative sqrt-pow2 rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 124
Calls
4 calls:
2.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
15.0ms
(cbrt (pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3))
52.0ms
(* (cbrt (pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3)) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
8.0ms
(pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3)

series184.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
37.0ms
(cbrt (pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3))
9.0ms
(* (cbrt (pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3)) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
107.0ms
(pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3)

simplify756.0ms

Counts
136 → 136

prune423.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

regimes164.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify905.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.8s3010×body2560valid
1.2s2476×body1280valid
795.0ms8064×body80nan
332.0ms1208×body640valid
115.0ms641×body320valid
57.0ms456×body160valid
15.0ms209×body80valid