Details

Time bar (total: 19.5s)

sample69.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
19.0ms238×body80nan

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01928
14428
216328
383928
4412928
done500028

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 5.0 (* v v))
0.2b
(* PI t)
0.3b
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
0.5b
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log add-cbrt-cube
18×associate-*r/
16×pow1
13×add-sqr-sqrt prod-exp cbrt-unprod
10×add-cube-cbrt *-un-lft-identity
8×flip3-- sqrt-div associate-*r* associate-/r/ flip--
7×associate-*l* pow-prod-down
4×cbrt-undiv expm1-log1p-u frac-times div-exp log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l*
2×associate-*l/ associate-/l/ unswap-sqr
1×frac-2neg div-sub clear-num associate-/r* sqrt-prod div-inv
Counts
4 → 102
Calls
4 calls:
33.0ms
(* 5.0 (* v v))
14.0ms
(* PI t)
172.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
45.0ms
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
50.0ms
(* 5.0 (* v v))
24.0ms
(* PI t)
877.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
309.0ms
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

simplify582.0ms

Counts
114 → 114
Iterations

Useful iterations: done (576.0ms)

IterNodesCost
02582497
18052336
done50002038

prune623.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 5.0 (* v v))
0.3b
(/ (- 1.0 (* 5.0 (* v v))) (* (/ (* PI (* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v 4))))))) (sqrt (+ 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))
0.4b
(* PI (* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v 4)))))))
0.4b
(* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v 4))))))

rewrite555.0ms

Algorithm
rewrite-expression-head
Rules
36×add-exp-log add-cbrt-cube
16×pow1
14×prod-exp cbrt-unprod
13×add-sqr-sqrt
12×associate-*r/
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×cbrt-undiv div-exp
7×pow-prod-down
6×associate-*r*
5×flip3-- associate-/r/ flip--
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l*
2×frac-times associate-/l/ unswap-sqr
1×frac-2neg div-sub associate-*l/ clear-num associate-/r* sqrt-prod div-inv
Counts
4 → 103
Calls
4 calls:
18.0ms
(* 5.0 (* v v))
349.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (/ (* PI (* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v 4))))))) (sqrt (+ 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))
135.0ms
(* PI (* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v 4)))))))
47.0ms
(* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v 4))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
38.0ms
(* 5.0 (* v v))
882.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (/ (* PI (* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v 4))))))) (sqrt (+ 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))
247.0ms
(* PI (* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v 4)))))))
209.0ms
(* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v 4))))))

simplify516.0ms

Counts
115 → 115
Iterations

Useful iterations: done (508.0ms)

IterNodesCost
02773589
18573369
done50002823

prune794.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 5.0 (* v v))
0.3b
(/ (- 1.0 (* 5.0 (* v v))) (* (/ (/ (* (* t (sqrt (* 2.0 (- (* 1.0 (pow 1.0 3)) (* (* (* 3.0 3.0) (* 3.0 3.0)) (pow v (* 2 4))))))) PI) (sqrt (+ (* 1.0 1.0) (* (* 3.0 3.0) (pow v 4))))) (sqrt (+ 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))
0.4b
(* (* t (sqrt (* 2.0 (- (* 1.0 (pow 1.0 3)) (* (* (* 3.0 3.0) (* 3.0 3.0)) (pow v (* 2 4))))))) PI)
0.4b
(* t (sqrt (* 2.0 (- (* 1.0 (pow 1.0 3)) (* (* (* 3.0 3.0) (* 3.0 3.0)) (pow v (* 2 4)))))))

rewrite864.0ms

Algorithm
rewrite-expression-head
Rules
43×add-exp-log add-cbrt-cube
16×pow1
15×prod-exp cbrt-unprod
13×cbrt-undiv add-sqr-sqrt div-exp
10×add-cube-cbrt *-un-lft-identity associate-*r/
8×associate-*r*
7×associate-*l* pow-prod-down
5×flip3-- associate-/r/ flip--
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×times-frac associate-*l/ *-commutative associate-/l*
2×frac-times associate-/l/ unswap-sqr
1×frac-2neg div-sub clear-num associate-/r* sqrt-prod div-inv
Counts
4 → 105
Calls
4 calls:
18.0ms
(* 5.0 (* v v))
587.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (/ (/ (* (* t (sqrt (* 2.0 (- (* 1.0 (pow 1.0 3)) (* (* (* 3.0 3.0) (* 3.0 3.0)) (pow v (* 2 4))))))) PI) (sqrt (+ (* 1.0 1.0) (* (* 3.0 3.0) (pow v 4))))) (sqrt (+ 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))
174.0ms
(* (* t (sqrt (* 2.0 (- (* 1.0 (pow 1.0 3)) (* (* (* 3.0 3.0) (* 3.0 3.0)) (pow v (* 2 4))))))) PI)
81.0ms
(* t (sqrt (* 2.0 (- (* 1.0 (pow 1.0 3)) (* (* (* 3.0 3.0) (* 3.0 3.0)) (pow v (* 2 4)))))))

series1.8s

Counts
4 → 12
Calls
4 calls:
28.0ms
(* 5.0 (* v v))
1.0s
(/ (- 1.0 (* 5.0 (* v v))) (* (/ (/ (* (* t (sqrt (* 2.0 (- (* 1.0 (pow 1.0 3)) (* (* (* 3.0 3.0) (* 3.0 3.0)) (pow v (* 2 4))))))) PI) (sqrt (+ (* 1.0 1.0) (* (* 3.0 3.0) (pow v 4))))) (sqrt (+ 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))
367.0ms
(* (* t (sqrt (* 2.0 (- (* 1.0 (pow 1.0 3)) (* (* (* 3.0 3.0) (* 3.0 3.0)) (pow v (* 2 4))))))) PI)
343.0ms
(* t (sqrt (* 2.0 (- (* 1.0 (pow 1.0 3)) (* (* (* 3.0 3.0) (* 3.0 3.0)) (pow v (* 2 4)))))))

simplify564.0ms

Counts
117 → 117
Iterations

Useful iterations: done (558.0ms)

IterNodesCost
03055389
19674829
done50013762

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 5.0 (* v v))
0.2b
(* PI t)
0.2b
(/ 1 (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
0.5b
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
37×add-exp-log
25×add-cbrt-cube
22×pow1
16×prod-exp
13×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity pow-prod-down cbrt-unprod
8×associate-*r/ associate-*r*
7×associate-*l*
6×div-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp pow-flip times-frac 1-exp *-commutative associate-/l*
2×flip3-- associate-/r/ flip-- unswap-sqr
1×frac-2neg clear-num associate-/r* sqrt-prod div-inv inv-pow
Counts
4 → 101
Calls
4 calls:
33.0ms
(* 5.0 (* v v))
10.0ms
(* PI t)
78.0ms
(/ 1 (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
55.0ms
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

series770.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* 5.0 (* v v))
29.0ms
(* PI t)
401.0ms
(/ 1 (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
311.0ms
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

simplify1.8s

Counts
113 → 113
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01931594
15171449
227901288
done50011284

prune469.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes239.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 2 (3.0ms)

IterNodesCost
02232
13032
23130
done3130

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.2s7921×body80nan
1.1s8000×body80valid