Details

Time bar (total: 27.0s)

sample216.0ms

Algorithm
intervals
Results
65.0ms298×body80nan
16.0ms168×body80valid
11.0ms24×body1280valid
10.0ms26×body640valid
6.0ms15×body1280nan
6.0ms19×body640nan
5.0ms20×body320valid
5.0ms18×body320nan
3.0ms18×body160valid
1.0ms9×body160nan

simplify6.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01827
13927
29327
318927
439727
566127
6112227
7262427
8413127
done500027

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b
(* (sqrt 2.0) t)
13.6b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.4b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
7×pow1
6×times-frac associate-*l* associate-/r* add-log-exp
4×sqrt-div
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate--l+ associate-/r/ cbrt-unprod unswap-sqr
1×distribute-rgt-in sub-neg rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 diff-log pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
89.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
22.0ms
(* (sqrt 2.0) t)
42.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
58.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.6s

Counts
4 → 12
Calls
4 calls:
564.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
57.0ms
(* (sqrt 2.0) t)
299.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.7s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.2s

Counts
92 → 92
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01682472
14142283
215522077
done50002025

prune462.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.3b

localize23.0ms

Local error

Found 4 expressions with local error:

5.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
6.7b
(/ (pow t 2) x)
6.7b
(/ (pow l 2) x)
29.0b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
16×associate-/l*
14×add-exp-log
8×associate-*r/ add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r* add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+
3×sqrt-prod
2×cbrt-undiv pow-to-exp associate-+r+ frac-2neg pow-exp clear-num div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log
Counts
4 → 130
Calls
4 calls:
22.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
9.0ms
(/ (pow t 2) x)
9.0ms
(/ (pow l 2) x)
19.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

series449.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
28.0ms
(/ (pow t 2) x)
33.0ms
(/ (pow l 2) x)
288.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

simplify1.3s

Counts
142 → 142
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02542317
15352084
217271868
done50001862

prune612.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
5.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
6.7b
(/ (pow t 2) x)
29.0b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x))))))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
9×add-exp-log
8×associate-*r/ associate-/l* add-log-exp
6×add-cbrt-cube
5×pow1 flip3-+ flip-+
4×sqrt-div frac-add unpow2 sqr-pow
3×div-exp associate-/r* sqrt-prod
2×+-commutative associate-+r+ sum-log
1×cbrt-undiv distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 92
Calls
4 calls:
16.0ms
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
25.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
17.0ms
(/ (pow t 2) x)
39.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x))))))

series372.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
76.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
33.0ms
(/ (pow t 2) x)
214.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x))))))

simplify1.3s

Counts
104 → 104
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02102163
15031885
217741702
done50001688

prune615.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize46.0ms

Local error

Found 4 expressions with local error:

3.2b
(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
5.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))))
6.7b
(/ (pow t 2) x)
29.0b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))))))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
34×times-frac
29×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
22×add-exp-log
18×associate-/l*
9×div-exp add-cbrt-cube
8×associate-*r/
6×cbrt-prod add-log-exp sqr-pow
5×pow1
4×flip3-+ sqrt-div frac-add associate-/r* flip-+ unpow2
3×cbrt-undiv pow-to-exp pow-exp prod-exp sqrt-prod
2×associate-+r+ frac-2neg clear-num div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log cbrt-unprod
Counts
4 → 120
Calls
4 calls:
37.0ms
(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
35.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))))
14.0ms
(/ (pow t 2) x)
19.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))))))

series578.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
137.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))))
21.0ms
(/ (pow t 2) x)
252.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))))))

simplify1.4s

Counts
132 → 132
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02863199
16432893
220942178
done50002098

prune788.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.3b

regimes827.0ms

Accuracy

75.7% (5.8b remaining)

Error of 9.6b against oracle of 3.8b and baseline of 27.8b

bsearch1.2s

Steps
ItersRangePoint
8
7.407251155982859e+145
4.879894848387411e+149
6.335165898555757e+148
6
-1.4231360660802614e-302
-2.7726430826687857e-303
-1.4020051272573528e-302
8
-2.3731648380204055e-262
-6.820981679032075e-265
-8.549619549454068e-265
5
-1.5004718450719783e+25
-4.978593612221029e+24
-8.54333635658851e+24

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
049178
159178
done59178

end0.0ms

sample6.5s

Algorithm
intervals
Results
1.8s10247×body80nan
1.0s851×body1280valid
686.0ms5159×body80valid
568.0ms1001×body640valid
379.0ms592×body640nan
378.0ms577×body1280nan
236.0ms635×body320valid
193.0ms334×body320nan
87.0ms179×body160nan
71.0ms354×body160valid