Details

Time bar (total: 28.3s)

sample370.0ms

Algorithm
intervals
Results
100.0ms338×body80nan
23.0ms40×body640valid
22.0ms156×body80valid
16.0ms19×body1280nan
16.0ms24×body1280valid
10.0ms24×body320valid
7.0ms20×body320nan
7.0ms14×body640nan
3.0ms12×body160valid
1.0ms5×body160nan

simplify6.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

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: 46.1b

localize26.0ms

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))))
0.5b
(* (sqrt 2.0) t)
13.9b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.6b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite271.0ms

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:
118.0ms
(/ (* (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)
46.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
76.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series3.0s

Counts
4 → 12
Calls
4 calls:
704.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
66.0ms
(* (sqrt 2.0) t)
343.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.8s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.5s

Counts
92 → 92
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01682472
14142283
215522077
done50002025

prune501.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.5b

localize35.0ms

Local error

Found 4 expressions with local error:

5.3b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
6.9b
(/ (pow l 2) x)
9.5b
(/ (pow t 2) x)
28.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

rewrite83.0ms

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:
23.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
18.0ms
(/ (pow l 2) x)
17.0ms
(/ (pow t 2) x)
20.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

series376.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
21.0ms
(/ (pow l 2) x)
22.0ms
(/ (pow t 2) x)
218.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

simplify1.2s

Counts
142 → 142
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02542317
15352084
217251868
done50011862

prune717.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.8b
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
5.3b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
9.5b
(/ (pow t 2) x)
28.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x))))))

rewrite118.0ms

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:
26.0ms
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
33.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
17.0ms
(/ (pow t 2) x)
36.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x))))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
87.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
22.0ms
(/ (pow t 2) x)
238.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x))))))

simplify1.4s

Counts
104 → 104
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02102163
15031885
217741702
done50001688

prune586.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

localize73.0ms

Local error

Found 4 expressions with local error:

4.2b
(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
5.3b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))))
9.5b
(/ (pow t 2) x)
28.2b
(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)))))))

rewrite119.0ms

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:
32.0ms
(/ (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))))))
9.0ms
(/ (pow t 2) x)
33.0ms
(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)))))))

series629.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
142.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))))
29.0ms
(/ (pow t 2) x)
287.0ms
(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)))))))

simplify2.1s

Counts
132 → 132
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02863199
16432893
220942178
done50002098

prune837.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

regimes598.0ms

Accuracy

76.6% (5.6b remaining)

Error of 9.5b against oracle of 3.9b and baseline of 27.9b

bsearch445.0ms

Steps
ItersRangePoint
9
9.324172023423285e+142
1.1012045087961449e+149
1.6421833813677545e+146
10
-1.1979006433782284e+85
-5.09199279650327e+67
-2.8442338941596414e+80

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
043107
153107
done53107

end0.0ms

sample6.7s

Algorithm
intervals
Results
2.0s10110×body80nan
840.0ms584×body640nan
836.0ms5091×body80valid
581.0ms1030×body640valid
525.0ms847×body1280valid
368.0ms601×body1280nan
210.0ms656×body320valid
162.0ms381×body320nan
81.0ms376×body160valid
38.0ms183×body160nan