Details

Time bar (total: 27.7s)

sample235.0ms

Algorithm
intervals
Results
62.0ms34×body640valid
30.0ms320×body80nan
15.0ms156×body80valid
11.0ms21×body1280valid
11.0ms31×body320valid
10.0ms22×body1280nan
7.0ms17×body640nan
4.0ms16×body320nan
3.0ms14×body160valid
1.0ms6×body160nan

simplify5.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01827
13927
29327
318927
439727
566127
6112227
7262427
8413127
done500027

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (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)
14.5b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.5b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite247.0ms

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:
87.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
12.0ms
(* (sqrt 2.0) t)
68.0ms
(- (* (/ (+ 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)))

series3.2s

Counts
4 → 12
Calls
4 calls:
638.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
59.0ms
(* (sqrt 2.0) t)
337.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
2.2s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.4s

Counts
92 → 92
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01682472
14142283
215522077
done50002025

prune492.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize42.0ms

Local error

Found 4 expressions with local error:

4.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
8.1b
(/ (pow l 2) x)
10.2b
(/ (pow t 2) x)
26.7b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

rewrite129.0ms

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:
45.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
17.0ms
(/ (pow l 2) x)
18.0ms
(/ (pow t 2) x)
39.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

series438.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
35.0ms
(/ (pow l 2) x)
36.0ms
(/ (pow t 2) x)
259.0ms
(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
217251868
done50011862

prune758.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.0b

localize45.0ms

Local error

Found 4 expressions with local error:

1.6b
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
4.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
10.2b
(/ (pow t 2) x)
26.7b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x))))))

rewrite85.0ms

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:
9.0ms
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
25.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
9.0ms
(/ (pow t 2) x)
38.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x))))))

series346.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
79.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))))
37.0ms
(/ (pow t 2) x)
187.0ms
(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 (1.2s)

IterNodesCost
02102163
15031885
217741702
done50001688

prune616.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.0b

localize36.0ms

Local error

Found 4 expressions with local error:

1.6b
(+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
4.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
10.2b
(/ (pow t 2) x)
26.7b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite70.0ms

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:
9.0ms
(+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
24.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
12.0ms
(/ (pow t 2) x)
19.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series514.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
134.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
23.0ms
(/ (pow t 2) x)
289.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify1.4s

Counts
104 → 104
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02002563
14752316
217282084
done50012029

prune648.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.0b

regimes1.0s

Accuracy

73.3% (6.4b remaining)

Error of 10.1b against oracle of 3.7b and baseline of 27.6b

bsearch861.0ms

Steps
ItersRangePoint
7
5.438827393303272e-47
3.255422209678199e-45
3.190616919639676e-45
9
-9.099259929633761e-243
-1.1388205652005344e-250
-4.3039381620799786e-243
8
-4.709429137726002e-147
-1.2135677083227269e-149
-1.2300651500007749e-149
8
-7.002515132037965e+150
-1.149067304892884e+146
-2.3034608226733973e+149

simplify17.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
061202
175202
done75202

end0.0ms

sample6.8s

Algorithm
intervals
Results
1.7s10338×body80nan
1.5s5100×body80valid
693.0ms655×body320valid
652.0ms910×body1280valid
523.0ms1003×body640valid
449.0ms564×body1280nan
351.0ms645×body640nan
114.0ms332×body160valid
110.0ms365×body320nan
29.0ms149×body160nan