Details

Time bar (total: 25.2s)

sample257.0ms

Algorithm
intervals
Results
44.0ms22×body640valid
27.0ms369×body80nan
14.0ms164×body80valid
11.0ms31×body1280valid
10.0ms31×body1280nan
10.0ms30×body640nan
6.0ms29×body320valid
3.0ms13×body320nan
1.0ms10×body160valid
1.0ms5×body160nan

simplify3.0s

Counts
1 → 1
Iterations
IterNodes
done5000
73799
61449
5797
4423
3199
293
139
018

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.4b

localize67.0ms

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)
11.8b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.1b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
7×pow1
6×associate-/r* times-frac associate-*l* 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 rem-sqrt-square clear-num sub-neg frac-2neg distribute-lft-in sqrt-pow1 pow1/2 diff-log pow-prod-down *-commutative div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
50.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
15.0ms
(* (sqrt 2.0) t)
30.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
63.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.9s

Counts
4 → 12
Calls
4 calls:
625.0ms
(/ (* (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)
333.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.9s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.4s

Counts
92 → 92
Iterations
IterNodes
done5000
22619
1455
0167

prune586.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.1b

localize44.0ms

Local error

Found 4 expressions with local error:

3.2b
(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
5.7b
(/ (* l l) x)
9.8b
(/ x (* t t))
27.7b
(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×times-frac add-log-exp
5×pow1
4×cbrt-undiv associate-/r* flip3-+ sqrt-div div-exp frac-add associate-*r/ flip-+ associate-/l*
3×sqrt-prod
2×associate-+l+ clear-num frac-2neg prod-exp cbrt-unprod div-inv
1×distribute-rgt-in +-commutative rem-sqrt-square sum-log distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 74
Calls
4 calls:
45.0ms
(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
15.0ms
(/ (* l l) x)
12.0ms
(/ x (* t t))
84.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

series534.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
22.0ms
(/ (* l l) x)
33.0ms
(/ x (* t t))
376.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

simplify1.5s

Counts
86 → 86
Iterations
IterNodes
done5001
23089
1509
0168

prune639.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* t t) (* l (/ l x)))
3.2b
(+ (* 2.0 (+ (* t t) (* l (/ l x)))) (/ 4.0 (/ x (* t t))))
9.8b
(/ x (* t t))
27.7b
(sqrt (+ (* 2.0 (+ (* t t) (* l (/ l x)))) (/ 4.0 (/ x (* t t)))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt add-log-exp
7×*-un-lft-identity add-cube-cbrt
5×pow1 flip3-+ flip-+
4×sqrt-div frac-add associate-*r/
3×times-frac sqrt-prod associate-/l*
2×cbrt-undiv +-commutative associate-+l+ sum-log div-exp
1×distribute-rgt-in rem-sqrt-square clear-num associate-/r* frac-2neg distribute-lft-in sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv
Counts
4 → 64
Calls
4 calls:
12.0ms
(+ (* t t) (* l (/ l x)))
30.0ms
(+ (* 2.0 (+ (* t t) (* l (/ l x)))) (/ 4.0 (/ x (* t t))))
11.0ms
(/ x (* t t))
56.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* l (/ l x)))) (/ 4.0 (/ x (* t t)))))

series576.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(+ (* t t) (* l (/ l x)))
110.0ms
(+ (* 2.0 (+ (* t t) (* l (/ l x)))) (/ 4.0 (/ x (* t t))))
44.0ms
(/ x (* t t))
358.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* l (/ l x)))) (/ 4.0 (/ x (* t t)))))

simplify1.2s

Counts
76 → 76
Iterations
IterNodes
done5001
22158
1435
0150

prune619.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* t t) (/ l (/ x l)))
3.2b
(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t))))
9.8b
(/ x (* t t))
27.7b
(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t)))))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt add-log-exp
7×*-un-lft-identity add-cube-cbrt
5×pow1 flip3-+ flip-+
4×sqrt-div frac-add associate-*r/
3×times-frac sqrt-prod associate-/l*
2×cbrt-undiv +-commutative associate-+l+ sum-log div-exp
1×distribute-rgt-in rem-sqrt-square clear-num associate-/r* frac-2neg distribute-lft-in sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv
Counts
4 → 64
Calls
4 calls:
28.0ms
(+ (* t t) (/ l (/ x l)))
70.0ms
(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t))))
12.0ms
(/ x (* t t))
96.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t)))))

series621.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ (* t t) (/ l (/ x l)))
118.0ms
(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t))))
34.0ms
(/ x (* t t))
416.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t)))))

simplify994.0ms

Counts
76 → 76
Iterations
IterNodes
done5000
22090
1432
0150

prune414.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.2b

regimes1.2s

Accuracy

71.1% (6.8b remaining)

Error of 10.6b against oracle of 3.8b and baseline of 27.2b

bsearch1.4s

Steps
ItersRangePoint
9
9.302190505211976e+16
7.445004787773374e+23
7.30958659336468e+23
10
9.657462100703732e-164
3.031856998694715e-153
8.463507043182295e-160
8
1.567848216510623e-295
4.048090763928206e-293
4.0088796644560363e-293
10
-3.4801109198288895e-286
-4.7771503152615563e-296
-1.6191443127207628e-287
8
-1.185302419643378e-162
-2.4464775612223304e-166
-8.68838282607017e-163
6
-8.884635004656325e+106
-1.469680632787173e+106
-8.435929301784522e+106

simplify25.0ms

Iterations
IterNodes
done76
376
270
154
043

end0.0ms

sample6.4s

Algorithm
intervals
Results
2.2s10213×body80nan
797.0ms5001×body80valid
653.0ms1064×body640valid
544.0ms885×body1280valid
383.0ms604×body1280nan
333.0ms624×body640nan
244.0ms656×body320valid
118.0ms394×body160valid
99.0ms338×body320nan
39.0ms202×body160nan