Details

Time bar (total: 13.9s)

sample87.0ms

Algorithm
intervals
Results
25.0ms317×body80nan
9.0ms160×body80valid
6.0ms23×body1280valid
6.0ms28×body640valid
6.0ms36×body320valid
4.0ms19×body640nan
4.0ms14×body1280nan
2.0ms12×body320nan
1.0ms9×body160nan
1.0ms9×body160valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01827
13927
28627
317727
434427
555027
689927
7159227
8322927
done500027

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize18.0ms

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)
13.6b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.1b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite71.0ms

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:
24.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
9.0ms
(* (sqrt 2.0) t)
12.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
435.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
40.0ms
(* (sqrt 2.0) t)
221.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify717.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (154.0ms)

IterNodesCost
01682472
14162283
215932085
done50002085

prune319.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.9b

localize19.0ms

Local error

Found 4 expressions with local error:

4.8b
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
8.8b
(/ (pow l 2) x)
11.1b
(/ (pow t 2) x)
26.9b
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite60.0ms

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
9×add-log-exp
8×add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r*
5×pow1
3×sum-log sqrt-prod
2×cbrt-undiv pow-to-exp frac-2neg flip3-+ sqrt-div pow-exp clear-num flip-+ div-inv
1×+-commutative rem-sqrt-square associate-+r+ sqrt-pow1 pow1/2
Counts
4 → 126
Calls
4 calls:
19.0ms
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow l 2) x)
4.0ms
(/ (pow t 2) x)
28.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

series374.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow l 2) x)
18.0ms
(/ (pow t 2) x)
270.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

simplify579.0ms

Counts
138 → 138
Iterations

Useful iterations: 2 (189.0ms)

IterNodesCost
02292129
14531871
215031692
done50001692

prune505.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt 2.0) t)
4.8b
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))
11.1b
(/ (pow t 2) x)
26.9b
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
24×times-frac
12×unpow-prod-down
11×add-exp-log
9×add-log-exp
8×add-cbrt-cube associate-/l*
7×pow1 sqrt-prod
6×associate-*l*
4×unpow2 sqr-pow
3×div-exp associate-*r* associate-/r* sum-log
2×flip3-+ sqrt-div flip-+ unswap-sqr
1×cbrt-undiv +-commutative pow-to-exp rem-sqrt-square associate-+r+ frac-2neg sqrt-pow1 pow1/2 pow-prod-down pow-exp prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 99
Calls
4 calls:
5.0ms
(* (sqrt 2.0) t)
28.0ms
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow t 2) x)
49.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))))

series271.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (sqrt 2.0) t)
56.0ms
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))
20.0ms
(/ (pow t 2) x)
149.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))))

simplify695.0ms

Counts
111 → 111
Iterations

Useful iterations: done (692.0ms)

IterNodesCost
02001866
14381600
215871465
done50001464

prune410.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
4.8b
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))
11.1b
(/ (pow t 2) x)
26.9b
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
24×times-frac
14×add-exp-log
12×unpow-prod-down sqrt-prod
11×add-cbrt-cube
10×pow1
9×associate-*l* add-log-exp
8×associate-/l*
4×unpow2 sqr-pow
3×div-exp pow-prod-down prod-exp associate-/r* sum-log cbrt-unprod
2×flip3-+ sqrt-div flip-+
1×cbrt-undiv +-commutative pow-to-exp rem-sqrt-square associate-+r+ frac-2neg sqrt-pow1 pow1/2 associate-*r* pow-exp clear-num *-commutative div-inv
Counts
4 → 101
Calls
4 calls:
16.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
26.0ms
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow t 2) x)
52.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))))

series262.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
60.0ms
(+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
143.0ms
(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))))

simplify685.0ms

Counts
113 → 113
Iterations

Useful iterations: done (676.0ms)

IterNodesCost
02092016
14781649
216011488
done50001487

prune405.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 2.8b

regimes544.0ms

Accuracy

76.7% (5.5b remaining)

Error of 9.3b against oracle of 3.8b and baseline of 27.6b

bsearch537.0ms

Steps
ItersRangePoint
8
1.4208256029707195e+117
1.7793028727278986e+120
3.3425130247455635e+119
8
-6.458455904138903e-289
-3.5220671154407477e-293
-6.34487891906004e-289
11
-9.166642237663663e-233
-1.562746242727e-252
-9.431458294677752e-250
10
-1.1264209325184682e+126
-7.95573321924467e+112
-5.627772131442995e+125

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
062188
181188
done81188

end0.0ms

sample2.1s

Algorithm
intervals
Results
509.0ms9832×body80nan
283.0ms5148×body80valid
224.0ms830×body1280valid
212.0ms1009×body640valid
149.0ms587×body1280nan
109.0ms556×body640nan
98.0ms641×body320valid
54.0ms354×body320nan
40.0ms372×body160valid
23.0ms187×body160nan