Details

Time bar (total: 9.4s)

sample74.0ms

Algorithm
intervals
Results
15.0ms329×body80nan
7.0ms154×body80valid
6.0ms28×body1280valid
5.0ms29×body640valid
4.0ms30×body320valid
4.0ms21×body640nan
2.0ms9×body1280nan
2.0ms12×body320nan
1.0ms15×body160valid
1.0ms7×body160nan

simplify84.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03914
19314
219314
341414
471814
5119214
6281614
7500114
done500114

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize27.0ms

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)
13.7b
(- (* (/ (+ 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)))

rewrite141.0ms

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:
53.0ms
(/ (* (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)
32.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
43.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
444.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
46.0ms
(* (sqrt 2.0) t)
228.0ms
(- (* (/ (+ 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)))

simplify59.0ms

Counts
92 → 92
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04171207
120511099
250021099
done50021099

prune314.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.0b

localize16.0ms

Local error

Found 4 expressions with local error:

3.0b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.7b
(/ (pow l 2) x)
9.0b
(/ (pow t 2) x)
29.0b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite57.0ms

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:
17.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
8.0ms
(/ (pow l 2) x)
11.0ms
(/ (pow t 2) x)
16.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series281.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
171.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify61.0ms

Counts
142 → 142
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05261067
12113984
25001978
done5001978

prune441.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
3.0b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
9.0b
(/ (pow t 2) x)
29.0b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite59.0ms

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:
14.0ms
(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
17.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
8.0ms
(/ (pow t 2) x)
17.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series349.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
87.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
25.0ms
(/ (pow t 2) x)
182.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify58.0ms

Counts
104 → 104
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04631321
120291213
250011210
done50011210

prune373.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize28.0ms

Local error

Found 4 expressions with local error:

2.0b
(/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))
3.0b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))))
9.0b
(/ (pow t 2) x)
29.0b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
477×times-frac
208×add-sqr-sqrt
207×add-cube-cbrt *-un-lft-identity
176×unpow-prod-down
63×cbrt-prod unpow2 sqr-pow
49×add-exp-log
40×associate-/r*
31×div-exp
14×associate-/l*
13×pow-exp
11×add-cbrt-cube
9×pow-to-exp div-inv
8×associate-*r/
6×add-log-exp
5×pow1
4×cbrt-undiv flip3-+ sqrt-div frac-add prod-exp flip-+
3×sqrt-prod
2×associate-+r+ frac-2neg clear-num
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log associate-/r/
Counts
4 → 375
Calls
4 calls:
26.0ms
(/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))
17.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))))
8.0ms
(/ (pow t 2) x)
16.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))))))

series363.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))
95.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))))
19.0ms
(/ (pow t 2) x)
197.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))))))

simplify72.0ms

Counts
387 → 387
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
016105656
150014964
done50014964

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

regimes471.0ms

Accuracy

73.5% (6.4b remaining)

Error of 10.3b against oracle of 4.0b and baseline of 28.0b

bsearch713.0ms

Steps
ItersRangePoint
6
1.4492506646584313e+85
1.822198397165114e+86
2.1749908664970245e+85
8
3.253872409851107e-130
5.196545289398966e-127
3.2912161221926835e-130
11
2.854009960629658e-293
6.144753180559701e-264
9.909309527651243e-270
8
-3.536926816114651e-240
-2.6493665622057615e-244
-3.0886340565384557e-240
9
-1.5401742513156077e-163
-1.1631287859066171e-170
-6.6963672441100204e-164
6
-2.8371712079202784e+139
-6.825323247239397e+138
-9.583977798108111e+138

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0118158
1118158
done118158

end0.0ms

sample2.1s

Algorithm
intervals
Results
468.0ms10055×body80nan
255.0ms5079×body80valid
197.0ms830×body1280valid
185.0ms1027×body640valid
125.0ms556×body1280nan
109.0ms627×body640nan
93.0ms687×body320valid
45.0ms350×body320nan
39.0ms377×body160valid
17.0ms196×body160nan