Details

Time bar (total: 1.6m)

sample340.0ms

Algorithm
intervals
Results
46.0ms306×body80nan
36.0ms11×body1280nan
26.0ms32×body1280valid
25.0ms156×body80valid
24.0ms37×body640valid
13.0ms22×body640nan
11.0ms24×body320valid
7.0ms15×body320nan
2.0ms9×body160nan
2.0ms7×body160valid

simplify362.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
360.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.4b

localize75.0ms

Local error

Found 4 expressions with local error:

19.1b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
13.8b
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.4b
(* (sqrt 2) t)
0.0b
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite200.0ms

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 insert-posit16
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 → 84
Calls
4 calls:
Slowest
89.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
76.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
24.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
7.0ms
(* (sqrt 2) t)

series2.7s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
943.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
231.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
82.0ms
(* (sqrt 2) t)

simplify22.8s

Counts
109 → 96
Calls
109 calls:
Slowest
738.0ms
(* (* (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)) (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
449.0ms
(- (+ (log (sqrt 2)) (log t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
433.0ms
(/ (* (sqrt 2) t) (sqrt (* (cbrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (cbrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))))
429.0ms
(- (* (/ (+ x 1) (- x 1)) (* 2 (* t t))) (* l l))
410.0ms
(* (cbrt (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))) (cbrt (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))))

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.5b

localize65.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x))))
0.4b
(* (sqrt 2) t)
0.2b
(+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x)))
0.1b
(* (* l 2) (/ l x))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×add-cbrt-cube add-exp-log
16×associate-*r*
15×*-un-lft-identity add-cube-cbrt
12×pow1
9×times-frac
8×associate-*l/
7×associate-*l* prod-exp sqrt-prod cbrt-unprod
6×add-log-exp
5×associate-*r/
4×flip3-+ sqrt-div pow-prod-down frac-add flip-+ insert-posit16
2×cbrt-undiv div-exp *-commutative unswap-sqr
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 div-inv
Counts
4 → 89
Calls
4 calls:
Slowest
85.0ms
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x))))
41.0ms
(+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x)))
33.0ms
(* (* l 2) (/ l x))
7.0ms
(* (sqrt 2) t)

series594.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
417.0ms
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x))))
77.0ms
(+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x)))
63.0ms
(* (sqrt 2) t)
37.0ms
(* (* l 2) (/ l x))

simplify14.5s

Counts
109 → 101
Calls
109 calls:
Slowest
581.0ms
(sqrt (sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x)))))
482.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
471.0ms
(sqrt (+ (* (* (* (- (* (/ 4 x) (/ 4 x)) (* 2 2)) t) t) x) (* (- (/ 4 x) 2) (* (* l 2) l))))
469.0ms
(+ (* (* (* (- (* (/ 4 x) (/ 4 x)) (* 2 2)) t) t) x) (* (- (/ 4 x) 2) (* (* l 2) l)))
408.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.0b

localize89.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (cbrt l) (cbrt x)))) (/ (cbrt l) (cbrt x)))))
0.6b
(cbrt l)
0.6b
(cbrt l)
0.6b
(cbrt l)

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
38×associate-*l/
18×associate-*r/
16×sqrt-div
14×frac-add
10×frac-times
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity flip3-+ add-cube-cbrt flip-+
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 66
Calls
4 calls:
Slowest
101.0ms
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (cbrt l) (cbrt x)))) (/ (cbrt l) (cbrt x)))))
1.0ms
(cbrt l)
1.0ms
(cbrt l)
1.0ms
(cbrt l)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
368.0ms
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (cbrt l) (cbrt x)))) (/ (cbrt l) (cbrt x)))))
302.0ms
(cbrt l)
252.0ms
(cbrt l)
245.0ms
(cbrt l)

simplify15.3s

Counts
101 → 78
Calls
101 calls:
Slowest
692.0ms
(sqrt (+ (* (* (* (- (* (/ 4 x) (/ 4 x)) (* 2 2)) t) t) (cbrt x)) (* (- (/ 4 x) 2) (* (* (* l 2) (* (cbrt l) (/ (cbrt l) (cbrt x)))) (/ (cbrt l) (cbrt x))))))
609.0ms
(sqrt (+ (* (* (* (+ (/ 4 x) 2) t) t) (* (* (+ (/ 4 x) 2) t) t)) (- (* (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (cbrt l) (cbrt x)))) (/ (cbrt l) (cbrt x))) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (cbrt l) (cbrt x)))) (/ (cbrt l) (cbrt x)))) (* (* (* (+ (/ 4 x) 2) t) t) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (cbrt l) (cbrt x)))) (/ (cbrt l) (cbrt x)))))))
579.0ms
(sqrt (- (* (* (* (+ (/ 4 x) 2) t) t) (* (* (+ (/ 4 x) 2) t) t)) (* (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (cbrt l) (cbrt x)))) (/ (cbrt l) (cbrt x))) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (cbrt l) (cbrt x)))) (/ (cbrt l) (cbrt x))))))
550.0ms
(* (* (sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (cbrt l) (cbrt x)))) (/ (cbrt l) (cbrt x))))) (sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (cbrt l) (cbrt x)))) (/ (cbrt l) (cbrt x)))))) (sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (cbrt l) (cbrt x)))) (/ (cbrt l) (cbrt x))))))
507.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))

prune1.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.0b

localize76.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (* (cbrt (* (cbrt l) (cbrt l))) (cbrt (cbrt l))) (cbrt x)))) (/ (cbrt l) (cbrt x)))))
0.6b
(cbrt l)
0.6b
(cbrt l)
0.6b
(cbrt l)

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
38×associate-*l/
18×associate-*r/
16×sqrt-div
14×frac-add
10×frac-times
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity flip3-+ add-cube-cbrt flip-+
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 66
Calls
4 calls:
Slowest
96.0ms
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (* (cbrt (* (cbrt l) (cbrt l))) (cbrt (cbrt l))) (cbrt x)))) (/ (cbrt l) (cbrt x)))))
1.0ms
(cbrt l)
1.0ms
(cbrt l)
1.0ms
(cbrt l)

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
374.0ms
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (* (cbrt (* (cbrt l) (cbrt l))) (cbrt (cbrt l))) (cbrt x)))) (/ (cbrt l) (cbrt x)))))
310.0ms
(cbrt l)
293.0ms
(cbrt l)
286.0ms
(cbrt l)

simplify15.4s

Counts
101 → 78
Calls
101 calls:
Slowest
1.1s
(sqrt (+ (* (* (* (+ (/ 4 x) 2) t) t) (* (* (+ (/ 4 x) 2) t) t)) (- (* (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (* (cbrt (* (cbrt l) (cbrt l))) (cbrt (cbrt l))) (cbrt x)))) (/ (cbrt l) (cbrt x))) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (* (cbrt (* (cbrt l) (cbrt l))) (cbrt (cbrt l))) (cbrt x)))) (/ (cbrt l) (cbrt x)))) (* (* (* (+ (/ 4 x) 2) t) t) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (* (cbrt (* (cbrt l) (cbrt l))) (cbrt (cbrt l))) (cbrt x)))) (/ (cbrt l) (cbrt x)))))))
961.0ms
(sqrt (- (* (* (* (+ (/ 4 x) 2) t) t) (* (* (+ (/ 4 x) 2) t) t)) (* (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (* (cbrt (* (cbrt l) (cbrt l))) (cbrt (cbrt l))) (cbrt x)))) (/ (cbrt l) (cbrt x))) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (* (cbrt (* (cbrt l) (cbrt l))) (cbrt (cbrt l))) (cbrt x)))) (/ (cbrt l) (cbrt x))))))
863.0ms
(sqrt (+ (pow (* (* (+ (/ 4 x) 2) t) t) 3) (pow (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (/ (* (cbrt (* (cbrt l) (cbrt l))) (cbrt (cbrt l))) (cbrt x)))) (/ (cbrt l) (cbrt x))) 3)))
537.0ms
(sqrt (+ (* (* (* (+ (pow (/ 4 x) 3) (pow 2 3)) t) t) (cbrt x)) (* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) (* (* (* l 2) (* (cbrt l) (/ (* (cbrt (* (cbrt l) (cbrt l))) (cbrt (cbrt l))) (cbrt x)))) (/ (cbrt l) (cbrt x))))))
512.0ms
(sqrt (+ (* (* (* (+ (pow (/ 4 x) 3) (pow 2 3)) t) t) (* (cbrt x) (cbrt x))) (* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) (* (* (* l 2) (* (/ (cbrt l) (cbrt x)) (* (cbrt (* (cbrt l) (cbrt l))) (cbrt (cbrt l))))) (cbrt l)))))

prune1.6s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 3.0b

regimes968.0ms

Accuracy

75% (6.0b remaining)

Error of 9.1b against oracle of 3.1b and baseline of 27.1b

bsearch2.3s

end0.0ms

sample8.8s

Algorithm
intervals
Results
2.5s10387×body80nan
1.5s5077×body80valid
1.3s857×body1280valid
786.0ms1051×body640valid
659.0ms554×body1280nan
569.0ms594×body640nan
389.0ms663×body320valid
226.0ms370×body320nan
221.0ms352×body160valid
62.0ms189×body160nan