Details

Time bar (total: 57.7s)

sample341.0ms

Algorithm
intervals
Results
80.0ms166×body80valid
52.0ms320×body80nan
42.0ms24×body640nan
24.0ms37×body640valid
17.0ms22×body1280valid
17.0ms20×body1280nan
10.0ms19×body320valid
6.0ms12×body160valid
6.0ms12×body320nan
2.0ms6×body160nan

simplify359.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
358.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.7b

localize70.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
9.9b
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.5b
(* (sqrt 2) t)
0.0b
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite194.0ms

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
85.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
63.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
32.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
10.0ms
(* (sqrt 2) t)

series2.4s

Counts
4 → 12
Calls
4 calls:
Slowest
1.6s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
476.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
274.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
75.0ms
(* (sqrt 2) t)

simplify11.6s

Counts
61 → 96
Calls
61 calls:
Slowest
420.0ms
(- (+ (log (sqrt 2)) (log t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
400.0ms
(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)))))
384.0ms
(/ (* (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* t t) t)) (* (* (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
380.0ms
(/ (sqrt 2) (* (cbrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (cbrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))))
374.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.9b

localize62.0ms

Local error

Found 4 expressions with local error:

24.7b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.5b
(* (sqrt 2) t)
0.1b
(* (* l 2) (/ l x))
0.1b
(/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
23×add-cbrt-cube add-exp-log
19×*-un-lft-identity add-cube-cbrt
16×associate-*r*
15×times-frac
13×sqrt-prod
12×pow1
9×associate-*r/
8×sqrt-div prod-exp cbrt-unprod
7×associate-*l*
6×associate-/r*
4×cbrt-undiv flip3-+ div-exp pow-prod-down frac-add associate-/r/ flip-+ insert-posit16 add-log-exp
2×*-commutative div-inv unswap-sqr
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l*
Counts
4 → 107
Calls
4 calls:
Slowest
56.0ms
(/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))
52.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
34.0ms
(* (* l 2) (/ l x))
14.0ms
(* (sqrt 2) t)

series626.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
326.0ms
(/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))
214.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
48.0ms
(* (sqrt 2) t)
38.0ms
(* (* l 2) (/ l x))

simplify10.1s

Counts
85 → 119
Calls
85 calls:
Slowest
440.0ms
(sqrt (+ (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (- (* (* (* l 2) (/ l x)) (* (* l 2) (/ l x))) (* (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))))
434.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
404.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
359.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))
323.0ms
(sqrt (- (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

localize67.0ms

Local error

Found 4 expressions with local error:

24.7b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.3b
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
0.2b
(* (cbrt (sqrt 2)) t)
0.1b
(* (* l 2) (/ l x))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log
24×pow1
23×add-sqr-sqrt add-cbrt-cube
17×associate-*r*
16×*-un-lft-identity add-cube-cbrt
15×prod-exp cbrt-unprod
12×pow-prod-down
11×associate-*l*
9×times-frac
8×cbrt-prod
7×sqrt-prod
5×associate-*r/
4×sqrt-div insert-posit16 add-log-exp
3×*-commutative unswap-sqr
2×cbrt-undiv flip3-+ div-exp frac-add flip-+
1×rem-sqrt-square sqrt-pow1 pow1/2 div-inv
Counts
4 → 102
Calls
4 calls:
Slowest
37.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
36.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
18.0ms
(* (* l 2) (/ l x))
15.0ms
(* (cbrt (sqrt 2)) t)

series756.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
437.0ms
(* (cbrt (sqrt 2)) t)
212.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
75.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
32.0ms
(* (* l 2) (/ l x))

simplify6.2s

Counts
76 → 114
Calls
76 calls:
Slowest
487.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
446.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
441.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))
360.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
325.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.9b

localize60.0ms

Local error

Found 4 expressions with local error:

24.7b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.3b
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
0.2b
(* (sqrt (sqrt 2)) t)
0.1b
(* (* l 2) (/ l x))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×sqrt-prod
23×add-cbrt-cube add-exp-log
19×*-un-lft-identity associate-*l* add-cube-cbrt
17×pow1 associate-*r*
10×prod-exp cbrt-unprod
9×times-frac
7×pow-prod-down
5×associate-*r/
4×sqrt-div insert-posit16 add-log-exp
3×*-commutative unswap-sqr
2×cbrt-undiv flip3-+ div-exp frac-add flip-+
1×rem-sqrt-square sqrt-pow1 pow1/2 div-inv
Counts
4 → 104
Calls
4 calls:
Slowest
59.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
46.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
37.0ms
(* (* l 2) (/ l x))
18.0ms
(* (sqrt (sqrt 2)) t)

series454.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
221.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
120.0ms
(* (sqrt (sqrt 2)) t)
85.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
28.0ms
(* (* l 2) (/ l x))

simplify5.3s

Counts
77 → 116
Calls
77 calls:
Slowest
483.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
389.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
345.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))
320.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* t t) t))
286.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) t) (* (sqrt (sqrt 2)) t)) (* (sqrt (sqrt 2)) t)))

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.9b

regimes886.0ms

Accuracy

75.7% (5.8b remaining)

Error of 9.1b against oracle of 3.3b and baseline of 27.0b

bsearch2.2s

end0.0ms

sample8.6s

Algorithm
intervals
Results
2.2s9953×body80nan
1.4s816×body1280valid
1.1s5179×body80valid
907.0ms1004×body640valid
646.0ms589×body1280nan
637.0ms627×body640nan
608.0ms329×body320nan
387.0ms630×body320valid
191.0ms371×body160valid
111.0ms201×body160nan