Details

Time bar (total: 1.0m)

sample517.0ms

Algorithm
intervals
Results
107.0ms29×body1280valid
104.0ms320×body80nan
40.0ms166×body80valid
24.0ms30×body640valid
20.0ms19×body1280nan
11.0ms18×body320valid
11.0ms12×body640nan
5.0ms13×body160valid
4.0ms7×body320nan
2.0ms4×body160nan

simplify280.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
279.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

localize61.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
13.1b
(- (* (/ (+ 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))))

rewrite112.0ms

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
42.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
32.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
28.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
7.0ms
(* (sqrt 2) t)

series2.8s

Counts
4 → 12
Calls
4 calls:
Slowest
1.6s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
901.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
260.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
76.0ms
(* (sqrt 2) t)

simplify10.3s

Counts
61 → 96
Calls
61 calls:
Slowest
410.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
382.0ms
(/ (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))))))
377.0ms
(- (log (* (sqrt 2) t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
367.0ms
(- (+ (log (sqrt 2)) (log t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
363.0ms
(/ t (sqrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.2b

localize32.0ms

Local error

Found 4 expressions with local error:

27.3b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.8b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.4b
(* (sqrt 2) t)
0.1b
(* (* l 2) (/ l x))

rewrite85.0ms

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 associate-*r/
7×associate-*l* prod-exp sqrt-prod cbrt-unprod
6×add-log-exp
4×flip3-+ sqrt-div pow-prod-down frac-add flip-+ insert-posit16
2×cbrt-undiv associate-+l+ div-exp *-commutative unswap-sqr
1×distribute-rgt-in +-commutative rem-sqrt-square sum-log distribute-lft-in sqrt-pow1 pow1/2 div-inv
Counts
4 → 91
Calls
4 calls:
Slowest
34.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
23.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
18.0ms
(* (* l 2) (/ l x))
7.0ms
(* (sqrt 2) t)

series397.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
188.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
114.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
55.0ms
(* (sqrt 2) t)
39.0ms
(* (* l 2) (/ l x))

simplify5.7s

Counts
65 → 103
Calls
65 calls:
Slowest
462.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
361.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))
346.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
287.0ms
(sqrt (- (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (* (* (* l 2) (/ l x)) (* (* l 2) (/ l x)))))
265.0ms
(* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) x)

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.7b

localize52.0ms

Local error

Found 4 expressions with local error:

27.3b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.8b
(+ (* (* 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)

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1
18×add-exp-log
16×add-sqr-sqrt
11×add-cbrt-cube
10×associate-*l*
9×*-un-lft-identity pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
8×cbrt-prod associate-*r/
7×sqrt-prod
6×add-log-exp
4×flip3-+ sqrt-div associate-*r* frac-add flip-+ insert-posit16
3×unswap-sqr
2×associate-+l+ *-commutative
1×distribute-rgt-in +-commutative rem-sqrt-square sum-log distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 84
Calls
4 calls:
Slowest
42.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
32.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
31.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
7.0ms
(* (cbrt (sqrt 2)) t)

series822.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
452.0ms
(* (cbrt (sqrt 2)) t)
213.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
94.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
64.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

simplify6.5s

Counts
60 → 96
Calls
60 calls:
Slowest
755.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
446.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))
445.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
413.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
320.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.7b

localize86.0ms

Local error

Found 4 expressions with local error:

27.3b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.8b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.5b
(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))
0.3b
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))

rewrite335.0ms

Algorithm
rewrite-expression-head
Rules
58×pow1
57×add-exp-log
39×pow-prod-down prod-exp cbrt-unprod
29×add-cbrt-cube
8×associate-*r/
6×add-sqr-sqrt add-log-exp
5×*-un-lft-identity add-cube-cbrt
4×flip3-+ sqrt-div frac-add flip-+ insert-posit16
3×sqrt-prod
2×associate-+l+ associate-*r* associate-*l* *-commutative
1×distribute-rgt-in +-commutative rem-sqrt-square sum-log distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 98
Calls
4 calls:
Slowest
165.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))
76.0ms
(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))
56.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
35.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))

series755.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
420.0ms
(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))
188.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
82.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
64.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))

simplify15.1s

Counts
73 → 110
Calls
73 calls:
Slowest
524.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (* (* t t) t))))
497.0ms
(* (* (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (cbrt (sqrt 2)) (* (* t t) t)))
434.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (* (* t t) t))))
424.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
418.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.7b

regimes674.0ms

Accuracy

73.9% (6.3b remaining)

Error of 9.3b against oracle of 3.0b and baseline of 27.0b

bsearch1.5s

end0.0ms

sample9.2s

Algorithm
intervals
Results
3.0s10171×body80nan
1.2s5104×body80valid
1.1s876×body1280valid
923.0ms1002×body640valid
712.0ms628×body1280nan
578.0ms645×body640nan
510.0ms655×body320valid
312.0ms345×body320nan
195.0ms363×body160valid
59.0ms166×body160nan