Details

Time bar (total: 40.0s)

sample564.0ms

Algorithm
intervals
Results
100.0ms284×body80nan
59.0ms150×body80valid
32.0ms27×body1280valid
27.0ms36×body640valid
22.0ms22×body1280nan
16.0ms21×body640nan
14.0ms24×body320valid
6.0ms19×body160valid
3.0ms8×body320nan
3.0ms7×body160nan

simplify1.1s

Calls
1 calls:
Slowest
1.1s
(/ (* (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: 45.0b

localize63.0ms

Local error

Found 4 expressions with local error:

20.4b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
13.4b
(- (* (/ (+ 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))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×sqrt-prod
6×associate-/r* times-frac add-cbrt-cube add-exp-log add-log-exp
4×pow1 sqrt-div insert-posit16
3×flip3-- associate-*l* flip--
2×associate--l+ associate-/r/
1×distribute-rgt-in cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg distribute-lft-in pow1/2 diff-log div-exp *-commutative div-inv associate-/l*
Calls
4 calls:
Slowest
22.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
19.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
10.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
2.0ms
(* (sqrt 2) t)

series1.3s

Calls
4 calls:
Slowest
908.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
243.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
157.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
23.0ms
(* (sqrt 2) t)

simplify9.2s

Calls
46 calls:
Slowest
424.0ms
(- (+ (* 2 (/ t (* (sqrt 2) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x))))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
401.0ms
(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)))))
366.0ms
(/ (sqrt 2) (sqrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
361.0ms
(- (log (* (sqrt 2) t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
354.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.1b

localize24.0ms

Local error

Found 4 expressions with local error:

29.2b
(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
0.4b
(* (sqrt 2) t)
0.4b
(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
0.2b
(/ (* l 2) (/ x l))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity associate-*r/ add-cube-cbrt
6×add-cbrt-cube add-exp-log add-log-exp
4×distribute-rgt-in pow1 associate-+r+ associate-/r* distribute-lft-in flip3-+ times-frac sqrt-div frac-add flip-+ insert-posit16
3×associate-*l* sqrt-prod div-inv
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg pow1/2 div-exp associate-/r/ *-commutative associate-/l*
Calls
4 calls:
Slowest
11.0ms
(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
7.0ms
(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
3.0ms
(/ (* l 2) (/ x l))
2.0ms
(* (sqrt 2) t)

series336.0ms

Calls
4 calls:
Slowest
240.0ms
(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
42.0ms
(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
33.0ms
(* (sqrt 2) t)
20.0ms
(/ (* l 2) (/ x l))

simplify3.9s

Calls
45 calls:
Slowest
331.0ms
(* (exp (/ (* l 2) (/ x l))) (exp (* t (* t (+ 2 (/ 4 x))))))
314.0ms
(+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3))))))
295.0ms
(sqrt (+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3)))))))
252.0ms
(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
244.0ms
(* (/ x l) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x)))))

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

localize15.0ms

Local error

Found 4 expressions with local error:

29.2b
(sqrt (+ (* (/ l x) (* 2 l)) (* t (* t (+ 2 (/ 4 x))))))
0.4b
(* (sqrt 2) t)
0.4b
(+ (* (/ l x) (* 2 l)) (* t (* t (+ 2 (/ 4 x)))))
0.1b
(* (/ l x) (* 2 l))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt associate-*r/
7×*-un-lft-identity associate-*l* add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log add-log-exp
5×associate-*l/
4×distribute-rgt-in associate-+r+ distribute-lft-in flip3-+ sqrt-div frac-add flip-+ insert-posit16
3×sqrt-prod
2×*-commutative
1×+-commutative rem-sqrt-square sum-log pow1/2 associate-*r* pow-prod-down prod-exp cbrt-unprod div-inv
Calls
4 calls:
Slowest
14.0ms
(+ (* (/ l x) (* 2 l)) (* t (* t (+ 2 (/ 4 x)))))
6.0ms
(sqrt (+ (* (/ l x) (* 2 l)) (* t (* t (+ 2 (/ 4 x))))))
5.0ms
(* (/ l x) (* 2 l))
3.0ms
(* (sqrt 2) t)

series384.0ms

Calls
4 calls:
Slowest
264.0ms
(sqrt (+ (* (/ l x) (* 2 l)) (* t (* t (+ 2 (/ 4 x))))))
64.0ms
(+ (* (/ l x) (* 2 l)) (* t (* t (+ 2 (/ 4 x)))))
35.0ms
(* (sqrt 2) t)
20.0ms
(* (/ l x) (* 2 l))

simplify3.7s

Calls
37 calls:
Slowest
360.0ms
(* x (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x)))))
330.0ms
(* (exp (* (/ l x) (* 2 l))) (exp (* t (* t (+ 2 (/ 4 x))))))
309.0ms
(sqrt (+ (* (* l (* 2 l)) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* x (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3)))))))
253.0ms
(+ (* (* l (* 2 l)) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* x (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3))))))
238.0ms
(sqrt (+ (pow (* (/ l x) (* 2 l)) 3) (pow (* t (* t (+ 2 (/ 4 x)))) 3)))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.4b

localize12.0ms

Local error

Found 4 expressions with local error:

29.2b
(sqrt (+ (* (/ l x) (* 2 l)) (* t (* t (+ 2 (/ 4 x))))))
0.4b
(+ (* (/ l x) (* 2 l)) (* t (* t (+ 2 (/ 4 x)))))
0.4b
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
0.2b
(* (sqrt (sqrt 2)) t)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-*l*
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt sqrt-prod
8×associate-*r/
6×pow1 add-cbrt-cube add-exp-log add-log-exp
4×distribute-rgt-in associate-+r+ distribute-lft-in flip3-+ sqrt-div associate-*l/ frac-add flip-+ insert-posit16
2×*-commutative
1×+-commutative rem-sqrt-square sum-log pow1/2 associate-*r* pow-prod-down prod-exp cbrt-unprod
Calls
4 calls:
Slowest
20.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
15.0ms
(+ (* (/ l x) (* 2 l)) (* t (* t (+ 2 (/ 4 x)))))
12.0ms
(sqrt (+ (* (/ l x) (* 2 l)) (* t (* t (+ 2 (/ 4 x))))))
7.0ms
(* (sqrt (sqrt 2)) t)

series372.0ms

Calls
4 calls:
Slowest
244.0ms
(sqrt (+ (* (/ l x) (* 2 l)) (* t (* t (+ 2 (/ 4 x))))))
46.0ms
(+ (* (/ l x) (* 2 l)) (* t (* t (+ 2 (/ 4 x)))))
44.0ms
(* (sqrt (sqrt 2)) t)
37.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))

simplify3.7s

Calls
42 calls:
Slowest
454.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) t) (* (sqrt (sqrt 2)) t)) (* (sqrt (sqrt 2)) t)))
386.0ms
(* (exp (* (/ l x) (* 2 l))) (exp (* t (* t (+ 2 (/ 4 x))))))
299.0ms
(* x (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x)))))
291.0ms
(+ (* (* l (* 2 l)) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* x (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3))))))
270.0ms
(sqrt (+ (* (* l (* 2 l)) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* x (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3)))))))

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.4b

regimes459.0ms

Accuracy

77.9% (5.6b remaining)

Error of 7.5b against oracle of 1.9b and baseline of 27.2b

bsearch1.2s

end0.0ms

sample8.6s

Algorithm
intervals
Results
2.7s10122×body80nan
1.4s1030×body640valid
1.0s5035×body80valid
970.0ms894×body1280valid
554.0ms587×body1280nan
529.0ms658×body640nan
459.0ms674×body320valid
237.0ms337×body320nan
129.0ms367×body160valid
100.0ms183×body160nan