Details

Time bar (total: 41.9s)

sample407.0ms

Algorithm
intervals
Results
153.0ms36×body640valid
110.0ms317×body80nan
27.0ms155×body80valid
19.0ms26×body1280valid
14.0ms16×body1280nan
12.0ms25×body320valid
6.0ms10×body640nan
5.0ms14×body160valid
3.0ms7×body320nan
3.0ms5×body160nan

simplify550.0ms

Calls
1 calls:
Slowest
549.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.0b

localize47.0ms

Local error

Found 4 expressions with local error:

19.6b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
14.2b
(- (* (/ (+ 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))))

rewrite47.0ms

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
18.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
14.0ms
(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))
3.0ms
(* (sqrt 2) t)

series2.3s

Calls
4 calls:
Slowest
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
521.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
273.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
71.0ms
(* (sqrt 2) t)

simplify9.4s

Calls
46 calls:
Slowest
466.0ms
(- (+ (* 2 (/ t (* (sqrt 2) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x))))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
376.0ms
(- (log (* (sqrt 2) t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
366.0ms
(sqrt (+ (* (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))) (+ (* (* l l) (* l l)) (* (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
356.0ms
(/ (sqrt 2) (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))))))
348.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize29.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
1.0b
(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
0.4b
(* (sqrt 2) t)
0.2b
(/ (* l 2) (/ x l))

rewrite34.0ms

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
15.0ms
(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
12.0ms
(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
3.0ms
(/ (* l 2) (/ x l))
3.0ms
(* (sqrt 2) t)

series697.0ms

Calls
4 calls:
Slowest
491.0ms
(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
111.0ms
(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
60.0ms
(* (sqrt 2) t)
35.0ms
(/ (* l 2) (/ x l))

simplify3.9s

Calls
45 calls:
Slowest
374.0ms
(* (exp (/ (* l 2) (/ x l))) (exp (* t (* t (+ 2 (/ 4 x))))))
285.0ms
(+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3))))))
285.0ms
(sqrt (+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3)))))))
231.0ms
(* (/ x l) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x)))))
228.0ms
(/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* (/ x l) (/ x l)) (/ x l)))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.4b

localize14.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (+ (* (/ (* l 2) x) l) (* t (* t (+ 2 (/ 4 x))))))
1.0b
(+ (* (/ (* l 2) x) l) (* t (* t (+ 2 (/ 4 x)))))
0.4b
(* (sqrt 2) t)
0.2b
(/ (* l 2) x)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-*r/
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt add-log-exp
4×distribute-rgt-in pow1 associate-+r+ distribute-lft-in flip3-+ add-cbrt-cube sqrt-div associate-*l/ frac-add add-exp-log flip-+ insert-posit16
3×associate-*l* sqrt-prod
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg pow1/2 *-commutative div-inv associate-/l*
Calls
4 calls:
Slowest
18.0ms
(sqrt (+ (* (/ (* l 2) x) l) (* t (* t (+ 2 (/ 4 x))))))
13.0ms
(+ (* (/ (* l 2) x) l) (* t (* t (+ 2 (/ 4 x)))))
5.0ms
(* (sqrt 2) t)
5.0ms
(/ (* l 2) x)

series648.0ms

Calls
4 calls:
Slowest
469.0ms
(sqrt (+ (* (/ (* l 2) x) l) (* t (* t (+ 2 (/ 4 x))))))
89.0ms
(+ (* (/ (* l 2) x) l) (* t (* t (+ 2 (/ 4 x)))))
70.0ms
(* (sqrt 2) t)
19.0ms
(/ (* l 2) x)

simplify3.4s

Calls
31 calls:
Slowest
344.0ms
(* x (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x)))))
323.0ms
(sqrt (+ (* (* (* l 2) l) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* x (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3)))))))
321.0ms
(+ (* (* (* l 2) l) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* x (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3))))))
271.0ms
(* (exp (* (/ (* l 2) x) l)) (exp (* t (* t (+ 2 (/ 4 x))))))
243.0ms
(sqrt (* (cbrt (+ (* (/ (* l 2) x) l) (* t (* t (+ 2 (/ 4 x)))))) (cbrt (+ (* (/ (* l 2) x) l) (* t (* t (+ 2 (/ 4 x))))))))

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.1b

localize23.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
1.0b
(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
0.3b
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
0.2b
(* (sqrt (sqrt 2)) t)

rewrite31.0ms

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 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
10.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
8.0ms
(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
8.0ms
(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
3.0ms
(* (sqrt (sqrt 2)) t)

series805.0ms

Calls
4 calls:
Slowest
514.0ms
(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
121.0ms
(* (sqrt (sqrt 2)) t)
102.0ms
(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
68.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))

simplify4.1s

Calls
42 calls:
Slowest
399.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) t) (* (sqrt (sqrt 2)) t)) (* (sqrt (sqrt 2)) t)))
379.0ms
(* (exp (/ (* l 2) (/ x l))) (exp (* t (* t (+ 2 (/ 4 x))))))
371.0ms
(+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3))))))
283.0ms
(* (/ x l) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x)))))
266.0ms
(sqrt (+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3)))))))

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.1b

regimes1.6s

Accuracy

71% (7.3b remaining)

Error of 9.2b against oracle of 1.8b and baseline of 27.1b

bsearch485.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
2.8s10002×body80nan
1.1s5172×body80valid
932.0ms1006×body640valid
911.0ms585×body640nan
871.0ms832×body1280valid
856.0ms606×body1280nan
348.0ms617×body320valid
205.0ms373×body320nan
142.0ms373×body160valid
67.0ms190×body160nan