Details

Time bar (total: 38.2s)

sample283.0ms

Algorithm
intervals
Results
46.0ms324×body80nan
34.0ms8×body160nan
24.0ms169×body80valid
22.0ms37×body640valid
17.0ms25×body1280valid
14.0ms20×body640nan
10.0ms15×body1280nan
6.0ms17×body320valid
6.0ms17×body320nan
3.0ms8×body160valid

simplify805.0ms

Calls
1 calls:
Slowest
805.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize56.0ms

Local error

Found 4 expressions with local error:

17.6b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
10.4b
(- (* (/ (+ 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))))

rewrite62.0ms

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
28.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
17.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
13.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
3.0ms
(* (sqrt 2) t)

series1.3s

Calls
4 calls:
Slowest
825.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
317.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
139.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
24.0ms
(* (sqrt 2) t)

simplify9.4s

Calls
46 calls:
Slowest
428.0ms
(- (+ (* 2 (/ t (* (sqrt 2) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x))))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
345.0ms
(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)))))
340.0ms
(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)))))
338.0ms
(/ (sqrt 2) (sqrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
332.0ms
(/ (sqrt 2) (sqrt (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: 4.7b

localize28.0ms

Local error

Found 4 expressions with local error:

24.7b
(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
0.6b
(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
0.4b
(* (sqrt 2) t)
0.2b
(/ (* l 2) (/ x l))

rewrite31.0ms

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
13.0ms
(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
7.0ms
(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
6.0ms
(/ (* l 2) (/ x l))
5.0ms
(* (sqrt 2) t)

series304.0ms

Calls
4 calls:
Slowest
225.0ms
(sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x))))))
41.0ms
(+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))
21.0ms
(* (sqrt 2) t)
17.0ms
(/ (* l 2) (/ x l))

simplify3.5s

Calls
45 calls:
Slowest
296.0ms
(* (exp (/ (* l 2) (/ x l))) (exp (* t (* t (+ 2 (/ 4 x))))))
277.0ms
(+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3))))))
270.0ms
(sqrt (+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3)))))))
227.0ms
(* (/ x l) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x)))))
219.0ms
(sqrt (sqrt (+ (/ (* l 2) (/ x l)) (* t (* t (+ 2 (/ 4 x)))))))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.2b

localize20.0ms

Local error

Found 4 expressions with local error:

24.7b
(sqrt (+ (* l (/ 2 (/ x l))) (* t (* t (+ 2 (/ 4 x))))))
0.7b
(/ 2 (/ x l))
0.6b
(+ (* l (/ 2 (/ x l))) (* t (* t (+ 2 (/ 4 x)))))
0.4b
(* (sqrt 2) t)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-*r/
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×add-log-exp
4×distribute-rgt-in pow1 associate-+r+ associate-/r* distribute-lft-in flip3-+ add-cbrt-cube sqrt-div frac-add add-exp-log flip-+ insert-posit16
3×associate-*l* sqrt-prod
2×div-inv
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg pow1/2 associate-/r/ *-commutative
Calls
4 calls:
Slowest
5.0ms
(+ (* l (/ 2 (/ x l))) (* t (* t (+ 2 (/ 4 x)))))
4.0ms
(sqrt (+ (* l (/ 2 (/ x l))) (* t (* t (+ 2 (/ 4 x))))))
3.0ms
(* (sqrt 2) t)
0.0ms
(/ 2 (/ x l))

series332.0ms

Calls
4 calls:
Slowest
236.0ms
(sqrt (+ (* l (/ 2 (/ x l))) (* t (* t (+ 2 (/ 4 x))))))
56.0ms
(+ (* l (/ 2 (/ x l))) (* t (* t (+ 2 (/ 4 x)))))
27.0ms
(* (sqrt 2) t)
13.0ms
(/ 2 (/ x l))

simplify3.2s

Calls
35 calls:
Slowest
347.0ms
(+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3))))))
275.0ms
(sqrt (+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3)))))))
259.0ms
(* (/ x l) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x)))))
241.0ms
(* (exp (* l (/ 2 (/ x l)))) (exp (* t (* t (+ 2 (/ 4 x))))))
213.0ms
(sqrt (+ (* l (/ 2 (/ x l))) (* t (* t (+ 2 (/ 4 x))))))

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.2b

localize26.0ms

Local error

Found 4 expressions with local error:

24.7b
(sqrt (+ (* l (/ 2 (/ x l))) (* t (* t (+ 2 (/ 4 x))))))
0.7b
(/ 2 (/ x l))
0.6b
(+ (* l (/ 2 (/ x l))) (* t (* t (+ 2 (/ 4 x)))))
0.3b
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-*r/
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube associate-*l* add-exp-log sqrt-prod add-log-exp
4×distribute-rgt-in associate-+r+ associate-/r* distribute-lft-in flip3-+ sqrt-div frac-add flip-+ insert-posit16
2×div-inv
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg pow1/2 associate-*r* pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
20.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
10.0ms
(+ (* l (/ 2 (/ x l))) (* t (* t (+ 2 (/ 4 x)))))
8.0ms
(sqrt (+ (* l (/ 2 (/ x l))) (* t (* t (+ 2 (/ 4 x))))))
1.0ms
(/ 2 (/ x l))

series309.0ms

Calls
4 calls:
Slowest
223.0ms
(sqrt (+ (* l (/ 2 (/ x l))) (* t (* t (+ 2 (/ 4 x))))))
41.0ms
(+ (* l (/ 2 (/ x l))) (* t (* t (+ 2 (/ 4 x)))))
29.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
15.0ms
(/ 2 (/ x l))

simplify3.7s

Calls
41 calls:
Slowest
360.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) t) (* (sqrt (sqrt 2)) t)) (* (sqrt (sqrt 2)) t)))
308.0ms
(+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3))))))
272.0ms
(sqrt (+ (* (* l 2) (+ (* 2 2) (- (* (/ 4 x) (/ 4 x)) (* 2 (/ 4 x))))) (* (/ x l) (* t (* t (+ (pow 2 3) (pow (/ 4 x) 3)))))))
266.0ms
(sqrt (+ (pow (* l (/ 2 (/ x l))) 3) (pow (* t (* t (+ 2 (/ 4 x)))) 3)))
257.0ms
(sqrt (+ (* l (/ 2 (/ x l))) (* t (* t (+ 2 (/ 4 x))))))

prune1.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.1b

regimes733.0ms

Accuracy

70.3% (7.4b remaining)

Error of 9.7b against oracle of 2.3b and baseline of 27.1b

bsearch1.6s

end0.0ms

sample8.1s

Algorithm
intervals
Results
2.5s10058×body80nan
1.3s1041×body640valid
1.1s5089×body80valid
818.0ms855×body1280valid
649.0ms585×body1280nan
513.0ms595×body640nan
411.0ms641×body320valid
183.0ms323×body320nan
151.0ms374×body160valid
56.0ms171×body160nan