Details

Time bar (total: 53.0s)

sample330.0ms

Algorithm
intervals
Results
46.0ms36×body640valid
45.0ms317×body80nan
21.0ms155×body80valid
20.0ms26×body1280valid
10.0ms16×body1280nan
9.0ms25×body320valid
5.0ms10×body640nan
4.0ms14×body160valid
3.0ms7×body320nan
1.0ms5×body160nan

simplify258.0ms

Calls
1 calls:
Slowest
257.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.0b

localize39.0ms

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))))

rewrite135.0ms

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*
Calls
4 calls:
Slowest
51.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
50.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
23.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
7.0ms
(* (sqrt 2) t)

series2.2s

Calls
4 calls:
Slowest
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
434.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
215.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
53.0ms
(* (sqrt 2) t)

simplify11.1s

Calls
61 calls:
Slowest
634.0ms
(cbrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
451.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
355.0ms
(- (+ (log (sqrt 2)) (log t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
341.0ms
(/ (* (* (* (sqrt 2) t) (* (sqrt 2) t)) (* (sqrt 2) 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)))))
341.0ms
(/ t (sqrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize39.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
1.0b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.4b
(* (sqrt 2) t)
0.1b
(* (* l 2) (/ l x))

rewrite123.0ms

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
Calls
4 calls:
Slowest
57.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
32.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
24.0ms
(* (* l 2) (/ l x))
8.0ms
(* (sqrt 2) t)

series423.0ms

Calls
4 calls:
Slowest
218.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
89.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
77.0ms
(* (sqrt 2) t)
39.0ms
(* (* l 2) (/ l x))

simplify5.8s

Calls
65 calls:
Slowest
463.0ms
(- (+ (* 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)))))
321.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))
297.0ms
(* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) x)
297.0ms
(sqrt (- (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (* (* (* l 2) (/ l x)) (* (* l 2) (/ l x)))))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.9b

localize61.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
1.0b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.4b
(* t (sqrt 2))
0.1b
(* (* l 2) (/ l x))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×associate-*r*
18×add-cbrt-cube add-exp-log
15×*-un-lft-identity add-cube-cbrt
12×pow1
9×times-frac associate-*r/
7×prod-exp sqrt-prod cbrt-unprod
6×add-log-exp
4×flip3-+ sqrt-div associate-*l* 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
Calls
4 calls:
Slowest
64.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
32.0ms
(* (* l 2) (/ l x))
26.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
7.0ms
(* t (sqrt 2))

series417.0ms

Calls
4 calls:
Slowest
240.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
76.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
52.0ms
(* t (sqrt 2))
50.0ms
(* (* l 2) (/ l x))

simplify5.9s

Calls
66 calls:
Slowest
476.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
409.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
321.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))
310.0ms
(sqrt (- (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (* (* (* l 2) (/ l x)) (* (* l 2) (/ l x)))))
268.0ms
(+ (* (* (* t t) (+ (pow (/ 4 x) 3) (pow 2 3))) x) (* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) (* (* l 2) l)))

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.9b

localize79.0ms

Local error

Found 4 expressions with local error:

31.7b
(cbrt (* (* l 2) (/ l x)))
31.7b
(cbrt (* (* l 2) (/ l x)))
31.7b
(cbrt (* (* l 2) (/ l x)))
27.6b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* (cbrt (* (* l 2) (/ l x))) (cbrt (* (* l 2) (/ l x)))) (cbrt (* (* l 2) (/ l x))))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
47×associate-*r/
27×cbrt-div
16×sqrt-div
14×frac-add
10×frac-times associate-*l/
8×flip3-+ flip-+
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-prod pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Calls
4 calls:
Slowest
85.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* (cbrt (* (* l 2) (/ l x))) (cbrt (* (* l 2) (/ l x)))) (cbrt (* (* l 2) (/ l x))))))
26.0ms
(cbrt (* (* l 2) (/ l x)))
12.0ms
(cbrt (* (* l 2) (/ l x)))
10.0ms
(cbrt (* (* l 2) (/ l x)))

series716.0ms

Calls
4 calls:
Slowest
265.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* (cbrt (* (* l 2) (/ l x))) (cbrt (* (* l 2) (/ l x)))) (cbrt (* (* l 2) (/ l x))))))
194.0ms
(cbrt (* (* l 2) (/ l x)))
135.0ms
(cbrt (* (* l 2) (/ l x)))
122.0ms
(cbrt (* (* l 2) (/ l x)))

simplify9.9s

Calls
39 calls:
Slowest
749.0ms
(* (exp (* 1/3 (- (* 2 (log l)) (log x)))) (cbrt 2))
481.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
462.0ms
(* (cbrt -2) (exp (* 1/3 (- (log (/ -1 x)) (* 2 (log (/ -1 l)))))))
434.0ms
(* (cbrt -2) (exp (* 1/3 (- (log (/ -1 x)) (* 2 (log (/ -1 l)))))))
424.0ms
(* (exp (* 1/3 (- (* 2 (log l)) (log x)))) (cbrt 2))

prune1.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.9b

regimes1.0s

Accuracy

75.2% (5.9b remaining)

Error of 9.1b against oracle of 3.2b and baseline of 27.1b

bsearch512.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
2.1s10002×body80nan
1.2s5172×body80valid
1.0s1006×body640valid
887.0ms832×body1280valid
825.0ms585×body640nan
665.0ms606×body1280nan
473.0ms190×body160nan
329.0ms617×body320valid
298.0ms373×body320nan
131.0ms373×body160valid