Details

Time bar (total: 53.7s)

sample422.0ms

Algorithm
intervals
Results
71.0ms295×body80nan
37.0ms155×body80valid
36.0ms3×body160nan
33.0ms27×body1280valid
32.0ms36×body640valid
25.0ms21×body1280nan
20.0ms21×body640nan
19.0ms26×body320valid
7.0ms10×body320nan
5.0ms12×body160valid

simplify349.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
348.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.8b

localize41.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
13.9b
(- (* (/ (+ 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))))

rewrite180.0ms

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
79.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
49.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
35.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
14.0ms
(* (sqrt 2) t)

series2.3s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
535.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
261.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
71.0ms
(* (sqrt 2) t)

simplify10.5s

Counts
61 → 96
Calls
61 calls:
Slowest
384.0ms
(/ (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))))))
367.0ms
(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)))))
366.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
365.0ms
(- (+ (log (sqrt 2)) (log t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
363.0ms
(- (* (/ (+ 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: 4.4b

localize33.0ms

Local error

Found 4 expressions with local error:

28.0b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
1.2b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.4b
(* (sqrt 2) t)
0.2b
(* (* l 2) (/ l x))

rewrite122.0ms

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
54.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
31.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
28.0ms
(* (* l 2) (/ l x))
7.0ms
(* (sqrt 2) t)

series388.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
196.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
111.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
55.0ms
(* (sqrt 2) t)
26.0ms
(* (* l 2) (/ l x))

simplify5.6s

Counts
65 → 103
Calls
65 calls:
Slowest
466.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
436.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))
431.0ms
(+ (* (* (* t t) (- (* (/ 4 x) (/ 4 x)) (* 2 2))) x) (* (- (/ 4 x) 2) (* (* l 2) l)))
332.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
286.0ms
(sqrt (- (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (* (* (* l 2) (/ l x)) (* (* l 2) (/ l x)))))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize70.0ms

Local error

Found 4 expressions with local error:

28.0b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* 2 (/ l x)) l)))
1.2b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* 2 (/ l x)) l))
0.4b
(* (sqrt 2) t)
0.2b
(* (* 2 (/ l x)) l)

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
15×add-cbrt-cube add-exp-log
14×add-sqr-sqrt
12×pow1
9×*-un-lft-identity associate-*r/ add-cube-cbrt
7×associate-*l* sqrt-prod
6×associate-*r* prod-exp cbrt-unprod add-log-exp
5×associate-*l/
4×flip3-+ sqrt-div pow-prod-down frac-add flip-+ insert-posit16
2×associate-+l+ *-commutative unswap-sqr
1×distribute-rgt-in cbrt-undiv +-commutative rem-sqrt-square sum-log distribute-lft-in sqrt-pow1 pow1/2 div-exp
Counts
4 → 79
Calls
4 calls:
Slowest
44.0ms
(* (* 2 (/ l x)) l)
40.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* 2 (/ l x)) l)))
36.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* 2 (/ l x)) l))
14.0ms
(* (sqrt 2) t)

series343.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
196.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* 2 (/ l x)) l)))
68.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* 2 (/ l x)) l))
51.0ms
(* (sqrt 2) t)
27.0ms
(* (* 2 (/ l x)) l)

simplify5.2s

Counts
53 → 91
Calls
53 calls:
Slowest
408.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
345.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
333.0ms
(sqrt (- (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (* (* (* 2 (/ l x)) l) (* (* 2 (/ l x)) l))))
263.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* 2 (/ l x)) l) 3)))
243.0ms
(sqrt (+ (* (* (* t t) (+ (pow (/ 4 x) 3) (pow 2 3))) x) (* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) (* (* 2 l) l))))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize87.0ms

Local error

Found 4 expressions with local error:

28.0b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* (* l 2) (/ 1 (* (cbrt x) (cbrt x)))) (/ l (cbrt x)))))
1.2b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* (* l 2) (/ 1 (* (cbrt x) (cbrt x)))) (/ l (cbrt x))))
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
32×associate-*r/
20×frac-add
12×flip3-+ sqrt-div flip-+
8×add-sqr-sqrt frac-times associate-*l/ un-div-inv
7×*-un-lft-identity add-cube-cbrt
6×cbrt-prod add-log-exp
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16
3×sqrt-prod
2×associate-+l+ pow1/3
1×distribute-rgt-in +-commutative rem-sqrt-square sum-log distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 74
Calls
4 calls:
Slowest
50.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* (* l 2) (/ 1 (* (cbrt x) (cbrt x)))) (/ l (cbrt x))))
40.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* (* l 2) (/ 1 (* (cbrt x) (cbrt x)))) (/ l (cbrt x)))))
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series960.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
306.0ms
(cbrt x)
282.0ms
(cbrt x)
251.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* (* l 2) (/ 1 (* (cbrt x) (cbrt x)))) (/ l (cbrt x)))))
121.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* (* l 2) (/ 1 (* (cbrt x) (cbrt x)))) (/ l (cbrt x))))

simplify11.0s

Counts
58 → 86
Calls
58 calls:
Slowest
676.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* (* l 2) (/ 1 (* (cbrt x) (cbrt x)))) (/ l (cbrt x))) 3)))
542.0ms
(sqrt (- (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (* (* (* (* l 2) (/ 1 (* (cbrt x) (cbrt x)))) (/ l (cbrt x))) (* (* (* l 2) (/ 1 (* (cbrt x) (cbrt x)))) (/ l (cbrt x))))))
416.0ms
(+ (* (* (* t t) (+ (pow (/ 4 x) 3) (pow 2 3))) (cbrt x)) (* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) (* (* (* l 2) (/ 1 (* (cbrt x) (cbrt x)))) l)))
391.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
364.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* (* l 2) (/ 1 (* (cbrt x) (cbrt x)))) (/ l (cbrt x)))))

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.6b

regimes1.3s

Accuracy

76.9% (5.5b remaining)

Error of 8.7b against oracle of 3.2b and baseline of 27.2b

bsearch404.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
2.5s10213×body80nan
1.4s878×body1280valid
1.2s5135×body80valid
832.0ms1003×body640valid
666.0ms628×body1280nan
559.0ms630×body640nan
353.0ms629×body320valid
261.0ms351×body320nan
178.0ms355×body160valid
86.0ms184×body160nan