Details

Time bar (total: 1.0m)

sample395.0ms

Algorithm
intervals
Results
121.0ms338×body80nan
38.0ms176×body80valid
23.0ms27×body640nan
22.0ms22×body1280valid
22.0ms28×body640valid
19.0ms17×body1280nan
14.0ms22×body320valid
5.0ms8×body320nan
3.0ms8×body160valid
1.0ms2×body160nan

simplify357.0ms

Calls
1 calls:
Slowest
356.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize71.0ms

Local error

Found 4 expressions with local error:

19.8b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
11.7b
(- (* (/ (+ 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))))

rewrite187.0ms

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
84.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
61.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
24.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
14.0ms
(* (sqrt 2) t)

series2.1s

Calls
4 calls:
Slowest
1.3s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
458.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
259.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
76.0ms
(* (sqrt 2) t)

simplify10.8s

Calls
61 calls:
Slowest
665.0ms
(/ (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))))))
371.0ms
(- (+ (log (sqrt 2)) (log t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
362.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
343.0ms
(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)))))
340.0ms
(/ (sqrt 2) (sqrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize36.0ms

Local error

Found 4 expressions with local error:

26.4b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.4b
(* (sqrt 2) t)
0.4b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.1b
(* (* l 2) (/ l x))

rewrite116.0ms

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
44.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
33.0ms
(* (* l 2) (/ l x))
28.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
8.0ms
(* (sqrt 2) t)

series417.0ms

Calls
4 calls:
Slowest
238.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
87.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
53.0ms
(* (sqrt 2) t)
39.0ms
(* (* l 2) (/ l x))

simplify5.6s

Calls
65 calls:
Slowest
483.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
390.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
355.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))
302.0ms
(sqrt (- (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (* (* (* l 2) (/ l x)) (* (* l 2) (/ l x)))))
234.0ms
(* (* (* (* l 2) (* l 2)) (* l 2)) (/ (* (* l l) l) (* (* x x) x)))

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.3b

localize63.0ms

Local error

Found 4 expressions with local error:

26.4b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.4b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.3b
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
0.2b
(* (cbrt (sqrt 2)) t)

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1
18×add-exp-log
16×add-sqr-sqrt
11×add-cbrt-cube
10×associate-*l*
9×*-un-lft-identity pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
8×cbrt-prod associate-*r/
7×sqrt-prod
6×add-log-exp
4×flip3-+ sqrt-div associate-*r* frac-add flip-+ insert-posit16
3×unswap-sqr
2×associate-+l+ *-commutative
1×distribute-rgt-in +-commutative rem-sqrt-square sum-log distribute-lft-in sqrt-pow1 pow1/2
Calls
4 calls:
Slowest
50.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
36.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
23.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
15.0ms
(* (cbrt (sqrt 2)) t)

series763.0ms

Calls
4 calls:
Slowest
415.0ms
(* (cbrt (sqrt 2)) t)
198.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
90.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
59.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

simplify6.2s

Calls
60 calls:
Slowest
458.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
447.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))
446.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
394.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
323.0ms
(sqrt (- (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (* (* (* l 2) (/ l x)) (* (* l 2) (/ l x)))))

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.3b

localize88.0ms

Local error

Found 4 expressions with local error:

26.4b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.4b
(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))
0.4b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.3b
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))

rewrite332.0ms

Algorithm
rewrite-expression-head
Rules
58×pow1
57×add-exp-log
39×pow-prod-down prod-exp cbrt-unprod
29×add-cbrt-cube
8×associate-*r/
6×add-sqr-sqrt add-log-exp
5×*-un-lft-identity add-cube-cbrt
4×flip3-+ sqrt-div frac-add flip-+ insert-posit16
3×sqrt-prod
2×associate-+l+ associate-*r* associate-*l* *-commutative
1×distribute-rgt-in +-commutative rem-sqrt-square sum-log distribute-lft-in sqrt-pow1 pow1/2
Calls
4 calls:
Slowest
190.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))
51.0ms
(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))
50.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
38.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))

series834.0ms

Calls
4 calls:
Slowest
463.0ms
(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))
186.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
111.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
73.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))

simplify15.6s

Calls
73 calls:
Slowest
568.0ms
(sqrt (* (cbrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) (cbrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))))
455.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))
454.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (* (* (cbrt (cbrt (sqrt 2))) t) (* (cbrt (cbrt (sqrt 2))) t)) (* (cbrt (cbrt (sqrt 2))) t))))
435.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (* (* t t) t))))
432.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))

prune1.8s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.3b

regimes1.1s

Accuracy

77.4% (5.5b remaining)

Error of 8.7b against oracle of 3.3b and baseline of 27.5b

bsearch2.4s

end0.0ms

sample8.6s

Algorithm
intervals
Results
2.5s10149×body80nan
1.4s5145×body80valid
1.3s1042×body640valid
970.0ms795×body1280valid
743.0ms568×body1280nan
459.0ms588×body640nan
401.0ms661×body320valid
199.0ms372×body320nan
127.0ms357×body160valid
63.0ms178×body160nan