Details

Time bar (total: 50.8s)

sample380.0ms

Algorithm
intervals
Results
65.0ms23×body640nan
59.0ms317×body80nan
39.0ms179×body80valid
25.0ms24×body1280valid
25.0ms32×body640valid
15.0ms15×body1280nan
8.0ms15×body320valid
4.0ms9×body320nan
3.0ms6×body160valid
1.0ms3×body160nan

simplify382.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
381.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.4b

localize67.0ms

Local error

Found 4 expressions with local error:

20.6b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
12.3b
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.5b
(* (sqrt 2) t)
0.0b
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite166.0ms

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
59.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
52.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
45.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
7.0ms
(* (sqrt 2) t)

series2.3s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
480.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
224.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
77.0ms
(* (sqrt 2) t)

simplify10.3s

Counts
61 → 96
Calls
61 calls:
Slowest
358.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
344.0ms
(- (log (* (sqrt 2) t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
341.0ms
(- (+ (log (sqrt 2)) (log t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
341.0ms
(/ (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))))))
335.0ms
(/ t (sqrt (cbrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.6b

localize43.0ms

Local error

Found 4 expressions with local error:

27.0b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.8b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.5b
(* (sqrt 2) t)
0.1b
(* (* l 2) (/ l x))

rewrite112.0ms

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
34.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
31.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
31.0ms
(* (* l 2) (/ l x))
14.0ms
(* (sqrt 2) t)

series388.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
206.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
97.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
53.0ms
(* (sqrt 2) t)
32.0ms
(* (* l 2) (/ l x))

simplify6.0s

Counts
65 → 103
Calls
65 calls:
Slowest
448.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
399.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
392.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))
379.0ms
(/ (cbrt l) (sqrt x))
303.0ms
(sqrt (- (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (* (* (* l 2) (/ l x)) (* (* l 2) (/ l x)))))

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize59.0ms

Local error

Found 4 expressions with local error:

27.0b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.8b
(+ (* (* 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)

rewrite183.0ms

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
Counts
4 → 84
Calls
4 calls:
Slowest
64.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
56.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
43.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
16.0ms
(* (cbrt (sqrt 2)) t)

series832.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
467.0ms
(* (cbrt (sqrt 2)) t)
201.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
106.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
58.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

simplify6.0s

Counts
60 → 96
Calls
60 calls:
Slowest
510.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
435.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
414.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))
324.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
318.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.1b

localize50.0ms

Local error

Found 4 expressions with local error:

27.0b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.8b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.3b
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
0.2b
(* (sqrt (sqrt 2)) t)

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-prod
19×add-sqr-sqrt
18×associate-*l*
12×pow1 *-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
8×associate-*r/
6×add-log-exp
4×flip3-+ sqrt-div associate-*r* pow-prod-down frac-add prod-exp cbrt-unprod 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
Counts
4 → 86
Calls
4 calls:
Slowest
52.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
51.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
31.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
13.0ms
(* (sqrt (sqrt 2)) t)

series475.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
194.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
112.0ms
(* (sqrt (sqrt 2)) t)
99.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
70.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))

simplify5.2s

Counts
61 → 98
Calls
61 calls:
Slowest
488.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
404.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
368.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))
308.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* t t) t))
290.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) t) (* (sqrt (sqrt 2)) t)) (* (sqrt (sqrt 2)) t)))

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.1b

regimes742.0ms

Accuracy

77.7% (5.2b remaining)

Error of 8.5b against oracle of 3.3b and baseline of 26.8b

bsearch2.3s

end0.0ms

sample8.5s

Algorithm
intervals
Results
2.5s10183×body80nan
1.4s5157×body80valid
910.0ms854×body1280valid
894.0ms1025×body640valid
735.0ms634×body1280nan
479.0ms611×body640nan
353.0ms611×body320valid
301.0ms353×body160valid
224.0ms316×body320nan
61.0ms186×body160nan