Details

Time bar (total: 1.7m)

sample341.0ms

Algorithm
intervals
Results
81.0ms341×body80nan
30.0ms164×body80valid
20.0ms31×body640valid
19.0ms26×body1280valid
16.0ms20×body1280nan
14.0ms23×body640nan
11.0ms23×body320valid
4.0ms9×body320nan
4.0ms12×body160valid
2.0ms6×body160nan

simplify403.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
402.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.1b

localize48.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
12.8b
(- (* (/ (+ 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))))

rewrite158.0ms

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 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
41.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
41.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
15.0ms
(* (sqrt 2) t)

series2.7s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
675.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
462.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
79.0ms
(* (sqrt 2) t)

simplify21.6s

Counts
109 → 96
Calls
109 calls:
Slowest
805.0ms
(* (* (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)) (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
418.0ms
(/ (* (sqrt 2) t) (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))))))
394.0ms
(exp (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
390.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
389.0ms
(- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3))

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.4b

localize34.0ms

Local error

Found 4 expressions with local error:

25.4b
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x))))
0.5b
(* (sqrt 2) t)
0.4b
(+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x)))
0.1b
(* (* l 2) (/ l x))

rewrite213.0ms

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
8×associate-*l/
7×associate-*l* prod-exp sqrt-prod cbrt-unprod
6×add-log-exp
5×associate-*r/
4×flip3-+ sqrt-div pow-prod-down frac-add flip-+ insert-posit16
2×cbrt-undiv div-exp *-commutative unswap-sqr
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 div-inv
Counts
4 → 89
Calls
4 calls:
Slowest
89.0ms
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x))))
74.0ms
(+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x)))
34.0ms
(* (* l 2) (/ l x))
13.0ms
(* (sqrt 2) t)

series671.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
455.0ms
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x))))
122.0ms
(+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x)))
62.0ms
(* (sqrt 2) t)
31.0ms
(* (* l 2) (/ l x))

simplify14.1s

Counts
109 → 101
Calls
109 calls:
Slowest
516.0ms
(log (sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x)))))
462.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
456.0ms
(sqrt (+ (* (* (* (- (* (/ 4 x) (/ 4 x)) (* 2 2)) t) t) x) (* (- (/ 4 x) 2) (* (* l 2) l))))
450.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
428.0ms
(+ (* (* (* (- (* (/ 4 x) (/ 4 x)) (* 2 2)) t) t) x) (* (- (/ 4 x) 2) (* (* l 2) l)))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.9b

localize54.0ms

Local error

Found 4 expressions with local error:

25.4b
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x))))
0.4b
(+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x)))
0.3b
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
0.2b
(* (cbrt (sqrt 2)) t)

rewrite171.0ms

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-*l/
7×sqrt-prod
6×add-log-exp
4×flip3-+ sqrt-div associate-*r* frac-add associate-*r/ flip-+ insert-posit16
3×unswap-sqr
2×*-commutative
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
4 → 82
Calls
4 calls:
Slowest
73.0ms
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x))))
48.0ms
(+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x)))
32.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
15.0ms
(* (cbrt (sqrt 2)) t)

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
447.0ms
(* (cbrt (sqrt 2)) t)
408.0ms
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x))))
102.0ms
(+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x)))
83.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

simplify14.1s

Counts
103 → 94
Calls
103 calls:
Slowest
950.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
621.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t)) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t)))
478.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
463.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
448.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.9b

localize89.0ms

Local error

Found 4 expressions with local error:

25.4b
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x))))
0.4b
(+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x)))
0.3b
(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))
0.3b
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))

rewrite415.0ms

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-*l/
6×add-sqr-sqrt add-log-exp
5×*-un-lft-identity add-cube-cbrt
4×flip3-+ sqrt-div frac-add associate-*r/ flip-+ insert-posit16
3×sqrt-prod
2×associate-*r* associate-*l* *-commutative
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
4 → 96
Calls
4 calls:
Slowest
157.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))
109.0ms
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x))))
75.0ms
(+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x)))
71.0ms
(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
470.0ms
(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))
399.0ms
(sqrt (+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x))))
113.0ms
(+ (* (* (+ (/ 4 x) 2) t) t) (* (* l 2) (/ l x)))
96.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))

simplify26.9s

Counts
114 → 108
Calls
114 calls:
Slowest
754.0ms
(sqrt (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))))
598.0ms
(* (* (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))
560.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))))
549.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (* (* t t) t))))
512.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))

prune1.8s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 2.9b

regimes1.0s

Accuracy

75.8% (5.9b remaining)

Error of 8.9b against oracle of 3.1b and baseline of 27.3b

bsearch909.0ms

end0.0ms

sample9.0s

Algorithm
intervals
Results
2.6s10227×body80nan
1.5s612×body1280nan
1.1s5156×body80valid
929.0ms1067×body640valid
921.0ms808×body1280valid
536.0ms591×body640nan
415.0ms645×body320valid
212.0ms323×body320nan
154.0ms324×body160valid
51.0ms148×body160nan