Details

Time bar (total: 1.1m)

sample442.0ms

Algorithm
intervals
Results
104.0ms322×body80nan
34.0ms34×body1280valid
30.0ms155×body80valid
24.0ms34×body640valid
23.0ms22×body1280nan
15.0ms21×body640nan
13.0ms21×body320valid
13.0ms14×body320nan
5.0ms12×body160valid
2.0ms8×body160nan

simplify326.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
325.0ms
(/ (* (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: 39.0b

localize34.0ms

Local error

Found 4 expressions with local error:

14.7b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
14.1b
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.4b
(* (sqrt 2) t)
0.3b
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite131.0ms

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
57.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ 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)))
24.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
7.0ms
(* (sqrt 2) t)

series2.4s

Counts
4 → 12
Calls
4 calls:
Slowest
1.6s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
496.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
245.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
56.0ms
(* (sqrt 2) t)

simplify10.5s

Counts
61 → 96
Calls
61 calls:
Slowest
408.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
360.0ms
(sqrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
356.0ms
(- (+ (log (sqrt 2)) (log t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
354.0ms
(/ t (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
343.0ms
(/ (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: 3.8b

localize60.0ms

Local error

Found 4 expressions with local error:

22.8b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.6b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.4b
(* (sqrt 2) t)
0.3b
(/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×*-un-lft-identity associate-*r/ add-cube-cbrt
11×add-cbrt-cube add-exp-log
8×sqrt-div
7×pow1
6×associate-/r* flip3-+ times-frac associate-*l* frac-add flip-+ add-log-exp
4×associate-/r/ insert-posit16
3×associate-*r*
2×cbrt-undiv associate-+l+ div-exp prod-exp cbrt-unprod unswap-sqr
1×distribute-rgt-in +-commutative rem-sqrt-square clear-num sum-log frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down *-commutative div-inv associate-/l*
Counts
4 → 89
Calls
4 calls:
Slowest
51.0ms
(/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))
43.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
28.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
7.0ms
(* (sqrt 2) t)

series645.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
286.0ms
(/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))
225.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
73.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
61.0ms
(* (sqrt 2) t)

simplify10.3s

Counts
69 → 101
Calls
69 calls:
Slowest
759.0ms
(/ (* (* (* (sqrt 2) t) (* (sqrt 2) t)) (* (sqrt 2) t)) (* (* (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))))
467.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
394.0ms
(sqrt (+ (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (- (* (* (* l 2) (/ l x)) (* (* l 2) (/ l x))) (* (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))))
391.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
371.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.0b

localize76.0ms

Local error

Found 4 expressions with local error:

22.8b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
22.8b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
22.8b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
3.5b
(cbrt (/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-div associate-*r/
14×cbrt-prod
13×add-sqr-sqrt
12×sqrt-prod
10×*-un-lft-identity add-cube-cbrt
8×flip3-+ frac-add flip-+
7×pow1
6×times-frac
4×add-cbrt-cube add-exp-log associate-/r/ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-div pow1/3 div-inv
Counts
4 → 78
Calls
4 calls:
Slowest
50.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
43.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
41.0ms
(cbrt (/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))))
30.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
719.0ms
(cbrt (/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))))
224.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
214.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
200.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))

simplify11.1s

Counts
54 → 90
Calls
54 calls:
Slowest
584.0ms
(- (* (* (exp (* 1/3 (+ (log t) (log (sqrt 2))))) (exp (* 1/6 (+ (log 1/2) (log x))))) (pow (/ 1 l) 1/3)) (+ (* 1/3 (* (* (pow t 2) (* (exp (* 1/3 (+ (log t) (log (sqrt 2))))) (exp (* 1/6 (+ (log 1/2) (log x)))))) (pow (/ 1 (pow l 7)) 1/3))) (* 1/6 (* (* (pow t 2) (* (exp (* 1/3 (+ (log t) (log (sqrt 2))))) (exp (* 1/6 (+ (log 1/2) (* 7 (log x))))))) (pow (/ 1 (pow l 7)) 1/3)))))
463.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
392.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
357.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
353.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))

prune1.7s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.0b

localize117.0ms

Local error

Found 4 expressions with local error:

22.8b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
22.8b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
22.8b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
3.5b
(cbrt (/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-div associate-*r/
14×cbrt-prod
13×add-sqr-sqrt
12×sqrt-prod
10×*-un-lft-identity add-cube-cbrt
8×flip3-+ frac-add flip-+
7×pow1
6×times-frac
4×add-cbrt-cube add-exp-log associate-/r/ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-div pow1/3 div-inv
Counts
4 → 78
Calls
4 calls:
Slowest
59.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
58.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
58.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
43.0ms
(cbrt (/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
615.0ms
(cbrt (/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))))
235.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
197.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
194.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))

simplify11.7s

Counts
54 → 90
Calls
54 calls:
Slowest
680.0ms
(- (* (* (exp (* 1/3 (+ (log t) (log (sqrt 2))))) (exp (* 1/6 (+ (log 1/2) (log x))))) (pow (/ 1 l) 1/3)) (+ (* 1/3 (* (* (pow t 2) (* (exp (* 1/3 (+ (log t) (log (sqrt 2))))) (exp (* 1/6 (+ (log 1/2) (log x)))))) (pow (/ 1 (pow l 7)) 1/3))) (* 1/6 (* (* (pow t 2) (* (exp (* 1/3 (+ (log t) (log (sqrt 2))))) (exp (* 1/6 (+ (log 1/2) (* 7 (log x))))))) (pow (/ 1 (pow l 7)) 1/3)))))
651.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))
501.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
468.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
413.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.0b

regimes716.0ms

Accuracy

73.5% (6.4b remaining)

Error of 9.6b against oracle of 3.2b and baseline of 27.2b

bsearch277.0ms

end0.0ms

sample8.7s

Algorithm
intervals
Results
2.1s10056×body80nan
1.5s5166×body80valid
1.2s822×body1280valid
945.0ms614×body640nan
885.0ms999×body640valid
629.0ms588×body1280nan
432.0ms646×body320valid
174.0ms343×body320nan
155.0ms367×body160valid
99.0ms207×body160nan