Details

Time bar (total: 49.4s)

sample725.0ms

Algorithm
intervals
Results
467.0ms28×body1280valid
59.0ms350×body80nan
25.0ms38×body640valid
24.0ms151×body80valid
15.0ms22×body640nan
12.0ms16×body1280nan
11.0ms22×body320valid
7.0ms9×body320nan
6.0ms17×body160valid
2.0ms4×body160nan

simplify305.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
305.0ms
(/ (* (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: 42.7b

localize52.0ms

Local error

Found 4 expressions with local error:

19.4b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
13.0b
(- (* (/ (+ 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))))

rewrite153.0ms

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
60.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
49.0ms
(/ (* (sqrt 2) t) (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))
7.0ms
(* (sqrt 2) t)

series2.1s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
463.0ms
(/ (* (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))
58.0ms
(* (sqrt 2) t)

simplify10.9s

Counts
61 → 96
Calls
61 calls:
Slowest
406.0ms
(- (log (* (sqrt 2) t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
398.0ms
(/ (* (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* t t) t)) (* (* (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
384.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
384.0ms
(- (+ (log (sqrt 2)) (log t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
367.0ms
(/ (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))))))

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.3b

localize71.0ms

Local error

Found 4 expressions with local error:

27.7b
(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))

rewrite117.0ms

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
55.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
29.0ms
(* (* l 2) (/ l x))
24.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
7.0ms
(* (sqrt 2) t)

series371.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
179.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
86.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
63.0ms
(* (sqrt 2) t)
43.0ms
(* (* l 2) (/ l x))

simplify5.5s

Counts
65 → 103
Calls
65 calls:
Slowest
482.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
389.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))
348.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
268.0ms
(+ (* (* (* t t) (+ (pow (/ 4 x) 3) (pow 2 3))) x) (* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) (* (* l 2) l)))
250.0ms
(* (* (* (* l 2) (* l 2)) (* l 2)) (/ (* (* l l) l) (* (* x x) x)))

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

localize53.0ms

Local error

Found 4 expressions with local error:

27.7b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.4b
(+ (* (* 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
46.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
45.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
37.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
16.0ms
(* (sqrt (sqrt 2)) t)

series415.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
209.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
88.0ms
(* (sqrt (sqrt 2)) t)
71.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
47.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))

simplify5.5s

Counts
61 → 98
Calls
61 calls:
Slowest
654.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* t t) t)))
461.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
339.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
328.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))
304.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) t) (* (sqrt (sqrt 2)) t)) (* (sqrt (sqrt 2)) t)))

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.6b

localize50.0ms

Local error

Found 4 expressions with local error:

27.7b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
1.0b
(* (sqrt (sqrt 2)) (sqrt (sqrt 2)))
0.4b
(* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) t)
0.4b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
69×sqrt-prod
50×add-sqr-sqrt
33×pow1 sqrt-pow1
18×*-un-lft-identity add-cube-cbrt
17×pow1/2
15×swap-sqr
12×associate-*r*
11×add-cbrt-cube add-exp-log
10×associate-*l* unswap-sqr
9×pow-prod-up
8×pow-prod-down associate-*r/
6×add-log-exp
5×pow-sqr
4×flip3-+ sqrt-div frac-add prod-exp cbrt-unprod flip-+ insert-posit16
2×associate-+l+ *-commutative
1×pow2 distribute-rgt-in +-commutative rem-sqrt-square sum-log rem-square-sqrt distribute-lft-in pow-plus sqrt-unprod
Counts
4 → 130
Calls
4 calls:
Slowest
52.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
46.0ms
(* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) t)
29.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
14.0ms
(* (sqrt (sqrt 2)) (sqrt (sqrt 2)))

series354.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
186.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
114.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
54.0ms
(* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) t)
0.0ms
(* (sqrt (sqrt 2)) (sqrt (sqrt 2)))

simplify5.9s

Counts
135 → 140
Calls
135 calls:
Slowest
605.0ms
(* (* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* t t) t))
510.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
407.0ms
(- (* 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)))
270.0ms
(sqrt (- (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (* (* (* l 2) (/ l x)) (* (* l 2) (/ l x)))))

prune1.9s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.6b

regimes752.0ms

Accuracy

75.3% (5.9b remaining)

Error of 9.0b against oracle of 3.1b and baseline of 26.9b

bsearch1.2s

end0.0ms

sample8.4s

Algorithm
intervals
Results
2.0s10019×body80nan
1.4s5129×body80valid
1.1s604×body1280nan
918.0ms866×body1280valid
880.0ms627×body320valid
757.0ms979×body640valid
503.0ms630×body640nan
207.0ms350×body320nan
132.0ms399×body160valid
55.0ms170×body160nan