Details

Time bar (total: 1.0m)

sample328.0ms

Algorithm
intervals
Results
77.0ms319×body80nan
62.0ms38×body1280valid
50.0ms22×body640nan
23.0ms156×body80valid
20.0ms33×body640valid
7.0ms15×body320valid
6.0ms10×body1280nan
5.0ms14×body320nan
4.0ms14×body160valid
1.0ms4×body160nan

simplify434.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
433.0ms
(/ (* (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: 45.3b

localize45.0ms

Local error

Found 4 expressions with local error:

21.8b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
13.2b
(- (* (/ (+ 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))))

rewrite176.0ms

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
77.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
47.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
33.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
16.0ms
(* (sqrt 2) t)

series2.2s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
453.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
284.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
45.0ms
(* (sqrt 2) t)

simplify11.4s

Counts
61 → 96
Calls
61 calls:
Slowest
756.0ms
(/ (sqrt 2) (sqrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
446.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
390.0ms
(sqrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
374.0ms
(- (log (* (sqrt 2) t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
367.0ms
(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)))))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.0b

localize64.0ms

Local error

Found 4 expressions with local error:

27.3b
(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))

rewrite133.0ms

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
52.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
33.0ms
(* (* l 2) (/ l x))
32.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
14.0ms
(* (sqrt 2) t)

series445.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
239.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
92.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
73.0ms
(* (sqrt 2) t)
42.0ms
(* (* l 2) (/ l x))

simplify5.7s

Counts
65 → 103
Calls
65 calls:
Slowest
389.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
374.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
327.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))
289.0ms
(sqrt (- (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (* (* (* l 2) (/ l x)) (* (* l 2) (/ l x)))))
270.0ms
(* (* (* (* l 2) (* l 2)) (* l 2)) (/ (* (* l l) l) (* (* x x) x)))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize58.0ms

Local error

Found 4 expressions with local error:

27.3b
(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)

rewrite157.0ms

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
69.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
44.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
31.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
10.0ms
(* (cbrt (sqrt 2)) t)

series895.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
460.0ms
(* (cbrt (sqrt 2)) t)
268.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
97.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
69.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

simplify6.0s

Counts
60 → 96
Calls
60 calls:
Slowest
551.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
411.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
351.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))
329.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
323.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.2b

localize66.0ms

Local error

Found 4 expressions with local error:

27.3b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
0.8b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.4b
(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))
0.3b
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))

rewrite329.0ms

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
Counts
4 → 98
Calls
4 calls:
Slowest
210.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))
44.0ms
(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))
44.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
28.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))

series869.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
462.0ms
(* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t))
226.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
97.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
83.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))

simplify15.7s

Counts
73 → 110
Calls
73 calls:
Slowest
566.0ms
(* (exp (* (* t t) (+ (/ 4 x) 2))) (exp (* (* l 2) (/ l x))))
484.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
479.0ms
(* (* (* (* (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 (sqrt 2)) (* (* t t) t)))
477.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))
469.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt 2))) t)))

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.1b

regimes668.0ms

Accuracy

76.6% (5.6b remaining)

Error of 9.0b against oracle of 3.4b and baseline of 27.3b

bsearch478.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
2.0s10004×body80nan
1.5s1050×body640valid
1.2s5010×body80valid
829.0ms909×body1280valid
628.0ms574×body1280nan
550.0ms352×body160valid
495.0ms679×body320valid
471.0ms614×body640nan
176.0ms306×body320nan
97.0ms181×body160nan