Details

Time bar (total: 1.1m)

sample733.0ms

Algorithm
intervals
Results
403.0ms29×body640valid
91.0ms324×body80nan
29.0ms32×body1280valid
26.0ms152×body80valid
20.0ms22×body1280nan
17.0ms24×body640nan
15.0ms25×body320valid
6.0ms10×body320nan
6.0ms18×body160valid
2.0ms6×body160nan

simplify244.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
243.0ms
(/ (* (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: 42.7b

localize91.0ms

Local error

Found 4 expressions with local error:

18.3b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
15.2b
(- (* (/ (+ 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))))

rewrite233.0ms

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
91.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
75.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
50.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
13.0ms
(* (sqrt 2) t)

series2.2s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
454.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
219.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
56.0ms
(* (sqrt 2) t)

simplify10.6s

Counts
61 → 96
Calls
61 calls:
Slowest
372.0ms
(- (log (* (sqrt 2) t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
370.0ms
(/ t (cbrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
361.0ms
(- (+ (log (sqrt 2)) (log t)) (log (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
352.0ms
(/ (* (* (* (sqrt 2) t) (* (sqrt 2) t)) (* (sqrt 2) 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)))))
350.0ms
(/ (sqrt 2) (sqrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.8b

localize39.0ms

Local error

Found 4 expressions with local error:

25.9b
(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
(/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))

rewrite154.0ms

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
80.0ms
(/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))
39.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
24.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
10.0ms
(* (sqrt 2) t)

series661.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
281.0ms
(/ (* (sqrt 2) t) (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))
195.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
109.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
76.0ms
(* (sqrt 2) t)

simplify10.0s

Counts
69 → 101
Calls
69 calls:
Slowest
680.0ms
(sqrt (cbrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))
481.0ms
(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))))))
459.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
341.0ms
(/ (* (* (* (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))))))
335.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.0b

localize52.0ms

Local error

Found 4 expressions with local error:

25.9b
(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)

rewrite132.0ms

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
66.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
31.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
25.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
8.0ms
(* (cbrt (sqrt 2)) t)

series799.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
409.0ms
(* (cbrt (sqrt 2)) t)
207.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
99.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
83.0ms
(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

simplify5.9s

Counts
60 → 96
Calls
60 calls:
Slowest
437.0ms
(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
431.0ms
(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))
415.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
367.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l 2) (/ l x)) 3)))
342.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.0b

localize44.0ms

Local error

Found 4 expressions with local error:

25.9b
(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)
0.3b
(* (* (sqrt 2) t) (/ 1 (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
29×associate-*r*
28×add-exp-log
26×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac add-cbrt-cube
16×sqrt-prod
13×prod-exp associate-*r/
12×pow1
8×sqrt-div
7×associate-*l* cbrt-unprod
6×flip3-+ frac-add flip-+ add-log-exp
4×div-exp pow-prod-down associate-/r/ insert-posit16
2×cbrt-undiv rec-exp associate-+l+ 1-exp *-commutative unswap-sqr
1×distribute-rgt-in +-commutative rem-sqrt-square sum-log distribute-lft-in sqrt-pow1 pow1/2 un-div-inv div-inv
Counts
4 → 109
Calls
4 calls:
Slowest
77.0ms
(* (* (sqrt 2) t) (/ 1 (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))))
29.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
24.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
8.0ms
(* (sqrt 2) t)

series720.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
322.0ms
(* (* (sqrt 2) t) (/ 1 (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))))
232.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
87.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
79.0ms
(* (sqrt 2) t)

simplify14.3s

Counts
85 → 121
Calls
85 calls:
Slowest
532.0ms
(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))))))
393.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
362.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
333.0ms
(+ (log (* (sqrt 2) t)) (- (log 1) (log (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))))
332.0ms
(+ (+ (log (sqrt 2)) (log t)) (- (log 1) (log (sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))))))

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.0b

regimes783.0ms

Accuracy

73.1% (6.4b remaining)

Error of 9.8b against oracle of 3.4b and baseline of 27.2b

bsearch1.0s

end0.0ms

sample8.4s

Algorithm
intervals
Results
2.8s10078×body80nan
1.3s5078×body80valid
1.1s868×body1280valid
888.0ms1051×body640valid
675.0ms615×body1280nan
450.0ms599×body640nan
399.0ms629×body320valid
166.0ms333×body320nan
166.0ms374×body160valid
91.0ms188×body160nan