Details

Time bar (total: 37.7s)

sample43.0ms

Algorithm
intervals
Results
11.0ms53×body1280valid
8.0ms209×body80nan
6.0ms36×body640valid
6.0ms137×body80valid
2.0ms19×body320valid
1.0ms11×body160valid

simplify11.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize10.0ms

Local error

Found 1 expressions with local error:

3.0b
(- (sqrt (+ x 1)) (sqrt x))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity sqrt-prod
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt insert-posit16 flip-- distribute-lft-out
Counts
1 → 20
Calls
1 calls:
Slowest
49.0ms
(- (sqrt (+ x 1)) (sqrt x))

series63.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
63.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify1.0s

Counts
29 → 23
Calls
29 calls:
Slowest
323.0ms
(* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x)))
233.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
51.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (+ (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
45.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
44.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))

prune228.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
20×sqrt-prod distribute-lft-out
18×times-frac
13×add-sqr-sqrt add-cube-cbrt
6×associate-/r* add-exp-log
4×add-cbrt-cube add-log-exp
3×pow1 associate-/l*
2×flip3-+ div-exp associate-/r/ flip-+ insert-posit16
1×cbrt-undiv +-commutative rec-exp clear-num sum-log frac-2neg 1-exp div-inv pow-flip inv-pow
Counts
2 → 61
Calls
2 calls:
Slowest
35.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
18.0ms
(+ (sqrt (+ x 1)) (sqrt x))

series155.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
86.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
68.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify2.9s

Counts
86 → 67
Calls
86 calls:
Slowest
439.0ms
(+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
389.0ms
(/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
316.0ms
(* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
206.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
170.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))

prune528.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
0.1b
(/ 1 (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
0.1b
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

rewrite281.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
74×*-un-lft-identity
37×pow1
32×distribute-lft-out
30×add-sqr-sqrt
28×sqrt-div
18×sqrt-pow1 pow1/2
17×add-exp-log
16×add-cube-cbrt
15×swap-sqr
14×flip3-+ flip-+ pow-flip
11×add-cbrt-cube
10×pow-prod-up
9×associate-*r* associate-*l*
8×frac-times associate-/r/
6×pow-prod-down pow-sqr
4×div-exp associate-*l/ prod-exp associate-*r/ insert-posit16 add-log-exp unswap-sqr
3×times-frac associate-/l*
2×pow2 cbrt-undiv rem-sqrt-square rec-exp pow-plus 1-exp cbrt-unprod
1×clear-num associate-/r* rem-square-sqrt frac-2neg sqrt-unprod *-commutative div-inv inv-pow
Counts
4 → 158
Calls
4 calls:
Slowest
138.0ms
(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
81.0ms
(/ 1 (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
33.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
26.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

series457.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
122.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
91.0ms
(/ 1 (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
84.0ms
(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify10.3s

Counts
205 → 170
Calls
205 calls:
Slowest
517.0ms
(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))))
459.0ms
(/ 1 (* (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
457.0ms
(sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
447.0ms
(* (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
435.0ms
(* (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))) (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))))

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) -1/2)
0.0b
(+ (sqrt (+ x 1)) (sqrt x))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite257.0ms

Algorithm
rewrite-expression-head
Rules
67×*-un-lft-identity
32×sqrt-prod distribute-lft-out
19×pow1
11×add-sqr-sqrt
10×swap-sqr
9×add-exp-log add-cube-cbrt
8×flip3-+ flip-+ add-log-exp
6×pow-pow add-cbrt-cube associate-*r* associate-*l*
4×frac-times insert-posit16
3×pow-unpow
2×pow2 +-commutative sum-log pow-plus pow-prod-down associate-*l/ pow-exp prod-exp associate-*r/ pow-sqr pow-prod-up
1×distribute-rgt-in pow-to-exp unpow-prod-down distribute-lft-in *-commutative cbrt-unprod unswap-sqr sqr-pow
Counts
4 → 101
Calls
4 calls:
Slowest
133.0ms
(* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x)))
62.0ms
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) -1/2)
36.0ms
(+ (sqrt (+ x 1)) (sqrt x))
25.0ms
(+ (sqrt (+ x 1)) (sqrt x))

series509.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
240.0ms
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) -1/2)
95.0ms
(* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x)))
89.0ms
(+ (sqrt (+ x 1)) (sqrt x))
85.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify15.3s

Counts
132 → 113
Calls
132 calls:
Slowest
930.0ms
(* (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
642.0ms
(* (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))))
574.0ms
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (* (cbrt -1/2) (cbrt -1/2)))
540.0ms
(* (* (pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) -1/2) (pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) -1/2)) (pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) -1/2))
462.0ms
(log (pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) -1/2))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes72.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch3.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
762.0ms4129×body80valid
614.0ms1648×body1280valid
450.0ms7809×body80nan
321.0ms1291×body640valid
184.0ms622×body320valid
35.0ms310×body160valid