Details

Time bar (total: 14.6s)

sample58.0ms

Algorithm
intervals
Results
15.0ms51×body1280valid
13.0ms277×body80nan
10.0ms49×body640valid
6.0ms125×body80valid
3.0ms20×body320valid
1.0ms11×body160valid

simplify10.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize10.0ms

Local error

Found 1 expressions with local error:

3.2b
(- (sqrt (+ x 1)) (sqrt x))

rewrite70.0ms

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
70.0ms
(- (sqrt (+ x 1)) (sqrt x))

series82.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
82.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify267.0ms

Counts
17 → 23
Calls
17 calls:
Slowest
55.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
26.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
24.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
24.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
23.0ms
(+ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

prune212.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 31.4b

localize25.0ms

Local error

Found 1 expressions with local error:

3.2b
(- (sqrt (+ x 1)) (sqrt x))

rewrite52.0ms

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
51.0ms
(- (sqrt (+ x 1)) (sqrt x))

series97.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
97.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify284.0ms

Counts
17 → 23
Calls
17 calls:
Slowest
61.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
24.0ms
(+ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
24.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
23.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
23.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

prune190.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 31.4b

localize38.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
0.5b
(* (sqrt x) (sqrt x))
0.3b
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
0.0b
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
64×sqrt-prod
56×add-sqr-sqrt
34×pow1
32×add-cube-cbrt
26×distribute-lft-out
24×times-frac
19×swap-sqr
16×sqrt-pow1 pow1/2
13×associate-*r* associate-*l*
12×sqrt-div
10×add-cbrt-cube add-exp-log pow-prod-up
8×difference-of-squares unswap-sqr
7×flip3-+ flip-+
6×associate-/r* pow-prod-down pow-sqr add-log-exp
4×frac-times insert-posit16 associate-/l*
2×pow2 rem-square-sqrt pow-plus flip3-- sqrt-unprod associate-*l/ prod-exp associate-*r/ associate-/r/ *-commutative cbrt-unprod flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
4 → 179
Calls
4 calls:
Slowest
89.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
28.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
21.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
9.0ms
(* (sqrt x) (sqrt x))

series182.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
24.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
18.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
17.0ms
(* (sqrt x) (sqrt x))

simplify6.6s

Counts
211 → 191
Calls
211 calls:
Slowest
734.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
392.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
268.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
217.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
208.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (+ (pow x 3) (pow 1 3))))

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite91.0ms

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
49.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
39.0ms
(+ (sqrt (+ x 1)) (sqrt x))

series186.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
103.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
83.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify1.2s

Counts
62 → 67
Calls
62 calls:
Slowest
247.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
160.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
59.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
35.0ms
(- 0 (log (+ (sqrt (+ x 1)) (sqrt x))))
29.0ms
(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

prune651.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes108.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
633.0ms1714×body1280valid
559.0ms7931×body80nan
390.0ms1263×body640valid
294.0ms4089×body80valid
140.0ms612×body320valid
38.0ms322×body160valid