Details

Time bar (total: 52.2s)

sample63.0ms

Algorithm
intervals
Results
16.0ms56×body1280valid
15.0ms271×body80nan
10.0ms43×body640valid
8.0ms129×body80valid
3.0ms18×body320valid
1.0ms10×body160valid

simplify21.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
21.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize11.0ms

Local error

Found 2 expressions with local error:

2.9b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity sqrt-prod
4×add-log-exp difference-of-squares
3×pow1 add-cube-cbrt distribute-lft-out--
2×add-cbrt-cube sqrt-div add-exp-log insert-posit16 distribute-lft-out
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Counts
2 → 37
Calls
2 calls:
Slowest
36.0ms
(- (sqrt (+ x 1)) (sqrt x))
4.0ms
(sqrt (+ x 1))

series101.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
63.0ms
(- (sqrt (+ x 1)) (sqrt x))
38.0ms
(sqrt (+ x 1))

simplify574.0ms

Counts
28 → 43
Calls
28 calls:
Slowest
128.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
66.0ms
(sqrt (+ (pow x 3) (pow 1 3)))
64.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
52.0ms
(sqrt (- (* x x) (* 1 1)))
24.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

prune444.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 29.2b

localize38.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (* (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)))

rewrite204.0ms

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
90.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
55.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
37.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
17.0ms
(* (sqrt x) (sqrt x))

series173.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
24.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
20.0ms
(* (sqrt x) (sqrt x))
18.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))

simplify6.5s

Counts
211 → 191
Calls
211 calls:
Slowest
411.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
367.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
328.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
219.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (+ x 1)))
217.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
24×sqrt-prod
21×distribute-lft-out
18×times-frac
16×add-sqr-sqrt
15×add-cube-cbrt
7×add-exp-log
6×associate-/r*
5×pow1 add-cbrt-cube add-log-exp
3×flip3-+ flip-+ insert-posit16 associate-/l*
2×sqrt-div div-exp associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp clear-num sum-log frac-2neg sqrt-pow1 pow1/2 1-exp div-inv pow-flip inv-pow
Counts
3 → 78
Calls
3 calls:
Slowest
40.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
18.0ms
(+ (sqrt (+ x 1)) (sqrt x))
4.0ms
(sqrt (+ x 1))

series163.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
75.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
50.0ms
(+ (sqrt (+ x 1)) (sqrt x))
38.0ms
(sqrt (+ x 1))

simplify1.5s

Counts
73 → 87
Calls
73 calls:
Slowest
282.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
147.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
121.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
79.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
35.0ms
(sqrt (+ (pow x 3) (pow 1 3)))

prune718.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
0.2b
(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
0.1b
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
700×sqrt-prod
594×times-frac
280×distribute-lft-out
254×add-sqr-sqrt
252×add-cube-cbrt
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
17×add-exp-log
15×pow1
14×flip3-+ flip-+
12×div-inv
11×add-cbrt-cube
8×div-exp pow-flip
7×sqrt-pow1 pow1/2
6×pow-div
4×cbrt-undiv insert-posit16 add-log-exp
2×rem-sqrt-square rec-exp clear-num frac-2neg 1-exp inv-pow
1×associate-/l/
Counts
4 → 463
Calls
4 calls:
Slowest
76.0ms
(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
28.0ms
(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
21.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
21.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

series457.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
130.0ms
(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
99.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
88.0ms
(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify32.2s

Counts
759 → 475
Calls
759 calls:
Slowest
662.0ms
(/ (* (* (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))) (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))) (* (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
429.0ms
(/ (/ (sqrt 1) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
392.0ms
(/ (/ 1 (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))) (* (cbrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (cbrt (sqrt (+ (sqrt (+ x 1)) (sqrt x))))))
391.0ms
(/ (/ 1 (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))) (sqrt (sqrt 1)))
380.0ms
(/ 1 (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))))

prune4.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes64.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
706.0ms4065×body80valid
536.0ms1739×body1280valid
375.0ms8063×body80nan
232.0ms1253×body640valid
87.0ms342×body160valid
82.0ms601×body320valid