Details

Time bar (total: 23.5s)

sample54.0ms

Algorithm
intervals
Results
14.0ms261×body80nan
12.0ms52×body1280valid
8.0ms43×body640valid
7.0ms131×body80valid
2.0ms18×body320valid
1.0ms12×body160valid

simplify12.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
12.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize13.0ms

Local error

Found 2 expressions with local error:

2.3b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite54.0ms

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
49.0ms
(- (sqrt (+ x 1)) (sqrt x))
4.0ms
(sqrt (+ x 1))

series104.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
63.0ms
(- (sqrt (+ x 1)) (sqrt x))
41.0ms
(sqrt (+ x 1))

simplify497.0ms

Counts
28 → 43
Calls
28 calls:
Slowest
121.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
42.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
35.0ms
(sqrt (+ (pow x 3) (pow 1 3)))
32.0ms
(sqrt (- (* x x) (* 1 1)))
24.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

prune450.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 28.6b

localize51.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* (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)))

rewrite178.0ms

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
74.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
43.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
39.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
17.0ms
(* (sqrt x) (sqrt x))

series171.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
26.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
19.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
16.0ms
(* (sqrt x) (sqrt x))

simplify7.0s

Counts
211 → 191
Calls
211 calls:
Slowest
446.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
355.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
340.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
244.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (+ x 1)))
241.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite57.0ms

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
31.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
21.0ms
(+ (sqrt (+ x 1)) (sqrt x))
4.0ms
(sqrt (+ x 1))

series163.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
83.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
56.0ms
(+ (sqrt (+ x 1)) (sqrt x))
24.0ms
(sqrt (+ x 1))

simplify1.4s

Counts
73 → 87
Calls
73 calls:
Slowest
170.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
161.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
89.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
50.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
49.0ms
(/ (sqrt 1) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))

prune645.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))
0.2b
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
0.1b
(sqrt (sqrt (+ x 1)))
0.1b
(sqrt (sqrt (+ x 1)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
62×add-sqr-sqrt
46×*-un-lft-identity
40×sqrt-pow1
32×pow1 sqrt-div
28×add-cube-cbrt
20×pow1/2
18×swap-sqr
10×associate-*r* associate-*l* add-exp-log
9×flip3-+ times-frac pow-prod-up flip-+ unswap-sqr
8×add-cbrt-cube distribute-lft-out
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square insert-posit16 add-log-exp
3×associate-/r* associate-/l*
2×div-exp associate-*l/ associate-*r/ associate-/r/
1×pow2 cbrt-undiv rec-exp clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod 1-exp prod-exp *-commutative cbrt-unprod div-inv pow-flip inv-pow
Counts
4 → 169
Calls
4 calls:
Slowest
30.0ms
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))
30.0ms
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
5.0ms
(sqrt (sqrt (+ x 1)))
5.0ms
(sqrt (sqrt (+ x 1)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
60.0ms
(sqrt (sqrt (+ x 1)))
45.0ms
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))
40.0ms
(sqrt (sqrt (+ x 1)))

simplify6.3s

Counts
195 → 181
Calls
195 calls:
Slowest
297.0ms
(/ (* (* 1 1) 1) (* (* (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)) (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x))) (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x))))
275.0ms
(+ (* (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))) (- (* (sqrt x) (sqrt x)) (* (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x))))
272.0ms
(* (sqrt (sqrt (+ (pow x 3) (pow 1 3)))) (sqrt (sqrt (- (* x x) (* 1 1)))))
267.0ms
(- (+ (pow (/ 1 x) -1/4) (* 1/4 (pow (/ 1 (pow x 3)) 1/4))) (* 3/32 (pow (/ 1 (pow x 7)) 1/4)))
267.0ms
(- (+ (pow (/ 1 x) -1/4) (* 1/4 (pow (/ 1 (pow x 3)) 1/4))) (* 3/32 (pow (/ 1 (pow x 7)) 1/4)))

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s1686×body1280valid
538.0ms8167×body80nan
332.0ms1272×body640valid
266.0ms4082×body80valid
110.0ms653×body320valid
61.0ms307×body160valid