Details

Time bar (total: 30.1s)

sample75.0ms

Algorithm
intervals
Results
18.0ms53×body1280valid
17.0ms273×body80nan
13.0ms47×body640valid
9.0ms130×body80valid
3.0ms15×body320valid
2.0ms11×body160valid

simplify20.0ms

Calls
1 calls:
Slowest
20.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize19.0ms

Local error

Found 2 expressions with local error:

2.8b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
55×*-un-lft-identity
43×add-sqr-sqrt
42×prod-diff
31×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
4×add-log-exp difference-of-squares
3×pow1 distribute-lft-out--
2×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log hypot-def insert-posit16 log1p-expm1-u
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Calls
2 calls:
Slowest
49.0ms
(- (sqrt (+ x 1)) (sqrt x))
10.0ms
(sqrt (+ x 1))

series114.0ms

Calls
2 calls:
Slowest
75.0ms
(- (sqrt (+ x 1)) (sqrt x))
39.0ms
(sqrt (+ x 1))

simplify5.3s

Calls
120 calls:
Slowest
180.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
165.0ms
(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
159.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
152.0ms
(fma 1 (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
143.0ms
(fma (- (cbrt (sqrt x))) (* (cbrt (sqrt x)) (cbrt (sqrt x))) (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))))

prune852.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 29.1b

localize30.0ms

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)))

rewrite238.0ms

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×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u 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 fma-neg diff-log div-sub div-exp prod-diff div-inv
Calls
4 calls:
Slowest
121.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
48.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
45.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
18.0ms
(* (sqrt x) (sqrt x))

series201.0ms

Calls
4 calls:
Slowest
115.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
33.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
28.0ms
(* (sqrt x) (sqrt x))
24.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))

simplify7.7s

Calls
214 calls:
Slowest
823.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
435.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
429.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
251.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (+ (pow x 3) (pow 1 3))))
240.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
28×sqrt-prod
22×distribute-lft-out
21×add-sqr-sqrt
18×times-frac
17×add-cube-cbrt
7×fma-def add-exp-log
6×associate-/r*
5×pow1 add-cbrt-cube add-log-exp
3×expm1-log1p-u flip3-+ flip-+ insert-posit16 log1p-expm1-u associate-/l*
2×sqrt-div div-exp associate-/r/ hypot-def
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
Calls
3 calls:
Slowest
37.0ms
(+ (sqrt (+ x 1)) (sqrt x))
26.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
5.0ms
(sqrt (+ x 1))

series209.0ms

Calls
3 calls:
Slowest
93.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
80.0ms
(+ (sqrt (+ x 1)) (sqrt x))
37.0ms
(sqrt (+ x 1))

simplify1.9s

Calls
81 calls:
Slowest
402.0ms
(/ (sqrt 1) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
236.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
157.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
125.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
59.0ms
(sqrt (- (* x x) (* 1 1)))

prune794.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

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×expm1-log1p-u frac-times rem-sqrt-square insert-posit16 log1p-expm1-u 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
Calls
4 calls:
Slowest
57.0ms
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
32.0ms
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))
12.0ms
(sqrt (sqrt (+ x 1)))
11.0ms
(sqrt (sqrt (+ x 1)))

series255.0ms

Calls
4 calls:
Slowest
109.0ms
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
61.0ms
(sqrt (sqrt (+ x 1)))
58.0ms
(sqrt (sqrt (+ x 1)))
26.0ms
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify6.2s

Calls
195 calls:
Slowest
327.0ms
(- (+ (pow (/ 1 x) -1/4) (* 1/4 (pow (/ 1 (pow x 3)) 1/4))) (* 3/32 (pow (/ 1 (pow x 7)) 1/4)))
270.0ms
(/ (* (* 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))))
268.0ms
(+ (* (* (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))))
260.0ms
(- (+ (pow (/ 1 x) -1/4) (* 1/4 (pow (/ 1 (pow x 3)) 1/4))) (* 3/32 (pow (/ 1 (pow x 7)) 1/4)))
243.0ms
(* (sqrt (sqrt (- (* x x) (* 1 1)))) (sqrt (sqrt (+ (pow x 3) (pow 1 3)))))

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

0% (0.1b remaining)

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

bsearch3.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
548.0ms1670×body1280valid
444.0ms8046×body80nan
405.0ms1320×body640valid
291.0ms4061×body80valid
129.0ms623×body320valid
35.0ms326×body160valid