Details

Time bar (total: 32.0s)

sample59.0ms

Algorithm
intervals
Results
14.0ms55×body1280valid
13.0ms251×body80nan
9.0ms39×body640valid
8.0ms135×body80valid
3.0ms17×body320valid
1.0ms10×body160valid

simplify12.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
11.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize19.0ms

Local error

Found 2 expressions with local error:

2.0b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite65.0ms

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--
Counts
2 → 92
Calls
2 calls:
Slowest
59.0ms
(- (sqrt (+ x 1)) (sqrt x))
5.0ms
(sqrt (+ x 1))

series493.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
453.0ms
(- (sqrt (+ x 1)) (sqrt x))
40.0ms
(sqrt (+ x 1))

simplify5.7s

Counts
120 → 98
Calls
120 calls:
Slowest
219.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
199.0ms
(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
178.0ms
(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
168.0ms
(fma (- (cbrt (sqrt x))) (* (cbrt (sqrt x)) (cbrt (sqrt x))) (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))))
166.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))

prune714.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 27.7b

localize24.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (* (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)))

rewrite233.0ms

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
Counts
4 → 189
Calls
4 calls:
Slowest
121.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
46.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
42.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
18.0ms
(* (sqrt x) (sqrt x))

series225.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
34.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
28.0ms
(* (sqrt x) (sqrt x))
24.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))

simplify7.9s

Counts
214 → 201
Calls
214 calls:
Slowest
790.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
487.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
383.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
237.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (+ (pow x 3) (pow 1 3))))
214.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

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))

rewrite77.0ms

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
Counts
3 → 93
Calls
3 calls:
Slowest
37.0ms
(+ (sqrt (+ x 1)) (sqrt x))
28.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
9.0ms
(sqrt (+ x 1))

series184.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
99.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
59.0ms
(+ (sqrt (+ x 1)) (sqrt x))
26.0ms
(sqrt (+ x 1))

simplify1.7s

Counts
81 → 102
Calls
81 calls:
Slowest
277.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
162.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
154.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
68.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
57.0ms
(sqrt (+ (pow x 3) (pow 1 3)))

prune853.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

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
Counts
4 → 177
Calls
4 calls:
Slowest
60.0ms
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
36.0ms
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))
9.0ms
(sqrt (sqrt (+ x 1)))
5.0ms
(sqrt (sqrt (+ x 1)))

series212.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
100.0ms
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
42.0ms
(sqrt (sqrt (+ x 1)))
39.0ms
(sqrt (sqrt (+ x 1)))
31.0ms
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify6.8s

Counts
195 → 189
Calls
195 calls:
Slowest
334.0ms
(/ (* (* 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))))
304.0ms
(* (sqrt (sqrt (- (* x x) (* 1 1)))) (sqrt (sqrt (+ (pow x 3) (pow 1 3)))))
300.0ms
(+ (* (* (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))))
291.0ms
(- (+ (pow (/ 1 x) -1/4) (* 1/4 (pow (/ 1 (pow x 3)) 1/4))) (* 3/32 (pow (/ 1 (pow x 7)) 1/4)))
261.0ms
(- (+ (pow (/ 1 x) -1/4) (* 1/4 (pow (/ 1 (pow x 3)) 1/4))) (* 3/32 (pow (/ 1 (pow x 7)) 1/4)))

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
716.0ms1261×body640valid
611.0ms1741×body1280valid
571.0ms7972×body80nan
290.0ms4092×body80valid
181.0ms608×body320valid
34.0ms298×body160valid