Details

Time bar (total: 32.5s)

sample81.0ms

Algorithm
intervals
Results
19.0ms132×body80valid
18.0ms53×body1280valid
16.0ms247×body80nan
9.0ms34×body640valid
4.0ms20×body320valid
2.0ms17×body160valid

simplify11.0ms

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: 29.3b

localize10.0ms

Local error

Found 2 expressions with local error:

5.2b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite39.0ms

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
30.0ms
(- (sqrt (+ x 1)) (sqrt x))
8.0ms
(sqrt (+ x 1))

series105.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
70.0ms
(- (sqrt (+ x 1)) (sqrt x))
35.0ms
(sqrt (+ x 1))

simplify5.8s

Counts
120 → 98
Calls
120 calls:
Slowest
201.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
195.0ms
(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
195.0ms
(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
180.0ms
(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
172.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))

prune853.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 28.3b

localize46.0ms

Local error

Found 4 expressions with local error:

4.1b
(- (* (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)))

rewrite553.0ms

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
439.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
53.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
40.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
18.0ms
(* (sqrt x) (sqrt x))

series181.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
29.0ms
(* (sqrt x) (sqrt x))
22.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
17.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))

simplify7.6s

Counts
214 → 201
Calls
214 calls:
Slowest
746.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
451.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
367.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
286.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
243.0ms
(/ (* (* (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))) (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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))

rewrite102.0ms

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
47.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
43.0ms
(+ (sqrt (+ x 1)) (sqrt x))
10.0ms
(sqrt (+ x 1))

series200.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
90.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
70.0ms
(+ (sqrt (+ x 1)) (sqrt x))
39.0ms
(sqrt (+ x 1))

simplify1.6s

Counts
81 → 102
Calls
81 calls:
Slowest
233.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
198.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
124.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
61.0ms
(sqrt (+ (pow x 3) (pow 1 3)))
60.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))

prune854.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite344.0ms

Algorithm
rewrite-expression-head
Rules
90×sqrt-prod
74×*-un-lft-identity
46×add-sqr-sqrt
37×pow1
32×distribute-lft-out
28×sqrt-div
18×sqrt-pow1 pow1/2
17×add-exp-log
16×add-cube-cbrt
15×swap-sqr
14×flip3-+ flip-+ pow-flip
11×add-cbrt-cube
10×pow-prod-up
9×associate-*r* associate-*l*
8×frac-times associate-/r/ hypot-def
6×pow-prod-down pow-sqr
4×expm1-log1p-u div-exp associate-*l/ prod-exp associate-*r/ insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×times-frac associate-/l*
2×pow2 cbrt-undiv rem-sqrt-square rec-exp pow-plus 1-exp cbrt-unprod
1×clear-num associate-/r* rem-square-sqrt frac-2neg sqrt-unprod *-commutative div-inv inv-pow
Counts
4 → 174
Calls
4 calls:
Slowest
163.0ms
(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
79.0ms
(/ 1 (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
49.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
48.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
121.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
92.0ms
(/ 1 (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
68.0ms
(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify7.2s

Counts
170 → 186
Calls
170 calls:
Slowest
415.0ms
(* (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
386.0ms
(sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
354.0ms
(* (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))) (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))))
310.0ms
(sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
304.0ms
(/ (* (* 1 1) 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))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))))

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes68.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
967.0ms1764×body1280valid
596.0ms7957×body80nan
352.0ms1209×body640valid
286.0ms4076×body80valid
146.0ms623×body320valid
43.0ms328×body160valid