Details

Time bar (total: 1.4m)

sample73.0ms

Algorithm
intervals
Results
17.0ms61×body640valid
16.0ms30×body1280valid
13.0ms218×body80nan
10.0ms133×body80valid
5.0ms24×body320valid
1.0ms8×body160valid

simplify19.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.3b

localize28.0ms

Local error

Found 4 expressions with local error:

3.4b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
1063×times-frac
902×*-un-lft-identity
788×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
580×sqrt-prod
74×distribute-lft-out
56×div-inv
48×sqrt-div
46×associate-/r/
25×difference-of-squares
24×flip3-+ flip-+
22×fma-neg
13×associate-/r* distribute-lft-out--
12×add-exp-log
9×pow1
8×add-cbrt-cube
6×pow-flip associate-/l* add-log-exp
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
3×sqrt-pow1 pow1/2
2×cbrt-undiv rec-exp clear-num frac-2neg 1-exp hypot-def inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 793
Calls
4 calls:
Slowest
30.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
10.0ms
(/ 1 (sqrt (+ x 1)))
5.0ms
(/ 1 (sqrt x))
5.0ms
(sqrt (+ x 1))

series232.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
90.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
51.0ms
(/ 1 (sqrt x))
49.0ms
(/ 1 (sqrt (+ x 1)))
41.0ms
(sqrt (+ x 1))

simplify797.0ms

Counts
805 → 805

prune7.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 19.7b

localize17.0ms

Local error

Found 4 expressions with local error:

3.4b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.0b
(sqrt (+ x 1))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
88×sqrt-prod
79×*-un-lft-identity
75×add-sqr-sqrt
42×prod-diff
39×add-cube-cbrt
12×distribute-lft-out difference-of-squares
11×add-cbrt-cube add-exp-log
10×times-frac associate-/l*
9×pow1 distribute-lft-out--
7×fma-neg associate-*r*
6×sqrt-div associate-*l* add-log-exp
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ cbrt-unprod hypot-def flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-unprod diff-log div-sub *-commutative div-inv
Counts
4 → 171
Calls
4 calls:
Slowest
66.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
40.0ms
(- (sqrt (+ x 1)) (sqrt x))
18.0ms
(* (sqrt x) (sqrt (+ x 1)))
5.0ms
(sqrt (+ x 1))

series309.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
156.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
64.0ms
(- (sqrt (+ x 1)) (sqrt x))
59.0ms
(* (sqrt x) (sqrt (+ x 1)))
29.0ms
(sqrt (+ x 1))

simplify464.0ms

Counts
183 → 183

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (/ (+ 1 (- x x)) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.2b
(/ (+ 1 (- x x)) (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
265×*-un-lft-identity
126×times-frac
108×distribute-lft-out
83×sqrt-prod
55×add-sqr-sqrt
47×add-cube-cbrt
41×associate-/l*
20×add-cbrt-cube add-exp-log
19×distribute-lft-out--
8×pow1 associate-/r/
7×cbrt-undiv associate-/r* fma-def flip3-+ div-exp associate-*r* flip-+
6×associate-*l* add-log-exp
4×expm1-log1p-u sqrt-div associate-*r/ insert-posit16 log1p-expm1-u div-inv unswap-sqr
3×div-sub pow-prod-down prod-exp cbrt-unprod associate-/l/
2×clear-num associate-+r- frac-2neg sqrt-pow1 pow1/2
1×+-commutative sum-log sqrt-unprod *-commutative
Counts
4 → 219
Calls
4 calls:
Slowest
81.0ms
(/ (/ (+ 1 (- x x)) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
56.0ms
(/ (+ 1 (- x x)) (+ (sqrt (+ x 1)) (sqrt x)))
23.0ms
(+ (sqrt (+ x 1)) (sqrt x))
17.0ms
(* (sqrt x) (sqrt (+ x 1)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
202.0ms
(/ (/ (+ 1 (- x x)) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
69.0ms
(/ (+ 1 (- x x)) (+ (sqrt (+ x 1)) (sqrt x)))
57.0ms
(* (sqrt x) (sqrt (+ x 1)))
55.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify591.0ms

Counts
231 → 231

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
24516×times-frac
22559×*-un-lft-identity
20666×sqrt-prod
8263×distribute-lft-out
5876×add-sqr-sqrt
5868×add-cube-cbrt
1487×distribute-lft-out--
410×associate-/r/
336×sqrt-div
245×div-inv
168×flip3-+ flip-+
101×associate-/r*
94×associate-/l*
51×add-cbrt-cube add-exp-log
29×cbrt-undiv div-exp
8×pow1
7×associate-*r*
6×sqrt-undiv associate-*l*
5×prod-exp cbrt-unprod associate-/l/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×clear-num frac-2neg pow-prod-down
2×sqrt-pow1 pow1/2 sqrt-unprod associate-*r/
1×*-commutative
Counts
4 → 6925
Calls
4 calls:
Slowest
125.0ms
(/ (/ (sqrt (+ 1 (- x x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (/ (* (sqrt x) (sqrt (+ x 1))) (/ (sqrt (+ 1 (- x x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))))
54.0ms
(/ (sqrt (+ 1 (- x x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
50.0ms
(/ (sqrt (+ 1 (- x x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
17.0ms
(* (sqrt x) (sqrt (+ x 1)))

series485.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
195.0ms
(/ (/ (sqrt (+ 1 (- x x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (/ (* (sqrt x) (sqrt (+ x 1))) (/ (sqrt (+ 1 (- x x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))))
119.0ms
(/ (sqrt (+ 1 (- x x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
117.0ms
(/ (sqrt (+ 1 (- x x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
54.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify8.3s

Counts
6937 → 6937

prune59.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch2.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
545.0ms4196×body80valid
474.0ms1804×body640valid
424.0ms7729×body80nan
327.0ms1083×body1280valid
116.0ms612×body320valid
33.0ms305×body160valid