Details

Time bar (total: 16.1s)

sample81.0ms

Algorithm
intervals
Results
19.0ms293×body80nan
18.0ms64×body640valid
13.0ms31×body1280valid
9.0ms116×body80valid
7.0ms33×body320valid
2.0ms12×body160valid

simplify54.0ms

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.4b

localize32.0ms

Local error

Found 4 expressions with local error:

4.0b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.2b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
113×add-sqr-sqrt
97×*-un-lft-identity times-frac
64×sqrt-prod
42×add-cube-cbrt
25×difference-of-squares
13×associate-/r* distribute-lft-out--
12×add-exp-log
9×pow1
8×add-cbrt-cube distribute-lft-out
6×div-inv pow-flip associate-/l* add-log-exp
4×sqrt-div div-exp insert-posit16
3×sqrt-pow1 pow1/2
2×cbrt-undiv rec-exp clear-num frac-2neg flip3-+ 1-exp associate-/r/ flip-+ inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 167
Calls
4 calls:
Slowest
33.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
13.0ms
(/ 1 (sqrt (+ x 1)))
5.0ms
(/ 1 (sqrt x))
4.0ms
(sqrt (+ x 1))

series198.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
81.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
41.0ms
(sqrt (+ x 1))
41.0ms
(/ 1 (sqrt x))
34.0ms
(/ 1 (sqrt (+ x 1)))

simplify837.0ms

Counts
179 → 179

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.6b

localize16.0ms

Local error

Found 4 expressions with local error:

4.2b
(- (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))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
39×sqrt-prod
36×*-un-lft-identity
12×difference-of-squares
11×add-cbrt-cube add-exp-log add-cube-cbrt
10×times-frac associate-/l*
9×pow1 distribute-lft-out--
7×associate-*r*
6×sqrt-div associate-*l* add-log-exp
5×distribute-lft-out
4×associate-*r/ insert-posit16 unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ cbrt-unprod 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 → 112
Calls
4 calls:
Slowest
77.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
37.0ms
(- (sqrt (+ x 1)) (sqrt x))
19.0ms
(* (sqrt x) (sqrt (+ x 1)))
8.0ms
(sqrt (+ x 1))

series443.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
234.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
97.0ms
(- (sqrt (+ x 1)) (sqrt x))
72.0ms
(* (sqrt x) (sqrt (+ x 1)))
40.0ms
(sqrt (+ x 1))

simplify2.2s

Counts
124 → 124

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
118×*-un-lft-identity
78×times-frac
55×sqrt-prod
47×add-sqr-sqrt
45×distribute-lft-out
39×add-cube-cbrt
32×add-exp-log
27×associate-/l*
20×add-cbrt-cube
14×div-exp
9×pow1
8×associate-/r/
7×cbrt-undiv associate-/r* associate-*r*
6×flip3-+ associate-*l* flip-+ add-log-exp
5×prod-exp
4×sqrt-div associate-*r/ insert-posit16 div-inv unswap-sqr
3×rec-exp 1-exp pow-prod-down cbrt-unprod
2×clear-num frac-2neg sqrt-pow1 pow1/2
1×+-commutative sum-log sqrt-unprod *-commutative pow-flip inv-pow associate-/l/
Counts
4 → 170
Calls
4 calls:
Slowest
48.0ms
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
32.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
18.0ms
(* (sqrt x) (sqrt (+ x 1)))
17.0ms
(+ (sqrt (+ x 1)) (sqrt x))

series456.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
243.0ms
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
92.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
65.0ms
(* (sqrt x) (sqrt (+ x 1)))
55.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify520.0ms

Counts
182 → 182

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

11.0b
(* (/ 1 (+ (* x (sqrt x)) (* (+ 1 x) (sqrt (+ 1 x))))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
4.0b
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
0.5b
(* (sqrt x) (sqrt x))
0.4b
(/ 1 (+ (* x (sqrt x)) (* (+ 1 x) (sqrt (+ 1 x)))))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
48×sqrt-div
34×frac-times
32×frac-add
31×*-un-lft-identity
30×add-cube-cbrt
28×flip3-+ flip-+
26×times-frac associate-*r/
24×associate-*l*
22×pow1
19×add-exp-log
18×sqrt-prod
17×flip3-- flip--
14×pow3
13×add-cbrt-cube
9×associate-*r* associate-*l/
8×sqrt-pow1 pow1/2 swap-sqr
7×sum-cubes unswap-sqr
6×add-log-exp
5×prod-exp pow-prod-up
4×associate-/r* div-exp pow-prod-down associate-/r/ insert-posit16
3×pow-sqr cbrt-unprod associate-/l*
2×cbrt-undiv rec-exp 1-exp *-commutative div-inv
1×pow2 distribute-rgt-in clear-num sub-neg rem-square-sqrt frac-2neg distribute-lft-in pow-plus distribute-rgt-out-- sqrt-unprod diff-log pow-flip inv-pow
Counts
4 → 181
Calls
4 calls:
Slowest
181.0ms
(* (/ 1 (+ (* x (sqrt x)) (* (+ 1 x) (sqrt (+ 1 x))))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
23.0ms
(/ 1 (+ (* x (sqrt x)) (* (+ 1 x) (sqrt (+ 1 x)))))
13.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
8.0ms
(* (sqrt x) (sqrt x))

series462.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(* (/ 1 (+ (* x (sqrt x)) (* (+ 1 x) (sqrt (+ 1 x))))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
131.0ms
(/ 1 (+ (* x (sqrt x)) (* (+ 1 x) (sqrt (+ 1 x)))))
93.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
30.0ms
(* (sqrt x) (sqrt x))

simplify663.0ms

Counts
193 → 193

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch6.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.0s1861×body640valid
564.0ms1171×body1280valid
556.0ms7822×body80nan
302.0ms4062×body80valid
160.0ms594×body320valid
77.0ms312×body160valid