Details

Time bar (total: 26.4s)

sample127.0ms

Algorithm
intervals
Results
34.0ms293×body80nan
29.0ms64×body640valid
18.0ms31×body1280valid
13.0ms116×body80valid
11.0ms33×body320valid
3.0ms12×body160valid

simplify32.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.4b

localize35.0ms

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))

rewrite103.0ms

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
45.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
9.0ms
(/ 1 (sqrt (+ x 1)))
6.0ms
(sqrt (+ x 1))
5.0ms
(/ 1 (sqrt x))

series208.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
102.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
46.0ms
(/ 1 (sqrt (+ x 1)))
31.0ms
(sqrt (+ x 1))
29.0ms
(/ 1 (sqrt x))

simplify907.0ms

Counts
805 → 805

prune10.1s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 21.6b

localize34.0ms

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))

rewrite204.0ms

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
125.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
35.0ms
(- (sqrt (+ x 1)) (sqrt x))
30.0ms
(* (sqrt x) (sqrt (+ x 1)))
9.0ms
(sqrt (+ x 1))

series459.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
218.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
103.0ms
(* (sqrt x) (sqrt (+ x 1)))
100.0ms
(- (sqrt (+ x 1)) (sqrt x))
35.0ms
(sqrt (+ x 1))

simplify666.0ms

Counts
183 → 183

prune1.7s

Pruning

3 alts after pruning (3 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))

rewrite245.0ms

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
124.0ms
(/ (/ (+ 1 (- x x)) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
78.0ms
(/ (+ 1 (- x x)) (+ (sqrt (+ x 1)) (sqrt x)))
20.0ms
(+ (sqrt (+ x 1)) (sqrt x))
16.0ms
(* (sqrt x) (sqrt (+ x 1)))

series589.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
299.0ms
(/ (/ (+ 1 (- x x)) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
117.0ms
(/ (+ 1 (- x x)) (+ (sqrt (+ x 1)) (sqrt x)))
88.0ms
(* (sqrt x) (sqrt (+ x 1)))
85.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify921.0ms

Counts
231 → 231

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

11.0b
(* (/ 1 (fma (sqrt (+ x 1)) (+ x 1) (* (sqrt x) 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 (fma (sqrt (+ x 1)) (+ x 1) (* (sqrt x) x)))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
48×sqrt-div
47×add-sqr-sqrt
34×frac-times
32×frac-add
29×*-un-lft-identity
28×add-cube-cbrt
26×flip3-+ associate-*r/ flip-+
22×pow1
20×times-frac
19×associate-*l* add-exp-log
18×sqrt-prod
17×flip3-- flip--
13×add-cbrt-cube
9×associate-*r* associate-*l/
8×sqrt-pow1 pow1/2 swap-sqr
7×unswap-sqr
6×add-log-exp
5×prod-exp pow-prod-up
4×expm1-log1p-u div-exp pow-prod-down insert-posit16 log1p-expm1-u
3×associate-/r* 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-- fma-neg sqrt-unprod diff-log prod-diff pow-flip inv-pow
Counts
4 → 180
Calls
4 calls:
Slowest
142.0ms
(* (/ 1 (fma (sqrt (+ x 1)) (+ x 1) (* (sqrt x) x))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
11.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
9.0ms
(* (sqrt x) (sqrt x))
6.0ms
(/ 1 (fma (sqrt (+ x 1)) (+ x 1) (* (sqrt x) x)))

series541.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
273.0ms
(* (/ 1 (fma (sqrt (+ x 1)) (+ x 1) (* (sqrt x) x))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
142.0ms
(/ 1 (fma (sqrt (+ x 1)) (+ x 1) (* (sqrt x) x)))
108.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
17.0ms
(* (sqrt x) (sqrt x))

simplify2.2s

Counts
192 → 192

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes59.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch6.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.0s1861×body640valid
517.0ms7822×body80nan
469.0ms1171×body1280valid
320.0ms4062×body80valid
143.0ms594×body320valid
62.0ms312×body160valid