Details

Time bar (total: 22.7s)

sample57.0ms

Algorithm
intervals
Results
13.0ms57×body640valid
12.0ms249×body80nan
10.0ms37×body1280valid
8.0ms138×body80valid
2.0ms12×body320valid
1.0ms12×body160valid

simplify19.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize38.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite114.0ms

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
39.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
15.0ms
(/ 1 (sqrt (+ x 1)))
9.0ms
(/ 1 (sqrt x))
8.0ms
(sqrt (+ x 1))

series221.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
44.0ms
(/ 1 (sqrt x))
41.0ms
(/ 1 (sqrt (+ x 1)))
37.0ms
(sqrt (+ x 1))

simplify1.0s

Counts
805 → 805

prune8.6s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 19.1b

localize17.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (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))

rewrite150.0ms

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
63.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
43.0ms
(- (sqrt (+ x 1)) (sqrt x))
37.0ms
(* (sqrt x) (sqrt (+ x 1)))
4.0ms
(sqrt (+ x 1))

series356.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
191.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
72.0ms
(- (sqrt (+ x 1)) (sqrt x))
68.0ms
(* (sqrt x) (sqrt (+ x 1)))
25.0ms
(sqrt (+ x 1))

simplify692.0ms

Counts
183 → 183

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

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))

rewrite228.0ms

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
100.0ms
(/ (/ (+ 1 (- x x)) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
68.0ms
(/ (+ 1 (- x x)) (+ (sqrt (+ x 1)) (sqrt x)))
32.0ms
(* (sqrt x) (sqrt (+ x 1)))
20.0ms
(+ (sqrt (+ x 1)) (sqrt x))

series433.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
221.0ms
(/ (/ (+ 1 (- x x)) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
83.0ms
(/ (+ 1 (- x x)) (+ (sqrt (+ x 1)) (sqrt x)))
64.0ms
(* (sqrt x) (sqrt (+ x 1)))
64.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify793.0ms

Counts
231 → 231

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

8.0b
(* (/ 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)))))
2.0b
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
0.5b
(* (sqrt x) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
50×sqrt-div
34×frac-times
32×frac-add
29×sqrt-prod
28×associate-*r/
27×*-un-lft-identity flip3-+ flip-+
25×pow1 associate-*l*
24×add-cube-cbrt
17×flip3-- add-exp-log flip--
16×associate-*r*
13×add-cbrt-cube
11×times-frac unswap-sqr
10×sqrt-pow1 pow1/2
9×associate-*l/
8×swap-sqr
7×pow-prod-down
6×prod-exp add-log-exp
5×pow-prod-up
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u
3×pow-sqr *-commutative
2×sqrt-unprod div-exp
1×pow2 distribute-rgt-in cbrt-undiv rec-exp sub-neg rem-square-sqrt distribute-lft-in pow-plus distribute-rgt-out-- fma-neg diff-log 1-exp prod-diff div-inv distribute-lft-out
Counts
4 → 182
Calls
4 calls:
Slowest
116.0ms
(* (/ 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)))))
16.0ms
(* (sqrt x) (sqrt (+ x 1)))
10.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
9.0ms
(* (sqrt x) (sqrt x))

series340.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
182.0ms
(* (/ 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)))))
83.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
58.0ms
(* (sqrt x) (sqrt (+ x 1)))
16.0ms
(* (sqrt x) (sqrt x))

simplify1.9s

Counts
194 → 194

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch4.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
781.0ms1871×body640valid
469.0ms7752×body80nan
467.0ms1128×body1280valid
290.0ms4077×body80valid
128.0ms617×body320valid
35.0ms307×body160valid