Details

Time bar (total: 18.4s)

sample114.0ms

Algorithm
intervals
Results
30.0ms52×body640valid
21.0ms36×body1280valid
20.0ms209×body80nan
16.0ms137×body80valid
7.0ms20×body320valid
3.0ms11×body160valid

simplify37.0ms

Counts
1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize30.0ms

Local error

Found 3 expressions with local error:

2.9b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
1063×times-frac
897×*-un-lft-identity
782×add-sqr-sqrt
712×add-cube-cbrt
594×prod-diff
576×sqrt-prod
73×distribute-lft-out
56×div-inv
46×sqrt-div associate-/r/
25×difference-of-squares
23×flip3-+ flip-+
22×fma-neg
13×associate-/r* distribute-lft-out--
11×add-exp-log
7×pow1 add-cbrt-cube
6×pow-flip associate-/l*
5×add-log-exp
4×div-exp
3×expm1-log1p-u insert-posit16 log1p-expm1-u
2×cbrt-undiv rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp inv-pow
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
3 → 772
Calls
3 calls:
Slowest
77.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
19.0ms
(/ 1 (sqrt (+ x 1)))
10.0ms
(/ 1 (sqrt x))

series172.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
91.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
48.0ms
(/ 1 (sqrt (+ x 1)))
33.0ms
(/ 1 (sqrt x))

simplify1.3s

Counts
1442 → 781

prune7.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 16.7b

localize15.0ms

Local error

Found 3 expressions with local error:

3.0b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
84×sqrt-prod
74×*-un-lft-identity
69×add-sqr-sqrt
42×prod-diff
37×add-cube-cbrt
12×difference-of-squares
11×distribute-lft-out
10×times-frac add-cbrt-cube add-exp-log associate-/l*
9×distribute-lft-out--
7×pow1 fma-neg associate-*r*
6×associate-*l*
5×add-log-exp
4×sqrt-div associate-*r/ unswap-sqr
3×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u
2×cbrt-undiv sqrt-pow1 flip3-+ flip3-- pow1/2 div-exp prod-exp associate-/r/ cbrt-unprod flip-+ flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg sqrt-unprod diff-log div-sub *-commutative div-inv
Counts
3 → 150
Calls
3 calls:
Slowest
63.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
31.0ms
(- (sqrt (+ x 1)) (sqrt x))
20.0ms
(* (sqrt x) (sqrt (+ x 1)))

series263.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
151.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
57.0ms
(* (sqrt x) (sqrt (+ x 1)))
55.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify436.0ms

Counts
222 → 159

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 16.3b

localize23.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (+ 1 x) x)
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.0b
(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
299×*-un-lft-identity
150×times-frac
104×add-sqr-sqrt
101×distribute-lft-out
87×sqrt-prod
56×add-cube-cbrt
48×associate-/l*
40×distribute-lft-out--
20×add-cbrt-cube add-exp-log difference-of-squares
12×prod-diff
9×add-log-exp
8×pow1 associate-/r/
7×cbrt-undiv associate-/r* div-exp associate-*r*
6×associate-*l*
5×flip3-+ flip-+
4×expm1-log1p-u fma-neg 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 frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log flip--
1×sum-log sub-neg sqrt-unprod associate--l+ *-commutative
Counts
4 → 250
Calls
4 calls:
Slowest
82.0ms
(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
70.0ms
(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
27.0ms
(- (+ 1 x) x)
23.0ms
(* (sqrt x) (sqrt (+ x 1)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
188.0ms
(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
72.0ms
(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
56.0ms
(* (sqrt x) (sqrt (+ x 1)))
1.0ms
(- (+ 1 x) x)

simplify354.0ms

Counts
362 → 262

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (* (sqrt x) (sqrt (+ x 1))))
0.1b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
29×add-sqr-sqrt
27×sqrt-prod
21×times-frac add-cube-cbrt
17×distribute-lft-out
15×add-exp-log
13×add-cbrt-cube
9×pow1
7×associate-/r* associate-*r*
6×associate-*l* associate-/l*
4×expm1-log1p-u sqrt-div div-exp associate-*r/ associate-/r/ insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×cbrt-undiv flip3-+ pow-prod-down flip-+
2×clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv expm1-udef
1×rec-exp expm1-log1p sqrt-unprod 1-exp div-sub *-commutative pow-flip inv-pow
Counts
4 → 123
Calls
4 calls:
Slowest
26.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
21.0ms
(* (sqrt x) (sqrt (+ x 1)))
11.0ms
(/ (expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (* (sqrt x) (sqrt (+ x 1))))
0.0ms
(expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

series582.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
308.0ms
(/ (expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (* (sqrt x) (sqrt (+ x 1))))
150.0ms
(expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
69.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
55.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify357.0ms

Counts
160 → 135

prune891.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes46.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
724.0ms7809×body80nan
476.0ms1862×body640valid
363.0ms1080×body1280valid
304.0ms4125×body80valid
127.0ms629×body320valid
52.0ms304×body160valid