Details

Time bar (total: 25.7s)

sample70.0ms

Algorithm
intervals
Results
15.0ms58×body640valid
15.0ms267×body80nan
12.0ms37×body1280valid
8.0ms133×body80valid
4.0ms19×body320valid
1.0ms9×body160valid

simplify29.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize36.0ms

Local error

Found 3 expressions with local error:

3.3b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.2b
(/ 1 (sqrt (+ x 1)))

rewrite94.0ms

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
44.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
9.0ms
(/ 1 (sqrt (+ x 1)))
5.0ms
(/ 1 (sqrt x))

series168.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
80.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
51.0ms
(/ 1 (sqrt (+ x 1)))
37.0ms
(/ 1 (sqrt x))

simplify1.2s

Counts
781 → 781

prune10.3s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 18.8b

localize34.0ms

Local error

Found 3 expressions with local error:

3.3b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))

rewrite122.0ms

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
64.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
37.0ms
(- (sqrt (+ x 1)) (sqrt x))
18.0ms
(* (sqrt x) (sqrt (+ x 1)))

series375.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
215.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
92.0ms
(- (sqrt (+ x 1)) (sqrt x))
68.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify2.3s

Counts
159 → 159

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.2b
(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
184×*-un-lft-identity
102×times-frac
77×distribute-lft-out
71×sqrt-prod
52×add-sqr-sqrt
44×add-cube-cbrt
34×associate-/l*
20×add-cbrt-cube add-exp-log
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×pow-prod-down prod-exp cbrt-unprod associate-/l/
2×clear-num frac-2neg sqrt-pow1 pow1/2
1×+-commutative sum-log sqrt-unprod *-commutative
Counts
4 → 198
Calls
4 calls:
Slowest
58.0ms
(/ (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
33.0ms
(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
21.0ms
(+ (sqrt (+ x 1)) (sqrt x))
20.0ms
(* (sqrt x) (sqrt (+ x 1)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
216.0ms
(/ (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
74.0ms
(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
60.0ms
(+ (sqrt (+ x 1)) (sqrt x))
58.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify537.0ms

Counts
210 → 210

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

9.4b
(* (/ 1 (fma (sqrt x) x (* (+ x 1) (sqrt (+ x 1))))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
3.0b
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
0.5b
(* (sqrt x) (sqrt x))
0.3b
(* (sqrt (+ x 1)) (sqrt (+ x 1)))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
60×sqrt-div
59×add-sqr-sqrt
44×sqrt-prod
43×*-un-lft-identity
38×frac-times
36×pow1
32×flip3-+ frac-add flip-+
28×associate-*r/ add-cube-cbrt
26×associate-*l*
19×swap-sqr
17×flip3-- add-exp-log flip--
16×sqrt-pow1 pow1/2 associate-*r*
13×add-cbrt-cube
11×times-frac associate-*l/ unswap-sqr
10×pow-prod-up
7×pow-prod-down
6×prod-exp pow-sqr distribute-lft-out add-log-exp
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u
3×*-commutative
2×pow2 rem-square-sqrt pow-plus sqrt-unprod div-exp
1×distribute-rgt-in cbrt-undiv rec-exp sub-neg distribute-lft-in distribute-rgt-out-- fma-neg diff-log 1-exp prod-diff div-inv
Counts
4 → 211
Calls
4 calls:
Slowest
118.0ms
(* (/ 1 (fma (sqrt x) x (* (+ x 1) (sqrt (+ x 1))))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
23.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
11.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
8.0ms
(* (sqrt x) (sqrt x))

series327.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
194.0ms
(* (/ 1 (fma (sqrt x) x (* (+ x 1) (sqrt (+ x 1))))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
90.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
25.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
18.0ms
(* (sqrt x) (sqrt x))

simplify1.8s

Counts
223 → 223

prune2.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

0% (0.6b remaining)

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

bsearch3.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
830.0ms7971×body80nan
503.0ms1837×body640valid
381.0ms1103×body1280valid
244.0ms4129×body80valid
149.0ms629×body320valid
34.0ms302×body160valid