Details

Time bar (total: 25.5s)

sample64.0ms

Algorithm
intervals
Results
17.0ms285×body80nan
14.0ms52×body1280valid
9.0ms45×body640valid
7.0ms126×body80valid
4.0ms22×body320valid
1.0ms11×body160valid

simplify13.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
13.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize9.0ms

Local error

Found 2 expressions with local error:

2.9b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
55×*-un-lft-identity
43×add-sqr-sqrt
42×prod-diff
31×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
4×add-log-exp difference-of-squares
3×pow1 distribute-lft-out--
2×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log hypot-def insert-posit16 log1p-expm1-u
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Counts
2 → 92
Calls
2 calls:
Slowest
70.0ms
(- (sqrt (+ x 1)) (sqrt x))
10.0ms
(sqrt (+ x 1))

series138.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
98.0ms
(- (sqrt (+ x 1)) (sqrt x))
39.0ms
(sqrt (+ x 1))

simplify5.8s

Counts
120 → 98
Calls
120 calls:
Slowest
214.0ms
(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
199.0ms
(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
189.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
181.0ms
(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
180.0ms
(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))

prune839.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 30.1b

localize21.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
0.5b
(* (sqrt x) (sqrt x))
0.3b
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
0.0b
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
64×sqrt-prod
56×add-sqr-sqrt
34×pow1
32×add-cube-cbrt
26×distribute-lft-out
24×times-frac
19×swap-sqr
16×sqrt-pow1 pow1/2
13×associate-*r* associate-*l*
12×sqrt-div
10×add-cbrt-cube add-exp-log pow-prod-up
8×difference-of-squares unswap-sqr
7×flip3-+ flip-+
6×associate-/r* pow-prod-down pow-sqr add-log-exp
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u associate-/l*
2×pow2 rem-square-sqrt pow-plus flip3-- sqrt-unprod associate-*l/ prod-exp associate-*r/ associate-/r/ *-commutative cbrt-unprod flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
4 → 189
Calls
4 calls:
Slowest
68.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
48.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
20.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
15.0ms
(* (sqrt x) (sqrt x))

series196.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
25.0ms
(* (sqrt x) (sqrt x))
24.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
22.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))

simplify7.9s

Counts
214 → 201
Calls
214 calls:
Slowest
730.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
452.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
316.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
231.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
227.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (+ (pow x 3) (pow 1 3))))

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
28×sqrt-prod
22×distribute-lft-out
21×add-sqr-sqrt
18×times-frac
17×add-cube-cbrt
7×fma-def add-exp-log
6×associate-/r*
5×pow1 add-cbrt-cube add-log-exp
3×expm1-log1p-u flip3-+ flip-+ insert-posit16 log1p-expm1-u associate-/l*
2×sqrt-div div-exp associate-/r/ hypot-def
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp clear-num sum-log frac-2neg sqrt-pow1 pow1/2 1-exp div-inv pow-flip inv-pow
Counts
3 → 93
Calls
3 calls:
Slowest
52.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
41.0ms
(+ (sqrt (+ x 1)) (sqrt x))
13.0ms
(sqrt (+ x 1))

series221.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
118.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
76.0ms
(+ (sqrt (+ x 1)) (sqrt x))
27.0ms
(sqrt (+ x 1))

simplify1.7s

Counts
81 → 102
Calls
81 calls:
Slowest
194.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
180.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
163.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
47.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
45.0ms
(sqrt (+ (pow x 3) (pow 1 3)))

prune840.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))
0.0b
(hypot (sqrt x) 1)
0.0b
(+ (hypot (sqrt x) 1) (sqrt x))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
13×add-sqr-sqrt add-cube-cbrt
12×times-frac
7×add-exp-log
5×add-cbrt-cube distribute-lft-out add-log-exp
4×pow1 associate-/r*
3×expm1-log1p-u fma-def insert-posit16 log1p-expm1-u associate-/l*
2×flip3-+ div-exp associate-/r/ flip-+
1×cbrt-undiv +-commutative rec-exp hypot-udef clear-num sum-log frac-2neg 1-exp div-inv pow-flip inv-pow
Counts
3 → 69
Calls
3 calls:
Slowest
12.0ms
(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))
10.0ms
(+ (hypot (sqrt x) 1) (sqrt x))
0.0ms
(hypot (sqrt x) 1)

series1.3s

Counts
3 → 9
Calls
3 calls:
Slowest
782.0ms
(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))
298.0ms
(+ (hypot (sqrt x) 1) (sqrt x))
206.0ms
(hypot (sqrt x) 1)

simplify921.0ms

Counts
49 → 78
Calls
49 calls:
Slowest
295.0ms
(/ (* (* 1 1) 1) (* (* (+ (hypot (sqrt x) 1) (sqrt x)) (+ (hypot (sqrt x) 1) (sqrt x))) (+ (hypot (sqrt x) 1) (sqrt x))))
78.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (hypot (sqrt x) 1) (sqrt x))) (cbrt (+ (hypot (sqrt x) 1) (sqrt x)))))
71.0ms
(+ (* (hypot (sqrt x) 1) (hypot (sqrt x) 1)) (- (* (sqrt x) (sqrt x)) (* (hypot (sqrt x) 1) (sqrt x))))
37.0ms
(- 0 (log (+ (hypot (sqrt x) 1) (sqrt x))))
35.0ms
(/ (sqrt 1) (* (cbrt (+ (hypot (sqrt x) 1) (sqrt x))) (cbrt (+ (hypot (sqrt x) 1) (sqrt x)))))

prune594.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes63.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch1.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
852.0ms1263×body640valid
617.0ms7851×body80nan
546.0ms1687×body1280valid
316.0ms4126×body80valid
120.0ms639×body320valid
36.0ms285×body160valid