Details

Time bar (total: 18.0s)

sample75.0ms

Algorithm
intervals
Results
18.0ms53×body1280valid
17.0ms273×body80nan
13.0ms47×body640valid
9.0ms130×body80valid
3.0ms15×body320valid
1.0ms11×body160valid

simplify21.0ms

Calls
1 calls:
Slowest
21.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize20.0ms

Local error

Found 2 expressions with local error:

2.8b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×*-un-lft-identity
18×prod-diff
17×add-cube-cbrt
16×sqrt-prod
6×fma-neg
4×add-log-exp
2×expm1-log1p-u pow1 add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
1×rem-sqrt-square sub-neg flip3-+ flip3-- pow1/2 diff-log flip-+ flip-- distribute-lft-out--
Calls
2 calls:
Slowest
15.0ms
(- (sqrt (+ x 1)) (sqrt x))
1.0ms
(sqrt (+ x 1))

series105.0ms

Calls
2 calls:
Slowest
81.0ms
(- (sqrt (+ x 1)) (sqrt x))
24.0ms
(sqrt (+ x 1))

simplify1.8s

Calls
59 calls:
Slowest
121.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
72.0ms
(fma (sqrt 1) (sqrt (+ x 1)) (- (* (sqrt x) 1)))
55.0ms
(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (* (sqrt (sqrt x)) (sqrt (sqrt x)))))
55.0ms
(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
54.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (sqrt (sqrt x)) (sqrt (sqrt x)))))

prune548.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 29.1b

localize18.0ms

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)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
20×add-sqr-sqrt add-cube-cbrt
16×times-frac
14×pow1
12×sqrt-div
10×add-cbrt-cube add-exp-log
9×associate-*r* associate-*l*
8×pow1/2
7×flip3-+ flip-+
6×sqrt-prod add-log-exp difference-of-squares
5×distribute-lft-out
4×expm1-log1p-u frac-times associate-/r* pow-prod-down pow-prod-up 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
Calls
4 calls:
Slowest
39.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
12.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
6.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
4.0ms
(* (sqrt x) (sqrt x))

series194.0ms

Calls
4 calls:
Slowest
134.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
26.0ms
(* (sqrt x) (sqrt x))
19.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
15.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))

simplify5.1s

Calls
111 calls:
Slowest
672.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
641.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
217.0ms
(/ (* (* (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))) (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
165.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
146.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

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))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
6×fma-def sqrt-prod
5×add-log-exp
4×pow1 associate-/r* add-exp-log
3×expm1-log1p-u flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u
2×sqrt-div associate-/r/ distribute-lft-out
1×+-commutative rem-sqrt-square rec-exp clear-num sum-log frac-2neg pow1/2 div-inv pow-flip inv-pow
Calls
3 calls:
Slowest
7.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
6.0ms
(+ (sqrt (+ x 1)) (sqrt x))
1.0ms
(sqrt (+ x 1))

series175.0ms

Calls
3 calls:
Slowest
89.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
60.0ms
(+ (sqrt (+ x 1)) (sqrt x))
26.0ms
(sqrt (+ x 1))

simplify611.0ms

Calls
29 calls:
Slowest
175.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
133.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
54.0ms
(sqrt (- (* x x) (* 1 1)))
24.0ms
(sqrt (+ (pow x 3) (pow 1 3)))
21.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

prune535.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))
0.1b
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
0.1b
(sqrt (sqrt (+ x 1)))
0.1b
(sqrt (sqrt (+ x 1)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
38×sqrt-prod
32×sqrt-div
19×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
10×pow1
9×flip3-+ associate-*r* associate-*l* flip-+
7×add-exp-log
6×add-cbrt-cube pow1/2
4×expm1-log1p-u frac-times rem-sqrt-square insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r*
2×pow-prod-down associate-*l/ associate-*r/ associate-/r/ pow-prod-up
1×pow2 rec-exp clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod div-inv pow-flip inv-pow
Calls
4 calls:
Slowest
14.0ms
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))
10.0ms
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
1.0ms
(sqrt (sqrt (+ x 1)))
1.0ms
(sqrt (sqrt (+ x 1)))

series228.0ms

Calls
4 calls:
Slowest
100.0ms
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
53.0ms
(sqrt (sqrt (+ x 1)))
46.0ms
(sqrt (sqrt (+ x 1)))
28.0ms
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify3.5s

Calls
78 calls:
Slowest
391.0ms
(- (+ (* 1/4 (/ (exp (* 1/4 (- (log -1) (log (/ -1 x))))) x)) (exp (* 1/4 (- (log -1) (log (/ -1 x)))))) (* 3/32 (/ (exp (* 1/4 (- (log -1) (log (/ -1 x))))) (pow x 2))))
369.0ms
(- (+ (* 1/4 (/ (exp (* 1/4 (- (log -1) (log (/ -1 x))))) x)) (exp (* 1/4 (- (log -1) (log (/ -1 x)))))) (* 3/32 (/ (exp (* 1/4 (- (log -1) (log (/ -1 x))))) (pow x 2))))
170.0ms
(- (+ (pow (/ 1 x) -1/4) (* 1/4 (pow (/ 1 (pow x 3)) 1/4))) (* 3/32 (pow (/ 1 (pow x 7)) 1/4)))
163.0ms
(- (+ (pow (/ 1 x) -1/4) (* 1/4 (pow (/ 1 (pow x 3)) 1/4))) (* 3/32 (pow (/ 1 (pow x 7)) 1/4)))
160.0ms
(+ (* (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))) (- (* (sqrt x) (sqrt x)) (* (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x))))

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
973.0ms8046×body80nan
483.0ms1670×body1280valid
379.0ms1320×body640valid
220.0ms4061×body80valid
131.0ms623×body320valid
35.0ms326×body160valid