Details

Time bar (total: 12.8s)

sample51.0ms

Algorithm
intervals
Results
12.0ms55×body1280valid
11.0ms269×body80nan
7.0ms41×body640valid
6.0ms129×body80valid
3.0ms20×body320valid
1.0ms11×body160valid

simplify36.0ms

Calls
1 calls:
Slowest
36.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize20.0ms

Local error

Found 2 expressions with local error:

2.6b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
5×*-un-lft-identity
4×sqrt-prod add-log-exp
3×add-cube-cbrt
2×pow1 add-cbrt-cube sqrt-div add-exp-log insert-posit16 difference-of-squares
1×rem-sqrt-square sub-neg flip3-+ flip3-- pow1/2 diff-log flip-+ flip-- distribute-lft-out--
Calls
2 calls:
Slowest
13.0ms
(- (sqrt (+ x 1)) (sqrt x))
1.0ms
(sqrt (+ x 1))

series52.0ms

Calls
2 calls:
Slowest
36.0ms
(- (sqrt (+ x 1)) (sqrt x))
17.0ms
(sqrt (+ x 1))

simplify459.0ms

Calls
18 calls:
Slowest
147.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
69.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
52.0ms
(sqrt (- (* x x) (* 1 1)))
24.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
23.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

prune340.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 29.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
0.5b
(* (sqrt x) (sqrt x))
0.3b
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
0.1b
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite72.0ms

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×frac-times associate-/r* pow-prod-down pow-prod-up insert-posit16 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 diff-log div-sub div-exp div-inv
Calls
4 calls:
Slowest
47.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
11.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
6.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
4.0ms
(* (sqrt x) (sqrt x))

series89.0ms

Calls
4 calls:
Slowest
48.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
15.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
13.0ms
(* (sqrt x) (sqrt x))
12.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))

simplify4.3s

Calls
108 calls:
Slowest
490.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
419.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
294.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
221.0ms
(/ (* (* (- (* (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))))
208.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×add-cube-cbrt add-log-exp
4×pow1 associate-/r* add-exp-log
3×flip3-+ add-cbrt-cube sqrt-prod flip-+ insert-posit16
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
11.0ms
(+ (sqrt (+ x 1)) (sqrt x))
10.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
1.0ms
(sqrt (+ x 1))

series76.0ms

Calls
3 calls:
Slowest
30.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
29.0ms
(+ (sqrt (+ x 1)) (sqrt x))
17.0ms
(sqrt (+ x 1))

simplify461.0ms

Calls
24 calls:
Slowest
168.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
91.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
33.0ms
(sqrt (- (* x x) (* 1 1)))
25.0ms
(* (exp (sqrt (+ x 1))) (exp (sqrt x)))
20.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune491.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-prod
15×*-un-lft-identity
12×add-sqr-sqrt
11×pow1 add-cube-cbrt
10×associate-/r/
9×associate-*r* associate-*l*
8×associate-/r* add-exp-log
6×add-cbrt-cube
5×flip3-+ pow1/2 sqrt-div flip-+ div-inv
4×insert-posit16 add-log-exp
2×rec-exp clear-num frac-2neg pow-prod-down pow-prod-up pow-flip distribute-lft-out inv-pow
1×pow2 frac-times rem-sqrt-square rem-square-sqrt pow-plus sqrt-unprod associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
15.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
12.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
6.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
2.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

series139.0ms

Calls
4 calls:
Slowest
47.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
36.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
29.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
27.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

simplify1.7s

Calls
66 calls:
Slowest
178.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
170.0ms
(sqrt (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
167.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
125.0ms
(* (* (* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (* (* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))))
71.0ms
(sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))))

prune928.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
943.0ms1722×body1280valid
430.0ms8068×body80nan
317.0ms1237×body640valid
304.0ms4100×body80valid
121.0ms612×body320valid
34.0ms329×body160valid