Details

Time bar (total: 15.3s)

sample85.0ms

Algorithm
intervals
Results
19.0ms54×body1280valid
17.0ms249×body80nan
10.0ms139×body80valid
8.0ms30×body640valid
5.0ms24×body320valid
1.0ms9×body160valid

simplify12.0ms

Calls
1 calls:
Slowest
12.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize10.0ms

Local error

Found 2 expressions with local error:

2.3b
(- (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))
2.0ms
(sqrt (+ x 1))

series39.0ms

Calls
2 calls:
Slowest
29.0ms
(- (sqrt (+ x 1)) (sqrt x))
10.0ms
(sqrt (+ x 1))

simplify1.8s

Calls
59 calls:
Slowest
145.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
64.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (sqrt (sqrt x)) (sqrt (sqrt x)))))
64.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (sqrt (sqrt x)) (sqrt (sqrt x)))))
59.0ms
(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
58.0ms
(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (* (sqrt (sqrt x)) (sqrt (sqrt x)))))

prune559.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 27.4b

localize13.0ms

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

rewrite108.0ms

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
60.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
20.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
14.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
10.0ms
(* (sqrt x) (sqrt x))

series65.0ms

Calls
4 calls:
Slowest
39.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
10.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
9.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
8.0ms
(* (sqrt x) (sqrt x))

simplify4.6s

Calls
111 calls:
Slowest
638.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
520.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
178.0ms
(/ (* (* (- (* (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))))
173.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
142.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

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
8.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
7.0ms
(+ (sqrt (+ x 1)) (sqrt x))
1.0ms
(sqrt (+ x 1))

series69.0ms

Calls
3 calls:
Slowest
32.0ms
(+ (sqrt (+ x 1)) (sqrt x))
26.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
10.0ms
(sqrt (+ x 1))

simplify623.0ms

Calls
29 calls:
Slowest
212.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
101.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
41.0ms
(sqrt (- (* x x) (* 1 1)))
21.0ms
(cbrt (+ (sqrt (+ x 1)) (sqrt x)))
20.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

prune592.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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
9.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
5.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
5.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
3.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

series155.0ms

Calls
4 calls:
Slowest
49.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
41.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
38.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
27.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.7s

Calls
66 calls:
Slowest
203.0ms
(sqrt (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
183.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
169.0ms
(* (* (* (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))))))
157.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
84.0ms
(* (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
746.0ms1267×body640valid
576.0ms1691×body1280valid
528.0ms7956×body80nan
318.0ms4125×body80valid
99.0ms591×body320valid
37.0ms326×body160valid