Details

Time bar (total: 9.9m)

sample111.0ms

Algorithm
intervals
Results
25.0ms56×body640valid
23.0ms253×body80nan
23.0ms42×body1280valid
14.0ms131×body80valid
7.0ms21×body320valid
2.0ms6×body160valid

simplify29.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize54.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.2b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
196×*-un-lft-identity
188×add-sqr-sqrt
175×associate-/r*
156×frac-sub
151×sqrt-prod
117×add-cube-cbrt
97×times-frac
81×associate-/l*
27×clear-num frac-2neg
25×difference-of-squares
20×distribute-lft-out
13×distribute-lft-out--
12×add-exp-log
9×pow1
8×add-cbrt-cube
6×div-inv pow-flip add-log-exp
4×sqrt-div div-exp insert-posit16
3×sqrt-pow1 pow1/2
2×cbrt-undiv rec-exp flip3-+ 1-exp associate-/r/ flip-+ inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log flip--
Calls
4 calls:
Slowest
58.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
10.0ms
(/ 1 (sqrt (+ x 1)))
10.0ms
(/ 1 (sqrt x))
5.0ms
(sqrt (+ x 1))

series198.0ms

Calls
4 calls:
Slowest
76.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
52.0ms
(/ 1 (sqrt x))
46.0ms
(/ 1 (sqrt (+ x 1)))
24.0ms
(sqrt (+ x 1))

simplify34.2s

Calls
514 calls:
Slowest
923.0ms
(- (* 1 (sqrt (sqrt (+ x 1)))) (* (sqrt x) (/ 1 (sqrt (sqrt (+ x 1))))))
589.0ms
(- (* 1 (cbrt (sqrt (+ x 1)))) (* (sqrt x) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
587.0ms
(- (* 1 (cbrt (sqrt (+ x 1)))) (* (/ (sqrt x) 1) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
583.0ms
(- (* (sqrt 1) (cbrt (sqrt (+ x 1)))) (* (/ (sqrt x) (sqrt 1)) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
546.0ms
(- (* (* (cbrt 1) (cbrt 1)) (cbrt (sqrt (+ x 1)))) (* (/ (sqrt x) (cbrt 1)) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))

prune2.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 18.2b

localize39.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))) (/ (sqrt (sqrt x)) (sqrt (sqrt (+ x 1)))))
0.3b
(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1))))
0.2b
(/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
0.2b
(/ (- (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))) (/ (sqrt (sqrt x)) (sqrt (sqrt (+ x 1))))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1)))))

rewrite874.0ms

Algorithm
rewrite-expression-head
Rules
22085×sqrt-prod
17002×add-sqr-sqrt
11470×times-frac
4544×*-un-lft-identity
3500×difference-of-squares
1506×add-cube-cbrt
1220×associate-*r*
1098×associate-*l* unswap-sqr
1056×frac-sub
1002×associate-/l*
918×associate-/r*
620×associate-/l/
595×distribute-lft-out--
504×distribute-lft-out
188×sqrt-div
122×*-commutative
94×clear-num frac-2neg
47×flip3-+ flip-+
13×add-cbrt-cube add-exp-log
10×pow1
8×sqrt-pow1
6×add-log-exp
5×pow-prod-down
4×pow1/2 associate-*r/ insert-posit16
3×cbrt-undiv div-exp
2×flip3-- prod-exp associate-/r/ cbrt-unprod div-inv flip--
1×sqrt-undiv sub-neg sqrt-unprod diff-log div-sub
Calls
4 calls:
Slowest
231.0ms
(/ (- (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))) (/ (sqrt (sqrt x)) (sqrt (sqrt (+ x 1))))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1)))))
91.0ms
(- (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))) (/ (sqrt (sqrt x)) (sqrt (sqrt (+ x 1)))))
40.0ms
(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1))))
24.0ms
(/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

series779.0ms

Calls
4 calls:
Slowest
375.0ms
(/ (- (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))) (/ (sqrt (sqrt x)) (sqrt (sqrt (+ x 1))))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1)))))
230.0ms
(- (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))) (/ (sqrt (sqrt x)) (sqrt (sqrt (+ x 1)))))
88.0ms
(/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
86.0ms
(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1))))

simplify9.2m

Calls
10162 calls:
Slowest
655.0ms
(- (* (sqrt (sqrt (+ (pow x 3) (pow 1 3)))) (sqrt (cbrt (sqrt (+ x 1))))) (* (* (sqrt (sqrt x)) (sqrt (sqrt (+ (* x x) (- (* 1 1) (* x 1)))))) (/ (sqrt (sqrt x)) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
607.0ms
(/ (+ (sqrt (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))) (sqrt (/ (sqrt (sqrt x)) (sqrt (sqrt (+ x 1)))))) (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt (+ x 1))))))
600.0ms
(- (* (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt (sqrt x)))) (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))) (* (sqrt (sqrt (sqrt x))) 1))
561.0ms
(/ (- (/ (sqrt (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (sqrt x)))) (/ (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt (+ x 1)))))) (* (sqrt (sqrt (cbrt x))) (sqrt (sqrt (+ x 1)))))
530.0ms
(/ (+ (/ (sqrt (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (sqrt x)))) (/ (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt (+ x 1)))))) (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt (+ x 1))))))