Details

Time bar (total: 2.0m)

sample84.0ms

Algorithm
intervals
Results
20.0ms59×body640valid
19.0ms271×body80nan
13.0ms32×body1280valid
12.0ms142×body80valid
4.0ms14×body320valid
1.0ms9×body160valid

simplify42.0ms

Calls
1 calls:
Slowest
42.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize14.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
1063×times-frac
902×*-un-lft-identity
788×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
580×sqrt-prod
74×distribute-lft-out
56×div-inv
48×sqrt-div
46×associate-/r/
25×difference-of-squares
24×flip3-+ flip-+
22×fma-neg
13×associate-/r* distribute-lft-out--
12×add-exp-log
9×pow1
8×add-cbrt-cube
6×pow-flip associate-/l* add-log-exp
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
3×sqrt-pow1 pow1/2
2×cbrt-undiv rec-exp clear-num frac-2neg 1-exp hypot-def inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip--
Calls
4 calls:
Slowest
34.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
25.0ms
(/ 1 (sqrt (+ x 1)))
10.0ms
(sqrt (+ x 1))
9.0ms
(/ 1 (sqrt x))

series226.0ms

Calls
4 calls:
Slowest
99.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
51.0ms
(/ 1 (sqrt x))
43.0ms
(/ 1 (sqrt (+ x 1)))
32.0ms
(sqrt (+ x 1))

simplify1.9m

Calls
1414 calls:
Slowest
506.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt x) (cbrt x)))) (/ (cbrt 1) (sqrt (cbrt x))) (- (* (/ (cbrt 1) (sqrt (+ x 1))) (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)))))
427.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (cbrt 1) (cbrt (sqrt x))) (- (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
396.0ms
(fma (/ (sqrt 1) (sqrt (* (cbrt x) (cbrt x)))) (/ (sqrt 1) (sqrt (cbrt x))) (- (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))
382.0ms
(fma (* (cbrt (/ 1 (sqrt x))) (cbrt (/ 1 (sqrt x)))) (cbrt (/ 1 (sqrt x))) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))
374.0ms
(fma (- (sqrt (+ (* x x) (- (* 1 1) (* x 1))))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))) (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3))))))

prune4.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.2b

localize22.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (/ 1 (sqrt (sqrt x))) (/ 1 (sqrt (sqrt (+ x 1)))))
0.3b
(* (+ (/ 1 (sqrt (sqrt x))) (/ 1 (sqrt (sqrt (+ x 1))))) (- (/ 1 (sqrt (sqrt x))) (/ 1 (sqrt (sqrt (+ x 1))))))
0.2b
(/ 1 (sqrt (sqrt x)))
0.2b
(/ 1 (sqrt (sqrt x)))

rewrite426.0ms

Algorithm
rewrite-expression-head
Rules
6342×sqrt-prod
6027×times-frac
4740×*-un-lft-identity
4287×add-sqr-sqrt
4005×add-cube-cbrt
3348×prod-diff
1118×distribute-rgt-in distribute-lft-in
372×sqrt-div
304×distribute-lft-out
216×div-inv
186×associate-/r/
98×difference-of-squares
97×flip3-+ flip-+
68×associate-*r*
32×distribute-lft-out--
31×fma-neg
19×associate-*l*
18×associate-/r*
14×add-exp-log
12×pow1
10×add-cbrt-cube pow-flip
9×frac-times
8×sqrt-pow1
6×associate-/l* add-log-exp
5×flip3-- frac-sub flip--
4×expm1-log1p-u pow1/2 div-exp frac-add insert-posit16 log1p-expm1-u
3×sub-neg associate-*l/ associate-*r/
2×cbrt-undiv rec-exp clear-num frac-2neg 1-exp inv-pow
1×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Calls
4 calls:
Slowest
175.0ms
(* (+ (/ 1 (sqrt (sqrt x))) (/ 1 (sqrt (sqrt (+ x 1))))) (- (/ 1 (sqrt (sqrt x))) (/ 1 (sqrt (sqrt (+ x 1))))))
37.0ms
(- (/ 1 (sqrt (sqrt x))) (/ 1 (sqrt (sqrt (+ x 1)))))
6.0ms
(/ 1 (sqrt (sqrt x)))
6.0ms
(/ 1 (sqrt (sqrt x)))

series643.0ms

Calls
4 calls:
Slowest
229.0ms
(* (+ (/ 1 (sqrt (sqrt x))) (/ 1 (sqrt (sqrt (+ x 1))))) (- (/ 1 (sqrt (sqrt x))) (/ 1 (sqrt (sqrt (+ x 1))))))
152.0ms
(/ 1 (sqrt (sqrt x)))
148.0ms
(/ 1 (sqrt (sqrt x)))
115.0ms
(- (/ 1 (sqrt (sqrt x))) (/ 1 (sqrt (sqrt (+ x 1)))))