Details

Time bar (total: 9.5m)

sample64.0ms

Algorithm
intervals
Results
19.0ms60×body640valid
13.0ms277×body80nan
12.0ms41×body1280valid
7.0ms125×body80valid
3.0ms20×body320valid
1.0ms10×body160valid

simplify31.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
31.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize41.0ms

Local error

Found 3 expressions with local error:

3.2b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.2b
(/ 1 (sqrt (+ x 1)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
1063×times-frac
897×*-un-lft-identity
782×add-sqr-sqrt
712×add-cube-cbrt
594×prod-diff
576×sqrt-prod
73×distribute-lft-out
56×div-inv
46×sqrt-div associate-/r/
25×difference-of-squares
23×flip3-+ flip-+
22×fma-neg
13×associate-/r* distribute-lft-out--
11×add-exp-log
pow1 add-cbrt-cube
pow-flip associate-/l*
add-log-exp
div-exp
expm1-log1p-u insert-posit16 log1p-expm1-u
cbrt-undiv rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp inv-pow
sub-neg flip3-- diff-log frac-sub flip--
Counts
3 → 772
Calls
3 calls:
Slowest
43.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
18.0ms
(/ 1 (sqrt (+ x 1)))
10.0ms
(/ 1 (sqrt x))

series159.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
82.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
39.0ms
(/ 1 (sqrt (+ x 1)))
38.0ms
(/ 1 (sqrt x))

simplify2.0m

Counts
1401 → 781
Calls
1401 calls:
Slowest
726.0ms
(fma (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt x))) (- (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
511.0ms
(fma 1 (/ 1 (sqrt x)) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))
392.0ms
(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)))))))
383.0ms
(fma (* (cbrt (/ 1 (sqrt x))) (cbrt (/ 1 (sqrt x)))) (cbrt (/ 1 (sqrt x))) (- (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
375.0ms
(fma (- (/ (cbrt 1) (cbrt (sqrt (+ x 1))))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))

prune4.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.4b

localize31.0ms

Local error

Found 4 expressions with local error:

3.2b
(- (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1)))))
0.3b
(/ 1 (sqrt x))
0.3b
(/ 1 (sqrt x))
0.2b
(* (+ (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))) (- (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))))

rewrite351.0ms

Algorithm
rewrite-expression-head
Rules
6052×sqrt-prod
3399×times-frac
3032×*-un-lft-identity
2647×add-sqr-sqrt
2453×add-cube-cbrt
2250×prod-diff
752×distribute-rgt-in distribute-lft-in
248×distribute-lft-out
180×div-inv
168×sqrt-div
150×associate-/r/
79×flip3-+ flip-+
72×difference-of-squares
53×associate-*r*
28×distribute-lft-out--
25×fma-neg
17×associate-*l*
14×add-exp-log
12×associate-/r*
10×pow1 add-cbrt-cube
frac-times
pow-flip associate-/l* add-log-exp
flip3-- frac-sub flip--
expm1-log1p-u div-exp frac-add insert-posit16 log1p-expm1-u
sub-neg associate-*l/ associate-*r/
cbrt-undiv rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp inv-pow
diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 2541
Calls
4 calls:
Slowest
173.0ms
(* (+ (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))) (- (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))))
32.0ms
(- (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1)))))
5.0ms
(/ 1 (sqrt x))
5.0ms
(/ 1 (sqrt x))

series386.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
216.0ms
(* (+ (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))) (- (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))))
110.0ms
(- (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1)))))
32.0ms
(/ 1 (sqrt x))
27.0ms
(/ 1 (sqrt x))

simplify6.9m

Counts
3339 → 2553
Calls
3339 calls:
Slowest
582.0ms
(* (+ (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))) (fma (- (sqrt (sqrt (- x 1)))) (sqrt (/ 1 (sqrt (- (* x x) (* 1 1))))) (* (sqrt (sqrt (- x 1))) (sqrt (/ 1 (sqrt (- (* x x) (* 1 1))))))))
566.0ms
(* (+ (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))) (fma (- (sqrt (/ (sqrt 1) (sqrt (cbrt (+ x 1)))))) (sqrt (/ (sqrt 1) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))) (* (sqrt (/ (sqrt 1) (sqrt (cbrt (+ x 1))))) (sqrt (/ (sqrt 1) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))))))
565.0ms
(* (+ (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))) (fma (- (sqrt (/ (sqrt 1) (cbrt (sqrt (+ x 1)))))) (sqrt (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))) (* (sqrt (/ (sqrt 1) (cbrt (sqrt (+ x 1))))) (sqrt (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))))
559.0ms
(* (+ (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))) (fma (- (sqrt (/ 1 (cbrt (sqrt (+ x 1)))))) (sqrt (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))) (* (sqrt (/ 1 (cbrt (sqrt (+ x 1))))) (sqrt (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))))
556.0ms
(* (+ (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))) (fma (- (sqrt (cbrt (/ 1 (sqrt (+ x 1)))))) (sqrt (* (cbrt (/ 1 (sqrt (+ x 1)))) (cbrt (/ 1 (sqrt (+ x 1)))))) (* (sqrt (cbrt (/ 1 (sqrt (+ x 1))))) (sqrt (* (cbrt (/ 1 (sqrt (+ x 1)))) (cbrt (/ 1 (sqrt (+ x 1)))))))))

prune27.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.3b

localize16.0ms

Local error

Found 2 expressions with local error:

10.7b
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt (+ x 1)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
231×*-un-lft-identity
203×add-sqr-sqrt
189×prod-diff
180×times-frac
172×add-cube-cbrt
106×sqrt-prod
89×unpow-prod-down
33×sqr-pow
25×distribute-lft-out
16×sqrt-div associate-/r/
15×difference-of-squares
div-inv
flip3-+ flip-+
associate-/r* fma-neg
add-exp-log
pow1 add-cbrt-cube add-log-exp
pow-flip associate-/l*
expm1-log1p-u div-exp insert-posit16 log1p-expm1-u distribute-lft-out--
cbrt-undiv rec-exp clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log 1-exp flip-- inv-pow
Counts
2 → 282
Calls
2 calls:
Slowest
25.0ms
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))
8.0ms
(/ 1 (sqrt (+ x 1)))

series83.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
51.0ms
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))
32.0ms
(/ 1 (sqrt (+ x 1)))