Details

Time bar (total: 9.6m)

sample77.0ms

Algorithm
intervals
Results
19.0ms61×body1280valid
17.0ms37×body640valid
15.0ms253×body80nan
8.0ms131×body80valid
4.0ms21×body320valid
1.0ms6×body160valid

simplify18.0ms

Calls
1 calls:
Slowest
18.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize19.0ms

Local error

Found 2 expressions with local error:

1.7b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity sqrt-prod
4×add-log-exp difference-of-squares
3×pow1 add-cube-cbrt distribute-lft-out--
2×add-cbrt-cube sqrt-div add-exp-log insert-posit16 distribute-lft-out
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Calls
2 calls:
Slowest
57.0ms
(- (sqrt (+ x 1)) (sqrt x))
5.0ms
(sqrt (+ x 1))

series97.0ms

Calls
2 calls:
Slowest
70.0ms
(- (sqrt (+ x 1)) (sqrt x))
28.0ms
(sqrt (+ x 1))

simplify491.0ms

Calls
28 calls:
Slowest
81.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
65.0ms
(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
60.0ms
(sqrt (- (* x x) (* 1 1)))
49.0ms
(sqrt (+ (pow x 3) (pow 1 3)))
24.0ms
(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

prune441.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 29.4b

localize43.0ms

Local error

Found 4 expressions with local error:

14.9b
(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (sqrt x))
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))

rewrite846.0ms

Algorithm
rewrite-expression-head
Rules
215×add-sqr-sqrt
129×sqrt-prod
84×unswap-sqr
68×cbrt-prod
62×difference-of-squares
21×*-un-lft-identity
12×swap-sqr
7×add-cube-cbrt
6×cbrt-div *-commutative add-log-exp
4×pow1 add-cbrt-cube associate-*l* add-exp-log insert-posit16 distribute-lft-out--
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×sub-neg flip3-- diff-log flip--
Calls
4 calls:
Slowest
835.0ms
(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (sqrt x))
3.0ms
(cbrt (+ x 1))
3.0ms
(cbrt (+ x 1))
3.0ms
(cbrt (+ x 1))

series276.0ms

Calls
4 calls:
Slowest
87.0ms
(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (sqrt x))
65.0ms
(cbrt (+ x 1))
63.0ms
(cbrt (+ x 1))
60.0ms
(cbrt (+ x 1))

simplify6.1s

Calls
161 calls:
Slowest
274.0ms
(/ (exp (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))))) (exp (sqrt x)))
252.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
239.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
210.0ms
(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2))))
206.0ms
(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2))))

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 29.3b

localize61.0ms

Local error

Found 4 expressions with local error:

16.1b
(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (sqrt x))
0.3b
(cbrt (cbrt (+ x 1)))
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))

rewrite3.3s

Algorithm
rewrite-expression-head
Rules
3028×add-sqr-sqrt
1903×cbrt-prod
1736×unswap-sqr
1521×sqrt-prod
642×difference-of-squares
248×swap-sqr
124×*-commutative
22×*-un-lft-identity
8×cbrt-div add-cube-cbrt
6×add-log-exp
4×pow1 add-cbrt-cube associate-*l* add-exp-log insert-posit16 distribute-lft-out--
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×sub-neg flip3-- diff-log flip--
Calls
4 calls:
Slowest
3.2s
(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (sqrt x))
3.0ms
(cbrt (cbrt (+ x 1)))
3.0ms
(cbrt (+ x 1))
3.0ms
(cbrt (+ x 1))

series243.0ms

Calls
4 calls:
Slowest
99.0ms
(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (sqrt x))
50.0ms
(cbrt (+ x 1))
49.0ms
(cbrt (cbrt (+ x 1)))
44.0ms
(cbrt (+ x 1))

simplify1.0m

Calls
1324 calls:
Slowest
302.0ms
(/ (exp (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))))) (exp (sqrt x)))
276.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
259.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
244.0ms
(- (+ (pow (/ 1 x) -1/9) (* 1/9 (pow (/ 1 (pow x 8)) 1/9))) (* 4/81 (pow (/ 1 (pow x 17)) 1/9)))
214.0ms
(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2))))

prune13.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 29.3b

localize50.0ms

Local error

Found 4 expressions with local error:

16.8b
(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (sqrt (cbrt (+ x 1)))) (cbrt (sqrt (cbrt (+ x 1)))))))) (sqrt x))
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))

rewrite6.7s

Algorithm
rewrite-expression-head
Rules
28147×add-sqr-sqrt
19336×cbrt-prod
17256×unswap-sqr
16481×sqrt-prod
5042×difference-of-squares
3208×swap-sqr
1204×*-commutative
21×*-un-lft-identity
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-cbrt-cube associate-*l* add-exp-log insert-posit16 distribute-lft-out--
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×sub-neg flip3-- diff-log flip--
Calls
4 calls:
Slowest
5.8s
(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (sqrt (cbrt (+ x 1)))) (cbrt (sqrt (cbrt (+ x 1)))))))) (sqrt x))
5.0ms
(cbrt (+ x 1))
5.0ms
(cbrt (+ x 1))
5.0ms
(cbrt (+ x 1))

series247.0ms

Calls
4 calls:
Slowest
77.0ms
(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* (cbrt (sqrt (cbrt (+ x 1)))) (cbrt (sqrt (cbrt (+ x 1)))))))) (sqrt x))
61.0ms
(cbrt (+ x 1))
59.0ms
(cbrt (+ x 1))
50.0ms
(cbrt (+ x 1))

simplify8.0m

Calls
10121 calls:
Slowest
755.0ms
(+ (* (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (sqrt (* (cbrt (* (sqrt (cbrt (+ x 1))) (sqrt (cbrt (+ x 1))))) (* (cbrt (sqrt (cbrt (sqrt (+ x 1))))) (cbrt (sqrt (cbrt (sqrt (+ x 1))))))))) (sqrt (sqrt x)))
726.0ms
(- (* (sqrt (cbrt (+ x 1))) (sqrt (* (cbrt (* (cbrt (sqrt (+ x 1))) (sqrt (cbrt (+ x 1))))) (* (sqrt (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (sqrt (+ x 1))))))))) (sqrt (sqrt x)))
504.0ms
(- (* (sqrt (* (sqrt (cbrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (sqrt (* (cbrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (sqrt (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (sqrt (+ x 1))))))))) (sqrt (sqrt x)))
500.0ms
(+ (* (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (sqrt (* (cbrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (sqrt (cbrt (sqrt (cbrt (+ x 1))))) (sqrt (cbrt (sqrt (cbrt (+ x 1))))))))) (sqrt (sqrt x)))
467.0ms
(+ (* (sqrt (cbrt (+ x 1))) (sqrt (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))))) (sqrt (sqrt x)))