Details

sample62.0ms

Algorithm

intervals

Results

15.0ms	288×	body	80	nan
14.0ms	54×	body	1280	valid
8.0ms	35×	body	640	valid
7.0ms	136×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify17.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

17.0ms

(- (sqrt (+ x 1)) (sqrt x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize10.0ms

Local error

Found 2 expressions with local error:

3.0b	(- (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))

rewrite39.0ms

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--`

Counts

2 → 37

Calls

2 calls:

Slowest

35.0ms	(- (sqrt (+ x 1)) (sqrt x))
4.0ms	(sqrt (+ x 1))

series114.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

69.0ms	(- (sqrt (+ x 1)) (sqrt x))
46.0ms	(sqrt (+ x 1))

simplify493.0ms

Counts

28 → 43

Calls

28 calls:

Slowest

101.0ms	(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
64.0ms	(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
44.0ms	(sqrt (+ (pow x 3) (pow 1 3)))
41.0ms	(sqrt (- (* x x) (* 1 1)))
22.0ms	(+ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

prune435.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 28.5b

localize46.0ms

Local error

Found 4 expressions with local error:

14.2b	(- (* (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))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 58

Calls

4 calls:

Slowest

62.0ms	(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (sqrt x))
7.0ms	(cbrt (+ x 1))
5.0ms	(cbrt (+ x 1))
5.0ms	(cbrt (+ x 1))

series247.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

93.0ms	(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (sqrt x))
59.0ms	(cbrt (+ x 1))
52.0ms	(cbrt (+ x 1))
43.0ms	(cbrt (+ x 1))

simplify2.0s

Counts

31 → 70

Calls

31 calls:

Slowest

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)))
227.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
212.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
190.0ms	(/ (exp (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))))) (exp (sqrt x)))
182.0ms	(- (+ (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))))

prune921.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 28.4b

localize51.0ms

Local error

Found 4 expressions with local error:

10.8b	(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))) (sqrt x))
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))
0.2b	(* (cbrt (+ x 1)) (cbrt (+ x 1)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-log-exp`
4×	`frac-times` `add-cbrt-cube` `insert-posit16` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip--`

Counts

4 → 97

Calls

4 calls:

Slowest

109.0ms	(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))) (sqrt x))
34.0ms	(* (cbrt (+ x 1)) (cbrt (+ x 1)))
2.0ms	(cbrt (+ x 1))
2.0ms	(cbrt (+ x 1))

series258.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

82.0ms	(- (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))) (sqrt x))
64.0ms	(* (cbrt (+ x 1)) (cbrt (+ x 1)))
57.0ms	(cbrt (+ x 1))
55.0ms	(cbrt (+ x 1))

simplify4.5s

Counts

89 → 109

Calls

89 calls:

Slowest

277.0ms	(* (cbrt (+ (pow x 3) (pow 1 3))) (cbrt (- (* x x) (* 1 1))))
274.0ms	(/ (exp (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))) (exp (sqrt x)))
266.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
263.0ms	(* (cbrt (- (* x x) (* 1 1))) (cbrt (+ (pow x 3) (pow 1 3))))
250.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune1.7s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 28.4b

localize57.0ms

Local error

Found 4 expressions with local error:

10.3b	(- (* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))) (* (sqrt x) (sqrt x)))
0.5b	(* (sqrt x) (sqrt x))
0.3b	(* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
0.3b	(cbrt (+ x 1))

rewrite3.6s

Algorithm

rewrite-expression-head

Rules

40824×	`sqrt-div`
34994×	`cbrt-div`
28432×	`frac-times`
17497×	`flip3-+` `flip-+`
7208×	`associate-l/` `associate-r/`
770×	`pow1`
548×	`sqrt-pow1`
458×	`pow-prod-down`
203×	`pow-prod-up`
115×	`pow-plus`
93×	`pow-sqr`
89×	`pow1/3`
36×	`pow1/2`
34×	`pow2`
25×	`add-sqr-sqrt`
18×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`swap-sqr` `prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-l`
6×	`sqrt-unprod` `add-log-exp`
4×	`cbrt-prod` `insert-posit16` `unswap-sqr`
2×	`rem-square-sqrt` `*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out` `difference-of-squares`

Counts

4 → 6818

Calls

4 calls:

Slowest

775.0ms	(- (* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))) (* (sqrt x) (sqrt x)))
661.0ms	(* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
16.0ms	(* (sqrt x) (sqrt x))
5.0ms	(cbrt (+ x 1))

series137.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

70.0ms	(cbrt (+ x 1))
32.0ms	(* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
18.0ms	(* (sqrt x) (sqrt x))
16.0ms	(- (* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))) (* (sqrt x) (sqrt x)))