Details

sample55.0ms

Algorithm

intervals

Results

19.0ms	58×	body	1280	valid
14.0ms	142×	body	80	valid
7.0ms	29×	body	640	valid
4.0ms	19×	body	320	valid
1.0ms	8×	body	160	valid

simplify20.0ms

Calls

1 calls:

Slowest

20.0ms

(- (cbrt (+ x 1)) (cbrt x))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize22.0ms

Local error

Found 3 expressions with local error:

2.3b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3` `distribute-lft-out`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Calls

3 calls:

Slowest

50.0ms	(- (cbrt (+ x 1)) (cbrt x))
15.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series507.0ms

Calls

3 calls:

Slowest

302.0ms	(cbrt x)
142.0ms	(- (cbrt (+ x 1)) (cbrt x))
63.0ms	(cbrt (+ x 1))

simplify2.0s

Calls

32 calls:

Slowest

385.0ms	(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (+ (* (pow (* x -1) 1/3) (cbrt -1)) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2)))))
279.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (* 5/81 (pow (/ 1 (pow x 8)) 1/3))) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
267.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
226.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
187.0ms	(- (+ (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))))

prune626.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))
0.3b	(cbrt (+ x 1))

rewrite839.0ms

Algorithm

rewrite-expression-head

Rules

224×	`cbrt-prod`
202×	`add-sqr-sqrt`
82×	`cbrt-div` `unswap-sqr`
44×	`*-un-lft-identity`
42×	`associate-l`
40×	`difference-of-squares`
28×	`frac-times` `flip3-+` `flip-+`
21×	`swap-sqr`
18×	`add-cube-cbrt`
14×	`associate-r` `associate-*l/`
9×	`*-commutative`
8×	`associate-*r/` `distribute-lft-out`
6×	`add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `distribute-lft-out--`
3×	`pow1/3`
2×	`pow3` `rem-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Calls

4 calls:

Slowest

698.0ms	(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt x))
126.0ms	(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))
5.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series503.0ms

Calls

4 calls:

Slowest

309.0ms	(cbrt x)
109.0ms	(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt x))
42.0ms	(cbrt (+ x 1))
42.0ms	(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))

simplify13.0s

Calls

199 calls:

Slowest

369.0ms	(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (+ (* (pow (* x -1) 1/3) (cbrt -1)) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2)))))
307.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
300.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (* 5/81 (pow (/ 1 (pow x 8)) 1/3))) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
292.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
283.0ms	(cbrt (* (* (cbrt (- (* x x) (* 1 1))) (cbrt (+ (pow x 3) (pow 1 3)))) (cbrt (+ (pow x 3) (pow 1 3)))))

prune2.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize58.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))) (* (cbrt x) (cbrt x)))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite5.7s

Algorithm

rewrite-expression-head

Rules

23563×	`add-sqr-sqrt`
18249×	`cbrt-prod`
15456×	`unswap-sqr`
3915×	`difference-of-squares`
2762×	`swap-sqr`
1236×	`*-commutative`
61×	`*-un-lft-identity`
31×	`associate-l`
17×	`distribute-lft-out--`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Calls

4 calls:

Slowest

4.7s	(- (* (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))) (* (cbrt x) (cbrt x)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.1s

Calls

4 calls:

Slowest

350.0ms	(cbrt x)
302.0ms	(cbrt x)
297.0ms	(cbrt x)
139.0ms	(- (* (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))) (* (cbrt x) (cbrt x)))