Details

sample31.0ms

Algorithm

intervals

Results

10.0ms	56×	body	1280	valid
5.0ms	127×	body	80	valid
5.0ms	39×	body	640	valid
2.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify23.0ms

Calls

1 calls:

Slowest

22.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize22.0ms

Local error

Found 3 expressions with local error:

2.5b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

3 calls:

Slowest

14.0ms	(- (cbrt (+ x 1)) (cbrt x))
1.0ms	(cbrt (+ x 1))
0.0ms	(cbrt x)

series426.0ms

Calls

3 calls:

Slowest

265.0ms	(cbrt x)
114.0ms	(- (cbrt (+ x 1)) (cbrt x))
48.0ms	(cbrt (+ x 1))

simplify1.4s

Calls

20 calls:

Slowest

280.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
256.0ms	(- (+ (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))))
167.0ms	(- (+ (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)))))
166.0ms	(- (+ (* 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)))
121.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune472.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize60.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.4b	(/ 1/9 x)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`cbrt-prod` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3`
1×	`clear-num` `neg-mul-1` `frac-2neg` `div-inv`

Calls

4 calls:

Slowest

1.0ms	(cbrt (- x))
0.0ms	(/ 1/9 x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)

series899.0ms

Calls

4 calls:

Slowest

305.0ms	(cbrt x)
296.0ms	(cbrt (- x))
280.0ms	(cbrt x)
17.0ms	(/ 1/9 x)

simplify110.0ms

Calls

16 calls:

Slowest

17.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
14.0ms	(* (pow x 1/3) (cbrt -1))
12.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
11.0ms	(pow (/ 1 x) -1/3)
10.0ms	(* (pow x 1/3) (cbrt -1))

prune592.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (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))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

82×	`cbrt-div`
28×	`frac-times` `flip3-+` `flip-+`
14×	`associate-*l/`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`cbrt-prod` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `pow3` `rem-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Calls

4 calls:

Slowest

21.0ms	(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt x))
11.0ms	(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))
1.0ms	(cbrt (+ x 1))
0.0ms	(cbrt x)

series486.0ms

Calls

4 calls:

Slowest

301.0ms	(cbrt x)
97.0ms	(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt x))
50.0ms	(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))
38.0ms	(cbrt (+ x 1))

simplify4.4s

Calls

49 calls:

Slowest

335.0ms	(- (+ (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))))
307.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
285.0ms	(- (+ (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))))
217.0ms	(- (+ (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)))))
158.0ms	(- (+ (* 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)))

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`cbrt-prod` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `add-log-exp`
1×	`neg-mul-1`

Calls

4 calls:

Slowest

1.0ms	(cbrt (- x))
0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)

series1.2s

Calls

4 calls:

Slowest

330.0ms	(cbrt (- x))
292.0ms	(cbrt x)
291.0ms	(cbrt x)
239.0ms	(cbrt x)

simplify112.0ms

Calls

16 calls:

Slowest

21.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
12.0ms	(pow (/ 1 x) -1/3)
12.0ms	(pow (/ 1 x) -1/3)
11.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
10.0ms	(* (pow (* x -1) 1/3) (cbrt -1))

prune510.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

regimes81.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 32.0b

bsearch138.0ms

end0.0ms

sample1.4s

Algorithm

intervals

Results

605.0ms	1729×	body	1280	valid
301.0ms	1213×	body	640	valid
292.0ms	4134×	body	80	valid
103.0ms	619×	body	320	valid
32.0ms	305×	body	160	valid