Details

sample49.0ms

Algorithm

intervals

Results

16.0ms	51×	body	1280	valid
11.0ms	46×	body	640	valid
8.0ms	135×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	9×	body	160	valid

simplify35.0ms

Calls

1 calls:

Slowest

35.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize10.0ms

Local error

Found 3 expressions with local error:

1.8b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))

rewrite9.0ms

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

7.0ms	(- (cbrt (+ x 1)) (cbrt x))
1.0ms	(cbrt (+ x 1))
0.0ms	(cbrt x)

series413.0ms

Calls

3 calls:

Slowest

275.0ms	(cbrt x)
106.0ms	(- (cbrt (+ x 1)) (cbrt x))
33.0ms	(cbrt (+ x 1))

simplify1.6s

Calls

20 calls:

Slowest

386.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
328.0ms	(- (+ (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))))
216.0ms	(- (+ (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)))))
147.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
139.0ms	(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))

prune470.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize1.0ms

Local error

Found 3 expressions with local error:

1.8b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))

rewrite16.0ms

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

13.0ms	(- (cbrt (+ x 1)) (cbrt x))
1.0ms	(cbrt (+ x 1))
0.0ms	(cbrt x)

series428.0ms

Calls

3 calls:

Slowest

296.0ms	(cbrt x)
101.0ms	(- (cbrt (+ x 1)) (cbrt x))
31.0ms	(cbrt (+ x 1))

simplify1.5s

Calls

20 calls:

Slowest

326.0ms	(- (+ (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))))
296.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
206.0ms	(- (+ (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)))))
167.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
145.0ms	(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))

prune352.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize28.0ms

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)

series753.0ms

Calls

4 calls:

Slowest

260.0ms	(cbrt (- x))
256.0ms	(cbrt x)
230.0ms	(cbrt x)
7.0ms	(/ 1/9 x)

simplify124.0ms

Calls

16 calls:

Slowest

20.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
19.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
15.0ms	(pow (/ 1 x) -1/3)
8.0ms	(pow (/ 1 x) -1/3)
7.0ms	(cbrt (* (cbrt (- x)) (cbrt (- x))))

prune556.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

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

4.0ms	(cbrt x)
1.0ms	(cbrt (- x))
0.0ms	(cbrt x)
0.0ms	(cbrt x)

series1.1s

Calls

4 calls:

Slowest

300.0ms	(cbrt (- x))
288.0ms	(cbrt x)
266.0ms	(cbrt x)
248.0ms	(cbrt x)

simplify144.0ms

Calls

16 calls:

Slowest

20.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
17.0ms	(pow (/ 1 x) -1/3)
16.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
14.0ms	(pow (/ 1 x) -1/3)
11.0ms	(* (pow x 1/3) (cbrt -1))

prune660.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.2b

regimes204.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 29.8b

bsearch6.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

523.0ms	1706×	body	1280	valid
302.0ms	1282×	body	640	valid
266.0ms	4096×	body	80	valid
120.0ms	616×	body	320	valid
28.0ms	300×	body	160	valid