Details

sample46.0ms

Algorithm

intervals

Results

17.0ms	59×	body	1280	valid
10.0ms	42×	body	640	valid
7.0ms	126×	body	80	valid
3.0ms	17×	body	320	valid
1.0ms	12×	body	160	valid

simplify11.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

11.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize14.0ms

Local error

Found 3 expressions with local error:

3.5b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))

rewrite75.0ms

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--`

Counts

3 → 47

Calls

3 calls:

Slowest

67.0ms	(- (cbrt (+ x 1)) (cbrt x))
5.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series450.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

268.0ms	(cbrt x)
147.0ms	(- (cbrt (+ x 1)) (cbrt x))
35.0ms	(cbrt (+ x 1))

simplify1.8s

Counts

32 → 56

Calls

32 calls:

Slowest

291.0ms	(- (+ (* 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)))
290.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
246.0ms	(- (+ (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)))))
184.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
155.0ms	(* (pow (* x -1) 1/3) (cbrt -1))

prune494.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize48.0ms

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)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`cbrt-prod`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `insert-posit16` `add-log-exp`
3×	`distribute-lft-neg-in` `associate-/r` `distribute-rgt-neg-in` `pow1/3` `associate-/l`
1×	`cbrt-undiv` `clear-num` `neg-mul-1` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 71

Calls

4 calls:

Slowest

4.0ms	(/ -1/9 x)
1.0ms	(cbrt (- x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series891.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

346.0ms	(cbrt x)
260.0ms	(cbrt (- x))
255.0ms	(cbrt x)
30.0ms	(/ -1/9 x)

simplify1.1s

Counts

52 → 83

Calls

52 calls:

Slowest

372.0ms	(/ (* (* -1/9 -1/9) -1/9) (* (* x x) x))
150.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
130.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
60.0ms	(/ (* (cbrt -1/9) (cbrt -1/9)) (* (cbrt x) (cbrt x)))
32.0ms	(pow (/ 1 x) -1/3)

prune936.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

Slowest

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

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

309.0ms	(cbrt x)
286.0ms	(cbrt x)
285.0ms	(cbrt (- x))
274.0ms	(cbrt x)

simplify707.0ms

Counts

31 → 67

Calls

31 calls:

Slowest

163.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
150.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
124.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
37.0ms	(* (pow x 1/3) (cbrt -1))
32.0ms	(pow (/ 1 x) -1/3)

prune925.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.2b

localize62.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* (cbrt x) (cbrt x)))
0.6b	(cbrt (- x))
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

Slowest

8.0ms	(cbrt (* (cbrt x) (cbrt x)))
3.0ms	(cbrt (- x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

443.0ms	(cbrt (* (cbrt x) (cbrt x)))
332.0ms	(cbrt x)
311.0ms	(cbrt x)
293.0ms	(cbrt (- x))

simplify669.0ms

Counts

29 → 65

Calls

29 calls:

Slowest

173.0ms	(* (pow (pow x 2) 1/9) (pow (pow (cbrt -1) 2) 1/3))
164.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
98.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
35.0ms	(* (pow x 1/3) (cbrt -1))
32.0ms	(pow (/ 1 x) -1/3)

prune931.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

regimes284.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 31.7b

bsearch7.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

924.0ms	1715×	body	1280	valid
368.0ms	1263×	body	640	valid
213.0ms	4095×	body	80	valid
90.0ms	596×	body	320	valid
33.0ms	331×	body	160	valid