Details

sample40.0ms

Algorithm

intervals

Results

12.0ms	56×	body	1280	valid
10.0ms	46×	body	640	valid
6.0ms	122×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	12×	body	160	valid

simplify20.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

19.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize22.0ms

Local error

Found 3 expressions with local error:

3.4b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))

rewrite70.0ms

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

63.0ms	(- (cbrt (+ x 1)) (cbrt x))
5.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series455.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

277.0ms	(cbrt x)
126.0ms	(- (cbrt (+ x 1)) (cbrt x))
51.0ms	(cbrt (+ x 1))

simplify2.0s

Counts

32 → 56

Calls

32 calls:

Slowest

299.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
282.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
265.0ms	(- (+ (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)))))
214.0ms	(- (+ (* 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)))
190.0ms	(- (+ (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))))

prune569.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.3b	(/ -1/9 x)

rewrite14.0ms

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

7.0ms	(/ -1/9 x)
3.0ms	(cbrt (- x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series917.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

323.0ms	(cbrt (- x))
309.0ms	(cbrt x)
257.0ms	(cbrt x)
29.0ms	(/ -1/9 x)

simplify962.0ms

Counts

52 → 83

Calls

52 calls:

Slowest

272.0ms	(/ (* (* -1/9 -1/9) -1/9) (* (* x x) x))
142.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
122.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
55.0ms	(/ (* (cbrt -1/9) (cbrt -1/9)) (* (cbrt x) (cbrt x)))
35.0ms	(* (pow x 1/3) (cbrt -1))

prune952.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite7.0ms

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

2.0ms	(cbrt (- x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

298.0ms	(cbrt (- x))
269.0ms	(cbrt x)
233.0ms	(cbrt x)
220.0ms	(cbrt x)

simplify712.0ms

Counts

31 → 67

Calls

31 calls:

Slowest

149.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
148.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
129.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
33.0ms	(pow (/ 1 x) -1/3)
31.0ms	(* (pow x 1/3) (cbrt -1))

prune925.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

localize82.0ms

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)

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

298.0ms	(cbrt (- x))
298.0ms	(cbrt x)
272.0ms	(cbrt x)
261.0ms	(cbrt x)

simplify596.0ms

Counts

31 → 67

Calls

31 calls:

Slowest

124.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
118.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
100.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
40.0ms	(* (pow x 1/3) (cbrt -1))
36.0ms	(* (pow x 1/3) (cbrt -1))

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.2b

regimes216.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 31.5b

bsearch13.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

645.0ms	4071×	body	80	valid
602.0ms	1761×	body	1280	valid
347.0ms	1217×	body	640	valid
105.0ms	641×	body	320	valid
33.0ms	310×	body	160	valid