Details

sample29.0ms

Algorithm

intervals

Results

10.0ms	59×	body	1280	valid
6.0ms	42×	body	640	valid
4.0ms	126×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	12×	body	160	valid

simplify20.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

20.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

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

24.0ms	(- (cbrt (+ x 1)) (cbrt x))
2.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series465.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

270.0ms	(cbrt x)
135.0ms	(- (cbrt (+ x 1)) (cbrt x))
59.0ms	(cbrt (+ x 1))

simplify1.9s

Counts

32 → 56

Calls

32 calls:

Slowest

321.0ms	(- (+ (* 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)))
287.0ms	(- (+ (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)))))
249.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
248.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
168.0ms	(- (+ (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))))

prune557.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize59.0ms

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)

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

series823.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

276.0ms	(cbrt (- x))
264.0ms	(cbrt x)
249.0ms	(cbrt x)
33.0ms	(/ -1/9 x)

simplify898.0ms

Counts

52 → 83

Calls

52 calls:

Slowest

246.0ms	(/ (* (* -1/9 -1/9) -1/9) (* (* x x) x))
143.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
130.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
37.0ms	(* (pow x 1/3) (cbrt -1))
32.0ms	(* (pow x 1/3) (cbrt -1))

prune847.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize87.0ms

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

304.0ms	(cbrt x)
282.0ms	(cbrt x)
272.0ms	(cbrt (- x))
262.0ms	(cbrt x)

simplify729.0ms

Counts

31 → 67

Calls

31 calls:

Slowest

148.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
146.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
144.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
35.0ms	(pow (/ 1 x) -1/3)
32.0ms	(pow (/ 1 x) -1/3)

prune840.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.2b

localize70.0ms

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)

rewrite7.0ms

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

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

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

457.0ms	(cbrt (* (cbrt x) (cbrt x)))
317.0ms	(cbrt (- x))
279.0ms	(cbrt x)
269.0ms	(cbrt x)

simplify720.0ms

Counts

29 → 65

Calls

29 calls:

Slowest

175.0ms	(* (pow (pow x 2) 1/9) (pow (pow (cbrt -1) 2) 1/3))
144.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
141.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
34.0ms	(* (pow x 1/3) (cbrt -1))
33.0ms	(pow (/ 1 x) -2/9)

prune868.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

regimes270.0ms

Accuracy

99.3% (0.2b remaining)

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

bsearch11.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.1s	1715×	body	1280	valid
263.0ms	1263×	body	640	valid
247.0ms	4095×	body	80	valid
137.0ms	596×	body	320	valid
36.0ms	331×	body	160	valid