Details

sample42.0ms

Algorithm

intervals

Results

13.0ms	47×	body	1280	valid
10.0ms	48×	body	640	valid
7.0ms	133×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	12×	body	160	valid

simplify19.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

19.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize22.0ms

Local error

Found 3 expressions with local error:

3.0b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.2b	(cbrt (+ x 1))

rewrite30.0ms

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

27.0ms	(- (cbrt (+ x 1)) (cbrt x))
3.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series409.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

252.0ms	(cbrt x)
101.0ms	(- (cbrt (+ x 1)) (cbrt x))
56.0ms	(cbrt (+ x 1))

simplify1.7s

Counts

32 → 56

Calls

32 calls:

Slowest

247.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
223.0ms	(- (+ (* 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)))
222.0ms	(- (+ (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)))))
204.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
193.0ms	(- (+ (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))))

prune629.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))
0.6b	(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`cbrt-prod` `*-un-lft-identity`
6×	`add-cube-cbrt` `add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `pow3` `rem-cbrt-cube` `flip--` `distribute-lft-out--`

Counts

4 → 51

Calls

4 calls:

Slowest

36.0ms	(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))
12.0ms	(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series948.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

315.0ms	(cbrt x)
278.0ms	(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
244.0ms	(cbrt x)
110.0ms	(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))

simplify1.5s

Counts

25 → 63

Calls

25 calls:

Slowest

330.0ms	(- (+ (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)))))
285.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
246.0ms	(- (+ (* 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)))
164.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
116.0ms	(* (pow (* x -1) 1/3) (cbrt -1))

prune744.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize63.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 50

Calls

4 calls:

Slowest

83.0ms	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series955.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

288.0ms	(cbrt x)
275.0ms	(cbrt x)
236.0ms	(cbrt x)
156.0ms	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))

simplify1.4s

Counts

24 → 62

Calls

24 calls:

Slowest

277.0ms	(- (+ (* 2/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 2/3)))
263.0ms	(- (+ (* 4/81 (pow (/ 1 (pow x 7)) 1/3)) (* 2/3 (pow (/ 1 x) 1/3))) (* 1/9 (pow (/ 1 (pow x 4)) 1/3)))
166.0ms	(/ (exp (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (exp (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))))
162.0ms	(- (+ (* 2/3 (pow (/ 1 x) 1/3)) (pow (/ -1 x) -2/3)) (+ (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)) (* 1/9 (pow (/ 1 (pow x 4)) 1/3))))
142.0ms	(* (pow (* x -1) 1/3) (cbrt -1))

prune727.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize72.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))
1.2b	(log (exp (- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))))
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

Slowest

73.0ms	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))
54.0ms	(log (exp (- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series841.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

276.0ms	(cbrt x)
257.0ms	(cbrt x)
160.0ms	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))
148.0ms	(log (exp (- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))))

simplify3.2s

Counts

32 → 70

Calls

32 calls:

Slowest

274.0ms	(- (+ (* 2/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 2/3)))
265.0ms	(- (+ (* 2/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 2/3)))
257.0ms	(- (+ (* 4/81 (pow (/ 1 (pow x 7)) 1/3)) (* 2/3 (pow (/ 1 x) 1/3))) (* 1/9 (pow (/ 1 (pow x 4)) 1/3)))
234.0ms	(/ (exp (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (exp (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))))
227.0ms	(- (+ (* 4/81 (pow (/ 1 (pow x 7)) 1/3)) (* 2/3 (pow (/ 1 x) 1/3))) (* 1/9 (pow (/ 1 (pow x 4)) 1/3)))

prune809.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

regimes56.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 30.3b

bsearch125.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

673.0ms	1262×	body	640	valid
557.0ms	1733×	body	1280	valid
236.0ms	4058×	body	80	valid
162.0ms	611×	body	320	valid
44.0ms	336×	body	160	valid