Details

sample40.0ms

Algorithm

intervals

Results

17.0ms	51×	body	1280	valid
6.0ms	143×	body	80	valid
5.0ms	31×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	12×	body	160	valid

simplify17.0ms

Calls

1 calls:

Slowest

17.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize26.0ms

Local error

Found 3 expressions with local error:

2.6b	(- (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

14.0ms	(- (cbrt (+ x 1)) (cbrt x))
1.0ms	(cbrt (+ x 1))
0.0ms	(cbrt x)

series459.0ms

Calls

3 calls:

Slowest

286.0ms	(cbrt x)
138.0ms	(- (cbrt (+ x 1)) (cbrt x))
35.0ms	(cbrt (+ x 1))

simplify1.6s

Calls

20 calls:

Slowest

364.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
303.0ms	(- (+ (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))))
212.0ms	(- (+ (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)))))
173.0ms	(- (+ (* 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)))
113.0ms	(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))

prune437.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (cbrt (+ 1 x)) (cbrt x))
2.0b	(log (exp (- (cbrt (+ 1 x)) (cbrt x))))
0.6b	(cbrt x)
0.3b	(cbrt (+ 1 x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

30.0ms	(log (exp (- (cbrt (+ 1 x)) (cbrt x))))
13.0ms	(- (cbrt (+ 1 x)) (cbrt x))
1.0ms	(cbrt (+ 1 x))
0.0ms	(cbrt x)

series527.0ms

Calls

4 calls:

Slowest

276.0ms	(cbrt x)
110.0ms	(- (cbrt (+ 1 x)) (cbrt x))
92.0ms	(log (exp (- (cbrt (+ 1 x)) (cbrt x))))
50.0ms	(cbrt (+ 1 x))

simplify2.6s

Calls

36 calls:

Slowest

384.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
335.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
285.0ms	(- (+ (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))))
212.0ms	(- (+ (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)))))
173.0ms	(- (+ (* 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)))

prune776.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

13.7b	(cbrt (+ -1 (* x x)))
13.1b	(- (/ (cbrt (+ -1 (* x x))) (cbrt (- x 1))) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (- x 1))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

18.0ms	(- (/ (cbrt (+ -1 (* x x))) (cbrt (- x 1))) (cbrt x))
1.0ms	(cbrt (+ -1 (* x x)))
1.0ms	(cbrt (- x 1))
0.0ms	(cbrt x)

series565.0ms

Calls

4 calls:

Slowest

260.0ms	(cbrt x)
137.0ms	(- (/ (cbrt (+ -1 (* x x))) (cbrt (- x 1))) (cbrt x))
114.0ms	(cbrt (+ -1 (* x x)))
53.0ms	(cbrt (- x 1))

simplify4.4s

Calls

34 calls:

Slowest

414.0ms	(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
405.0ms	(- (* (pow (* x -1) 1/3) (cbrt -1)) (+ (* 1/9 (* (pow (/ -1 (pow x 5)) 1/3) (cbrt -1))) (* 1/3 (* (pow (/ -1 (pow x 2)) 1/3) (cbrt -1)))))
356.0ms	(cbrt (- (* -1 -1) (* (* x x) (* x x))))
323.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
293.0ms	(- (+ (* 1/3 (* (pow (/ -1 (pow x 2)) 1/3) (/ 1 (cbrt -1)))) (* (pow (* x -1) 1/3) (/ 1 (cbrt -1)))) (+ (* 1/9 (* (pow (/ -1 (pow x 5)) 1/3) (/ 1 (cbrt -1)))) (* (pow (* x -1) 1/3) (cbrt -1))))

prune636.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

13.6b	(- (pow (+ 1 x) 1/3) (cbrt x))
4.2b	(log (exp (- (pow (+ 1 x) 1/3) (cbrt x))))
1.1b	(pow (+ 1 x) 1/3)
0.6b	(cbrt x)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
7×	`log-pow` `add-cube-cbrt`
6×	`pow1` `exp-prod` `add-log-exp`
5×	`log-prod` `unpow-prod-down` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `difference-of-squares`
2×	`sub-neg` `exp-sum` `distribute-lft-out--`
1×	`pow-to-exp` `log-div` `pow-pow` `flip3--` `exp-diff` `unpow1/3` `pow1/3` `diff-log` `rem-log-exp` `pow-exp` `flip--`

Calls

4 calls:

Slowest

16.0ms	(log (exp (- (pow (+ 1 x) 1/3) (cbrt x))))
8.0ms	(- (pow (+ 1 x) 1/3) (cbrt x))
1.0ms	(pow (+ 1 x) 1/3)
0.0ms	(cbrt x)

series543.0ms

Calls

4 calls:

Slowest

279.0ms	(cbrt x)
119.0ms	(- (pow (+ 1 x) 1/3) (cbrt x))
108.0ms	(log (exp (- (pow (+ 1 x) 1/3) (cbrt x))))
36.0ms	(pow (+ 1 x) 1/3)

simplify2.5s

Calls

36 calls:

Slowest

355.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
334.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
264.0ms	(- (+ (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))))
242.0ms	(- (+ (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	(- (+ (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)))))

prune641.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes67.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 30.2b

bsearch119.0ms

end0.0ms

sample1.4s

Algorithm

intervals

Results

524.0ms	1737×	body	1280	valid
363.0ms	1199×	body	640	valid
242.0ms	4092×	body	80	valid
96.0ms	646×	body	320	valid
33.0ms	326×	body	160	valid