Details

sample42.0ms

Algorithm

intervals

Results

14.0ms	56×	body	1280	valid
11.0ms	127×	body	80	valid
7.0ms	39×	body	640	valid
3.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify12.0ms

Calls

1 calls:

Slowest

12.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize22.0ms

Local error

Found 3 expressions with local error:

2.5b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`prod-diff` `add-cube-cbrt`
16×	`cbrt-prod`
6×	`fma-neg`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-div` `pow1/3` `difference-of-squares`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--` `distribute-lft-out--`

Calls

3 calls:

Slowest

16.0ms	(- (cbrt (+ x 1)) (cbrt x))
1.0ms	(cbrt (+ x 1))
0.0ms	(cbrt x)

series502.0ms

Calls

3 calls:

Slowest

301.0ms	(cbrt x)
133.0ms	(- (cbrt (+ x 1)) (cbrt x))
67.0ms	(cbrt (+ x 1))

simplify3.0s

Calls

61 calls:

Slowest

387.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
306.0ms	(- (+ (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))))
189.0ms	(- (+ (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)))))
161.0ms	(- (+ (* 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)))
131.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune747.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.9b

localize15.0ms

Local error

Found 4 expressions with local error:

30.7b	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt x)))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `cbrt-div` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`flip3-+` `flip-+`
1×	`fma-udef`

Calls

4 calls:

Slowest

1.0ms	(cbrt (+ x 1))
1.0ms	(cbrt (+ x 1))
0.0ms	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt x)))
0.0ms	(cbrt x)

series457.0ms

Calls

4 calls:

Slowest

246.0ms	(cbrt x)
128.0ms	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt x)))
43.0ms	(cbrt (+ x 1))
40.0ms	(cbrt (+ x 1))

simplify2.1s

Calls

22 calls:

Slowest

362.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow x 1/3)) (+ (pow (/ 1 x) -1/3) (* 1/9 (pow (/ 1 (pow x 5)) 1/3))))
327.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
305.0ms	(- (+ (* 1/3 (* (pow (/ 1 (pow x 7)) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x))))))) (* (pow (pow x 2) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x))))))) (+ (* (pow (* x -1) 1/3) (cbrt -1)) (* 1/9 (* (pow (/ 1 (pow x 16)) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x)))))))))
266.0ms	(- (+ (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))))
228.0ms	(- (+ (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))))

prune845.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.9b

localize25.0ms

Local error

Found 4 expressions with local error:

30.7b	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))) (- (cbrt x)))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `cbrt-div` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`flip3-+` `flip-+`
1×	`fma-udef`

Calls

4 calls:

Slowest

1.0ms	(cbrt (+ x 1))
1.0ms	(cbrt (+ x 1))
0.0ms	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))) (- (cbrt x)))
0.0ms	(cbrt x)

series498.0ms

Calls

4 calls:

Slowest

208.0ms	(cbrt x)
157.0ms	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))) (- (cbrt x)))
71.0ms	(cbrt (+ x 1))
62.0ms	(cbrt (+ x 1))

simplify2.6s

Calls

22 calls:

Slowest

486.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
373.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow x 1/3)) (+ (pow (/ 1 x) -1/3) (* 1/9 (pow (/ 1 (pow x 5)) 1/3))))
339.0ms	(- (+ (* 1/3 (* (pow (/ 1 (pow x 7)) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x))))))) (* (pow (pow x 2) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x))))))) (+ (* (pow (* x -1) 1/3) (cbrt -1)) (* 1/9 (* (pow (/ 1 (pow x 16)) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x)))))))))
331.0ms	(- (+ (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))))
255.0ms	(- (+ (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))))

prune887.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.9b

localize15.0ms

Local error

Found 4 expressions with local error:

30.7b	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Calls

4 calls:

Slowest

0.0ms	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))
0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)

series961.0ms

Calls

4 calls:

Slowest

298.0ms	(cbrt x)
275.0ms	(cbrt x)
262.0ms	(cbrt x)
125.0ms	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))))

simplify1.6s

Calls

12 calls:

Slowest

786.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow x 1/3)) (+ (pow (/ 1 x) -1/3) (* 1/9 (pow (/ 1 (pow x 5)) 1/3))))
396.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
357.0ms	(- (+ (* 1/3 (* (pow (/ 1 (pow x 7)) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x))))))) (* (pow (pow x 2) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x))))))) (+ (* (pow (* x -1) 1/3) (cbrt -1)) (* 1/9 (* (pow (/ 1 (pow x 16)) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x)))))))))
21.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
17.0ms	(* (pow (* x -1) 1/3) (cbrt -1))

prune800.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.9b

regimes87.0ms

Accuracy

99.6% (0.1b remaining)

Error of 15.6b against oracle of 15.6b and baseline of 29.7b

bsearch137.0ms

end0.0ms

sample1.4s

Algorithm

intervals

Results

545.0ms	1729×	body	1280	valid
345.0ms	1213×	body	640	valid
313.0ms	4134×	body	80	valid
95.0ms	619×	body	320	valid
32.0ms	305×	body	160	valid