Details

sample52.0ms

Algorithm

intervals

Results

19.0ms	51×	body	1280	valid
11.0ms	46×	body	640	valid
8.0ms	135×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	9×	body	160	valid

simplify20.0ms

Calls

1 calls:

Slowest

20.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize15.0ms

Local error

Found 3 expressions with local error:

1.8b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))

rewrite9.0ms

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

7.0ms	(- (cbrt (+ x 1)) (cbrt x))
1.0ms	(cbrt (+ x 1))
0.0ms	(cbrt x)

series381.0ms

Calls

3 calls:

Slowest

241.0ms	(cbrt x)
102.0ms	(- (cbrt (+ x 1)) (cbrt x))
38.0ms	(cbrt (+ x 1))

simplify3.1s

Calls

61 calls:

Slowest

418.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
338.0ms	(- (+ (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))))
258.0ms	(- (+ (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)))))
183.0ms	(- (+ (* 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)))
140.0ms	(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))

prune634.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.8b

localize11.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))
0.3b	(cbrt (+ x 1))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

82×	`cbrt-div`
28×	`frac-times` `flip3-+` `flip-+`
15×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`associate-*l/`
13×	`add-cube-cbrt`
12×	`prod-diff`
8×	`cbrt-prod` `associate-*r/`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `pow3` `rem-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Calls

4 calls:

Slowest

16.0ms	(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt x))
11.0ms	(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))
1.0ms	(cbrt (+ x 1))
0.0ms	(cbrt x)

series463.0ms

Calls

4 calls:

Slowest

253.0ms	(cbrt x)
104.0ms	(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt x))
54.0ms	(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))
50.0ms	(cbrt (+ x 1))

simplify6.1s

Calls

76 calls:

Slowest

449.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
359.0ms	(- (+ (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))))
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))))
228.0ms	(- (+ (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)))))
180.0ms	(- (+ (* 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)))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.7b

localize11.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (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)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `prod-diff`
23×	`cbrt-prod`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `pow3` `rem-cbrt-cube` `flip--` `distribute-lft-out--`

Calls

4 calls:

Slowest

14.0ms	(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))
10.0ms	(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
0.0ms	(cbrt x)
0.0ms	(cbrt x)

series940.0ms

Calls

4 calls:

Slowest

318.0ms	(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
279.0ms	(cbrt x)
254.0ms	(cbrt x)
89.0ms	(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))

simplify3.9s

Calls

72 calls:

Slowest

353.0ms	(- (+ (* 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))) (+ (* (pow (* x -1) 1/3) (cbrt -1)) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2)))))
222.0ms	(- (+ (* 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)))
99.0ms	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (* (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))) 1)))
93.0ms	(fma (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (* (cbrt (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))) (cbrt (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))))))

prune763.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 15.7b

localize12.0ms

Local error

Found 4 expressions with local error:

8.6b	(- (cbrt (+ x 1)) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))
0.6b	(cbrt (* (cbrt x) (cbrt x)))
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod`
6×	`fma-neg` `prod-diff` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Calls

4 calls:

Slowest

18.0ms	(- (cbrt (+ x 1)) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))
2.0ms	(cbrt (* (cbrt x) (cbrt x)))
0.0ms	(cbrt x)
0.0ms	(cbrt x)

series1.1s

Calls

4 calls:

Slowest

396.0ms	(cbrt (* (cbrt x) (cbrt x)))
304.0ms	(cbrt x)
264.0ms	(cbrt x)
98.0ms	(- (cbrt (+ x 1)) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))

simplify1.6s

Calls

31 calls:

Slowest

425.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
204.0ms	(- (+ (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)))))
176.0ms	(- (+ (* 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)))
78.0ms	(fma 1 (cbrt (+ x 1)) (- (* (cbrt (cbrt x)) (cbrt (* (cbrt x) (cbrt x))))))
67.0ms	(/ (exp (cbrt (+ x 1))) (exp (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x)))))

prune814.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.7b

regimes150.0ms

Accuracy

99.7% (0.0b remaining)

Error of 15.4b against oracle of 15.4b and baseline of 29.9b

bsearch135.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

545.0ms	1706×	body	1280	valid
363.0ms	1282×	body	640	valid
292.0ms	4096×	body	80	valid
96.0ms	616×	body	320	valid
76.0ms	300×	body	160	valid