Details

sample41.0ms

Algorithm

intervals

Results

14.0ms	57×	body	1280	valid
8.0ms	44×	body	640	valid
6.0ms	132×	body	80	valid
3.0ms	17×	body	320	valid
1.0ms	6×	body	160	valid

simplify13.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

13.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
56×	`*-un-lft-identity`
42×	`prod-diff`
41×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
5×	`add-log-exp`
4×	`difference-of-squares`
3×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

3 → 102

Calls

3 calls:

Slowest

66.0ms	(- (cbrt (+ x 1)) (cbrt x))
5.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series415.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

280.0ms	(cbrt x)
89.0ms	(- (cbrt (+ x 1)) (cbrt x))
46.0ms	(cbrt (+ x 1))

simplify7.2s

Counts

122 → 111

Calls

122 calls:

Slowest

365.0ms	(- (+ (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)))))
315.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
288.0ms	(- (+ (* 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)))
244.0ms	(fma (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (cbrt x)) (* (cbrt (cbrt x)) (cbrt (cbrt x))))))
227.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune943.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.2b

localize39.0ms

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))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

82×	`cbrt-div`
28×	`cbrt-prod` `frac-times` `flip3-+` `flip-+`
25×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`prod-diff`
21×	`add-cube-cbrt`
14×	`associate-*l/`
8×	`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`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `pow3` `rem-cbrt-cube` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

Slowest

64.0ms	(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))
22.0ms	(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt x))
5.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series453.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

253.0ms	(cbrt x)
115.0ms	(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt x))
44.0ms	(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))
41.0ms	(cbrt (+ x 1))

simplify11.6s

Counts

106 → 128

Calls

106 calls:

Slowest

373.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
365.0ms	(- (+ (* 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)))
334.0ms	(- (+ (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)))))
292.0ms	(cbrt (* (* (cbrt (+ (pow x 3) (pow 1 3))) (cbrt (- (* x x) (* 1 1)))) (cbrt (- (* x x) (* 1 1)))))
280.0ms	(cbrt (* (* (cbrt (+ x 1)) (cbrt (- (* x x) (* 1 1)))) (cbrt (+ (pow x 3) (pow 1 3)))))

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.2b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

1434×	`cbrt-div`
568×	`frac-times`
406×	`flip3-+` `flip-+`
188×	`associate-*l/`
152×	`associate-*r/`
35×	`cbrt-prod`
26×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`prod-diff`
22×	`add-cube-cbrt`
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`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 334

Calls

4 calls:

Slowest

103.0ms	(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (cbrt x))
83.0ms	(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))))
3.0ms	(cbrt (cbrt (+ x 1)))
1.0ms	(cbrt x)

series501.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

274.0ms	(cbrt x)
124.0ms	(- (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (cbrt x))
55.0ms	(cbrt (cbrt (+ x 1)))
48.0ms	(cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))))

simplify1.3m

Counts

324 → 346

Calls

324 calls:

Slowest

792.0ms	(cbrt (* (* (cbrt (- (* x x) (* 1 1))) (cbrt (+ (pow x 3) (pow 1 3)))) (* (cbrt (* (cbrt (+ (pow x 3) (pow 1 3))) (cbrt (+ (pow x 3) (pow 1 3))))) (cbrt (cbrt (+ x 1))))))
689.0ms	(cbrt (* (* (cbrt (- (* x x) (* 1 1))) (cbrt (+ x 1))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ (pow x 3) (pow 1 3))))) (cbrt (cbrt (+ (pow x 3) (pow 1 3)))))))
418.0ms	(cbrt (* (* (cbrt (+ (pow x 3) (pow 1 3))) (cbrt (+ x 1))) (* (cbrt (* (cbrt (+ (pow x 3) (pow 1 3))) (cbrt (- (* x x) (* 1 1))))) (cbrt (cbrt (+ x 1))))))
415.0ms	(cbrt (* (* (cbrt (- (* x x) (* 1 1))) (cbrt (+ (pow x 3) (pow 1 3)))) (* (cbrt (* (cbrt (- (* x x) (* 1 1))) (cbrt (+ x 1)))) (cbrt (cbrt (- (* x x) (* 1 1)))))))
406.0ms	(cbrt (* (* (cbrt (+ (pow x 3) (pow 1 3))) (cbrt (+ x 1))) (* (cbrt (* (cbrt (- (* x x) (* 1 1))) (cbrt (+ (pow x 3) (pow 1 3))))) (cbrt (cbrt (+ (pow x 3) (pow 1 3)))))))

prune6.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.2b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`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--` `fma-neg` `diff-log` `prod-diff` `flip--` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

Slowest

124.0ms	(- (* (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))) (* (cbrt x) (cbrt x)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

339.0ms	(cbrt x)
268.0ms	(cbrt x)
261.0ms	(cbrt x)
147.0ms	(- (* (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1))))) (* (cbrt x) (cbrt x)))

simplify1.6s

Counts

27 → 72

Calls

27 calls:

Slowest

305.0ms	(- (+ (* 2/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 2/3)))
259.0ms	(- (+ (* 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)))
220.0ms	(/ (exp (* (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))) (cbrt (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))))) (exp (* (cbrt x) (cbrt x))))
164.0ms	(- (+ (* 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))))
130.0ms	(* (pow (* x -1) 1/3) (cbrt -1))

prune837.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

regimes83.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 29.5b

bsearch219.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

665.0ms	1194×	body	640	valid
471.0ms	1700×	body	1280	valid
285.0ms	4155×	body	80	valid
83.0ms	624×	body	320	valid
33.0ms	327×	body	160	valid