Details

sample33.0ms

Algorithm

intervals

Results

10.0ms	56×	body	1280	valid
8.0ms	122×	body	80	valid
6.0ms	46×	body	640	valid
2.0ms	20×	body	320	valid
1.0ms	12×	body	160	valid

simplify21.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

21.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize22.0ms

Local error

Found 3 expressions with local error:

3.4b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))

rewrite81.0ms

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

71.0ms	(- (cbrt (+ x 1)) (cbrt x))
6.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series853.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

698.0ms	(cbrt x)
106.0ms	(- (cbrt (+ x 1)) (cbrt x))
49.0ms	(cbrt (+ x 1))

simplify7.4s

Counts

122 → 111

Calls

122 calls:

Slowest

337.0ms	(- (+ (* 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)))
335.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 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)))))
223.0ms	(fma (* (cbrt (cbrt (+ x 1))) (cbrt (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (* (cbrt (cbrt x)) (* (cbrt (cbrt x)) (cbrt (cbrt x))))))
213.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.7b

localize24.0ms

Local error

Found 4 expressions with local error:

10.2b	(- (cbrt (+ x 1)) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

Slowest

62.0ms	(- (cbrt (+ x 1)) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series897.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

268.0ms	(cbrt x)
267.0ms	(cbrt x)
262.0ms	(cbrt x)
100.0ms	(- (cbrt (+ x 1)) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))

simplify2.5s

Counts

42 → 83

Calls

42 calls:

Slowest

362.0ms	(- (+ (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)))))
343.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
297.0ms	(- (+ (* 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)))
213.0ms	(/ (exp (cbrt (+ x 1))) (exp (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x)))))
171.0ms	(* (pow (* x -1) 1/3) (cbrt -1))

prune977.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.7b

localize37.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (cbrt (+ x 1)) (cbrt x))
3.4b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

120×	`cbrt-prod`
104×	`*-un-lft-identity`
84×	`prod-diff`
78×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
16×	`distribute-lft-out`
14×	`fma-neg`
8×	`add-log-exp` `difference-of-squares`
6×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--`

Counts

4 → 170

Calls

4 calls:

Slowest

66.0ms	(- (cbrt (+ x 1)) (cbrt x))
33.0ms	(- (cbrt (+ x 1)) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series829.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

312.0ms	(cbrt x)
266.0ms	(cbrt x)
146.0ms	(- (cbrt (+ x 1)) (cbrt x))
105.0ms	(- (cbrt (+ x 1)) (cbrt x))

simplify12.9s

Counts

226 → 182

Calls

226 calls:

Slowest

340.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
339.0ms	(- (+ (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)))))
335.0ms	(- (+ (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)))))
328.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
290.0ms	(- (+ (* 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)))

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.7b

localize31.0ms

Local error

Found 4 expressions with local error:

31.9b	(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))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod` `*-un-lft-identity`
7×	`add-sqr-sqrt` `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-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 59

Calls

4 calls:

Slowest

3.0ms	(cbrt (+ x 1))
3.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)
0.0ms	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt x)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

279.0ms	(cbrt x)
172.0ms	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt x)))
68.0ms	(cbrt (+ x 1))
43.0ms	(cbrt (+ x 1))

simplify2.7s

Counts

27 → 71

Calls

27 calls:

Slowest

360.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
348.0ms	(- (+ (* 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)))))))))
332.0ms	(- (+ (* 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))))
234.0ms	(- (+ (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))))
232.0ms	(- (+ (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))))

prune829.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.6b

regimes157.0ms

Accuracy

99.6% (0.1b remaining)

Error of 15.8b against oracle of 15.8b and baseline of 30.0b

bsearch197.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

706.0ms	4071×	body	80	valid
522.0ms	1761×	body	1280	valid
265.0ms	1217×	body	640	valid
94.0ms	641×	body	320	valid
30.0ms	310×	body	160	valid