Details

sample48.0ms

Algorithm

intervals

Results

16.0ms	54×	body	1280	valid
10.0ms	41×	body	640	valid
8.0ms	130×	body	80	valid
3.0ms	19×	body	320	valid
1.0ms	12×	body	160	valid

simplify20.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

20.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize17.0ms

Local error

Found 3 expressions with local error:

3.5b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.2b	(cbrt (+ x 1))

rewrite55.0ms

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

50.0ms	(- (cbrt (+ x 1)) (cbrt x))
3.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series428.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

272.0ms	(cbrt x)
106.0ms	(- (cbrt (+ x 1)) (cbrt x))
50.0ms	(cbrt (+ x 1))

simplify7.1s

Counts

122 → 111

Calls

122 calls:

Slowest

356.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
331.0ms	(- (+ (* 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)))
295.0ms	(- (+ (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)))))
204.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
198.0ms	(fma (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (cbrt x)) (* (cbrt (cbrt x)) (cbrt (cbrt x))))))

prune903.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.0b

localize35.0ms

Local error

Found 4 expressions with local error:

3.5b	(- (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)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

35×	`cbrt-prod` `*-un-lft-identity`
28×	`prod-diff`
27×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
7×	`fma-neg`
6×	`add-log-exp`
5×	`distribute-lft-out`
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--`

Counts

4 → 94

Calls

4 calls:

Slowest

40.0ms	(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))
24.0ms	(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

358.0ms	(cbrt (* (* (cbrt x) (cbrt x)) (cbrt x)))
287.0ms	(cbrt x)
246.0ms	(cbrt x)
144.0ms	(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))

simplify6.5s

Counts

87 → 106

Calls

87 calls:

Slowest

375.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
372.0ms	(- (+ (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)))))
288.0ms	(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))))))))
285.0ms	(- (+ (* 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)))
210.0ms	(fma (cbrt 1) (cbrt (+ 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))))))))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.0b

localize47.0ms

Local error

Found 4 expressions with local error:

7.0b	(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

37×	`cbrt-prod`
36×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `prod-diff`
24×	`add-cube-cbrt`
7×	`fma-neg`
6×	`add-log-exp`
5×	`distribute-lft-out`
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` `flip--` `distribute-lft-out--`

Counts

4 → 95

Calls

4 calls:

Slowest

85.0ms	(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series985.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

307.0ms	(cbrt x)
291.0ms	(cbrt x)
274.0ms	(cbrt x)
113.0ms	(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))))

simplify19.3s

Counts

89 → 107

Calls

89 calls:

Slowest

754.0ms	(fma (* (cbrt (cbrt (+ x 1))) (cbrt (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (* (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))) 1)))
428.0ms	(fma (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))) 1)))
414.0ms	(fma (cbrt 1) (cbrt (+ x 1)) (- (* (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))) 1)))
400.0ms	(fma (cbrt 1) (cbrt (+ x 1)) (- (* (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))) 1)))
392.0ms	(fma (- (sqrt (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))))) (sqrt (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))) (* (sqrt (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))) (sqrt (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))))))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.0b

localize91.0ms

Local error

Found 4 expressions with local error:

7.0b	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))) (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite322.0ms

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

319.0ms	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))) (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series994.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

315.0ms	(cbrt x)
280.0ms	(cbrt x)
252.0ms	(cbrt x)
147.0ms	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))) (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))))

simplify3.1s

Counts

27 → 72

Calls

27 calls:

Slowest

419.0ms	(fma (cbrt (+ x 1)) (cbrt (+ x 1)) (- (* (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))) (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))))))
370.0ms	(/ (exp (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (exp (* (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))) (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))))))
338.0ms	(- (+ (* 2/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 2/3)))
308.0ms	(- (+ (* 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)))
308.0ms	(+ (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))))

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

regimes74.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 30.2b

bsearch257.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.0s	1747×	body	1280	valid
277.0ms	1230×	body	640	valid
247.0ms	4064×	body	80	valid
93.0ms	645×	body	320	valid
30.0ms	314×	body	160	valid