Details

sample43.0ms

Algorithm

intervals

Results

14.0ms	54×	body	1280	valid
7.0ms	36×	body	640	valid
7.0ms	137×	body	80	valid
3.0ms	19×	body	320	valid
1.0ms	10×	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: 28.4b

localize22.0ms

Local error

Found 3 expressions with local error:

3.2b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.2b	(cbrt (+ x 1))

rewrite63.0ms

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

59.0ms	(- (cbrt (+ x 1)) (cbrt x))
2.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series434.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

273.0ms	(cbrt x)
100.0ms	(- (cbrt (+ x 1)) (cbrt x))
60.0ms	(cbrt (+ x 1))

simplify9.4s

Counts

166 → 111

Calls

166 calls:

Slowest

464.0ms	(* (* (- (cbrt (+ x 1)) (cbrt x)) (- (cbrt (+ x 1)) (cbrt x))) (- (cbrt (+ x 1)) (cbrt x)))
429.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
420.0ms	(fma (cbrt 1) (cbrt (+ x 1)) (- (* (sqrt (cbrt x)) (sqrt (cbrt x)))))
349.0ms	(- (+ (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)))))
311.0ms	(- (+ (* 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)))

prune976.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.2b	(* (+ (cbrt (+ 1 x)) (cbrt x)) (cbrt x))
0.2b	(cbrt (+ 1 x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
18×	`cbrt-prod`
14×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
6×	`pow1` `associate-r` `associate-l` `add-exp-log`
5×	`add-cbrt-cube` `distribute-lft-out`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`cbrt-div` `flip3-+` `associate-*l/` `flip-+` `unswap-sqr`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 75

Calls

4 calls:

Slowest

75.0ms	(* (+ (cbrt (+ 1 x)) (cbrt x)) (cbrt x))
2.0ms	(cbrt (+ 1 x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series843.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

322.0ms	(cbrt x)
290.0ms	(cbrt x)
171.0ms	(* (+ (cbrt (+ 1 x)) (cbrt x)) (cbrt x))
60.0ms	(cbrt (+ 1 x))

simplify5.9s

Counts

97 → 87

Calls

97 calls:

Slowest

976.0ms	(* (* (* (+ (cbrt (+ 1 x)) (cbrt x)) (cbrt x)) (* (+ (cbrt (+ 1 x)) (cbrt x)) (cbrt x))) (* (+ (cbrt (+ 1 x)) (cbrt x)) (cbrt x)))
571.0ms	(* (* (* (+ (cbrt (+ 1 x)) (cbrt x)) (+ (cbrt (+ 1 x)) (cbrt x))) (+ (cbrt (+ 1 x)) (cbrt x))) x)
474.0ms	(- (+ (* 1/3 (* (* (cbrt -1) (exp (* 1/3 (- (log -1) (log (/ -1 x)))))) (pow (/ -1 (pow x 2)) 1/3))) (+ (* (pow (* x -1) 1/3) (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (cbrt -1))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)))) (* 1/9 (* (pow (/ -1 (pow x 5)) 1/3) (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (cbrt -1)))))
449.0ms	(* (+ (pow (cbrt (+ 1 x)) 3) (pow (cbrt x) 3)) (cbrt x))
436.0ms	(* (- (* (cbrt (+ 1 x)) (cbrt (+ 1 x))) (* (cbrt x) (cbrt x))) (cbrt x))

prune917.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.2b	(* (cbrt x) (+ (cbrt (+ 1 x)) (cbrt x)))
0.2b	(cbrt (+ 1 x))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
18×	`cbrt-prod`
14×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
6×	`pow1` `associate-r` `associate-l` `add-exp-log`
5×	`add-cbrt-cube` `distribute-lft-out`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`cbrt-div` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 77

Calls

4 calls:

Slowest

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

series723.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

304.0ms	(cbrt x)
240.0ms	(cbrt x)
129.0ms	(* (cbrt x) (+ (cbrt (+ 1 x)) (cbrt x)))
49.0ms	(cbrt (+ 1 x))

simplify4.4s

Counts

101 → 89

Calls

101 calls:

Slowest

455.0ms	(- (+ (* 1/3 (* (* (cbrt -1) (exp (* 1/3 (- (log -1) (log (/ -1 x)))))) (pow (/ -1 (pow x 2)) 1/3))) (+ (* (pow (* x -1) 1/3) (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (cbrt -1))) (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)))) (* 1/9 (* (pow (/ -1 (pow x 5)) 1/3) (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (cbrt -1)))))
402.0ms	(* (cbrt x) (- (* (cbrt (+ 1 x)) (cbrt (+ 1 x))) (* (cbrt x) (cbrt x))))
332.0ms	(- (+ (* 1/3 (pow (pow x 4) 1/3)) (+ (pow x 1/3) (pow (pow x 2) 1/3))) (* 1/9 (pow (pow x 7) 1/3)))
263.0ms	(* (cbrt x) (+ (pow (cbrt (+ 1 x)) 3) (pow (cbrt x) 3)))
261.0ms	(exp (* (cbrt x) (+ (cbrt (+ 1 x)) (cbrt x))))

prune1.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 59

Calls

4 calls:

Slowest

2.0ms	(cbrt (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

408.0ms	(cbrt (cbrt x))
331.0ms	(cbrt x)
331.0ms	(cbrt x)
258.0ms	(cbrt x)

simplify1.6s

Counts

82 → 71

Calls

82 calls:

Slowest

720.0ms	(* (pow (* x -1) 1/9) (pow (cbrt -1) 1/3))
156.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
145.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
130.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
62.0ms	(* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))

prune899.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes185.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch3.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

730.0ms	1267×	body	640	valid
518.0ms	1705×	body	1280	valid
244.0ms	4112×	body	80	valid
131.0ms	614×	body	320	valid
33.0ms	302×	body	160	valid