Details

sample34.0ms

Algorithm

intervals

Results

11.0ms	60×	body	1280	valid
7.0ms	49×	body	640	valid
5.0ms	114×	body	80	valid
2.0ms	21×	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))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize22.0ms

Local error

Found 3 expressions with local error:

2.6b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3` `distribute-lft-out`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

3 → 47

Calls

3 calls:

Slowest

64.0ms	(- (cbrt (+ x 1)) (cbrt x))
6.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series444.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

264.0ms	(cbrt x)
120.0ms	(- (cbrt (+ x 1)) (cbrt x))
60.0ms	(cbrt (+ x 1))

simplify2.1s

Counts

32 → 56

Calls

32 calls:

Slowest

332.0ms	(- (+ (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)))))
317.0ms	(- (+ (* 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)))
273.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
247.0ms	(- (+ (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	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune603.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.4b	(* (/ (cbrt x) x) (+ 1/3 (/ -1/9 x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
26×	`cbrt-prod`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
22×	`associate-l`
20×	`times-frac`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`pow1`
4×	`associate-r` `insert-posit16` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `pow1/3` `unswap-sqr`
2×	`frac-times` `flip3-+` `prod-exp` `associate-*r/` `cbrt-unprod` `flip-+`
1×	`distribute-rgt-in` `cbrt-undiv` `neg-mul-1` `distribute-lft-in` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 93

Calls

4 calls:

Slowest

36.0ms	(* (/ (cbrt x) x) (+ 1/3 (/ -1/9 x)))
3.0ms	(cbrt (- x))
2.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

549.0ms	(* (/ (cbrt x) x) (+ 1/3 (/ -1/9 x)))
292.0ms	(cbrt (- x))
283.0ms	(cbrt x)
252.0ms	(cbrt x)

simplify3.5s

Counts

73 → 105

Calls

73 calls:

Slowest

374.0ms	(* x (+ (* 1/3 1/3) (- (* (/ -1/9 x) (/ -1/9 x)) (* 1/3 (/ -1/9 x)))))
301.0ms	(* (* (* (/ (cbrt x) x) (/ (cbrt x) x)) (/ (cbrt x) x)) (* (* (+ 1/3 (/ -1/9 x)) (+ 1/3 (/ -1/9 x))) (+ 1/3 (/ -1/9 x))))
282.0ms	(* (cbrt x) (- (* 1/3 1/3) (* (/ -1/9 x) (/ -1/9 x))))
272.0ms	(* (cbrt x) (+ (pow 1/3 3) (pow (/ -1/9 x) 3)))
265.0ms	(- (* 1/9 (* (pow (/ 1 (pow x 5)) 1/3) (cbrt -1))) (* 1/3 (* (pow (/ 1 (pow x 2)) 1/3) (cbrt -1))))

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
0.4b	(* (/ (cbrt x) x) (+ 1/3 (/ -1/9 x)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`associate-l`
21×	`add-cube-cbrt`
20×	`times-frac`
19×	`cbrt-prod`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`pow1`
4×	`associate-r` `insert-posit16` `add-log-exp`
3×	`pow1/3` `unswap-sqr`
2×	`frac-times` `flip3-+` `prod-exp` `associate-*r/` `cbrt-unprod` `flip-+`
1×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

Slowest

54.0ms	(* (/ (cbrt x) x) (+ 1/3 (/ -1/9 x)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

566.0ms	(* (/ (cbrt x) x) (+ 1/3 (/ -1/9 x)))
315.0ms	(cbrt x)
259.0ms	(cbrt x)
259.0ms	(cbrt x)

simplify3.6s

Counts

66 → 98

Calls

66 calls:

Slowest

332.0ms	(* (cbrt x) (- (* 1/3 1/3) (* (/ -1/9 x) (/ -1/9 x))))
307.0ms	(- (* 1/9 (* (pow (/ 1 (pow x 5)) 1/3) (cbrt -1))) (* 1/3 (* (pow (/ 1 (pow x 2)) 1/3) (cbrt -1))))
295.0ms	(* (* (* (/ (cbrt x) x) (/ (cbrt x) x)) (/ (cbrt x) x)) (* (* (+ 1/3 (/ -1/9 x)) (+ 1/3 (/ -1/9 x))) (+ 1/3 (/ -1/9 x))))
287.0ms	(* x (+ (* 1/3 1/3) (- (* (/ -1/9 x) (/ -1/9 x)) (* 1/3 (/ -1/9 x)))))
219.0ms	(* (/ x (* (* x x) x)) (* (* (+ 1/3 (/ -1/9 x)) (+ 1/3 (/ -1/9 x))) (+ 1/3 (/ -1/9 x))))

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (cbrt x) (- 1/9 (* (/ -1/9 x) (/ -1/9 x))))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`cbrt-prod`
10×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `associate-l` `add-exp-log`
5×	`add-cbrt-cube`
4×	`associate-r` `insert-posit16` `add-log-exp`
3×	`pow1/3`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/` `unswap-sqr`
1×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

Slowest

34.0ms	(* (cbrt x) (- 1/9 (* (/ -1/9 x) (/ -1/9 x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series2.1s

Counts

4 → 12

Calls

4 calls:

Slowest

1.2s	(* (cbrt x) (- 1/9 (* (/ -1/9 x) (/ -1/9 x))))
277.0ms	(cbrt x)
274.0ms	(cbrt x)
256.0ms	(cbrt x)

simplify4.8s

Counts

43 → 78

Calls

43 calls:

Slowest

451.0ms	(* x (* (* (- 1/9 (* (/ -1/9 x) (/ -1/9 x))) (- 1/9 (* (/ -1/9 x) (/ -1/9 x)))) (- 1/9 (* (/ -1/9 x) (/ -1/9 x)))))
423.0ms	(* (cbrt x) (- (* (/ -1/9 x) (/ -1/9 x))))
416.0ms	(- (* 1/9 (pow x 1/3)) (* 1/81 (pow (/ 1 (pow x 5)) 1/3)))
397.0ms	(- (* 1/9 (pow x 1/3)) (* 1/81 (pow (/ 1 (pow x 5)) 1/3)))
388.0ms	(+ (* 1/9 1/9) (+ (* (* (/ -1/9 x) (/ -1/9 x)) (* (/ -1/9 x) (/ -1/9 x))) (* 1/9 (* (/ -1/9 x) (/ -1/9 x)))))

prune829.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.0b

regimes211.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.6b

bsearch107.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

448.0ms	1762×	body	1280	valid
391.0ms	1235×	body	640	valid
273.0ms	4069×	body	80	valid
86.0ms	618×	body	320	valid
30.0ms	316×	body	160	valid