Details

sample63.0ms

Algorithm

intervals

Results

19.0ms	52×	body	1280	valid
13.0ms	246×	body	80	nan
9.0ms	42×	body	640	valid
7.0ms	126×	body	80	valid
3.0ms	23×	body	320	valid
1.0ms	13×	body	160	valid

simplify10.0ms

Calls

1 calls:

Slowest

10.0ms

(- (sqrt (+ x 1)) (sqrt x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize10.0ms

Local error

Found 2 expressions with local error:

3.4b	(- (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

7.0ms	(- (sqrt (+ x 1)) (sqrt x))
1.0ms	(sqrt (+ x 1))

series70.0ms

Calls

2 calls:

Slowest

39.0ms	(- (sqrt (+ x 1)) (sqrt x))
31.0ms	(sqrt (+ x 1))

simplify314.0ms

Calls

18 calls:

Slowest

111.0ms	(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
46.0ms	(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
35.0ms	(sqrt (- (* x x) (* 1 1)))
19.0ms	(- (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
18.0ms	(sqrt (+ (pow x 3) (pow 1 3)))

prune297.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 30.2b

localize11.0ms

Local error

Found 4 expressions with local error:

24.1b	(- (* (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (sqrt x))
0.3b	(cbrt (sqrt (+ x 1)))
0.3b	(cbrt (sqrt (+ x 1)))
0.3b	(cbrt (sqrt (+ x 1)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-prod`
6×	`cbrt-div` `sqrt-div` `add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`flip3-+` `pow1/3` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Calls

4 calls:

Slowest

37.0ms	(- (* (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (sqrt x))
1.0ms	(cbrt (sqrt (+ x 1)))
1.0ms	(cbrt (sqrt (+ x 1)))
1.0ms	(cbrt (sqrt (+ x 1)))

series155.0ms

Calls

4 calls:

Slowest

51.0ms	(cbrt (sqrt (+ x 1)))
43.0ms	(cbrt (sqrt (+ x 1)))
33.0ms	(cbrt (sqrt (+ x 1)))
27.0ms	(- (* (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (sqrt x))

simplify2.2s

Calls

37 calls:

Slowest

354.0ms	(- (+ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (* 1/6 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) x))) (* 5/72 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (pow x 2))))
316.0ms	(- (+ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (* 1/6 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) x))) (* 5/72 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (pow x 2))))
292.0ms	(- (+ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (* 1/6 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) x))) (* 5/72 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (pow x 2))))
134.0ms	(- (+ (* 1/6 (pow (/ 1 (pow x 5)) 1/6)) (pow (/ 1 x) -1/6)) (* 5/72 (pow (/ 1 (pow x 11)) 1/6)))
129.0ms	(- (+ (* 1/6 (pow (/ 1 (pow x 5)) 1/6)) (pow (/ 1 x) -1/6)) (* 5/72 (pow (/ 1 (pow x 11)) 1/6)))

prune834.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 30.0b

localize62.0ms

Local error

Found 4 expressions with local error:

21.7b	(- (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (sqrt x))
0.3b	(cbrt (sqrt (+ x 1)))
0.3b	(cbrt (sqrt (+ x 1)))
0.3b	(cbrt (+ x 1))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div` `sqrt-prod` `add-log-exp`
4×	`pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16`
3×	`flip3-+` `pow1/3` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Calls

4 calls:

Slowest

161.0ms	(- (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (sqrt x))
1.0ms	(cbrt (sqrt (+ x 1)))
1.0ms	(cbrt (sqrt (+ x 1)))
1.0ms	(cbrt (+ x 1))

series164.0ms

Calls

4 calls:

Slowest

55.0ms	(cbrt (sqrt (+ x 1)))
53.0ms	(cbrt (sqrt (+ x 1)))
32.0ms	(cbrt (+ x 1))
24.0ms	(- (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (sqrt x))

simplify2.3s

Calls

34 calls:

Slowest

357.0ms	(- (+ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (* 1/6 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) x))) (* 5/72 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (pow x 2))))
324.0ms	(- (+ (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))))
319.0ms	(- (+ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (* 1/6 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) x))) (* 5/72 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (pow x 2))))
138.0ms	(/ (exp (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))))) (exp (sqrt x)))
136.0ms	(- (+ (* 1/6 (pow (/ 1 (pow x 5)) 1/6)) (pow (/ 1 x) -1/6)) (* 5/72 (pow (/ 1 (pow x 11)) 1/6)))

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 30.0b

localize40.0ms

Local error

Found 4 expressions with local error:

21.3b	(- (* (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))))) (* (sqrt x) (sqrt x)))
0.5b	(* (sqrt x) (sqrt x))
0.3b	(cbrt (sqrt (+ x 1)))
0.3b	(cbrt (sqrt (+ x 1)))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
6×	`add-cbrt-cube` `add-exp-log` `sqrt-prod` `add-log-exp`
4×	`cbrt-div` `pow1/2` `sqrt-div` `insert-posit16`
3×	`associate-r` `associate-l`
2×	`flip3-+` `pow1/3` `pow-prod-down` `pow-prod-up` `flip-+`
1×	`pow2` `sub-neg` `rem-square-sqrt` `pow-plus` `flip3--` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `difference-of-squares`

Calls

4 calls:

Slowest

2.3s	(- (* (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))))) (* (sqrt x) (sqrt x)))
9.0ms	(* (sqrt x) (sqrt x))
2.0ms	(cbrt (sqrt (+ x 1)))
2.0ms	(cbrt (sqrt (+ x 1)))

series131.0ms

Calls

4 calls:

Slowest

53.0ms	(cbrt (sqrt (+ x 1)))
52.0ms	(cbrt (sqrt (+ x 1)))
14.0ms	(- (* (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))))) (* (sqrt x) (sqrt x)))
12.0ms	(* (sqrt x) (sqrt x))

simplify2.1s

Calls

45 calls:

Slowest

431.0ms	(/ (exp (* (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))))) (exp (* (sqrt x) (sqrt x))))
342.0ms	(- (+ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (* 1/6 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) x))) (* 5/72 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (pow x 2))))
332.0ms	(- (+ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (* 1/6 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) x))) (* 5/72 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (pow x 2))))
122.0ms	(- (+ (* 1/6 x) 1) (* 5/72 (pow x 2)))
121.0ms	(- (+ (* 1/6 x) 1) (* 5/72 (pow x 2)))

prune1.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

regimes43.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

644.0ms	7996×	body	80	nan
490.0ms	1717×	body	1280	valid
346.0ms	1248×	body	640	valid
298.0ms	4095×	body	80	valid
123.0ms	601×	body	320	valid
37.0ms	339×	body	160	valid