Details

sample59.0ms

Algorithm

intervals

Results

20.0ms	62×	body	640	valid
16.0ms	132×	body	80	valid
11.0ms	44×	body	320	valid
3.0ms	18×	body	160	valid

simplify21.0ms

Calls

1 calls:

Slowest

21.0ms

(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize19.0ms

Local error

Found 3 expressions with local error:

2.4b	(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
0.0b	(/ 1 (- x 1))
0.0b	(/ 1 (+ x 1))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
32×	`associate-/r/`
22×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
19×	`div-inv`
18×	`add-cube-cbrt`
9×	`flip-+` `flip--`
8×	`flip3-+` `flip3--`
6×	`associate-/r*` `fma-neg`
5×	`pow1` `add-exp-log` `distribute-lft-out--` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `pow-flip` `inv-pow`
1×	`sub-neg` `diff-log` `frac-sub` `difference-of-squares`

Calls

3 calls:

Slowest

10.0ms	(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
1.0ms	(/ 1 (- x 1))
1.0ms	(/ 1 (+ x 1))

series136.0ms

Calls

3 calls:

Slowest

108.0ms	(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
14.0ms	(/ 1 (- x 1))
13.0ms	(/ 1 (+ x 1))

simplify13.9s

Calls

108 calls:

Slowest

941.0ms	(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))
726.0ms	(fma (/ 1 (- (* x x) (* 1 1))) (- x 1) (- (* (+ x 1) (/ 1 (- (* x x) (* 1 1))))))
499.0ms	(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))
496.0ms	(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))
480.0ms	(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))

prune718.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ -2 (fma x (+ x -1) (+ x -1)))
0.0b	(fma x (+ x -1) (+ x -1))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `associate-/r` `-un-lft-identity` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`clear-num` `frac-2neg` `fma-udef` `div-inv`

Calls

2 calls:

Slowest

1.0ms	(/ -2 (fma x (+ x -1) (+ x -1)))
0.0ms	(fma x (+ x -1) (+ x -1))

series206.0ms

Calls

2 calls:

Slowest

121.0ms	(fma x (+ x -1) (+ x -1))
85.0ms	(/ -2 (fma x (+ x -1) (+ x -1)))

simplify889.0ms

Calls

9 calls:

Slowest

311.0ms	(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
285.0ms	(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
108.0ms	(+ (* 2 (pow x 2)) (+ (* 2 (pow x 4)) 2))
55.0ms	(cbrt (fma x (+ x -1) (+ x -1)))
52.0ms	(sqrt (fma x (+ x -1) (+ x -1)))

prune284.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

16.9b	(cbrt (fma x (+ x -1) (+ x -1)))
16.9b	(cbrt (fma x (+ x -1) (+ x -1)))
16.9b	(cbrt (fma x (+ x -1) (+ x -1)))
0.2b	(/ -2 (* (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))) (cbrt (fma x (+ x -1) (+ x -1)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Calls

4 calls:

Slowest

10.0ms	(/ -2 (* (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))) (cbrt (fma x (+ x -1) (+ x -1)))))
2.0ms	(cbrt (fma x (+ x -1) (+ x -1)))
1.0ms	(cbrt (fma x (+ x -1) (+ x -1)))
1.0ms	(cbrt (fma x (+ x -1) (+ x -1)))

series656.0ms

Calls

4 calls:

Slowest

236.0ms	(cbrt (fma x (+ x -1) (+ x -1)))
176.0ms	(cbrt (fma x (+ x -1) (+ x -1)))
165.0ms	(cbrt (fma x (+ x -1) (+ x -1)))
78.0ms	(/ -2 (* (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))) (cbrt (fma x (+ x -1) (+ x -1)))))

simplify4.6s

Calls

22 calls:

Slowest

412.0ms	(cbrt (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
375.0ms	(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
358.0ms	(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
351.0ms	(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
342.0ms	(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))

prune685.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

17.2b	(cbrt (/ -2 (fma x (+ x -1) (+ x -1))))
17.2b	(cbrt (/ -2 (fma x (+ x -1) (+ x -1))))
17.2b	(cbrt (/ -2 (fma x (+ x -1) (+ x -1))))
0.3b	(* (cbrt (/ -2 (fma x (+ x -1) (+ x -1)))) (cbrt (/ -2 (fma x (+ x -1) (+ x -1)))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
7×	`cbrt-div` `pow1/3` `associate-r` `associate-l`
6×	`add-exp-log`
5×	`div-inv`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

13.0ms	(* (cbrt (/ -2 (fma x (+ x -1) (+ x -1)))) (cbrt (/ -2 (fma x (+ x -1) (+ x -1)))))
1.0ms	(cbrt (/ -2 (fma x (+ x -1) (+ x -1))))
1.0ms	(cbrt (/ -2 (fma x (+ x -1) (+ x -1))))
1.0ms	(cbrt (/ -2 (fma x (+ x -1) (+ x -1))))

series1.0s

Calls

4 calls:

Slowest

272.0ms	(* (cbrt (/ -2 (fma x (+ x -1) (+ x -1)))) (cbrt (/ -2 (fma x (+ x -1) (+ x -1)))))
255.0ms	(cbrt (/ -2 (fma x (+ x -1) (+ x -1))))
245.0ms	(cbrt (/ -2 (fma x (+ x -1) (+ x -1))))
241.0ms	(cbrt (/ -2 (fma x (+ x -1) (+ x -1))))

simplify11.8s

Calls

53 calls:

Slowest

495.0ms	(* (/ -2 (fma x (+ x -1) (+ x -1))) (/ -2 (fma x (+ x -1) (+ x -1))))
440.0ms	(+ (* 5/9 (* (pow (/ 1 (pow x 16)) 1/3) (pow (cbrt -2) 2))) (+ (* 2/3 (* (pow (/ 1 (pow x 10)) 1/3) (pow (cbrt -2) 2))) (* (pow (/ 1 (pow x 4)) 1/3) (pow (cbrt -2) 2))))
414.0ms	(* (/ -2 (fma x (+ x -1) (+ x -1))) (/ -2 (fma x (+ x -1) (+ x -1))))
395.0ms	(+ (* 2/3 (* (pow x 2) (pow (cbrt -2) 2))) (+ (pow (cbrt -2) 2) (* 5/9 (* (pow x 4) (pow (cbrt -2) 2)))))
390.0ms	(* (cbrt -2) (cbrt (/ -2 (fma x (+ x -1) (+ x -1)))))

prune1.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

781.0ms	4247×	body	80	valid
727.0ms	1907×	body	640	valid
378.0ms	1211×	body	320	valid
101.0ms	635×	body	160	valid