Details

sample95.0ms

Algorithm

intervals

Results

44.0ms	83×	body	1280	valid
25.0ms	50×	body	640	valid
10.0ms	24×	body	2560	valid
4.0ms	19×	body	320	valid
4.0ms	69×	body	80	valid
1.0ms	11×	body	160	valid

simplify19.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.5b

localize9.0ms

Local error

Found 3 expressions with local error:

2.4b	(log (+ x (hypot 1 x)))
1.0b	(+ x (hypot 1 x))
0.0b	(hypot 1 x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
4×	`pow1` `log-prod` `add-exp-log`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `hypot-udef` `sum-log` `rem-log-exp` `log-pow`

Counts

3 → 47

Calls

3 calls:

Slowest

4.0ms	(+ x (hypot 1 x))
3.0ms	(log (+ x (hypot 1 x)))
0.0ms	(hypot 1 x)

series270.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

162.0ms	(log (+ x (hypot 1 x)))
63.0ms	(+ x (hypot 1 x))
45.0ms	(hypot 1 x)

simplify1.4s

Counts: 56 → 56

prune548.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

13.7b	(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.3b	(* x -1/6)
0.1b	(fma 3/40 (pow x 5) x)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

Slowest

6.0ms	(* x -1/6)
0.0ms	(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.0ms	(fma 3/40 (pow x 5) x)

series274.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

197.0ms	(fma 3/40 (pow x 5) x)
62.0ms	(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
15.0ms	(* x -1/6)

simplify1.6s

Counts: 52 → 52

prune414.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

19.5b	(+ (/ -1/16 (pow x 5)) (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)))
10.9b	(log (+ (/ -1/16 (pow x 5)) (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x))))
0.2b	(/ 1/8 (* x x))
0.2b	(/ -1/16 (pow x 5))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

666×	`times-frac`
416×	`*-un-lft-identity`
394×	`add-sqr-sqrt` `add-cube-cbrt`
327×	`associate-+r+`
325×	`prod-diff`
80×	`div-inv`
25×	`fma-def`
21×	`unpow-prod-down`
15×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`add-log-exp`
8×	`associate-/r*` `frac-add`
7×	`sqr-pow`
6×	`log-div` `log-prod` `distribute-lft-out` `associate-/l*`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`cbrt-undiv`
2×	`clear-num` `sum-log` `frac-2neg` `flip3-+` `flip3--` `frac-sub` `flip-+` `flip--` `sub-div`
1×	`pow-to-exp` `+-commutative` `associate-+r-` `sub-neg` `diff-log` `rem-log-exp` `pow-exp` `prod-exp` `log-pow` `cbrt-unprod`

Counts

4 → 471

Calls

4 calls:

Slowest

154.0ms	(+ (/ -1/16 (pow x 5)) (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)))
66.0ms	(log (+ (/ -1/16 (pow x 5)) (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x))))
6.0ms	(/ 1/8 (* x x))
5.0ms	(/ -1/16 (pow x 5))

series333.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

139.0ms	(log (+ (/ -1/16 (pow x 5)) (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x))))
96.0ms	(+ (/ -1/16 (pow x 5)) (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)))
60.0ms	(/ -1/16 (pow x 5))
38.0ms	(/ 1/8 (* x x))

simplify1.4s

Counts: 483 → 483

prune4.8s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

18.0b	(fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x))
17.2b	(log (fma (- (hypot 1 x) x) (hypot 1 x) (* x x)))
10.4b	(log (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)))
1.6b	(- (hypot 1 x) x)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow1` `log-prod` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`rem-log-exp` `log-pow`
1×	`sub-neg` `flip3--` `diff-log` `fma-udef` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

Slowest

16.0ms	(- (hypot 1 x) x)
2.0ms	(log (fma (- (hypot 1 x) x) (hypot 1 x) (* x x)))
2.0ms	(log (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)))
1.0ms	(fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x))

series893.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

301.0ms	(log (fma (- (hypot 1 x) x) (hypot 1 x) (* x x)))
292.0ms	(log (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)))
214.0ms	(fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x))
85.0ms	(- (hypot 1 x) x)

simplify853.0ms

Counts: 82 → 82

prune897.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes65.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.9b

bsearch97.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.0s	2268×	body	1280	valid
797.0ms	802×	body	2560	valid
771.0ms	1551×	body	640	valid
251.0ms	754×	body	320	valid
227.0ms	2236×	body	80	valid
70.0ms	389×	body	160	valid