Details

sample90.0ms

Algorithm

intervals

Results

20.0ms	270×	body	80	nan
19.0ms	58×	body	640	valid
15.0ms	38×	body	1280	valid
11.0ms	125×	body	80	valid
6.0ms	25×	body	320	valid
2.0ms	10×	body	160	valid

simplify58.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize16.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b	(/ 1 (sqrt x))
0.2b	(/ 1 (sqrt (+ x 1)))
0.0b	(sqrt (+ x 1))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

1063×	`times-frac`
902×	`*-un-lft-identity`
788×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
580×	`sqrt-prod`
74×	`distribute-lft-out`
56×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
25×	`difference-of-squares`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*` `distribute-lft-out--`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube`
6×	`pow-flip` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `hypot-def` `inv-pow`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 793

Calls

4 calls:

Slowest

34.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
23.0ms	(/ 1 (sqrt (+ x 1)))
10.0ms	(sqrt (+ x 1))
5.0ms	(/ 1 (sqrt x))

series214.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

96.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
45.0ms	(/ 1 (sqrt x))
38.0ms	(/ 1 (sqrt (+ x 1)))
35.0ms	(sqrt (+ x 1))

simplify1.2s

Counts: 805 → 805

prune9.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 18.4b

localize19.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))
0.3b	(/ 1 (sqrt x))
0.2b	(/ 1 (hypot (sqrt x) 1))
0.0b	(hypot (sqrt x) 1)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

505×	`times-frac`
406×	`add-sqr-sqrt`
386×	`*-un-lft-identity`
365×	`add-cube-cbrt`
286×	`prod-diff`
144×	`sqrt-prod`
42×	`div-inv`
22×	`fma-neg`
15×	`difference-of-squares`
12×	`add-exp-log`
9×	`associate-/r*`
8×	`add-cbrt-cube`
7×	`pow1` `distribute-lft-out--`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `pow-flip`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `inv-pow`
1×	`hypot-udef` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 439

Calls

4 calls:

Slowest

28.0ms	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))
5.0ms	(/ 1 (sqrt x))
4.0ms	(/ 1 (hypot (sqrt x) 1))
0.0ms	(hypot (sqrt x) 1)

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

716.0ms	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))
269.0ms	(/ 1 (hypot (sqrt x) 1))
204.0ms	(hypot (sqrt x) 1)
36.0ms	(/ 1 (sqrt x))

simplify1.2s

Counts: 451 → 451

prune3.2s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 18.4b

localize17.0ms

Local error

Found 3 expressions with local error:

12.8b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))
0.2b	(/ 1 (sqrt (+ x 1)))
0.0b	(sqrt (+ x 1))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

236×	`*-un-lft-identity`
209×	`add-sqr-sqrt`
189×	`prod-diff`
180×	`times-frac`
174×	`add-cube-cbrt`
110×	`sqrt-prod`
89×	`unpow-prod-down`
33×	`sqr-pow`
26×	`distribute-lft-out`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`difference-of-squares`
9×	`flip3-+` `flip-+` `div-inv`
7×	`associate-/r*` `fma-neg` `add-exp-log`
6×	`pow1`
5×	`add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `pow-flip` `associate-/l*`
2×	`sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `1-exp` `flip--` `inv-pow`

Counts

3 → 303

Calls

3 calls:

Slowest

22.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))
8.0ms	(/ 1 (sqrt (+ x 1)))
4.0ms	(sqrt (+ x 1))

series113.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

56.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))
29.0ms	(/ 1 (sqrt (+ x 1)))
28.0ms	(sqrt (+ x 1))

simplify739.0ms

Counts: 312 → 312

prune2.2s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 18.4b

localize67.0ms

Local error

Found 4 expressions with local error:

33.7b	(fma (- (/ 1 (sqrt (cbrt (+ x 1))))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))))
31.0b	(fma (pow (* (cbrt x) (cbrt x)) -1/2) (pow (cbrt x) -1/2) (- (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `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`
2×	`pow1/3` `fma-udef`

Counts

4 → 50

Calls

4 calls:

Slowest

1.0ms	(cbrt x)
1.0ms	(cbrt x)
0.0ms	(fma (- (/ 1 (sqrt (cbrt (+ x 1))))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))))
0.0ms	(fma (pow (* (cbrt x) (cbrt x)) -1/2) (pow (cbrt x) -1/2) (- (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))

series726.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

206.0ms	(fma (- (/ 1 (sqrt (cbrt (+ x 1))))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))))
193.0ms	(cbrt x)
190.0ms	(cbrt x)
136.0ms	(fma (pow (* (cbrt x) (cbrt x)) -1/2) (pow (cbrt x) -1/2) (- (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))

simplify695.0ms

Counts: 62 → 62

prune643.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 18.3b

regimes132.0ms

Accuracy

0% (0.7b remaining)

Error of 19.8b against oracle of 19.1b and baseline of 19.8b

bsearch1.0ms

end0.0ms

sample2.2s

Algorithm

intervals

Results

633.0ms	1160×	body	1280	valid
451.0ms	8156×	body	80	nan
431.0ms	1790×	body	640	valid
308.0ms	4032×	body	80	valid
144.0ms	660×	body	320	valid
37.0ms	358×	body	160	valid