Details

sample77.0ms

Algorithm

intervals

Results

16.0ms	57×	body	640	valid
16.0ms	245×	body	80	nan
13.0ms	130×	body	80	valid
13.0ms	35×	body	1280	valid
5.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid

simplify29.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.2b

localize40.0ms

Local error

Found 3 expressions with local error:

3.2b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b	(/ 1 (sqrt x))
0.1b	(/ 1 (sqrt (+ x 1)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

1063×	`times-frac`
897×	`*-un-lft-identity`
782×	`add-sqr-sqrt`
712×	`add-cube-cbrt`
594×	`prod-diff`
576×	`sqrt-prod`
73×	`distribute-lft-out`
56×	`div-inv`
46×	`sqrt-div` `associate-/r/`
25×	`difference-of-squares`
23×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*` `distribute-lft-out--`
11×	`add-exp-log`
7×	`pow1` `add-cbrt-cube`
6×	`pow-flip` `associate-/l*`
5×	`add-log-exp`
4×	`div-exp`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

3 → 772

Calls

3 calls:

Slowest

59.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
18.0ms	(/ 1 (sqrt (+ x 1)))
11.0ms	(/ 1 (sqrt x))

series171.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

97.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
45.0ms	(/ 1 (sqrt (+ x 1)))
29.0ms	(/ 1 (sqrt x))

simplify1.1s

Counts: 781 → 781

prune8.9s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 20.5b

localize28.0ms

Local error

Found 2 expressions with local error:

11.1b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))
0.1b	(/ 1 (sqrt (+ x 1)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

231×	`*-un-lft-identity`
203×	`add-sqr-sqrt`
189×	`prod-diff`
180×	`times-frac`
172×	`add-cube-cbrt`
106×	`sqrt-prod`
89×	`unpow-prod-down`
33×	`sqr-pow`
25×	`distribute-lft-out`
16×	`sqrt-div` `associate-/r/`
15×	`difference-of-squares`
9×	`div-inv`
8×	`flip3-+` `flip-+`
7×	`associate-/r*` `fma-neg`
6×	`add-exp-log`
4×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`pow-flip` `associate-/l*`
2×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
1×	`cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `1-exp` `flip--` `inv-pow`

Counts

2 → 282

Calls

2 calls:

Slowest

23.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))
11.0ms	(/ 1 (sqrt (+ x 1)))

series101.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

65.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))
36.0ms	(/ 1 (sqrt (+ x 1)))

simplify1.1s

Counts: 288 → 288

prune2.9s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 20.5b

localize18.0ms

Local error

Found 2 expressions with local error:

3.2b	(- (pow x -1/2) (pow (+ x 1) -1/2))
0.0b	(pow (+ x 1) -1/2)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

69×	`unpow-prod-down`
59×	`*-un-lft-identity`
56×	`prod-diff`
48×	`add-sqr-sqrt`
36×	`add-cube-cbrt`
23×	`sqr-pow`
9×	`distribute-lft-out` `difference-of-squares`
7×	`fma-neg`
4×	`add-log-exp`
3×	`pow1` `pow-unpow` `add-exp-log` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
1×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `flip--`

Counts

2 → 111

Calls

2 calls:

Slowest

36.0ms	(- (pow x -1/2) (pow (+ x 1) -1/2))
6.0ms	(pow (+ x 1) -1/2)

series153.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

104.0ms	(- (pow x -1/2) (pow (+ x 1) -1/2))
49.0ms	(pow (+ x 1) -1/2)

simplify1.4s

Counts: 117 → 117

prune993.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize67.0ms

Local error

Found 4 expressions with local error:

32.3b	(fma (- (/ (sqrt 1) (cbrt (sqrt (+ x 1))))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
19.8b	(fma 1 (pow x -1/2) (- (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
0.3b	(cbrt (sqrt (+ x 1)))
0.3b	(cbrt (sqrt (+ x 1)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
12×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `pow1` `cbrt-div` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `pow1/3` `flip-+` `fma-udef` `distribute-lft-out`

Counts

4 → 62

Calls

4 calls:

Slowest

3.0ms	(cbrt (sqrt (+ x 1)))
3.0ms	(cbrt (sqrt (+ x 1)))
0.0ms	(fma (- (/ (sqrt 1) (cbrt (sqrt (+ x 1))))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
0.0ms	(fma 1 (pow x -1/2) (- (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

275.0ms	(fma (- (/ (sqrt 1) (cbrt (sqrt (+ x 1))))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
61.0ms	(fma 1 (pow x -1/2) (- (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
40.0ms	(cbrt (sqrt (+ x 1)))
35.0ms	(cbrt (sqrt (+ x 1)))

simplify1.1s

Counts: 74 → 74

prune802.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

regimes48.0ms

Accuracy

98.2% (0.5b remaining)

Error of 1.5b against oracle of 1.0b and baseline of 30.2b

bsearch65.0ms

end0.0ms

sample2.4s

Algorithm

intervals

Results

550.0ms	1894×	body	640	valid
474.0ms	7827×	body	80	nan
461.0ms	1174×	body	1280	valid
341.0ms	329×	body	160	valid
292.0ms	4009×	body	80	valid
102.0ms	594×	body	320	valid