Details

sample45.0ms

Algorithm

intervals

Results

17.0ms	64×	body	640	valid
9.0ms	134×	body	80	valid
7.0ms	37×	body	320	valid
3.0ms	21×	body	160	valid

simplify23.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize22.0ms

Local error

Found 3 expressions with local error:

3.6b	(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
0.0b	(/ 1 (- x 1))
0.0b	(/ 1 (+ x 1))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

850×	`*-un-lft-identity`
783×	`times-frac`
710×	`add-sqr-sqrt`
486×	`prod-diff`
454×	`add-cube-cbrt`
125×	`difference-of-squares`
98×	`associate-/r/`
94×	`distribute-lft-out`
81×	`distribute-lft-out--`
58×	`difference-of-sqr-1`
52×	`div-inv`
30×	`flip-+`
29×	`flip3-+`
21×	`flip--`
20×	`flip3--`
18×	`fma-neg`
11×	`associate-/r*` `add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`pow1` `add-log-exp`
4×	`div-exp`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `pow-flip` `inv-pow`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 638

Calls

3 calls:

Slowest

85.0ms	(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
24.0ms	(/ 1 (- x 1))
16.0ms	(/ 1 (+ x 1))

series104.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

75.0ms	(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
15.0ms	(/ 1 (- x 1))
14.0ms	(/ 1 (+ x 1))

simplify893.0ms

Counts: 647 → 647

prune6.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

6.4b	(- (/ (/ 1 (sqrt (+ x 1))) (sqrt (+ x 1))) (/ 1 (- x 1)))
0.1b	(/ (/ 1 (sqrt (+ x 1))) (sqrt (+ x 1)))
0.1b	(/ 1 (sqrt (+ x 1)))
0.0b	(/ 1 (- x 1))

rewrite657.0ms

Algorithm

rewrite-expression-head

Rules

13988×	`times-frac`
11239×	`*-un-lft-identity`
9108×	`add-sqr-sqrt`
6629×	`add-cube-cbrt`
5627×	`sqrt-prod`
5265×	`prod-diff`
1400×	`distribute-lft-out`
1214×	`difference-of-squares`
860×	`associate-/r/`
597×	`distribute-lft-out--`
589×	`difference-of-sqr-1`
468×	`sqrt-div`
436×	`div-inv`
234×	`flip3-+` `flip-+`
197×	`flip3--` `flip--`
195×	`fma-neg`
33×	`associate-/l*`
21×	`associate-/r*` `add-exp-log`
14×	`pow1`
13×	`add-cbrt-cube`
10×	`div-exp`
9×	`pow-flip`
6×	`add-log-exp` `pow-div`
5×	`cbrt-undiv` `sqrt-pow1` `pow1/2`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `inv-pow`
1×	`sub-neg` `diff-log` `frac-sub` `associate-/l/`

Counts

4 → 5875

Calls

4 calls:

Slowest

149.0ms	(- (/ (/ 1 (sqrt (+ x 1))) (sqrt (+ x 1))) (/ 1 (- x 1)))
19.0ms	(/ (/ 1 (sqrt (+ x 1))) (sqrt (+ x 1)))
9.0ms	(/ 1 (- x 1))
8.0ms	(/ 1 (sqrt (+ x 1)))

series175.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

87.0ms	(- (/ (/ 1 (sqrt (+ x 1))) (sqrt (+ x 1))) (/ 1 (- x 1)))
44.0ms	(/ 1 (sqrt (+ x 1)))
23.0ms	(/ (/ 1 (sqrt (+ x 1))) (sqrt (+ x 1)))
20.0ms	(/ 1 (- x 1))

simplify9.1s

Counts: 5887 → 5887

prune1.2m

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 2 (* x x))
0.2b	(/ 2 (* (* (* x x) x) (* (* x x) x)))
0.1b	(* (* x x) (* x x))
0.1b	(* (* (* x x) x) (* (* x x) x))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

657×	`pow1`
314×	`pow-prod-up`
209×	`pow-plus`
114×	`pow-prod-down`
108×	`pow-sqr`
104×	`add-cbrt-cube` `add-exp-log`
66×	`pow2`
63×	`prod-exp` `cbrt-unprod`
22×	`pow3`
12×	`cbrt-undiv` `div-exp`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `associate-/r` `frac-2neg` `swap-sqr` `associate-r` `associate-l` `-commutative` `div-inv`
1×	`unswap-sqr`

Counts

4 → 324

Calls

4 calls:

Slowest

77.0ms	(* (* (* x x) x) (* (* x x) x))
72.0ms	(/ 2 (* (* (* x x) x) (* (* x x) x)))
22.0ms	(* (* x x) (* x x))
6.0ms	(/ 2 (* x x))

series183.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

52.0ms	(/ 2 (* (* (* x x) x) (* (* x x) x)))
47.0ms	(* (* (* x x) x) (* (* x x) x))
42.0ms	(* (* x x) (* x x))
42.0ms	(/ 2 (* x x))

simplify2.2s

Counts: 336 → 336

prune2.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2 (* (* (* x x) x) (* (* x x) x)))
0.1b	(/ (/ 2 x) x)
0.1b	(* (* x x) (* x x))
0.1b	(* (* (* x x) x) (* (* x x) x))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

657×	`pow1`
314×	`pow-prod-up`
209×	`pow-plus`
114×	`pow-prod-down`
108×	`pow-sqr`
104×	`add-cbrt-cube` `add-exp-log`
78×	`times-frac`
66×	`pow2`
62×	`prod-exp` `cbrt-unprod`
48×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
22×	`pow3`
16×	`associate-/l*`
13×	`cbrt-undiv` `div-exp`
6×	`div-inv`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `swap-sqr` `associate-r` `associate-l` `*-commutative`
1×	`unswap-sqr` `associate-/l/`

Counts

4 → 373

Calls

4 calls:

Slowest

100.0ms	(* (* (* x x) x) (* (* x x) x))
69.0ms	(/ 2 (* (* (* x x) x) (* (* x x) x)))
40.0ms	(* (* x x) (* x x))
8.0ms	(/ (/ 2 x) x)

series207.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

66.0ms	(/ 2 (* (* (* x x) x) (* (* x x) x)))
65.0ms	(* (* (* x x) x) (* (* x x) x))
48.0ms	(* (* x x) (* x x))
28.0ms	(/ (/ 2 x) x)

simplify717.0ms

Counts: 385 → 385

prune3.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 26.4b

bsearch154.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

603.0ms	1902×	body	640	valid
364.0ms	4223×	body	80	valid
327.0ms	1278×	body	320	valid
80.0ms	597×	body	160	valid