Details

sample70.0ms

Algorithm

intervals

Results

25.0ms	66×	body	640	valid
12.0ms	122×	body	80	valid
10.0ms	20×	body	1280	valid
10.0ms	31×	body	320	valid
3.0ms	17×	body	160	valid

simplify288.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize36.0ms

Local error

Found 4 expressions with local error:

3.3b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
0.0b	(/ 1 (+ x 1))
0.0b	(/ 1 (- x 1))

rewrite311.0ms

Algorithm

rewrite-expression-head

Rules

743×	`*-un-lft-identity`
715×	`times-frac`
544×	`add-sqr-sqrt`
494×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
99×	`distribute-lft-out`
72×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
22×	`distribute-lft-out--`
20×	`difference-of-squares`
18×	`fma-neg`
13×	`fma-def`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `difference-of-sqr-1` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `1-exp` `frac-sub` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 648

Calls

4 calls:

Slowest

220.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
46.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
9.0ms	(/ 1 (- x 1))
8.0ms	(/ 1 (+ x 1))

series198.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

116.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
42.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
22.0ms	(/ 1 (+ x 1))
17.0ms	(/ 1 (- x 1))

simplify1.9s

Counts: 660 → 660

prune6.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

14.9b	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
3.2b	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
0.3b	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
0.2b	(* (/ 1 (- x 1)) (/ 1 (- x 1)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

1672×	`*-un-lft-identity`
1578×	`times-frac`
1191×	`add-sqr-sqrt`
1002×	`add-cube-cbrt`
937×	`prod-diff`
472×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
196×	`frac-sub`
172×	`distribute-lft-out`
164×	`div-inv`
146×	`distribute-lft-out--`
117×	`associate-/r/`
112×	`frac-times`
87×	`difference-of-squares`
80×	`flip3--` `flip--`
62×	`swap-sqr` `associate-/l/`
58×	`associate-l/` `associate-r/`
52×	`flip3-+` `flip-+`
48×	`add-exp-log`
40×	`associate-r` `associate-l`
31×	`un-div-inv`
26×	`pow1`
20×	`add-cbrt-cube`
18×	`difference-of-sqr-1`
17×	`div-exp` `prod-exp`
16×	`associate-/r*`
10×	`unswap-sqr`
8×	`rec-exp` `1-exp` `pow-flip` `inv-pow`
6×	`pow-prod-up` `add-log-exp`
5×	`cbrt-undiv` `sub-neg` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `pow-sqr` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`pow2` `pow-plus` `*-commutative`
1×	`clear-num` `frac-2neg` `fma-neg` `diff-log` `div-sub`

Counts

4 → 1422

Calls

4 calls:

Slowest

532.0ms	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
203.0ms	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
121.0ms	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
48.0ms	(* (/ 1 (- x 1)) (/ 1 (- x 1)))

series592.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

356.0ms	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
141.0ms	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
61.0ms	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
34.0ms	(* (/ 1 (- x 1)) (/ 1 (- x 1)))

simplify3.7s

Counts: 1434 → 1434

prune19.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

3.3b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
0.0b	(/ 1 (+ x 1))
0.0b	(/ 1 (- x 1))

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

743×	`*-un-lft-identity`
715×	`times-frac`
544×	`add-sqr-sqrt`
494×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
99×	`distribute-lft-out`
72×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
22×	`distribute-lft-out--`
20×	`difference-of-squares`
18×	`fma-neg`
13×	`fma-def`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `difference-of-sqr-1` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `1-exp` `frac-sub` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 648

Calls

4 calls:

Slowest

194.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
46.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
15.0ms	(/ 1 (- x 1))
8.0ms	(/ 1 (+ x 1))

series175.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

121.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
25.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
16.0ms	(/ 1 (- x 1))
14.0ms	(/ 1 (+ x 1))

simplify1.6s

Counts: 660 → 660

prune5.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2 (pow x 5))
0.1b	(/ 2 (* x (* x x)))
0.1b	(/ 2 (pow x 7))
0.1b	(* x (* x x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
40×	`add-sqr-sqrt`
39×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-exp-log`
24×	`unpow-prod-down`
22×	`add-cbrt-cube`
18×	`pow1`
15×	`associate-/r*`
9×	`div-exp` `associate-/l*`
8×	`sqr-pow`
6×	`prod-exp` `cbrt-unprod`
5×	`cbrt-undiv` `pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `pow-prod-down` `div-inv`
2×	`pow-to-exp` `pow-exp`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

Slowest

18.0ms	(/ 2 (* x (* x x)))
13.0ms	(* x (* x x))
5.0ms	(/ 2 (pow x 7))
5.0ms	(/ 2 (pow x 5))

series200.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

69.0ms	(/ 2 (pow x 7))
57.0ms	(/ 2 (pow x 5))
39.0ms	(/ 2 (* x (* x x)))
34.0ms	(* x (* x x))

simplify1.4s

Counts: 161 → 161

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes71.0ms

Accuracy

98.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 9.9b

bsearch121.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

641.0ms	1893×	body	640	valid
347.0ms	4071×	body	80	valid
250.0ms	584×	body	1280	valid
231.0ms	945×	body	320	valid
67.0ms	508×	body	160	valid