Details

sample78.0ms

Algorithm

intervals

Results

25.0ms	60×	body	640	valid
15.0ms	128×	body	80	valid
13.0ms	21×	body	1280	valid
12.0ms	37×	body	320	valid
2.0ms	10×	body	160	valid

simplify193.0ms

Counts

1 → 1

Iterations

Iter	Nodes
11	195
10	195
9	187
8	132
7	94
6	83
5	75
4	63
3	43
2	33
1	19
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1))
0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
2.3b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite383.0ms

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:

10.0ms	(/ 1 (- x 1))
10.0ms	(/ 1 (+ x 1))
66.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
264.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ 1 (- x 1))
21.0ms	(/ 1 (+ x 1))
42.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
161.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify4.6s

Counts

660 → 660

Iterations

Iter	Nodes
2	2750
1	1122
0	495

prune6.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (- x 1)) (/ 1 (- x 1)))
0.3b	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
2.3b	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
13.9b	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

rewrite1.2s

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:

69.0ms	(* (/ 1 (- x 1)) (/ 1 (- x 1)))
285.0ms	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
154.0ms	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
533.0ms	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

series666.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (/ 1 (- x 1)) (/ 1 (- x 1)))
43.0ms	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
158.0ms	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
440.0ms	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

simplify3.7s

Counts

1434 → 1434

Iterations

Iter	Nodes
1	3689
0	1359

prune20.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1))
0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
2.3b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite315.0ms

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:

9.0ms	(/ 1 (- x 1))
9.0ms	(/ 1 (+ x 1))
53.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
218.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 1 (- x 1))
15.0ms	(/ 1 (+ x 1))
33.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
154.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify4.5s

Counts

660 → 660

Iterations

Iter	Nodes
2	2750
1	1122
0	495

prune7.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2 (pow x 7))
0.1b	(* (* x x) x)
0.2b	(/ 2 (pow x 5))
0.6b	(/ 2 (* (* x x) x))

rewrite59.0ms

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`
23×	`pow1`
22×	`add-cbrt-cube`
15×	`associate-/r*`
9×	`div-exp` `associate-/l*`
8×	`sqr-pow`
6×	`pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `pow-prod-down` `div-inv`
2×	`pow2` `pow-to-exp` `pow-exp` `pow-sqr`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

4 → 153

Calls

4 calls:

6.0ms	(/ 2 (pow x 7))
26.0ms	(* (* x x) x)
10.0ms	(/ 2 (pow x 5))
15.0ms	(/ 2 (* (* x x) x))

series231.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 2 (pow x 7))
35.0ms	(* (* x x) x)
86.0ms	(/ 2 (pow x 5))
42.0ms	(/ 2 (* (* x x) x))

simplify1.8s

Counts

165 → 165

Iterations

Iter	Nodes
3	3844
2	1291
1	411
0	215

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes111.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 9.5b

bsearch124.0ms

Steps

Iters	Range		Point
7	15.597049771107491	3862.7483140020904	109.3629970410856
10	-1231591086050.0088	-0.0006858147917088189	-119.2186693862327

simplify8.0ms

Iterations

Iter	Nodes
2	40
1	40
0	32

end0.0ms

sample2.0s

Algorithm

intervals

Results

747.0ms	1890×	body	640	valid
503.0ms	4183×	body	80	valid
253.0ms	912×	body	320	valid
251.0ms	561×	body	1280	valid
101.0ms	455×	body	160	valid