Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	57×	body	640	valid
4.0ms	134×	body	80	valid
2.0ms	31×	body	320	valid
2.0ms	17×	body	1280	valid
1.0ms	17×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7
done	209	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.0b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite475.0ms

Algorithm

rewrite-expression-head

Rules

725×	`*-un-lft-identity`
703×	`times-frac`
524×	`add-sqr-sqrt`
492×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
11×	`add-log-exp`
10×	`fma-def`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

11.0ms	(/ 1.0 (- x 1.0))
10.0ms	(/ 1.0 (+ x 1.0))
75.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
324.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1.0 (- x 1.0))
25.0ms	(/ 1.0 (+ x 1.0))
45.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
216.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify142.0ms

Counts

630 → 630

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	1156	10955
1	3607	8288
2	5001	7670
done	5001	7670

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.8b	(exp (log (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))))
2.0b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite625.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
700×	`times-frac`
508×	`add-sqr-sqrt`
484×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
103×	`distribute-lft-out`
64×	`div-inv`
56×	`associate-/r/`
30×	`flip3-+` `flip-+`
20×	`distribute-lft-out--`
18×	`fma-neg`
11×	`add-log-exp`
10×	`fma-def`
9×	`log-prod` `exp-sum`
8×	`difference-of-squares`
6×	`add-exp-log` `frac-add` `add-cbrt-cube`
5×	`pow1` `log-div` `exp-diff`
4×	`expm1-log1p-u` `exp-prod` `associate-/r*` `log1p-expm1-u`
3×	`flip3--` `frac-sub` `flip--` `associate-/l*`
2×	`sub-neg` `diff-log` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `clear-num` `log-pow` `rem-exp-log`

Counts

4 → 607

Calls

4 calls:

11.0ms	(/ 1.0 (+ x 1.0))
72.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
167.0ms	(exp (log (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))))
322.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1.0 (+ x 1.0))
47.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
223.0ms	(exp (log (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))))
232.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify150.0ms

Counts

619 → 619

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	1120	11110
1	3404	8427
2	5002	7809
done	5002	7809

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.0b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite468.0ms

Algorithm

rewrite-expression-head

Rules

725×	`*-un-lft-identity`
703×	`times-frac`
524×	`add-sqr-sqrt`
492×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
11×	`add-log-exp`
10×	`fma-def`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

10.0ms	(/ 1.0 (- x 1.0))
11.0ms	(/ 1.0 (+ x 1.0))
75.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
319.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1.0 (- x 1.0))
31.0ms	(/ 1.0 (+ x 1.0))
44.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
243.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify153.0ms

Counts

630 → 630

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	1156	10955
1	3607	8288
2	5001	7670
done	5001	7670

prune1.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
0.2b	(/ 1 (pow x 5))
0.2b	(/ 1 (pow x 7))
0.2b	(/ 2.0 (pow x 3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`unpow-prod-down`
27×	`add-exp-log`
26×	`associate-/r*`
15×	`div-exp`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`associate-/l*`
7×	`pow-to-exp` `pow-exp`
6×	`rec-exp` `1-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
2×	`pow-flip` `inv-pow`
1×	`fma-udef`

Counts

4 → 187

Calls

4 calls:

0.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
8.0ms	(/ 1 (pow x 5))
8.0ms	(/ 1 (pow x 7))
11.0ms	(/ 2.0 (pow x 3))

series222.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
52.0ms	(/ 1 (pow x 5))
63.0ms	(/ 1 (pow x 7))
39.0ms	(/ 2.0 (pow x 3))

simplify57.0ms

Counts

199 → 199

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	460	970
1	2326	837
2	5001	837
done	5001	837

prune400.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes75.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 9.4b

bsearch103.0ms

Steps

Iters	Range		Point
9	7.055123656280252	892369.0132880388	109.89750468235896
10	-1.8070707071506563e+17	-0.15939393977811658	-111.02026224228146

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	27
1	48	27
2	48	27
done	48	27

end0.0ms

sample620.0ms

Algorithm

intervals

Results

197.0ms	1861×	body	640	valid
123.0ms	4112×	body	80	valid
77.0ms	598×	body	1280	valid
72.0ms	938×	body	320	valid
26.0ms	491×	body	160	valid