Details

sample34.0ms

Algorithm

intervals

Results

10.0ms	70×	body	640	valid
4.0ms	122×	body	80	valid
4.0ms	24×	body	1280	valid
3.0ms	29×	body	320	valid
1.0ms	11×	body	160	valid

simplify4.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
10	4810
9	1188
8	437
7	210
6	162
5	135
4	89
3	41
2	31
1	18
0	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize36.0ms

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))
0.0b	(/ 1.0 (- x 1.0))
2.1b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite590.0ms

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-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

15.0ms	(/ 1.0 (+ x 1.0))
98.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
16.0ms	(/ 1.0 (- x 1.0))
377.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 1.0 (+ x 1.0))
63.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
47.0ms	(/ 1.0 (- x 1.0))
333.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.5s

Counts

630 → 630

Iterations

Iter	Nodes
done	5000
2	4183
1	1192
0	501

prune3.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 2.0 (* x x)) x)
0.3b	(/ 2.0 (pow x 7))
0.3b	(/ 2.0 (pow x 5))
0.7b	(/ 2.0 (* x x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
54×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
28×	`add-exp-log`
24×	`unpow-prod-down`
22×	`add-cbrt-cube`
18×	`associate-/r*`
16×	`associate-/l*`
13×	`div-exp`
9×	`cbrt-undiv`
8×	`div-inv` `sqr-pow`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod`
1×	`associate-/l/`

Counts

4 → 167

Calls

4 calls:

20.0ms	(/ (/ 2.0 (* x x)) x)
6.0ms	(/ 2.0 (pow x 7))
6.0ms	(/ 2.0 (pow x 5))
8.0ms	(/ 2.0 (* x x))

series247.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (/ 2.0 (* x x)) x)
80.0ms	(/ 2.0 (pow x 7))
64.0ms	(/ 2.0 (pow x 5))
51.0ms	(/ 2.0 (* x x))

simplify1.6s

Counts

179 → 179

Iterations

Iter	Nodes
done	5001
2	2898
1	549
0	256

prune944.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (/ (/ 2.0 x) (* x x)) (/ 2.0 (pow x 7))) (/ 2.0 (pow x 5)))
0.2b	(/ (/ 2.0 x) (* x x))
0.3b	(/ 2.0 (pow x 7))
0.3b	(/ 2.0 (pow x 5))

rewrite443.0ms

Algorithm

rewrite-expression-head

Rules

73×	`times-frac`
58×	`*-un-lft-identity`
51×	`add-sqr-sqrt` `add-cube-cbrt`
26×	`add-exp-log`
24×	`unpow-prod-down`
20×	`add-cbrt-cube`
19×	`associate-/l*`
15×	`associate-/r*`
12×	`div-exp`
9×	`add-log-exp`
8×	`cbrt-undiv` `sqr-pow`
5×	`div-inv`
4×	`expm1-log1p-u` `pow1` `fma-def` `frac-add` `log1p-expm1-u` `distribute-lft-out`
3×	`clear-num` `sum-log` `frac-2neg`
2×	`pow-to-exp` `flip3-+` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+`
1×	`+-commutative` `associate-+l+` `associate-/l/`

Counts

4 → 166

Calls

4 calls:

404.0ms	(+ (+ (/ (/ 2.0 x) (* x x)) (/ 2.0 (pow x 7))) (/ 2.0 (pow x 5)))
15.0ms	(/ (/ 2.0 x) (* x x))
6.0ms	(/ 2.0 (pow x 7))
10.0ms	(/ 2.0 (pow x 5))

series363.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(+ (+ (/ (/ 2.0 x) (* x x)) (/ 2.0 (pow x 7))) (/ 2.0 (pow x 5)))
78.0ms	(/ (/ 2.0 x) (* x x))
95.0ms	(/ 2.0 (pow x 7))
90.0ms	(/ 2.0 (pow x 5))

simplify2.0s

Counts

178 → 178

Iterations

Iter	Nodes
done	5000
2	3261
1	699
0	297

prune1.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 2.0 (* x x))
0.7b	(/ 2.0 (* x x))
26.6b	(sqrt (/ 2.0 (* x x)))
26.6b	(sqrt (/ 2.0 (* x x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`times-frac` `add-cbrt-cube` `add-exp-log` `sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `rem-sqrt-square` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `prod-exp` `cbrt-unprod`

Counts

4 → 88

Calls

4 calls:

6.0ms	(/ 2.0 (* x x))
6.0ms	(/ 2.0 (* x x))
5.0ms	(sqrt (/ 2.0 (* x x)))
6.0ms	(sqrt (/ 2.0 (* x x)))

series159.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 2.0 (* x x))
39.0ms	(/ 2.0 (* x x))
39.0ms	(sqrt (/ 2.0 (* x x)))
52.0ms	(sqrt (/ 2.0 (* x x)))

simplify855.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	665
1	143
0	67

prune568.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes180.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 9.7b

bsearch196.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	108.74599921555445
10	-17239113253358.373	-4.96108325192681e-05	-137.43678957349164

simplify9.0ms

Iterations

Iter	Nodes
done	36
1	36
0	30

end0.0ms

sample1.8s

Algorithm

intervals

Results

530.0ms	555×	body	1280	valid
469.0ms	1910×	body	640	valid
369.0ms	4156×	body	80	valid
240.0ms	916×	body	320	valid
50.0ms	463×	body	160	valid