Details

sample41.0ms

Algorithm

intervals

Results

13.0ms	70×	body	640	valid
6.0ms	24×	body	1280	valid
5.0ms	122×	body	80	valid
4.0ms	29×	body	320	valid
1.0ms	11×	body	160	valid

simplify179.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	198
9	198
8	170
7	103
6	83
5	72
4	60
3	41
2	31
1	18
0	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize37.0ms

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)))

rewrite655.0ms

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:

9.0ms	(/ 1.0 (+ x 1.0))
90.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
17.0ms	(/ 1.0 (- x 1.0))
484.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1.0 (+ x 1.0))
62.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
47.0ms	(/ 1.0 (- x 1.0))
319.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.4s

Counts

630 → 630

Iterations

Iter	Nodes
done	5007
2	3115
1	1189
0	501

prune3.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.2b	(/ 2.0 (* x (* x x)))
0.3b	(/ 2.0 (pow x 7))
0.3b	(/ 2.0 (pow x 5))

rewrite64.0ms

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` `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 → 145

Calls

4 calls:

24.0ms	(* x (* x x))
20.0ms	(/ 2.0 (* x (* x x)))
5.0ms	(/ 2.0 (pow x 7))
7.0ms	(/ 2.0 (pow x 5))

series230.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* x (* x x))
59.0ms	(/ 2.0 (* x (* x x)))
66.0ms	(/ 2.0 (pow x 7))
57.0ms	(/ 2.0 (pow x 5))

simplify1.2s

Counts

157 → 157

Iterations

Iter	Nodes
done	5009
2	1731
1	422
0	215

prune622.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize41.0ms

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))

rewrite502.0ms

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:

457.0ms	(+ (+ (/ (/ 2.0 x) (* x x)) (/ 2.0 (pow x 7))) (/ 2.0 (pow x 5)))
17.0ms	(/ (/ 2.0 x) (* x x))
9.0ms	(/ 2.0 (pow x 7))
9.0ms	(/ 2.0 (pow x 5))

series379.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(+ (+ (/ (/ 2.0 x) (* x x)) (/ 2.0 (pow x 7))) (/ 2.0 (pow x 5)))
74.0ms	(/ (/ 2.0 x) (* x x))
96.0ms	(/ 2.0 (pow x 7))
100.0ms	(/ 2.0 (pow x 5))

simplify1.8s

Counts

178 → 178

Iterations

Iter	Nodes
done	5042
2	2526
1	678
0	297

prune958.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (pow x 7))
0.3b	(/ 2.0 (pow x 5))
0.5b	(/ (sqrt 2.0) x)
0.5b	(/ (sqrt 2.0) x)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
66×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
24×	`unpow-prod-down` `sqrt-prod`
20×	`associate-/r*`
18×	`add-exp-log` `associate-/l*`
12×	`add-cbrt-cube`
8×	`div-exp` `sqr-pow`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `clear-num` `frac-2neg` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-to-exp` `pow-exp`

Counts

4 → 176

Calls

4 calls:

11.0ms	(/ 2.0 (pow x 7))
9.0ms	(/ 2.0 (pow x 5))
10.0ms	(/ (sqrt 2.0) x)
10.0ms	(/ (sqrt 2.0) x)

series340.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ 2.0 (pow x 7))
88.0ms	(/ 2.0 (pow x 5))
98.0ms	(/ (sqrt 2.0) x)
64.0ms	(/ (sqrt 2.0) x)

simplify2.6s

Counts

188 → 188

Iterations

Iter	Nodes
done	5000
3	4317
2	1149
1	366
0	210

prune1.1s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0b

regimes137.0ms

Accuracy

99.5% (0.1b remaining)

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

bsearch201.0ms

Steps

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

simplify4.0ms

Iterations

Iter	Nodes
done	33
1	33
0	26

end0.0ms

sample1.9s

Algorithm

intervals

Results

550.0ms	916×	body	320	valid
474.0ms	1910×	body	640	valid
358.0ms	4156×	body	80	valid
228.0ms	555×	body	1280	valid
95.0ms	463×	body	160	valid