Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	68×	body	640	valid
4.0ms	125×	body	80	valid
4.0ms	39×	body	320	valid
2.0ms	13×	body	1280	valid
1.0ms	11×	body	160	valid

simplify77.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	15
1	18	15
2	31	15
3	41	15
4	52	15
5	59	15
6	68	15
7	86	15
8	107	15
9	117	15
done	117	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.6b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite347.0ms

Algorithm

rewrite-expression-head

Rules

707×	`*-un-lft-identity`
691×	`times-frac`
514×	`add-sqr-sqrt`
482×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
91×	`distribute-lft-out`
64×	`div-inv`
56×	`associate-/r/`
28×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
10×	`fma-def` `add-log-exp`
5×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `flip3--` `frac-add` `flip--` `log1p-expm1-u` `associate-/l*`
2×	`sub-neg` `diff-log` `sum-log` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `clear-num`

Counts

3 → 583

Calls

3 calls:

5.0ms	(/ 1.0 (- x 1.0))
51.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
236.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series324.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ 1.0 (- x 1.0))
47.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
244.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.2s

Counts

592 → 592

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	485	19448
1	1053	16993
2	2785	12566
done	5001	12442

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.2b	(/ 1.0 (- (* x x) (* 1.0 1.0)))
10.2b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0)))
15.6b	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0))

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

689×	`times-frac`
677×	`*-un-lft-identity`
520×	`add-sqr-sqrt`
491×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
84×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
36×	`flip3-+` `flip-+`
18×	`fma-neg` `associate-l`
15×	`frac-add` `difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
10×	`fma-def`
8×	`frac-times` `flip3--` `associate-*r/` `flip--`
6×	`pow1` `frac-sub` `distribute-lft-out--`
4×	`expm1-log1p-u` `associate-r` `associate-l/` `associate-/r` `log1p-expm1-u`
3×	`associate-/l*`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in` `diff-log` `div-exp` `prod-exp` `sum-log` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+l-` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 633

Calls

4 calls:

49.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
222.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0)))
24.0ms	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0))

series482.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
53.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
320.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0)))
58.0ms	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0))

simplify582.0ms

Counts

645 → 645

Iterations

Useful iterations: done (550.0ms)

Iter	Nodes	Cost
0	602	23464
1	1577	20867
done	5000	18714

prune1.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
0.0b	(/ 1 (pow x 7))
0.1b	(/ 1 (pow x 5))
0.1b	(/ 1 (pow x 3))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

105×	`times-frac`
87×	`*-un-lft-identity`
77×	`add-sqr-sqrt` `add-cube-cbrt`
45×	`unpow-prod-down`
31×	`add-exp-log`
26×	`associate-/r*`
25×	`fma-def`
18×	`div-exp`
15×	`sqr-pow`
12×	`cube-prod`
10×	`add-cbrt-cube`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
8×	`div-inv`
7×	`distribute-lft-out`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `inv-pow`
1×	`+-commutative` `flip3-+` `frac-add` `sum-log` `flip-+`

Counts

4 → 231

Calls

4 calls:

60.0ms	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
4.0ms	(/ 1 (pow x 7))
4.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 3))

series246.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
63.0ms	(/ 1 (pow x 7))
46.0ms	(/ 1 (pow x 5))
39.0ms	(/ 1 (pow x 3))

simplify1.4s

Counts

243 → 243

Iterations

Useful iterations: 2 (270.0ms)

Iter	Nodes	Cost
0	250	2254
1	487	1703
2	1023	1646
done	5001	1646

prune445.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (/ 1 (pow x 5)) (pow x -3)) (/ 1 (pow x 7)))
0.0b	(+ (/ 1 (pow x 5)) (pow x -3))
0.0b	(/ 1 (pow x 7))
0.1b	(/ 1 (pow x 5))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

68×	`*-un-lft-identity`
63×	`times-frac`
51×	`add-sqr-sqrt` `add-cube-cbrt`
33×	`unpow-prod-down`
30×	`fma-def`
22×	`add-exp-log`
14×	`associate-/r*` `distribute-lft-out`
12×	`div-exp`
11×	`add-log-exp` `sqr-pow`
10×	`div-inv`
8×	`add-cbrt-cube`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
4×	`pow1` `expm1-log1p-u` `sum-log` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `+-commutative` `pow-flip` `frac-2neg` `frac-add` `clear-num` `inv-pow`
1×	`associate-+l+`

Counts

4 → 178

Calls

4 calls:

155.0ms	(+ (+ (/ 1 (pow x 5)) (pow x -3)) (/ 1 (pow x 7)))
26.0ms	(+ (/ 1 (pow x 5)) (pow x -3))
4.0ms	(/ 1 (pow x 7))
4.0ms	(/ 1 (pow x 5))

series284.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (+ (/ 1 (pow x 5)) (pow x -3)) (/ 1 (pow x 7)))
115.0ms	(+ (/ 1 (pow x 5)) (pow x -3))
60.0ms	(/ 1 (pow x 7))
46.0ms	(/ 1 (pow x 5))

simplify1.7s

Counts

190 → 190

Iterations

Useful iterations: 3 (605.0ms)

Iter	Nodes	Cost
0	207	1977
1	440	1645
2	1027	1570
3	4070	1562
done	5001	1562

prune410.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 26.3b

bsearch93.0ms

Steps

Iters	Range		Point
8	0.44834868164545755	179.5191949529741	111.79023992954416
7	-436.72743869654124	-4.891764506654909	-118.86664556304571

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	31	65
1	42	49
done	42	49

end0.0ms

sample680.0ms

Algorithm

intervals

Results

236.0ms	1919×	body	640	valid
140.0ms	4135×	body	80	valid
91.0ms	971×	body	320	valid
80.0ms	522×	body	1280	valid
28.0ms	455×	body	160	valid