Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	60×	body	640	valid
4.0ms	133×	body	80	valid
3.0ms	21×	body	1280	valid
3.0ms	32×	body	320	valid
1.0ms	10×	body	160	valid

simplify96.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	18	15
2	31	15
3	41	15
4	50	15
5	55	15
6	64	15
7	82	15
8	99	15
9	109	15
done	109	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.5b

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))
2.4b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite480.0ms

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))
77.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
324.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1.0 (- x 1.0))
26.0ms	(/ 1.0 (+ x 1.0))
50.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
222.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.0s

Counts

630 → 630

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	502	19834
1	1149	17345
2	2799	12902
done	5001	10138

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x))
0.0b	(/ 1.0 (sqrt (+ x 1.0)))
0.1b	(/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
7.5b	(+ (- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite3.1s

Algorithm

rewrite-expression-head

Rules

13024×	`times-frac`
9784×	`*-un-lft-identity`
7160×	`add-sqr-sqrt`
7050×	`add-cube-cbrt`
5428×	`sqrt-prod`
5070×	`prod-diff`
2537×	`associate-+l+`
1356×	`distribute-lft-out`
616×	`div-inv`
452×	`sqrt-div` `associate-/r/`
227×	`flip3-+` `flip-+`
195×	`fma-neg`
30×	`associate-/l*`
28×	`difference-of-squares`
19×	`fma-def`
14×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`distribute-lft-out--`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`frac-add`
2×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `sum-log` `frac-sub` `flip--`
1×	`+-commutative` `associate-+l-` `associate-/l/`

Counts

4 → 5628

Calls

4 calls:

359.0ms	(- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x))
12.0ms	(/ 1.0 (sqrt (+ x 1.0)))
41.0ms	(/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
1.6s	(+ (- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x))
74.0ms	(/ 1.0 (sqrt (+ x 1.0)))
25.0ms	(/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
223.0ms	(+ (- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.2s

Counts

5640 → 5640

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	1947	238083
1	4206	201722
done	5000	163009

prune11.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (sqrt (+ x 1.0)))
0.1b	(* (/ 1.0 (sqrt (+ x 1.0))) x)
4.8b	(/ (fma (- (* (/ 1.0 (sqrt (+ x 1.0))) x) (* (sqrt (+ x 1.0)) 2.0)) (- x 1.0) (* (* (sqrt (+ x 1.0)) x) 1.0)) (* (* (sqrt (+ x 1.0)) x) (- x 1.0)))
12.4b	(fma (- (* (/ 1.0 (sqrt (+ x 1.0))) x) (* (sqrt (+ x 1.0)) 2.0)) (- x 1.0) (* (* (sqrt (+ x 1.0)) x) 1.0))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
47×	`times-frac`
45×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
29×	`sqrt-prod`
27×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
10×	`sqrt-div`
9×	`associate-*l/`
8×	`associate-/r*`
7×	`distribute-lft-out`
6×	`pow1` `associate-/l*`
5×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `associate-r` `flip--` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `clear-num`
1×	`pow-prod-down` `*-commutative` `fma-udef`

Counts

4 → 139

Calls

4 calls:

12.0ms	(/ 1.0 (sqrt (+ x 1.0)))
33.0ms	(* (/ 1.0 (sqrt (+ x 1.0))) x)
45.0ms	(/ (fma (- (* (/ 1.0 (sqrt (+ x 1.0))) x) (* (sqrt (+ x 1.0)) 2.0)) (- x 1.0) (* (* (sqrt (+ x 1.0)) x) 1.0)) (* (* (sqrt (+ x 1.0)) x) (- x 1.0)))
0.0ms	(fma (- (* (/ 1.0 (sqrt (+ x 1.0))) x) (* (sqrt (+ x 1.0)) 2.0)) (- x 1.0) (* (* (sqrt (+ x 1.0)) x) 1.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

280.0ms	(/ 1.0 (sqrt (+ x 1.0)))
130.0ms	(* (/ 1.0 (sqrt (+ x 1.0))) x)
934.0ms	(/ (fma (- (* (/ 1.0 (sqrt (+ x 1.0))) x) (* (sqrt (+ x 1.0)) 2.0)) (- x 1.0) (* (* (sqrt (+ x 1.0)) x) 1.0)) (* (* (sqrt (+ x 1.0)) x) (- x 1.0)))
298.0ms	(fma (- (* (/ 1.0 (sqrt (+ x 1.0))) x) (* (sqrt (+ x 1.0)) 2.0)) (- x 1.0) (* (* (sqrt (+ x 1.0)) x) 1.0))

simplify1.4s

Counts

151 → 151

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	292	3504
1	725	3369
2	2417	2922
done	5001	2913

prune414.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 5)))
0.2b	(/ 2.0 (pow x 5))
0.2b	(/ 2.0 (pow x 7))
0.3b	(/ 2.0 (pow x 3))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 205

Calls

4 calls:

57.0ms	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 5)))
7.0ms	(/ 2.0 (pow x 5))
7.0ms	(/ 2.0 (pow x 7))
8.0ms	(/ 2.0 (pow x 3))

series309.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 5)))
49.0ms	(/ 2.0 (pow x 5))
62.0ms	(/ 2.0 (pow x 7))
40.0ms	(/ 2.0 (pow x 3))

simplify777.0ms

Counts

217 → 217

Iterations

Useful iterations: done (772.0ms)

Iter	Nodes	Cost
0	263	2139
1	498	1870
2	1343	1802
done	5001	1801

prune551.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 25.6b

bsearch95.0ms

Steps

Iters	Range		Point
10	0.0001820196720056695	1126179.5725289274	120.6357054631159
9	-76786.820650899	-0.0002772006047103471	-0.9952950592534084

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	29	67
1	36	49
done	36	49

end0.0ms

sample664.0ms

Algorithm

intervals

Results

204.0ms	1803×	body	640	valid
136.0ms	4221×	body	80	valid
83.0ms	566×	body	1280	valid
79.0ms	956×	body	320	valid
26.0ms	456×	body	160	valid