Details

sample35.0ms

Algorithm

intervals

Results

14.0ms	69×	body	640	valid
5.0ms	120×	body	80	valid
3.0ms	31×	body	320	valid
3.0ms	15×	body	1280	valid
1.0ms	21×	body	160	valid

simplify158.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize13.0ms

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)))

rewrite681.0ms

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:

24.0ms	(/ 1.0 (- x 1.0))
24.0ms	(/ 1.0 (+ x 1.0))
111.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
423.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series545.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1.0 (- x 1.0))
46.0ms	(/ 1.0 (+ x 1.0))
72.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
371.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.8s

Counts

630 → 630

Iterations

Useful iterations: done (2.7s)

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

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

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:

91.0ms	(+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 7)))
14.0ms	(/ 2.0 (pow x 5))
8.0ms	(/ 2.0 (pow x 7))
8.0ms	(/ 2.0 (pow x 3))

series516.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 7)))
104.0ms	(/ 2.0 (pow x 5))
75.0ms	(/ 2.0 (pow x 7))
57.0ms	(/ 2.0 (pow x 3))

simplify1.1s

Counts

217 → 217

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	263	2139
1	498	1870
2	1342	1802
done	5000	1801

prune850.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 7)))
0.0b	(/ 2.0 (pow x 5))
0.1b	(/ (/ 2.0 x) (* x x))
0.2b	(/ 2.0 (pow x 7))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 186

Calls

4 calls:

104.0ms	(+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 7)))
8.0ms	(/ 2.0 (pow x 5))
22.0ms	(/ (/ 2.0 x) (* x x))
15.0ms	(/ 2.0 (pow x 7))

series481.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 7)))
81.0ms	(/ 2.0 (pow x 5))
74.0ms	(/ (/ 2.0 x) (* x x))
99.0ms	(/ 2.0 (pow x 7))

simplify1.5s

Counts

198 → 198

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	271	1954
1	563	1761
2	1498	1641
done	5001	1640

prune996.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (pow x 5))
0.1b	(* (sqrt 2.0) (/ (sqrt 2.0) (pow x 3)))
0.2b	(/ 2.0 (pow x 7))
0.3b	(/ (sqrt 2.0) (pow x 3))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

202×	`times-frac`
176×	`add-sqr-sqrt`
128×	`add-cube-cbrt` `*-un-lft-identity`
95×	`sqrt-prod`
76×	`associate-r`
67×	`unpow-prod-down`
43×	`cube-prod`
29×	`add-exp-log`
26×	`associate-/r*`
25×	`sqr-pow`
18×	`unswap-sqr`
15×	`add-cbrt-cube`
13×	`cube-mult` `unpow3`
12×	`div-exp` `associate-/l*`
6×	`pow1` `associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `pow-to-exp` `pow-exp` `prod-exp` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`cbrt-unprod`
1×	`associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 318

Calls

4 calls:

15.0ms	(/ 2.0 (pow x 5))
98.0ms	(* (sqrt 2.0) (/ (sqrt 2.0) (pow x 3)))
15.0ms	(/ 2.0 (pow x 7))
21.0ms	(/ (sqrt 2.0) (pow x 3))

series404.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ 2.0 (pow x 5))
157.0ms	(* (sqrt 2.0) (/ (sqrt 2.0) (pow x 3)))
77.0ms	(/ 2.0 (pow x 7))
80.0ms	(/ (sqrt 2.0) (pow x 3))

simplify1.5s

Counts

330 → 330

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	345	4137
1	629	3346
2	2078	3108
done	5001	3082

prune1.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch154.0ms

Steps

Iters	Range		Point
9	0.0033303272193615503	311302.39110615524	104.14959850437234
7	-1204.6599638446712	-30.191575632521864	-97.23298484104902

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	29	64
1	36	46
done	36	46

end0.0ms

sample2.0s

Algorithm

intervals

Results

706.0ms	937×	body	320	valid
447.0ms	1935×	body	640	valid
312.0ms	4122×	body	80	valid
239.0ms	530×	body	1280	valid
101.0ms	480×	body	160	valid