Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	60×	body	640	valid
3.0ms	130×	body	80	valid
3.0ms	46×	body	320	valid
1.0ms	20×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	15	11
done	15	11

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
3.6b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

662×	`*-un-lft-identity`
589×	`times-frac`
496×	`add-sqr-sqrt`
378×	`prod-diff`
368×	`add-cube-cbrt`
86×	`associate-/r/`
79×	`distribute-lft-out--`
76×	`distribute-lft-out`
62×	`difference-of-squares`
44×	`div-inv`
24×	`flip-+`
23×	`flip3-+`
21×	`flip--`
20×	`flip3--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 504

Calls

3 calls:

5.0ms	(/ 1.0 (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
68.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series230.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(/ 1.0 (+ x 1.0))
27.0ms	(/ 1.0 (- x 1.0))
174.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify1.4s

Counts

513 → 513

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	525	24322
1	1180	21760
2	2919	16672
done	5000	16240

prune640.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ 1.0 (- (* x x) (* 1.0 1.0)))
3.2b	(- (- x 1.0) (+ x 1.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
39×	`add-sqr-sqrt`
29×	`prod-diff`
27×	`add-cube-cbrt`
14×	`add-log-exp`
12×	`times-frac`
11×	`associate--l+` `distribute-lft-out--`
10×	`difference-of-squares`
7×	`distribute-lft-out`
6×	`diff-log`
5×	`fma-neg`
4×	`add-exp-log` `flip3--` `associate-/r*` `frac-sub` `add-cbrt-cube` `flip--`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `sub-neg` `flip3-+` `sum-log` `associate-/r/` `flip-+` `log1p-expm1-u`
1×	`cbrt-undiv` `associate--l-` `frac-2neg` `div-exp` `clear-num` `div-inv` `associate--r+`

Counts

2 → 99

Calls

2 calls:

5.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
30.0ms	(- (- x 1.0) (+ x 1.0))

series60.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
7.0ms	(- (- x 1.0) (+ x 1.0))

simplify937.0ms

Counts

105 → 105

Iterations

Useful iterations: done (934.0ms)

Iter	Nodes	Cost
0	196	1915
1	495	1569
2	1858	1323
done	5001	1314

prune194.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 2.0 (pow x 2)) (/ 2.0 (pow x 4)))
0.1b	(/ 2.0 (pow x 4))
0.3b	(/ 2.0 (pow x 6))
0.5b	(/ 2.0 (pow x 2))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
78×	`*-un-lft-identity`
70×	`add-sqr-sqrt` `add-cube-cbrt`
45×	`unpow-prod-down`
28×	`fma-def`
22×	`associate-/r*`
19×	`add-exp-log`
15×	`sqr-pow`
10×	`add-cbrt-cube`
9×	`div-exp` `associate-/l*`
7×	`unpow2`
6×	`div-inv` `add-log-exp`
5×	`distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `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 → 192

Calls

4 calls:

47.0ms	(+ (/ 2.0 (pow x 2)) (/ 2.0 (pow x 4)))
6.0ms	(/ 2.0 (pow x 4))
4.0ms	(/ 2.0 (pow x 6))
4.0ms	(/ 2.0 (pow x 2))

series206.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (/ 2.0 (pow x 2)) (/ 2.0 (pow x 4)))
38.0ms	(/ 2.0 (pow x 4))
48.0ms	(/ 2.0 (pow x 6))
30.0ms	(/ 2.0 (pow x 2))

simplify1.5s

Counts

204 → 204

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	257	1945
1	488	1763
2	1293	1610
done	5000	1589

prune533.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (/ 2.0 x) (pow x (/ 2 2))) (/ 2.0 (pow x 4)))
0.1b	(/ 2.0 (pow x 4))
0.1b	(/ (/ 2.0 x) (pow x (/ 2 2)))
0.3b	(/ 2.0 (pow x 6))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

361×	`times-frac`
202×	`*-un-lft-identity`
196×	`add-sqr-sqrt` `add-cube-cbrt`
105×	`unpow-prod-down`
95×	`fma-def`
35×	`sqr-pow`
27×	`add-exp-log`
21×	`associate-/r*`
19×	`div-inv` `associate-/l*`
15×	`div-exp`
13×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `pow-to-exp` `pow-exp` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`distribute-lft-out`
1×	`+-commutative` `flip3-+` `frac-add` `sum-log` `flip-+` `associate-/l/`

Counts

4 → 337

Calls

4 calls:

131.0ms	(+ (/ (/ 2.0 x) (pow x (/ 2 2))) (/ 2.0 (pow x 4)))
4.0ms	(/ 2.0 (pow x 4))
8.0ms	(/ (/ 2.0 x) (pow x (/ 2 2)))
4.0ms	(/ 2.0 (pow x 6))

series206.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (/ (/ 2.0 x) (pow x (/ 2 2))) (/ 2.0 (pow x 4)))
36.0ms	(/ 2.0 (pow x 4))
29.0ms	(/ (/ 2.0 x) (pow x (/ 2 2)))
48.0ms	(/ 2.0 (pow x 6))

simplify1.6s

Counts

349 → 349

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	415	4158
1	885	3224
2	2559	2582
done	5000	2578

prune929.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes41.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 14.3b

bsearch84.0ms

Steps

Iters	Range		Point
7	1766.3470775505596	94269.73169533648	14237.069114952126
10	-5.579151754068455e+22	-2572101730117.1323	-9124183958286494.0

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	31	69
1	39	48
done	39	48

end0.0ms

sample462.0ms

Algorithm

intervals

Results

157.0ms	1907×	body	640	valid
96.0ms	4137×	body	80	valid
85.0ms	1274×	body	320	valid
29.0ms	682×	body	160	valid