Details

sample63.0ms

Algorithm

intervals

Results

24.0ms	51×	body	1280	valid
9.0ms	41×	body	640	valid
7.0ms	124×	body	80	valid
5.0ms	30×	body	320	valid
1.0ms	10×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
12	4085
11	1745
10	535
9	183
8	79
7	58
6	39
5	27
4	21
3	19
2	16
1	12
0	7

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite329.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

17.0ms	(/ x (+ x 1.0))
38.0ms	(/ (+ x 1.0) (- x 1.0))
192.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series281.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(/ x (+ x 1.0))
40.0ms	(/ (+ x 1.0) (- x 1.0))
185.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.0s

Counts

605 → 605

Iterations

Iter	Nodes
done	5000
2	4599
1	1252
0	523

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 3.0 x) (/ 1.0 (* x x)))
0.1b	(/ 3.0 (pow x 3))
0.5b	(/ 1.0 (* x x))
5.8b	(- (- (/ 3.0 (pow x 3))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

527×	`*-un-lft-identity`
408×	`times-frac`
349×	`add-sqr-sqrt`
347×	`add-cube-cbrt`
336×	`prod-diff`
202×	`distribute-rgt-neg-in`
200×	`distribute-lft-neg-in`
102×	`unpow-prod-down` `cube-prod`
87×	`distribute-lft-out`
84×	`fma-neg`
34×	`cube-mult` `unpow3` `sqr-pow`
16×	`add-log-exp`
14×	`add-exp-log`
13×	`associate-/r*` `fma-def` `div-inv`
11×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`neg-mul-1` `div-exp`
4×	`expm1-log1p-u` `pow1` `diff-log` `log1p-expm1-u` `distribute-lft-out--`
3×	`cbrt-undiv` `sum-log` `frac-sub` `distribute-neg-frac`
2×	`clear-num` `frac-2neg` `flip3-+` `neg-log` `frac-add` `flip-+`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `+-commutative` `sub-neg` `flip3--` `pow-exp` `prod-exp` `cbrt-unprod` `flip--` `associate--r+` `difference-of-squares`

Counts

4 → 565

Calls

4 calls:

18.0ms	(+ (/ 3.0 x) (/ 1.0 (* x x)))
9.0ms	(/ 3.0 (pow x 3))
6.0ms	(/ 1.0 (* x x))
205.0ms	(- (- (/ 3.0 (pow x 3))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

series172.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+ (/ 3.0 x) (/ 1.0 (* x x)))
39.0ms	(/ 3.0 (pow x 3))
32.0ms	(/ 1.0 (* x x))
36.0ms	(- (- (/ 3.0 (pow x 3))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

simplify521.0ms

Counts

577 → 577

Iterations

Iter	Nodes
done	5000
1	1228
0	471

prune977.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.5b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
3.6b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite929.0ms

Algorithm

rewrite-expression-head

Rules

2796×	`*-un-lft-identity`
2108×	`times-frac`
1668×	`add-sqr-sqrt`
1404×	`prod-diff`
1190×	`add-cube-cbrt`
940×	`exp-sum`
537×	`distribute-lft-out`
473×	`log-prod`
268×	`associate-/r/`
260×	`distribute-lft-out--`
233×	`difference-of-squares`
134×	`div-inv`
80×	`flip3-+` `flip-+`
56×	`flip3--` `flip--`
32×	`exp-prod`
18×	`fma-neg`
17×	`log-pow`
9×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`sub-neg`
2×	`exp-diff` `diff-log` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `div-exp` `rem-log-exp` `frac-sub`

Counts

4 → 1560

Calls

4 calls:

269.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
27.0ms	(/ (+ x 1.0) (- x 1.0))
365.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
100.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series593.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
57.0ms	(/ (+ x 1.0) (- x 1.0))
185.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
167.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify873.0ms

Counts

1572 → 1572

Iterations

Iter	Nodes
done	5000
1	1876
0	1132

prune4.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(- (/ x (+ x 1.0)) (- (fma 2.0 x (fma 2.0 (* x x) 1.0))))
0.0b	(fma 2.0 x (fma 2.0 (* x x) 1.0))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

232×	`*-un-lft-identity`
180×	`prod-diff`
159×	`add-sqr-sqrt`
154×	`add-cube-cbrt`
145×	`times-frac`
55×	`distribute-rgt-neg-in`
54×	`distribute-lft-neg-in`
37×	`distribute-lft-out`
24×	`associate-/r/`
18×	`neg-mul-1` `fma-neg`
12×	`flip3-+` `flip-+` `div-inv`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`associate-/r*`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `associate-/l*`
2×	`diff-log` `fma-udef` `distribute-lft-out--` `difference-of-squares`
1×	`neg-sub0` `cbrt-undiv` `distribute-neg-in` `clear-num` `sub-neg` `frac-2neg` `flip3--` `div-exp` `neg-log` `flip--` `associate--r+` `associate--r-`

Counts

3 → 264

Calls

3 calls:

14.0ms	(/ x (+ x 1.0))
93.0ms	(- (/ x (+ x 1.0)) (- (fma 2.0 x (fma 2.0 (* x x) 1.0))))
0.0ms	(fma 2.0 x (fma 2.0 (* x x) 1.0))

series145.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ x (+ x 1.0))
53.0ms	(- (/ x (+ x 1.0)) (- (fma 2.0 x (fma 2.0 (* x x) 1.0))))
39.0ms	(fma 2.0 x (fma 2.0 (* x x) 1.0))

simplify2.4s

Counts

273 → 273

Iterations

Iter	Nodes
done	5000
2	3389
1	725
0	306

prune551.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes116.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.8b

bsearch2.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	26
1	26
0	22

end0.0ms

sample1.2s

Algorithm

intervals

Results

363.0ms	1694×	body	1280	valid
279.0ms	4092×	body	80	valid
209.0ms	1237×	body	640	valid
67.0ms	339×	body	160	valid
66.0ms	638×	body	320	valid