Details

sample69.0ms

Algorithm

intervals

Results

27.0ms	74×	body	1280	valid
12.0ms	49×	body	640	valid
9.0ms	191×	body	80	valid
5.0ms	29×	body	320	valid
1.0ms	7×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
2.1b	(- (exp x) 1.0)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

66.0ms	(/ (- (exp x) 1.0) x)
12.0ms	(- (exp x) 1.0)

series68.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- (exp x) 1.0) x)
17.0ms	(- (exp x) 1.0)

simplify2.1s

Counts

74 → 74

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	127	854
1	281	745
2	612	665
3	1785	619
done	5001	605

prune255.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma x (fma 1/6 x 1/2) 1)
0.1b	(fma 1/6 x 1/2)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma x (fma 1/6 x 1/2) 1)
1.0ms	(fma 1/6 x 1/2)

series58.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(fma x (fma 1/6 x 1/2) 1)
34.0ms	(fma 1/6 x 1/2)

simplify2.6s

Counts

26 → 26

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	33	213
1	53	204
2	114	176
3	381	175
4	1753	175
done	5001	175

prune89.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) x)
0.0b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
2.3b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite473.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
139×	`*-un-lft-identity`
107×	`add-sqr-sqrt`
85×	`add-cube-cbrt`
44×	`difference-of-squares`
31×	`associate-/l*`
27×	`distribute-lft-out`
24×	`exp-sum`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
8×	`add-log-exp`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `fma-neg` `div-exp` `prod-diff` `log1p-expm1-u`
3×	`fma-def` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`+-commutative` `sub-neg` `diff-log` `sum-log`

Counts

4 → 214

Calls

4 calls:

7.0ms	(+ 1.0 (exp x))
196.0ms	(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) x)
195.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
63.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series222.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ 1.0 (exp x))
86.0ms	(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) x)
85.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
37.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.5s

Counts

226 → 226

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	319	4871
1	771	4677
2	2336	4400
done	5000	4386

prune811.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(/ (/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x)))) x)
0.0b	(pow (exp x) 3)
2.0b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite287.0ms

Algorithm

rewrite-expression-head

Rules

592×	`add-sqr-sqrt`
537×	`times-frac`
412×	`*-un-lft-identity`
280×	`add-cube-cbrt`
234×	`unpow-prod-down` `cube-prod`
208×	`difference-of-squares`
144×	`prod-diff`
130×	`sqr-pow`
79×	`associate-/l*`
65×	`distribute-lft-out--`
26×	`cube-mult` `unpow3`
13×	`difference-cubes`
12×	`fma-neg`
10×	`add-cbrt-cube`
9×	`add-exp-log`
8×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-unpow` `exp-prod` `fma-def` `div-exp` `associate-/r*`
2×	`div-sub`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `pow-exp` `clear-num` `sum-log` `flip--` `flip-+` `associate-/l/` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 574

Calls

4 calls:

20.0ms	(+ (exp x) 1.0)
149.0ms	(/ (/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x)))) x)
8.0ms	(pow (exp x) 3)
54.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series307.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (exp x) 1.0)
222.0ms	(/ (/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x)))) x)
29.0ms	(pow (exp x) 3)
40.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify2.9s

Counts

586 → 586

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	684	20648
1	1534	16838
2	4319	15766
done	5000	15762

prune1.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.6b

bsearch30.0ms

Steps

Iters	Range		Point
9	-0.12398824387462552	-4.403108084983288e-07	-0.00010118150260600152

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	26
1	21	26
done	21	26

end0.0ms

sample1.9s

Algorithm

intervals

Results

841.0ms	2259×	body	1280	valid
347.0ms	1643×	body	640	valid
264.0ms	5491×	body	80	valid
113.0ms	828×	body	320	valid
33.0ms	395×	body	160	valid