Details

sample54.0ms

Algorithm

intervals

Results

18.0ms	65×	body	1280	valid
12.0ms	62×	body	640	valid
6.0ms	182×	body	80	valid
4.0ms	33×	body	320	valid
1.0ms	12×	body	160	valid

simplify19.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.8b	(- (exp x) 1.0)

rewrite48.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*` `fma-neg`
2×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 68

Calls

2 calls:

27.0ms	(/ (- (exp x) 1.0) x)
18.0ms	(- (exp x) 1.0)

series88.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(/ (- (exp x) 1.0) x)
22.0ms	(- (exp x) 1.0)

simplify733.0ms

Counts

74 → 74

Iterations

Useful iterations: done (731.0ms)

Iter	Nodes	Cost
0	127	854
1	296	749
2	1006	668
done	5000	648

prune284.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/2 x (fma 1/6 (pow x 2) 1))
0.0b	(fma 1/6 (pow x 2) 1)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

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

series112.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(fma 1/2 x (fma 1/6 (pow x 2) 1))
88.0ms	(fma 1/6 (pow x 2) 1)

simplify910.0ms

Counts

26 → 26

Iterations

Useful iterations: done (909.0ms)

Iter	Nodes	Cost
0	30	266
1	52	257
2	189	226
3	1293	224
done	5000	199

prune169.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (fma x 1/6 1/2))
0.1b	(fma x 1/6 1/2)
0.9b	(exp (log1p (* x (fma x 1/6 1/2))))
10.0b	(log1p (* x (fma x 1/6 1/2)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`expm1-log1p-u` `add-log-exp`
4×	`log1p-expm1-u`
3×	`exp-prod` `associate-r` `associate-l` `fma-udef`
2×	`log1p-udef` `rem-exp-log`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

6.0ms	(* x (fma x 1/6 1/2))
0.0ms	(fma x 1/6 1/2)
2.0ms	(exp (log1p (* x (fma x 1/6 1/2))))
1.0ms	(log1p (* x (fma x 1/6 1/2)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* x (fma x 1/6 1/2))
44.0ms	(fma x 1/6 1/2)
86.0ms	(exp (log1p (* x (fma x 1/6 1/2))))
72.0ms	(log1p (* x (fma x 1/6 1/2)))

simplify597.0ms

Counts

69 → 69

Iterations

Useful iterations: done (595.0ms)

Iter	Nodes	Cost
0	112	695
1	255	659
2	914	580
done	5001	568

prune386.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 3)
0.0b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (* x (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x)))))
0.0b	(* x (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x))))
3.7b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

161×	`add-sqr-sqrt`
144×	`prod-diff`
117×	`*-un-lft-identity`
114×	`unpow-prod-down` `cube-prod`
87×	`add-cube-cbrt`
50×	`sqr-pow`
48×	`difference-of-squares`
26×	`cube-mult` `unpow3`
25×	`times-frac` `associate-/l*`
15×	`distribute-lft-out--`
12×	`add-cbrt-cube` `fma-neg`
11×	`add-exp-log`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`difference-cubes` `pow-unpow` `exp-prod` `associate-r` `associate-l`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `cbrt-unprod` `fma-udef` `flip--` `associate-/l/`
1×	`distribute-rgt-in` `pow-to-exp` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `div-sub` `pow-prod-down` `pow-exp` `-commutative` `div-inv` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 312

Calls

4 calls:

3.0ms	(pow (exp x) 3)
115.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (* x (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x)))))
11.0ms	(* x (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x))))
52.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series424.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (exp x) 3)
214.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (* x (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x)))))
119.0ms	(* x (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x))))
66.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify2.6s

Counts

324 → 324

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	341	8898
1	869	6044
2	4203	4879
done	5000	4878

prune875.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes71.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.2b

bsearch55.0ms

Steps

Iters	Range		Point
8	-0.00181011214377754	-1.6902992745682556e-06	-0.00016704963527402913

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	54
1	34	54
done	34	54

end0.0ms

sample1.8s

Algorithm

intervals

Results

827.0ms	2317×	body	1280	valid
325.0ms	1622×	body	640	valid
177.0ms	5413×	body	80	valid
108.0ms	833×	body	320	valid
66.0ms	402×	body	160	valid