Details

sample69.0ms

Algorithm

intervals

Results

22.0ms	96×	body	10240	exit
16.0ms	64×	body	1280	valid
11.0ms	63×	body	640	valid
3.0ms	32×	body	320	valid
3.0ms	86×	body	80	valid
1.0ms	12×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.8b

localize6.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
3.8b	(- (exp x) 1.0)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 67

Calls

2 calls:

28.0ms	(/ (exp x) (- (exp x) 1.0))
11.0ms	(- (exp x) 1.0)

series80.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (exp x) (- (exp x) 1.0))
28.0ms	(- (exp x) 1.0)

simplify625.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	897
1	253
0	117

prune310.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp x) (fma (pow x 3) 1/6 (fma (* x x) 1/2 x)))
0.0b	(fma (* x x) 1/2 x)
10.3b	(fma (pow x 3) 1/6 (fma (* x x) 1/2 x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube`
4×	`add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 49

Calls

3 calls:

11.0ms	(/ (exp x) (fma (pow x 3) 1/6 (fma (* x x) 1/2 x)))
0.0ms	(fma (* x x) 1/2 x)
1.0ms	(fma (pow x 3) 1/6 (fma (* x x) 1/2 x))

series214.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (exp x) (fma (pow x 3) 1/6 (fma (* x x) 1/2 x)))
99.0ms	(fma (* x x) 1/2 x)
39.0ms	(fma (pow x 3) 1/6 (fma (* x x) 1/2 x))

simplify2.5s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	4162
2	683
1	187
0	97

prune337.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(/ 1.0 (exp x))
3.8b	(- 1 (/ 1.0 (exp x)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
70×	`times-frac`
59×	`add-cube-cbrt`
39×	`prod-diff`
20×	`difference-of-squares`
11×	`associate-/r*`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`div-inv` `distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `fma-neg` `div-exp` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `associate-/r/` `flip--`
1×	`rec-exp` `sub-neg` `diff-log` `1-exp` `pow-flip` `inv-pow`

Counts

3 → 145

Calls

3 calls:

35.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
6.0ms	(/ 1.0 (exp x))
32.0ms	(- 1 (/ 1.0 (exp x)))

series147.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
16.0ms	(/ 1.0 (exp x))
55.0ms	(- 1 (/ 1.0 (exp x)))

simplify2.1s

Counts

154 → 154

Iterations

Iter	Nodes
done	5001
2	2401
1	609
0	257

prune378.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 3)
0.4b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x))))
0.5b	(/ (exp x) (/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x)))))
3.7b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite355.0ms

Algorithm

rewrite-expression-head

Rules

717×	`add-sqr-sqrt`
612×	`times-frac`
479×	`*-un-lft-identity`
309×	`add-cube-cbrt`
282×	`unpow-prod-down` `cube-prod`
272×	`difference-of-squares`
162×	`sqr-pow`
144×	`prod-diff`
85×	`distribute-lft-out--`
82×	`associate-/r*`
28×	`associate-/l*`
26×	`cube-mult` `unpow3`
17×	`difference-cubes`
12×	`add-cbrt-cube` `fma-neg`
9×	`add-exp-log`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `pow-pow` `div-exp` `log1p-expm1-u`
3×	`pow-unpow` `exp-prod`
2×	`clear-num` `frac-2neg` `flip3--` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `diff-log` `div-sub` `pow-exp` `associate-/r/` `rem-cube-cbrt`

Counts

4 → 676

Calls

4 calls:

7.0ms	(pow (exp x) 3)
123.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x))))
102.0ms	(/ (exp x) (/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x)))))
58.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series369.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (exp x) 3)
125.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x))))
158.0ms	(/ (exp x) (/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x)))))
60.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify1.4s

Counts

688 → 688

Iterations

Iter	Nodes
done	5000
1	1899
0	691

prune2.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes114.0ms

Accuracy

94% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 11.5b

bsearch1.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	33
1	33
0	30

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	2519×	body	10240	exit
825.0ms	2308×	body	1280	valid
324.0ms	1612×	body	640	valid
109.0ms	2859×	body	80	valid
108.0ms	827×	body	320	valid
32.0ms	396×	body	160	valid