Details

sample59.0ms

Algorithm

intervals

Results

21.0ms	65×	body	1280	valid
15.0ms	70×	body	640	valid
6.0ms	178×	body	80	valid
3.0ms	19×	body	320	valid
1.0ms	14×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.0b	(- (exp x) 1.0)

rewrite70.0ms

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:

52.0ms	(/ (- (exp x) 1.0) x)
14.0ms	(- (exp x) 1.0)

series72.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- (exp x) 1.0) x)
27.0ms	(- (exp x) 1.0)

simplify2.4s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
3	2361
2	721
1	292
0	127

prune272.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(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×	`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 x (fma 1/6 x 1/2) 1)
0.0ms	(fma 1/6 x 1/2)

series87.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(fma x (fma 1/6 x 1/2) 1)
46.0ms	(fma 1/6 x 1/2)

simplify2.8s

Counts

26 → 26

Iterations

Iter	Nodes
done	5000
4	2796
3	498
2	133
1	57
0	33

prune162.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) x)
2.7b	(- (/ (exp x) x) (/ 1.0 x))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

262×	`times-frac`
213×	`add-sqr-sqrt`
209×	`*-un-lft-identity`
201×	`add-cube-cbrt`
169×	`prod-diff`
30×	`div-inv`
13×	`fma-neg`
4×	`add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `add-exp-log` `associate-/l`
2×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `distribute-rgt-out--` `diff-log` `div-exp` `frac-sub` `flip--` `sub-div`

Counts

2 → 236

Calls

2 calls:

10.0ms	(/ (exp x) x)
33.0ms	(- (/ (exp x) x) (/ 1.0 x))

series88.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (exp x) x)
53.0ms	(- (/ (exp x) x) (/ 1.0 x))

simplify2.2s

Counts

242 → 242

Iterations

Iter	Nodes
done	5000
2	1919
1	782
0	342

prune975.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (exp (fma x 2 x)) (* 1.0 (* 1.0 1.0))) (fma (exp x) (exp x) (* 1.0 (+ (exp x) 1.0)))) x)
0.0b	(fma (exp x) (exp x) (* 1.0 (+ (exp x) 1.0)))
0.0b	(/ (- (exp (fma x 2 x)) (* 1.0 (* 1.0 1.0))) (fma (exp x) (exp x) (* 1.0 (+ (exp x) 1.0))))
2.9b	(- (exp (fma x 2 x)) (* 1.0 (* 1.0 1.0)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `fma-neg` `div-exp` `prod-diff` `log1p-expm1-u`
3×	`div-sub` `fma-udef` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `exp-sum` `flip--`
1×	`sub-neg` `diff-log`

Counts

4 → 137

Calls

4 calls:

25.0ms	(/ (/ (- (exp (fma x 2 x)) (* 1.0 (* 1.0 1.0))) (fma (exp x) (exp x) (* 1.0 (+ (exp x) 1.0)))) x)
0.0ms	(fma (exp x) (exp x) (* 1.0 (+ (exp x) 1.0)))
41.0ms	(/ (- (exp (fma x 2 x)) (* 1.0 (* 1.0 1.0))) (fma (exp x) (exp x) (* 1.0 (+ (exp x) 1.0))))
20.0ms	(- (exp (fma x 2 x)) (* 1.0 (* 1.0 1.0)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (/ (- (exp (fma x 2 x)) (* 1.0 (* 1.0 1.0))) (fma (exp x) (exp x) (* 1.0 (+ (exp x) 1.0)))) x)
64.0ms	(fma (exp x) (exp x) (* 1.0 (+ (exp x) 1.0)))
149.0ms	(/ (- (exp (fma x 2 x)) (* 1.0 (* 1.0 1.0))) (fma (exp x) (exp x) (* 1.0 (+ (exp x) 1.0))))
40.0ms	(- (exp (fma x 2 x)) (* 1.0 (* 1.0 1.0)))

simplify2.0s

Counts

149 → 149

Iterations

Iter	Nodes
done	5001
2	1594
1	582
0	243

prune860.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.5b

bsearch83.0ms

Steps

Iters	Range		Point
10	-733100.9210806559	-4.034181863829644e-08	-9.248950464724179e-05

simplify8.0ms

Iterations

Iter	Nodes
done	40
1	40
0	31

end0.0ms

sample1.8s

Algorithm

intervals

Results

708.0ms	2264×	body	1280	valid
438.0ms	1639×	body	640	valid
219.0ms	5476×	body	80	valid
142.0ms	836×	body	320	valid
33.0ms	405×	body	160	valid