Details

sample89.0ms

Algorithm

intervals

Results

52.0ms	93×	body	10240	exit
15.0ms	275×	body	80	valid
2.0ms	6×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	1280	valid
0.0ms	4×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
3	23
2	19
1	12
0	8

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.5b	(log (+ 1.0 (exp x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `log-prod` `add-cube-cbrt`
6×	`pow1` `add-log-exp`
4×	`log-div` `fma-neg` `prod-diff` `associate--l+` `add-exp-log`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `add-cbrt-cube` `log-pow` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--`

Counts

3 → 62

Calls

3 calls:

11.0ms	(+ 1.0 (exp x))
20.0ms	(- (log (+ 1.0 (exp x))) (* x y))
9.0ms	(log (+ 1.0 (exp x)))

series188.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(+ 1.0 (exp x))
62.0ms	(- (log (+ 1.0 (exp x))) (* x y))
113.0ms	(log (+ 1.0 (exp x)))

simplify2.5s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
3	3790
2	755
1	242
0	105

prune427.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (exp x) 1.0) (exp x))
0.4b	(/ (fma 1.0 (* 1.0 1.0) (exp (* 3 x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x))))
0.5b	(log (/ (fma 1.0 (* 1.0 1.0) (exp (* 3 x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x)))))
3.9b	(- (exp x) 1.0)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`times-frac`
13×	`log-prod`
10×	`add-exp-log`
9×	`prod-diff`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `fma-neg` `associate-r` `associate-/l`
2×	`flip3--` `div-exp` `rem-log-exp` `associate-*l/` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `log-div` `clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 107

Calls

4 calls:

32.0ms	(* (- (exp x) 1.0) (exp x))
4.0ms	(/ (fma 1.0 (* 1.0 1.0) (exp (* 3 x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x))))
2.0ms	(log (/ (fma 1.0 (* 1.0 1.0) (exp (* 3 x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x)))))
9.0ms	(- (exp x) 1.0)

series463.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (- (exp x) 1.0) (exp x))
159.0ms	(/ (fma 1.0 (* 1.0 1.0) (exp (* 3 x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x))))
247.0ms	(log (/ (fma 1.0 (* 1.0 1.0) (exp (* 3 x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x)))))
19.0ms	(- (exp x) 1.0)

simplify1.3s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	1551
1	425
0	199

prune933.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (+ 1.0 (exp x)))
0.2b	(sqrt (+ 1.0 (exp x)))
1.0b	(log (sqrt (+ 1.0 (exp x))))
1.0b	(log (sqrt (+ 1.0 (exp x))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `sqrt-prod`
14×	`log-prod`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `log-div` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp` `hypot-def`

Counts

4 → 82

Calls

4 calls:

9.0ms	(sqrt (+ 1.0 (exp x)))
16.0ms	(sqrt (+ 1.0 (exp x)))
11.0ms	(log (sqrt (+ 1.0 (exp x))))
12.0ms	(log (sqrt (+ 1.0 (exp x))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (+ 1.0 (exp x)))
54.0ms	(sqrt (+ 1.0 (exp x)))
127.0ms	(log (sqrt (+ 1.0 (exp x))))
139.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify1.7s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
3	2750
2	542
1	175
0	90

prune601.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ (fma (* x x) 1/2 2.0) x)) (* x y))
0.0b	(+ (fma (* x x) 1/2 2.0) x)
6.6b	(log (+ (fma (* x x) 1/2 2.0) x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `log-prod` `add-cube-cbrt`
6×	`pow1` `add-log-exp`
4×	`log-div` `fma-neg` `prod-diff` `associate--l+` `add-exp-log`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `add-cbrt-cube` `log-pow` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `associate-+l+` `sum-log` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `fma-udef` `flip--`

Counts

3 → 63

Calls

3 calls:

18.0ms	(- (log (+ (fma (* x x) 1/2 2.0) x)) (* x y))
8.0ms	(+ (fma (* x x) 1/2 2.0) x)
7.0ms	(log (+ (fma (* x x) 1/2 2.0) x))

series207.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(- (log (+ (fma (* x x) 1/2 2.0) x)) (* x y))
24.0ms	(+ (fma (* x x) 1/2 2.0) x)
97.0ms	(log (+ (fma (* x x) 1/2 2.0) x))

simplify1.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1371
1	300
0	122

prune411.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes175.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.7s	2554×	body	10240	exit
902.0ms	8468×	body	80	valid
125.0ms	254×	body	640	valid
86.0ms	120×	body	1280	valid
76.0ms	183×	body	320	valid
13.0ms	93×	body	160	valid