Details

sample108.0ms

Algorithm

intervals

Results

66.0ms	93×	body	10240	exit
18.0ms	275×	body	80	valid
3.0ms	6×	body	640	valid
2.0ms	2×	body	1280	valid
2.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

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)))

rewrite65.0ms

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:

32.0ms	(+ 1.0 (exp x))
19.0ms	(- (log (+ 1.0 (exp x))) (* x y))
9.0ms	(log (+ 1.0 (exp x)))

series208.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ 1.0 (exp x))
91.0ms	(- (log (+ 1.0 (exp x))) (* x y))
102.0ms	(log (+ 1.0 (exp x)))

simplify2.3s

Counts

71 → 71

Iterations

Iter	Nodes
done	5004
3	1882
2	606
1	242
0	105

prune382.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log (/ (fma 1.0 (* 1.0 1.0) (exp (fma 2 x x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x))))) (* x y))
0.4b	(/ (fma 1.0 (* 1.0 1.0) (exp (fma 2 x x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x))))
0.5b	(log (/ (fma 1.0 (* 1.0 1.0) (exp (fma 2 x x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x)))))
3.9b	(- (exp x) 1.0)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt` `*-un-lft-identity`
35×	`add-cube-cbrt`
27×	`times-frac`
26×	`log-prod`
13×	`prod-diff` `associate--l+`
9×	`add-exp-log`
7×	`pow1` `fma-neg` `add-log-exp`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `log-pow` `div-inv` `associate-/l`
2×	`log-div` `sub-neg` `flip3--` `diff-log` `div-exp` `rem-log-exp` `flip--`
1×	`associate--l-` `cbrt-undiv` `clear-num` `frac-2neg` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 119

Calls

4 calls:

13.0ms	(- (log (/ (fma 1.0 (* 1.0 1.0) (exp (fma 2 x x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x))))) (* x y))
4.0ms	(/ (fma 1.0 (* 1.0 1.0) (exp (fma 2 x x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x))))
2.0ms	(log (/ (fma 1.0 (* 1.0 1.0) (exp (fma 2 x x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x)))))
9.0ms	(- (exp x) 1.0)

series518.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(- (log (/ (fma 1.0 (* 1.0 1.0) (exp (fma 2 x x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x))))) (* x y))
113.0ms	(/ (fma 1.0 (* 1.0 1.0) (exp (fma 2 x x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x))))
199.0ms	(log (/ (fma 1.0 (* 1.0 1.0) (exp (fma 2 x x))) (fma 1.0 1.0 (* (- (exp x) 1.0) (exp x)))))
17.0ms	(- (exp x) 1.0)

simplify2.5s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
3	4006
2	1191
1	486
0	225

prune940.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize23.0ms

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))))

rewrite43.0ms

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:

8.0ms	(sqrt (+ 1.0 (exp x)))
15.0ms	(sqrt (+ 1.0 (exp x)))
10.0ms	(log (sqrt (+ 1.0 (exp x))))
9.0ms	(log (sqrt (+ 1.0 (exp x))))

series358.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (+ 1.0 (exp x)))
36.0ms	(sqrt (+ 1.0 (exp x)))
144.0ms	(log (sqrt (+ 1.0 (exp x))))
132.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify2.2s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
4	4487
3	1305
2	452
1	174
0	90

prune534.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x (fma 0.5 x 1.0) 2.0)
0.0b	(- (log (fma x (fma 0.5 x 1.0) 2.0)) (* x y))
6.6b	(log (fma x (fma 0.5 x 1.0) 2.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `log-prod`
4×	`fma-neg` `prod-diff` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `associate--l+` `log-pow` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `fma-udef` `flip--`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma x (fma 0.5 x 1.0) 2.0)
12.0ms	(- (log (fma x (fma 0.5 x 1.0) 2.0)) (* x y))
2.0ms	(log (fma x (fma 0.5 x 1.0) 2.0))

series327.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(fma x (fma 0.5 x 1.0) 2.0)
157.0ms	(- (log (fma x (fma 0.5 x 1.0) 2.0)) (* x y))
141.0ms	(log (fma x (fma 0.5 x 1.0) 2.0))

simplify2.9s

Counts

58 → 58

Iterations

Iter	Nodes
done	5002
3	2580
2	744
1	267
0	111

prune298.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes141.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.8s	2554×	body	10240	exit
1.1s	8468×	body	80	valid
97.0ms	254×	body	640	valid
87.0ms	120×	body	1280	valid
45.0ms	183×	body	320	valid
13.0ms	93×	body	160	valid