Details

sample85.0ms

Algorithm

intervals

Results

45.0ms	61×	body	10240	exit
14.0ms	260×	body	80	valid
7.0ms	9×	body	1280	valid
3.0ms	8×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	263
1	12	263
2	19	263
3	23	263
done	23	263

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.3b	(log (+ 1.0 (exp x)))

rewrite39.0ms

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:

10.0ms	(+ 1.0 (exp x))
20.0ms	(- (log (+ 1.0 (exp x))) (* x y))
7.0ms	(log (+ 1.0 (exp x)))

series196.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(+ 1.0 (exp x))
80.0ms	(- (log (+ 1.0 (exp x))) (* x y))
102.0ms	(log (+ 1.0 (exp x)))

simplify2.2s

Counts

71 → 71

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	105	20528
1	242	18197
2	755	17850
3	3790	17587
done	5000	17507

prune335.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

50×	`log-pow`
40×	`pow1`
37×	`*-un-lft-identity`
26×	`fma-neg` `prod-diff`
20×	`distribute-rgt-out`
19×	`add-sqr-sqrt` `add-cube-cbrt` `distribute-lft-out`
14×	`log-prod` `sqrt-pow1` `pow1/2`
9×	`add-log-exp`
8×	`log-div` `sqrt-div` `sqrt-prod`
6×	`add-exp-log`
5×	`flip3-+` `flip-+`
4×	`associate--l-` `expm1-log1p-u` `distribute-lft1-in` `add-cbrt-cube` `distribute-rgt1-in` `log1p-expm1-u`
3×	`fma-def`
2×	`associate-+r-` `sum-log` `count-2` `diff-log` `rem-log-exp` `associate-+l-`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

4 → 133

Calls

4 calls:

10.0ms	(+ 1.0 (exp x))
142.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
11.0ms	(log (sqrt (+ 1.0 (exp x))))
11.0ms	(log (sqrt (+ 1.0 (exp x))))

series626.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ 1.0 (exp x))
237.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
186.0ms	(log (sqrt (+ 1.0 (exp x))))
188.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify1.5s

Counts

145 → 145

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	160	50181
1	364	44364
2	1325	40543
done	5000	40054

prune811.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

21×	`log-prod`
16×	`*-un-lft-identity`
12×	`sqrt-prod`
10×	`add-sqr-sqrt` `pow1` `add-cube-cbrt`
9×	`log-pow`
7×	`add-exp-log`
6×	`log-div` `sqrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 76

Calls

4 calls:

0.0ms	(fma (sqrt (log (sqrt (+ 1.0 (exp x))))) (+ (sqrt (log (sqrt (+ 1.0 (exp x))))) (sqrt (log (sqrt (+ 1.0 (exp x)))))) (- (* x y)))
6.0ms	(log (sqrt (+ 1.0 (exp x))))
5.0ms	(log (sqrt (+ 1.0 (exp x))))
10.0ms	(log (sqrt (+ 1.0 (exp x))))

series960.0ms

Counts

4 → 12

Calls

4 calls:

506.0ms	(fma (sqrt (log (sqrt (+ 1.0 (exp x))))) (+ (sqrt (log (sqrt (+ 1.0 (exp x))))) (sqrt (log (sqrt (+ 1.0 (exp x)))))) (- (* x y)))
170.0ms	(log (sqrt (+ 1.0 (exp x))))
151.0ms	(log (sqrt (+ 1.0 (exp x))))
133.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify1.7s

Counts

88 → 88

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	96	35651
1	186	31116
2	503	29709
3	2480	29401
done	5001	29157

prune564.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize92.0ms

Local error

Found 4 expressions with local error:

1.0b	(log (sqrt (+ (exp x) 1.0)))
1.0b	(log (sqrt (+ (pow 1.0 3) (pow (exp x) 3))))
4.2b	(- (exp x) 1.0)
4.4b	(log (sqrt (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
25×	`log-prod`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
16×	`sqrt-prod`
10×	`pow1`
9×	`prod-diff` `log-pow`
7×	`add-exp-log`
6×	`distribute-lft-out` `add-log-exp`
4×	`expm1-log1p-u` `log-div` `unpow-prod-down` `add-cbrt-cube` `sqrt-div` `cube-prod` `log1p-expm1-u`
3×	`sqrt-pow1` `pow1/2` `fma-neg` `rem-log-exp`
2×	`flip3-+` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `sum-cubes` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 96

Calls

4 calls:

6.0ms	(log (sqrt (+ (exp x) 1.0)))
23.0ms	(log (sqrt (+ (pow 1.0 3) (pow (exp x) 3))))
13.0ms	(- (exp x) 1.0)
3.0ms	(log (sqrt (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0)))))

series587.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(log (sqrt (+ (exp x) 1.0)))
162.0ms	(log (sqrt (+ (pow 1.0 3) (pow (exp x) 3))))
18.0ms	(- (exp x) 1.0)
254.0ms	(log (sqrt (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0)))))

simplify1.6s

Counts

108 → 108

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	228	55031
1	444	39745
2	1384	37030
done	5000	36140

prune806.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes121.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	438
1	18	438
2	20	438
done	20	438

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.7s	2501×	body	10240	exit
1.1s	8406×	body	80	valid
153.0ms	139×	body	1280	valid
114.0ms	264×	body	640	valid
49.0ms	202×	body	320	valid
16.0ms	104×	body	160	valid