Details

sample129.0ms

Algorithm

intervals

Results

68.0ms	81×	body	10240	exit
22.0ms	272×	body	80	valid
7.0ms	7×	body	1280	valid
4.0ms	8×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	19	9
3	23	9
done	23	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 45

Calls

2 calls:

14.0ms	(- (log (+ 1.0 (exp x))) (* x y))
6.0ms	(log (+ 1.0 (exp x)))

series176.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(- (log (+ 1.0 (exp x))) (* x y))
104.0ms	(log (+ 1.0 (exp x)))

simplify2.0s

Counts

51 → 51

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	94	602
1	207	571
2	623	528
3	3161	511
done	5000	507

prune144.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp x)))
0.0b	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
0.7b	(log (sqrt (+ 1.0 (exp x))))
0.7b	(log (sqrt (+ 1.0 (exp x))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

10.0ms	(sqrt (+ 1.0 (exp x)))
117.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
7.0ms	(log (sqrt (+ 1.0 (exp x))))
7.0ms	(log (sqrt (+ 1.0 (exp x))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ 1.0 (exp x)))
180.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
114.0ms	(log (sqrt (+ 1.0 (exp x))))
117.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify953.0ms

Counts

147 → 147

Iterations

Useful iterations: done (947.0ms)

Iter	Nodes	Cost
0	164	2106
1	370	1789
2	1388	1524
done	5001	1470

prune852.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`log-prod`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt`
2×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`flip3-+` `rem-log-exp` `log-pow` `flip-+` `fma-udef` `distribute-lft-out`

Counts

2 → 27

Calls

2 calls:

1.0ms	(fma (- x) y (log (+ (exp x) 1.0)))
24.0ms	(log (+ (exp x) 1.0))

series188.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(fma (- x) y (log (+ (exp x) 1.0)))
93.0ms	(log (+ (exp x) 1.0))

simplify1.1s

Counts

33 → 33

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	71	346
1	138	336
2	341	303
3	1294	299
done	5000	295

prune114.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp x)))
0.7b	(log (sqrt (+ 1.0 (exp x))))
0.7b	(log (sqrt (sqrt (+ 1.0 (exp x)))))
0.7b	(log (sqrt (sqrt (+ 1.0 (exp x)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

10.0ms	(sqrt (+ 1.0 (exp x)))
7.0ms	(log (sqrt (+ 1.0 (exp x))))
13.0ms	(log (sqrt (sqrt (+ 1.0 (exp x)))))
12.0ms	(log (sqrt (sqrt (+ 1.0 (exp x)))))

series682.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ 1.0 (exp x)))
131.0ms	(log (sqrt (+ 1.0 (exp x))))
266.0ms	(log (sqrt (sqrt (+ 1.0 (exp x)))))
252.0ms	(log (sqrt (sqrt (+ 1.0 (exp x)))))

simplify2.3s

Counts

107 → 107

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	144	1241
1	269	1136
2	805	1062
3	4221	1056
done	5000	1055

prune580.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes48.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	9	9
done	9	9

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.0s	2412×	body	10240	exit
636.0ms	8357×	body	80	valid
132.0ms	270×	body	640	valid
92.0ms	135×	body	1280	valid
46.0ms	205×	body	320	valid
13.0ms	105×	body	160	valid