Details

sample95.0ms

Algorithm

intervals

Results

53.0ms	79×	body	10240	exit
18.0ms	278×	body	80	valid
3.0ms	8×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	1×	body	1280	valid
0.0ms	2×	body	160	valid

simplify10.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.6b	(log (+ 1.0 (exp x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

7.0ms	(+ 1.0 (exp x))
6.0ms	(log (+ 1.0 (exp x)))

series121.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(+ 1.0 (exp x))
112.0ms	(log (+ 1.0 (exp x)))

simplify986.0ms

Counts

40 → 40

Iterations

Useful iterations: done (984.0ms)

Iter	Nodes	Cost
0	65	314
1	141	297
2	416	275
3	1718	273
done	5000	270

prune184.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(log (+ 1.0 (exp x)))
0.7b	(sqrt (log (+ 1.0 (exp x))))
0.7b	(sqrt (log (+ 1.0 (exp x))))
0.7b	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (log (+ 1.0 (exp x)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
30×	`pow1`
29×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`swap-sqr`
10×	`sqrt-pow1` `pow1/2`
9×	`log-pow`
7×	`add-exp-log` `associate-r` `associate-l`
6×	`add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log-prod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `log-div`
1×	`pow2` `flip3-+` `pow-plus` `sqrt-unprod` `rem-log-exp` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 105

Calls

4 calls:

11.0ms	(log (+ 1.0 (exp x)))
15.0ms	(sqrt (log (+ 1.0 (exp x))))
18.0ms	(sqrt (log (+ 1.0 (exp x))))
37.0ms	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (log (+ 1.0 (exp x)))))

series404.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(log (+ 1.0 (exp x)))
127.0ms	(sqrt (log (+ 1.0 (exp x))))
138.0ms	(sqrt (log (+ 1.0 (exp x))))
69.0ms	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (log (+ 1.0 (exp x)))))

simplify964.0ms

Counts

117 → 117

Iterations

Useful iterations: done (961.0ms)

Iter	Nodes	Cost
0	122	1551
1	270	1073
2	944	987
done	5001	960

prune386.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(sqrt (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))))
0.7b	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x)))))))
1.3b	(log (sqrt (+ 1.0 (exp x))))
1.3b	(log (sqrt (+ 1.0 (exp x))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

68×	`sqrt-prod`
51×	`log-pow`
46×	`pow1`
37×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
29×	`associate-r`
21×	`add-cube-cbrt`
20×	`distribute-rgt-out`
18×	`distribute-lft-out`
17×	`sqrt-pow1` `pow1/2`
14×	`log-prod`
8×	`add-exp-log` `sqrt-div`
7×	`associate-l`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log-div` `distribute-lft1-in` `flip3-+` `distribute-rgt1-in` `flip-+` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down`
2×	`count-2` `associate-*r/` `rem-log-exp`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

4 → 143

Calls

4 calls:

38.0ms	(sqrt (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))))
79.0ms	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x)))))))
13.0ms	(log (sqrt (+ 1.0 (exp x))))
7.0ms	(log (sqrt (+ 1.0 (exp x))))

series1.3s

Counts

4 → 12

Calls

4 calls:

385.0ms	(sqrt (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))))
635.0ms	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x)))))))
109.0ms	(log (sqrt (+ 1.0 (exp x))))
130.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify1.2s

Counts

155 → 155

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	245	2886
1	540	2163
2	1941	2046
done	5001	2033

prune767.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
0.0b	(fma (fma 1/2 x 1) x 2.0)
5.6b	(log (fma (fma 1/2 x 1) x 2.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

9.0ms	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
0.0ms	(fma (fma 1/2 x 1) x 2.0)
1.0ms	(log (fma (fma 1/2 x 1) x 2.0))

series228.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
33.0ms	(fma (fma 1/2 x 1) x 2.0)
68.0ms	(log (fma (fma 1/2 x 1) x 2.0))

simplify664.0ms

Counts

58 → 58

Iterations

Useful iterations: done (661.0ms)

Iter	Nodes	Cost
0	102	851
1	238	807
2	881	738
done	5000	705

prune214.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes93.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	25
1	17	25
done	17	25

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.5s	2539×	body	10240	exit
988.0ms	8426×	body	80	valid
95.0ms	273×	body	640	valid
78.0ms	128×	body	1280	valid
60.0ms	171×	body	320	valid
13.0ms	107×	body	160	valid