Details

sample82.0ms

Algorithm

intervals

Results

41.0ms	70×	body	10240	exit
15.0ms	255×	body	80	valid
3.0ms	9×	body	640	valid
2.0ms	2×	body	1280	valid
2.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify15.0ms

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

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)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

12.0ms	(+ 1.0 (exp x))
21.0ms	(- (log (+ 1.0 (exp x))) (* x y))
6.0ms	(log (+ 1.0 (exp x)))

series188.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(+ 1.0 (exp x))
74.0ms	(- (log (+ 1.0 (exp x))) (* x y))
97.0ms	(log (+ 1.0 (exp x)))

simplify2.5s

Counts

71 → 71

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	105	724
1	240	686
2	761	635
3	3881	618
done	5000	614

prune273.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp x) 3)
0.3b	(log (+ (pow 1.0 3) (pow (exp x) 3)))
5.7b	(- (exp x) 1.0)
6.0b	(log (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
12×	`log-prod`
9×	`prod-diff`
7×	`pow1` `unpow-prod-down` `cube-prod`
6×	`add-exp-log` `add-log-exp`
5×	`add-cbrt-cube` `distribute-lft-out`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`pow-unpow` `exp-prod` `fma-neg`
2×	`log-div` `rem-log-exp` `log-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `flip3-+` `diff-log` `unpow3` `pow-exp` `sum-cubes` `flip--` `flip-+` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

8.0ms	(pow (exp x) 3)
41.0ms	(log (+ (pow 1.0 3) (pow (exp x) 3)))
20.0ms	(- (exp x) 1.0)
3.0ms	(log (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0))))

series319.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow (exp x) 3)
139.0ms	(log (+ (pow 1.0 3) (pow (exp x) 3)))
23.0ms	(- (exp x) 1.0)
127.0ms	(log (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0))))

simplify2.5s

Counts

104 → 104

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	183	1228
1	441	1024
2	1794	899
done	5000	890

prune395.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt (+ 1.0 (exp x)))
0.3b	(sqrt (+ 1.0 (exp x)))
0.7b	(log (sqrt (+ 1.0 (exp x))))
0.7b	(log (sqrt (+ 1.0 (exp x))))

rewrite57.0ms

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-+` `pow1/2` `add-cbrt-cube` `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:

13.0ms	(sqrt (+ 1.0 (exp x)))
17.0ms	(sqrt (+ 1.0 (exp x)))
12.0ms	(log (sqrt (+ 1.0 (exp x))))
12.0ms	(log (sqrt (+ 1.0 (exp x))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (+ 1.0 (exp x)))
47.0ms	(sqrt (+ 1.0 (exp x)))
144.0ms	(log (sqrt (+ 1.0 (exp x))))
111.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify1.2s

Counts

94 → 94

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	90	962
1	176	876
2	552	816
3	2814	812
done	5001	810

prune354.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
0.0b	(fma 1/2 (pow x 2) (+ x 2.0))
8.5b	(log (fma 1/2 (pow x 2) (+ 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 1/2 (pow x 2) (+ x 2.0))) (* x y))
0.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
2.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

series151.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
18.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
55.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify612.0ms

Counts

58 → 58

Iterations

Useful iterations: done (610.0ms)

Iter	Nodes	Cost
0	100	911
1	233	865
2	881	790
done	5000	757

prune244.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes64.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	25
1	19	25
done	19	25

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.8s	2429×	body	10240	exit
667.0ms	8343×	body	80	valid
134.0ms	282×	body	640	valid
80.0ms	121×	body	1280	valid
40.0ms	181×	body	320	valid
17.0ms	120×	body	160	valid