Details

sample58.0ms

Algorithm

intervals

Results

32.0ms	80×	body	10240	exit
10.0ms	274×	body	80	valid
2.0ms	7×	body	640	valid
2.0ms	3×	body	1280	valid
1.0ms	6×	body	320	valid
0.0ms	5×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	23	5
3	23	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite14.0ms

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:

6.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(+ 1.0 (exp x))
3.0ms	(log (+ 1.0 (exp x)))

series134.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(- (log (+ 1.0 (exp x))) (* x y))
8.0ms	(+ 1.0 (exp x))
66.0ms	(log (+ 1.0 (exp x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	236	404
1	702	369
2	2284	367
3	5002	340

prune164.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(log (+ 1.0 (exp x)))
1.2b	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
1.2b	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
1.2b	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

3.0ms	(log (+ 1.0 (exp x)))
2.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
2.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
3.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))

series1.2s

Counts

4 → 12

Calls

4 calls:

59.0ms	(log (+ 1.0 (exp x)))
453.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
314.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
345.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))

simplify44.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	349	970
1	1259	923
2	5002	905

prune269.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

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))
4.9b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite7.0ms

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:

4.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
1.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
17.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
57.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	229	423
1	763	380
2	3267	376
3	5001	356

prune157.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.3b	(cbrt (log (fma 1/2 (pow x 2) (+ x 2.0))))
4.9b	(log (fma 1/2 (pow x 2) (+ x 2.0)))
4.9b	(log (fma 1/2 (pow x 2) (+ x 2.0)))
4.9b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
8×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`add-exp-log`
4×	`cbrt-prod` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
1×	`pow1/3`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt (log (fma 1/2 (pow x 2) (+ x 2.0))))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt (log (fma 1/2 (pow x 2) (+ x 2.0))))
55.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))
50.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))
56.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify141.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (134.0ms)

Iter	Nodes	Cost
0	307	613
1	1079	545
2	4907	517
3	5001	514

prune263.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes69.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

end0.0ms

sample1.7s

Algorithm

intervals

Results

984.0ms	2439×	body	10240	exit
316.0ms	8416×	body	80	valid
67.0ms	250×	body	640	valid
59.0ms	117×	body	1280	valid
33.0ms	208×	body	320	valid
11.0ms	117×	body	160	valid