Details

sample100.0ms

Algorithm

intervals

Results

54.0ms	80×	body	10240	exit
20.0ms	274×	body	80	valid
3.0ms	7×	body	640	valid
3.0ms	3×	body	1280	valid
2.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize14.0ms

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)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 45

Calls

3 calls:

10.0ms	(- (log (+ 1.0 (exp x))) (* x y))
6.0ms	(+ 1.0 (exp x))
6.0ms	(log (+ 1.0 (exp x)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(- (log (+ 1.0 (exp x))) (* x y))
12.0ms	(+ 1.0 (exp x))
100.0ms	(log (+ 1.0 (exp x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	207	322
1	584	301
2	1729	298
3	5001	297

prune124.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

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)))

rewrite13.0ms

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×	`log-prod` `add-cbrt-cube` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`
2×	`log-div`
1×	`flip3-+` `rem-log-exp` `log-pow` `flip-+` `distribute-lft-out`

Counts

4 → 54

Calls

4 calls:

4.0ms	(log (+ 1.0 (exp x)))
3.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
3.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
3.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))

series980.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(log (+ 1.0 (exp x)))
309.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
309.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
302.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))

simplify40.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	335	921
1	1197	877
2	5002	855

prune263.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow x 2))
0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
4.9b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`add-exp-log` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r`
6×	`log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `log-div` `unswap-sqr`
3×	`flip3-+` `associate-l` `prod-exp` `associate--l+` `sum-log` `flip-+`
2×	`associate--l-` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 71

Calls

4 calls:

6.0ms	(* 1/2 (pow x 2))
9.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
7.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
11.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 1/2 (pow x 2))
77.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
22.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
49.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	371	584
1	1401	529
2	5001	520

prune206.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
8×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`add-exp-log`
6×	`log-div`
4×	`cbrt-prod` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `rem-log-exp` `flip-+`
1×	`pow1/3`

Counts

4 → 54

Calls

4 calls:

1.0ms	(cbrt (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))
7.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
7.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
7.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))
56.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
49.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
56.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	363	755
1	1304	677
2	5001	644

prune441.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes73.0ms

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

983.0ms	2439×	body	10240	exit
317.0ms	8416×	body	80	valid
66.0ms	250×	body	640	valid
58.0ms	117×	body	1280	valid
33.0ms	208×	body	320	valid
11.0ms	117×	body	160	valid