Details

sample58.0ms

Algorithm

intervals

Results

30.0ms	76×	body	10240	exit
9.0ms	255×	body	80	valid
4.0ms	7×	body	1280	valid
3.0ms	12×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	5×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.8b	(log (+ 1.0 (exp x)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

3.0ms	(+ 1.0 (exp x))
3.0ms	(log (+ 1.0 (exp x)))

series72.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(+ 1.0 (exp x))
64.0ms	(log (+ 1.0 (exp x)))

simplify99.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	128	169
1	337	152
2	897	151
3	3150	150
4	5002	150

prune75.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(+ 1.0 (exp x))
1.5b	(log (sqrt (+ 1.0 (exp x))))
1.5b	(log (sqrt (+ 1.0 (exp x))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`log-prod`
8×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `sqrt-prod` `add-log-exp`
6×	`add-exp-log` `log-pow`
4×	`log-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`+-commutative` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log`

Counts

4 → 64

Calls

4 calls:

4.0ms	(+ 1.0 (exp x))
3.0ms	(+ 1.0 (exp x))
4.0ms	(log (sqrt (+ 1.0 (exp x))))
4.0ms	(log (sqrt (+ 1.0 (exp x))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ 1.0 (exp x))
8.0ms	(+ 1.0 (exp x))
103.0ms	(log (sqrt (+ 1.0 (exp x))))
104.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify40.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	155	476
1	390	434
2	1073	422
3	5002	414

prune207.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize10.0ms

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))
8.3b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite31.0ms

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:

5.0ms	(* 1/2 (pow x 2))
8.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
6.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
6.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 1/2 (pow x 2))
78.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
18.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
51.0ms	(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	575
1	1439	529
2	5001	520

prune197.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (log (+ (pow (* 1/2 (pow x 2)) 3) (pow (+ x 2.0) 3))) (log (+ (* (* 1/2 (pow x 2)) (* 1/2 (pow x 2))) (- (* (+ x 2.0) (+ x 2.0)) (* (* 1/2 (pow x 2)) (+ x 2.0))))))
9.2b	(+ (pow (* 1/2 (pow x 2)) 3) (pow (+ x 2.0) 3))
11.9b	(log (+ (* (* 1/2 (pow x 2)) (* 1/2 (pow x 2))) (- (* (+ x 2.0) (+ x 2.0)) (* (* 1/2 (pow x 2)) (+ x 2.0)))))
12.6b	(log (+ (pow (* 1/2 (pow x 2)) 3) (pow (+ x 2.0) 3)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

28.0ms	(- (log (+ (pow (* 1/2 (pow x 2)) 3) (pow (+ x 2.0) 3))) (log (+ (* (* 1/2 (pow x 2)) (* 1/2 (pow x 2))) (- (* (+ x 2.0) (+ x 2.0)) (* (* 1/2 (pow x 2)) (+ x 2.0))))))
12.0ms	(+ (pow (* 1/2 (pow x 2)) 3) (pow (+ x 2.0) 3))
13.0ms	(log (+ (* (* 1/2 (pow x 2)) (* 1/2 (pow x 2))) (- (* (+ x 2.0) (+ x 2.0)) (* (* 1/2 (pow x 2)) (+ x 2.0)))))
11.0ms	(log (+ (pow (* 1/2 (pow x 2)) 3) (pow (+ x 2.0) 3)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(- (log (+ (pow (* 1/2 (pow x 2)) 3) (pow (+ x 2.0) 3))) (log (+ (* (* 1/2 (pow x 2)) (* 1/2 (pow x 2))) (- (* (+ x 2.0) (+ x 2.0)) (* (* 1/2 (pow x 2)) (+ x 2.0))))))
48.0ms	(+ (pow (* 1/2 (pow x 2)) 3) (pow (+ x 2.0) 3))
58.0ms	(log (+ (* (* 1/2 (pow x 2)) (* 1/2 (pow x 2))) (- (* (+ x 2.0) (+ x 2.0)) (* (* 1/2 (pow x 2)) (+ x 2.0)))))
126.0ms	(log (+ (pow (* 1/2 (pow x 2)) 3) (pow (+ x 2.0) 3)))

simplify67.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	476	1691
1	1786	1582
2	5002	1544

prune348.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes65.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

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

976.0ms	2445×	body	10240	exit
318.0ms	8428×	body	80	valid
66.0ms	254×	body	640	valid
66.0ms	134×	body	1280	valid
26.0ms	160×	body	320	valid
13.0ms	110×	body	160	valid