Details

sample31.0ms

Algorithm

intervals

Results

13.0ms	299×	body	80	valid
4.0ms	105×	body	80	overflowed
1.0ms	1×	body	640	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	19	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

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

rewrite26.0ms

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:

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

series126.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(- (log (+ 1.0 (exp x))) (* x y))
7.0ms	(+ 1.0 (exp x))
62.0ms	(log (+ 1.0 (exp x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (47.0ms)

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

prune157.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

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:

12.0ms	(+ 1.0 (exp x))
15.0ms	(+ 1.0 (exp x))
12.0ms	(log (sqrt (+ 1.0 (exp x))))
12.0ms	(log (sqrt (+ 1.0 (exp x))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ 1.0 (exp x))
7.0ms	(+ 1.0 (exp x))
94.0ms	(log (sqrt (+ 1.0 (exp x))))
98.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify40.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (34.0ms)

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

prune187.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow x 2))
0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
6.8b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite75.0ms

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:

12.0ms	(* 1/2 (pow x 2))
19.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
23.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
18.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* 1/2 (pow x 2))
18.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
66.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
67.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	371	575
1	1439	529
2	5001	520

prune182.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp (log (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))) (* x y))
0.0b	(log (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))
0.3b	(exp (log (log (+ (* 1/2 (pow x 2)) (+ x 2.0)))))
6.8b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

21.0ms	(- (exp (log (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))) (* x y))
1.0ms	(log (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))
3.0ms	(exp (log (log (+ (* 1/2 (pow x 2)) (+ x 2.0)))))
17.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (exp (log (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))) (* x y))
96.0ms	(log (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))
49.0ms	(exp (log (log (+ (* 1/2 (pow x 2)) (+ x 2.0)))))
46.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	404	731
1	1440	654
2	5002	617

prune190.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes44.0ms

Accuracy

0% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	11
1	12	11

end0.0ms

sample759.0ms

Algorithm

intervals

Results

329.0ms	9173×	body	80	valid
113.0ms	3428×	body	80	overflowed
6.0ms	10×	body	1280	valid
3.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid