Details

sample47.0ms

Algorithm

intervals

Results

22.0ms	55×	body	10240	exit
10.0ms	265×	body	80	valid
2.0ms	4×	body	1280	valid
2.0ms	7×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	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

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite12.0ms

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:

3.0ms	(+ 1.0 (exp x))
5.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(log (+ 1.0 (exp x)))

series128.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ 1.0 (exp x))
58.0ms	(- (log (+ 1.0 (exp x))) (* x y))
63.0ms	(log (+ 1.0 (exp x)))

simplify47.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (42.0ms)

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

prune119.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp x)))
0.0b	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
1.4b	(log (sqrt (+ 1.0 (exp x))))
1.4b	(log (sqrt (+ 1.0 (exp x))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
14×	`log-prod`
12×	`sqrt-prod`
10×	`add-sqr-sqrt` `sqrt-div`
9×	`pow1` `add-cube-cbrt`
8×	`log-div`
7×	`add-log-exp`
6×	`add-exp-log` `log-pow`
5×	`flip3-+` `flip-+`
4×	`associate--l-` `add-cbrt-cube`
3×	`sqrt-pow1` `pow1/2` `distribute-lft-out`
2×	`associate-+l-` `associate-+r-` `diff-log` `rem-log-exp`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

4 → 74

Calls

4 calls:

6.0ms	(sqrt (+ 1.0 (exp x)))
49.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
6.0ms	(log (sqrt (+ 1.0 (exp x))))
3.0ms	(log (sqrt (+ 1.0 (exp x))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ 1.0 (exp x)))
150.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
101.0ms	(log (sqrt (+ 1.0 (exp x))))
104.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify109.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	279	765
1	942	666
2	3612	627
3	5001	617

prune245.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
0.0b	(* 1/2 (pow x 2))
7.5b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite32.0ms

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:

8.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
10.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
5.0ms	(* 1/2 (pow x 2))
8.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series168.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
75.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
23.0ms	(* 1/2 (pow x 2))
53.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (38.0ms)

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

prune233.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(log (+ 1.0 (exp x)))
0.7b	(log (+ 1.0 (exp x)))
0.7b	(log (+ 1.0 (exp x)))
11.9b	(/ (- (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (* (* x y) (* x y))) (+ (log (+ 1.0 (exp x))) (* x y)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`log-prod` `times-frac`
9×	`add-exp-log`
7×	`pow1`
6×	`log-div` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `associate-/l*` `add-log-exp` `difference-of-squares`
3×	`rem-log-exp` `associate-/r*` `log-pow` `distribute-lft-out`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 81

Calls

4 calls:

9.0ms	(log (+ 1.0 (exp x)))
5.0ms	(log (+ 1.0 (exp x)))
4.0ms	(log (+ 1.0 (exp x)))
36.0ms	(/ (- (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (* (* x y) (* x y))) (+ (log (+ 1.0 (exp x))) (* x y)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(log (+ 1.0 (exp x)))
62.0ms	(log (+ 1.0 (exp x)))
62.0ms	(log (+ 1.0 (exp x)))
181.0ms	(/ (- (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (* (* x y) (* x y))) (+ (log (+ 1.0 (exp x))) (* x y)))

simplify51.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	318	1230
1	1389	1140
2	5001	1118

prune243.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes34.0ms

Accuracy

0% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 1.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	11
1	12	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

906.0ms	2274×	body	10240	exit
320.0ms	8417×	body	80	valid
68.0ms	258×	body	640	valid
58.0ms	116×	body	1280	valid
32.0ms	205×	body	320	valid
10.0ms	112×	body	160	valid