Details

sample79.0ms

Algorithm

intervals

Results

42.0ms	80×	body	10240	exit
21.0ms	277×	body	80	valid
2.0ms	3×	body	1280	valid
2.0ms	5×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	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))
0.8b	(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))
6.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(log (+ 1.0 (exp x)))

series135.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ 1.0 (exp x))
62.0ms	(- (log (+ 1.0 (exp x))) (* x y))
65.0ms	(log (+ 1.0 (exp x)))

simplify46.0ms

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

prune120.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp x)))
0.0b	(sqrt (+ 1.0 (exp x)))
1.4b	(log (sqrt (+ 1.0 (exp x))))
1.4b	(log (sqrt (+ 1.0 (exp x))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

5.0ms	(sqrt (+ 1.0 (exp x)))
5.0ms	(sqrt (+ 1.0 (exp x)))
3.0ms	(log (sqrt (+ 1.0 (exp x))))
4.0ms	(log (sqrt (+ 1.0 (exp x))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (+ 1.0 (exp x)))
38.0ms	(sqrt (+ 1.0 (exp x)))
106.0ms	(log (sqrt (+ 1.0 (exp x))))
106.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify52.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	162	564
1	453	528
2	1549	508
3	5001	496

prune233.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp x)))
0.7b	(* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x)))))
1.4b	(log (* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x))))))
1.4b	(log (sqrt (+ 1.0 (exp x))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

90×	`sqrt-prod`
66×	`sqrt-pow1`
54×	`pow1`
52×	`sqrt-div`
50×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
34×	`pow1/2`
25×	`log-pow`
19×	`add-cube-cbrt`
18×	`swap-sqr` `pow-prod-up`
14×	`flip3-+` `flip-+`
10×	`add-exp-log` `log-div` `associate-r` `associate-l` `pow-prod-down` `pow-sqr`
9×	`unswap-sqr`
8×	`frac-times` `log-prod` `distribute-lft-out`
6×	`add-cbrt-cube`
4×	`associate-r/` `associate-l/` `add-log-exp`
3×	`rem-log-exp`
2×	`pow2` `pow-plus` `prod-exp`
1×	`rem-sqrt-square` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 164

Calls

4 calls:

5.0ms	(sqrt (+ 1.0 (exp x)))
32.0ms	(* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x)))))
19.0ms	(log (* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x))))))
4.0ms	(log (sqrt (+ 1.0 (exp x))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ 1.0 (exp x)))
32.0ms	(* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x)))))
112.0ms	(log (* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x))))))
109.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify54.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	325	1226
1	1161	1136
2	5001	1100

prune380.0ms

Pruning

4 alts after pruning (1 fresh and 3 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))
6.8b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite36.0ms

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

series180.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 1/2 (pow x 2))
80.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
18.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
56.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (38.0ms)

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

prune198.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes64.0ms

Accuracy

0% (0.3b 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	16	17
1	16	17

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	2366×	body	10240	exit
653.0ms	8487×	body	80	valid
88.0ms	239×	body	640	valid
61.0ms	93×	body	1280	valid
42.0ms	169×	body	320	valid
17.0ms	107×	body	160	valid