Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
6.0ms	272×	pre	80	false
3.0ms	256×	pre	80	true

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	47	7
2	106	7
3	265	7
4	1495	7
5	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
14.6b	(/ (- (* a a) (* b b)) (* a a))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-log-exp`
4×	`pow1` `times-frac` `associate-/l*`
3×	`sqrt-prod` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

3 → 52

Calls

3 calls:

2.0ms	(- (* a a) (* b b))
1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
8.0ms	(/ (- (* a a) (* b b)) (* a a))

series99.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(- (* a a) (* b b))
17.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
52.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify166.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (160.0ms)

Iter	Nodes	Cost
0	228	417
1	970	368
2	4781	367
3	5001	366

prune143.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
0.0b	(/ (- a b) a)
0.0b	(/ (+ a b) a)
0.0b	(* (/ (+ a b) a) (/ (- a b) a))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
58×	`times-frac`
41×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-r`
16×	`associate-l`
9×	`associate-/l*`
7×	`pow1` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+`

Counts

4 → 143

Calls

4 calls:

1.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
9.0ms	(/ (- a b) a)
7.0ms	(/ (+ a b) a)
27.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series131.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
30.0ms	(/ (- a b) a)
26.0ms	(/ (+ a b) a)
59.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify64.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	493	951
1	2505	870
2	5001	867

prune349.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ a (+ a b)))
0.0b	(/ (- a b) a)
0.0b	(/ a (+ a b))
0.0b	(* (/ 1 (/ a (+ a b))) (/ (- a b) a))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

251×	`times-frac`
194×	`*-un-lft-identity`
173×	`add-sqr-sqrt`
126×	`add-cube-cbrt`
64×	`add-exp-log`
59×	`associate-l`
34×	`add-cbrt-cube`
30×	`div-exp`
25×	`associate-/r*` `distribute-lft-out`
19×	`associate-r`
18×	`associate-/r/`
14×	`cbrt-undiv` `prod-exp`
12×	`div-inv`
11×	`associate-/l*`
10×	`unswap-sqr`
8×	`flip3-+` `flip-+`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`rec-exp` `1-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/l/`
1×	`frac-times` `flip3--` `pow-flip` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `inv-pow`

Counts

4 → 287

Calls

4 calls:

9.0ms	(/ 1 (/ a (+ a b)))
7.0ms	(/ (- a b) a)
5.0ms	(/ a (+ a b))
53.0ms	(* (/ 1 (/ a (+ a b))) (/ (- a b) a))

series361.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(/ 1 (/ a (+ a b)))
30.0ms	(/ (- a b) a)
45.0ms	(/ a (+ a b))
59.0ms	(* (/ 1 (/ a (+ a b))) (/ (- a b) a))

simplify48.0ms

Algorithm

egg-herbie

Counts

299 → 299

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	958	2115
1	5001	1843

prune657.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (/ (/ (- a b) (/ a (+ a b))) a)))
0.0b	(/ a (+ a b))
0.0b	(/ (- a b) (/ a (+ a b)))
0.0b	(/ (/ (- a b) (/ a (+ a b))) a)

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

1059×	`times-frac`
759×	`*-un-lft-identity`
596×	`add-sqr-sqrt`
413×	`add-cube-cbrt`
103×	`associate-/l*`
91×	`distribute-lft-out--` `difference-of-squares`
82×	`distribute-lft-out`
59×	`associate-/r/`
33×	`div-inv`
27×	`flip3-+` `flip-+`
25×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `div-sub` `clear-num` `sqrt-prod` `associate-/l/`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 578

Calls

4 calls:

1.0ms	(sqrt (fabs (/ (/ (- a b) (/ a (+ a b))) a)))
8.0ms	(/ a (+ a b))
14.0ms	(/ (- a b) (/ a (+ a b)))
35.0ms	(/ (/ (- a b) (/ a (+ a b))) a)

series182.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (fabs (/ (/ (- a b) (/ a (+ a b))) a)))
39.0ms	(/ a (+ a b))
58.0ms	(/ (- a b) (/ a (+ a b)))
68.0ms	(/ (/ (- a b) (/ a (+ a b))) a)

simplify100.0ms

Algorithm

egg-herbie

Counts

590 → 590

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1768	6750
1	5001	6593

prune1.3s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes93.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

end0.0ms

sample593.0ms

Algorithm

intervals

Results

190.0ms	8000×	body	80	valid
93.0ms	8000×	pre	80	true
91.0ms	8050×	pre	80	false