Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
3.0ms	249×	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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 15.1b

Counts

2 → 1

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:

3.0ms	(- (* a a) (* b b))
1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
7.0ms	(/ (- (* a a) (* b b)) (* a a))

series100.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(- (* a a) (* b b))
17.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
53.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify162.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (156.0ms)

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

prune124.0ms

Filtered

61 candidates to 45 candidates (73.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	2	62

Merged error: 0.0b

Counts

62 → 2

localize8.0ms

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))

rewrite36.0ms

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))))
5.0ms	(/ (+ a b) a)
5.0ms	(/ (- a b) a)
19.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series130.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
21.0ms	(/ (+ a b) a)
30.0ms	(/ (- a b) a)
62.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify70.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	493	952
1	2505	870
2	5001	867

prune270.0ms

Filtered

155 candidates to 106 candidates (68.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	154	3	157

Merged error: 0b

Counts

157 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ a b) a)
0.0b	(/ (- a b) a)
0.0b	(/ (- a b) a)
0.1b	(* (* (/ (+ a b) a) (sqrt (/ (- a b) a))) (sqrt (/ (- a b) a)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
65×	`add-sqr-sqrt`
57×	`times-frac`
43×	`add-cube-cbrt`
22×	`associate-r`
19×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
14×	`associate-/l*`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`pow1` `associate-/r*`
8×	`sqrt-div`
6×	`associate-/l/`
5×	`frac-times` `associate-*l/` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `div-inv` `distribute-lft-out` `add-log-exp`
3×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num`
2×	`flip3--` `div-sub` `flip--`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

4 → 155

Calls

4 calls:

5.0ms	(/ (+ a b) a)
6.0ms	(/ (- a b) a)
6.0ms	(/ (- a b) a)
19.0ms	(* (* (/ (+ a b) a) (sqrt (/ (- a b) a))) (sqrt (/ (- a b) a)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (+ a b) a)
35.0ms	(/ (- a b) a)
30.0ms	(/ (- a b) a)
77.0ms	(* (* (/ (+ a b) a) (sqrt (/ (- a b) a))) (sqrt (/ (- a b) a)))

simplify68.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	457	1079
1	2323	952
2	5001	944

prune356.0ms

Filtered

167 candidates to 113 candidates (67.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	167	3	170

Merged error: 0b

Counts

170 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

129×	`times-frac`
126×	`add-sqr-sqrt`
84×	`sqrt-prod`
82×	`add-cube-cbrt` `*-un-lft-identity`
31×	`swap-sqr`
25×	`associate-r` `associate-l`
18×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
13×	`pow1`
9×	`unswap-sqr`
7×	`associate-/l*`
6×	`sqrt-div`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3--` `associate-/r*` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 191

Calls

4 calls:

6.0ms	(/ (sqrt (- (* a a) (* b b))) a)
21.0ms	(* (/ (sqrt (- (* a a) (* b b))) a) (/ (sqrt (- (* a a) (* b b))) a))
4.0ms	(sqrt (- (* a a) (* b b)))
4.0ms	(sqrt (- (* a a) (* b b)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (sqrt (- (* a a) (* b b))) a)
55.0ms	(* (/ (sqrt (- (* a a) (* b b))) a) (/ (sqrt (- (* a a) (* b b))) a))
45.0ms	(sqrt (- (* a a) (* b b)))
51.0ms	(sqrt (- (* a a) (* b b)))

simplify83.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	618	2481
1	3024	2161
2	5001	1973

prune394.0ms

Filtered

203 candidates to 133 candidates (65.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	203	3	206

Merged error: 0b

Counts

206 → 3

regimes47.0ms

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	11	7
1	11	7

end0.0ms

sample615.0ms

Algorithm

intervals

Results

194.0ms	8000×	body	80	valid
100.0ms	8000×	pre	80	true
95.0ms	7994×	pre	80	false