Details

sample83.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 96.856734%

Space saved by search: 93.762201%

Guaranteed chance to sample good point: 0%

Results

9.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true
0.0ms	3×	pre	80	false

simplify47.0ms

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

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: 13.4b

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))))
13.0b	(/ (- (* a a) (* b b)) (* a a))

rewrite12.0ms

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))

series24.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(- (* a a) (* b b))
10.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
8.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify153.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (145.0ms)

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

prune80.0ms

Filtered

45 candidates to 61 candidates (-35.6%)

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))

rewrite35.0ms

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)
6.0ms	(/ (- a b) a)
16.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series28.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
4.0ms	(/ (+ a b) a)
5.0ms	(/ (- a b) a)
10.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify66.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	493	951
1	2505	870
2	5002	867

prune154.0ms

Filtered

106 candidates to 155 candidates (-46.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	153	4	157

Merged error: 0b

Counts

157 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-sqr-sqrt`
94×	`sqrt-prod`
84×	`*-un-lft-identity`
81×	`times-frac`
67×	`pow1`
52×	`add-cube-cbrt`
45×	`associate-r`
41×	`pow-prod-down`
40×	`sqrt-div`
39×	`associate-l`
22×	`add-exp-log` `add-cbrt-cube`
20×	`sqrt-pow1` `pow1/2`
19×	`frac-times`
18×	`unswap-sqr`
13×	`associate-r/` `associate-l/`
10×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
8×	`pow-prod-up`
7×	`sqrt-unprod`
6×	`pow-sqr` `distribute-lft-out`
5×	`div-inv` `associate-/l*`
4×	`add-log-exp`
3×	`associate-/r` `-commutative`
2×	`pow-plus` `associate-/l/`
1×	`cbrt-undiv` `pow2` `flip3--` `frac-2neg` `div-sub` `swap-sqr` `div-exp` `clear-num` `rem-square-sqrt` `flip--`

Counts

4 → 231

Calls

4 calls:

6.0ms	(/ (- a b) a)
20.0ms	(* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a)))
22.0ms	(* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a)))
28.0ms	(* (* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a))) (* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a))))

series48.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ (- a b) a)
17.0ms	(* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a)))
14.0ms	(* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a)))
12.0ms	(* (* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a))) (* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a))))

simplify78.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	483	2038
1	2187	1821
2	5002	1791

prune231.0ms

Filtered

153 candidates to 243 candidates (-58.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	243	4	247

Merged error: 0b

Counts

247 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
169×	`sqrt-prod`
159×	`*-un-lft-identity`
138×	`times-frac`
75×	`add-cube-cbrt`
58×	`associate-r`
52×	`difference-of-squares`
49×	`add-exp-log` `add-cbrt-cube`
26×	`distribute-lft-out--`
18×	`prod-exp` `cbrt-unprod`
16×	`distribute-lft-out`
15×	`cbrt-undiv` `div-exp`
14×	`associate-/l*`
12×	`associate-/r*`
9×	`pow1`
6×	`add-log-exp`
5×	`frac-times` `associate-*l/`
4×	`associate-/l/`
3×	`associate-*r/` `pow-prod-down` `div-inv`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`+-commutative` `flip3--` `div-sub` `associate-l` `sum-log` `*-commutative` `flip--`

Counts

4 → 248

Calls

4 calls:

33.0ms	(* (* (/ (+ a b) a) (/ (+ (sqrt a) (sqrt b)) (sqrt a))) (/ (- (sqrt a) (sqrt b)) (sqrt a)))
9.0ms	(/ (+ (sqrt a) (sqrt b)) (sqrt a))
5.0ms	(+ (sqrt a) (sqrt b))
10.0ms	(/ (- (sqrt a) (sqrt b)) (sqrt a))

series87.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* (/ (+ a b) a) (/ (+ (sqrt a) (sqrt b)) (sqrt a))) (/ (- (sqrt a) (sqrt b)) (sqrt a)))
13.0ms	(/ (+ (sqrt a) (sqrt b)) (sqrt a))
6.0ms	(+ (sqrt a) (sqrt b))
12.0ms	(/ (- (sqrt a) (sqrt b)) (sqrt a))

simplify50.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	880	3338
1	5001	2934

prune215.0ms

Filtered

147 candidates to 260 candidates (-76.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	260	0	260
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	260	4	264

Merged error: 0b

Counts

264 → 4

regimes80.0ms

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

sample609.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 96.856734%

Space saved by search: 93.762201%

Guaranteed chance to sample good point: 0%

Results

271.0ms	8000×	body	80	valid
144.0ms	8000×	pre	80	true
1.0ms	64×	pre	80	false

Details

sample83.0ms

simplify47.0ms

prune3.0ms

localize7.0ms

rewrite12.0ms

series24.0ms

simplify153.0ms

prune80.0ms

localize8.0ms

rewrite35.0ms

series28.0ms

simplify66.0ms

prune154.0ms

localize12.0ms

rewrite87.0ms

series48.0ms

simplify78.0ms

prune231.0ms

localize14.0ms

rewrite70.0ms

series87.0ms

simplify50.0ms

prune215.0ms

regimes80.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample609.0ms

Profiling