Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

sample38.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5022	33

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow (fabs x) 5) 5.0)
0.1b	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
0.1b	(/ (pow (fabs x) 3) 3.0)
1.0b	(sqrt PI)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

77×	`times-frac`
69×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
32×	`associate-*r/`
24×	`unpow-prod-down`
22×	`associate-l`
19×	`add-exp-log` `associate-/l*`
16×	`frac-add`
13×	`sqrt-prod` `add-cbrt-cube`
12×	`flip3-+` `cube-prod` `flip-+`
8×	`frac-times` `sqr-pow`
7×	`pow1` `div-exp`
6×	`associate-/r*`
4×	`cube-mult` `unpow3` `add-log-exp`
3×	`cbrt-undiv` `associate-r` `div-inv` `unswap-sqr`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `prod-exp` `clear-num` `cbrt-unprod`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 183

Calls

4 calls:

5.0ms	(/ (pow (fabs x) 5) 5.0)
25.0ms	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
5.0ms	(/ (pow (fabs x) 3) 3.0)
1.0ms	(sqrt PI)

series75.0ms

Counts

4 → 10

Calls

4 calls:

10.0ms	(/ (pow (fabs x) 5) 5.0)
58.0ms	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
7.0ms	(/ (pow (fabs x) 3) 3.0)
0.0ms	(sqrt PI)

simplify73.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4975	4274
1	4975	4274

prune558.0ms

Filtered

133 candidates to 193 candidates (-45.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	189	4	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	190	4	194

Merged error: 0b

Counts

194 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ 1 (/ 3.0 (pow (fabs x) 3))))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
0.1b	(/ 3.0 (pow (fabs x) 3))
0.6b	(/ 1 (/ 3.0 (pow (fabs x) 3)))
1.0b	(sqrt PI)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
182×	`add-sqr-sqrt`
173×	`add-cube-cbrt` `*-un-lft-identity`
52×	`associate-/r*`
48×	`unpow-prod-down` `cube-prod`
36×	`add-exp-log`
32×	`associate-*r/`
22×	`associate-l`
21×	`div-exp`
16×	`cube-mult` `unpow3` `frac-add` `add-cbrt-cube` `sqr-pow`
13×	`sqrt-prod`
12×	`flip3-+` `flip-+`
8×	`pow1` `frac-times`
7×	`div-inv`
6×	`associate-/l*`
5×	`cbrt-undiv`
4×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`distribute-rgt-in` `rem-sqrt-square` `pow-flip` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `inv-pow`

Counts

4 → 328

Calls

4 calls:

43.0ms	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ 1 (/ 3.0 (pow (fabs x) 3))))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
5.0ms	(/ 3.0 (pow (fabs x) 3))
11.0ms	(/ 1 (/ 3.0 (pow (fabs x) 3)))
1.0ms	(sqrt PI)

series79.0ms

Counts

4 → 10

Calls

4 calls:

54.0ms	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ 1 (/ 3.0 (pow (fabs x) 3))))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
17.0ms	(/ 3.0 (pow (fabs x) 3))
7.0ms	(/ 1 (/ 3.0 (pow (fabs x) 3)))
0.0ms	(sqrt PI)

simplify85.0ms

Algorithm

egg-herbie

Counts

338 → 338

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5004	6220

prune814.0ms

Filtered

175 candidates to 338 candidates (-93.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	338	0	338
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	338	4	342

Merged error: 0b

Counts

342 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow (fabs x) 5) 5.0)
0.1b	(/ (pow (fabs x) 3) 3.0)
0.3b	(/ (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt PI))
1.0b	(sqrt PI)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
62×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
22×	`associate-/l*`
16×	`add-exp-log`
15×	`sqrt-prod`
12×	`cube-prod` `associate-r/` `associate-/r`
10×	`add-cbrt-cube`
8×	`frac-add` `associate-/l/` `sqr-pow`
7×	`div-exp`
6×	`flip3-+` `flip-+`
5×	`pow1`
4×	`cube-mult` `unpow3` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
2×	`pow-to-exp` `pow-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 170

Calls

4 calls:

5.0ms	(/ (pow (fabs x) 5) 5.0)
6.0ms	(/ (pow (fabs x) 3) 3.0)
21.0ms	(/ (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt PI))
1.0ms	(sqrt PI)

series64.0ms

Counts

4 → 10

Calls

4 calls:

9.0ms	(/ (pow (fabs x) 5) 5.0)
7.0ms	(/ (pow (fabs x) 3) 3.0)
47.0ms	(/ (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt PI))
0.0ms	(sqrt PI)

simplify46.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5607	3447

prune452.0ms

Filtered

119 candidates to 180 candidates (-51.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	180	4	184

Merged error: 0b

Counts

184 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow (fabs x) 3) 3.0)
0.3b	(/ (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

39×	`times-frac`
35×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-/l*`
14×	`add-exp-log`
12×	`unpow-prod-down` `cube-prod` `associate-*r/`
11×	`add-cbrt-cube`
8×	`frac-add` `associate-/l/`
6×	`pow1` `flip3-+` `sqrt-prod` `flip-+`
5×	`div-exp`
4×	`cube-mult` `unpow3` `associate-/r*` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod`

Counts

4 → 120

Calls

4 calls:

5.0ms	(/ (pow (fabs x) 3) 3.0)
30.0ms	(/ (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
1.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series56.0ms

Counts

4 → 8

Calls

4 calls:

10.0ms	(/ (pow (fabs x) 3) 3.0)
45.0ms	(/ (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify35.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5600	1922

prune285.0ms

Filtered

83 candidates to 128 candidates (-54.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	128	4	132

Merged error: 0b

Counts

132 → 4

regimes81.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	35
1	35	35

end0.0ms

sample982.0ms

Algorithm

intervals

Results

783.0ms	8000×	body	80	valid
90.0ms	8000×	pre	80	true

Details

analyze5.0ms

sample38.0ms

simplify43.0ms

prune9.0ms

localize21.0ms

rewrite43.0ms

series75.0ms

simplify73.0ms

prune558.0ms

localize22.0ms

rewrite76.0ms

series79.0ms

simplify85.0ms

prune814.0ms

localize23.0ms

rewrite39.0ms

series64.0ms

simplify46.0ms

prune452.0ms

localize23.0ms

rewrite43.0ms

series56.0ms

simplify35.0ms

prune285.0ms

regimes81.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample982.0ms

Profiling