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

sample34.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
3.0ms	257×	pre	80	true
0.0ms	1×	body	80	invalid

simplify62.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5023	53

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

localize27.0ms

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)

rewrite74.0ms

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:

10.0ms	(/ (pow (fabs x) 5) 5.0)
41.0ms	(* (/ 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)))))
6.0ms	(/ (pow (fabs x) 3) 3.0)
1.0ms	(sqrt PI)

series76.0ms

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)

simplify150.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5002	6808

prune758.0ms

Filtered

133 candidates to 193 candidates (-45.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	188	5	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	189	5	194

Merged error: 0b

Counts

194 → 5

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow (fabs x) 7) 0.047619047619047616)
0.1b	(* (pow (fabs x) 5) 0.2)
0.1b	(* (+ (* (pow (fabs x) 7) 0.047619047619047616) (+ (* (pow (fabs x) 5) 0.2) (+ (* (pow (fabs x) 3) 0.6666666666666666) (* (fabs x) 2.0)))) (sqrt (/ 1 PI)))
0.1b	(* (pow (fabs x) 3) 0.6666666666666666)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
29×	`associate-l`
25×	`associate-r`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`add-exp-log`
16×	`sqrt-prod`
14×	`unswap-sqr`
12×	`unpow-prod-down` `add-cbrt-cube`
11×	`times-frac`
10×	`prod-exp`
6×	`pow1` `sqr-pow`
4×	`cube-prod` `*-commutative` `cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `sqrt-div` `pow-exp`
2×	`frac-times` `flip3-+` `associate-*l/` `flip-+`
1×	`cube-mult` `unpow3` `associate-*r/` `pow-prod-down` `div-inv`

Counts

4 → 120

Calls

4 calls:

5.0ms	(* (pow (fabs x) 7) 0.047619047619047616)
7.0ms	(* (pow (fabs x) 5) 0.2)
27.0ms	(* (+ (* (pow (fabs x) 7) 0.047619047619047616) (+ (* (pow (fabs x) 5) 0.2) (+ (* (pow (fabs x) 3) 0.6666666666666666) (* (fabs x) 2.0)))) (sqrt (/ 1 PI)))
6.0ms	(* (pow (fabs x) 3) 0.6666666666666666)

series125.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (pow (fabs x) 7) 0.047619047619047616)
23.0ms	(* (pow (fabs x) 5) 0.2)
73.0ms	(* (+ (* (pow (fabs x) 7) 0.047619047619047616) (+ (* (pow (fabs x) 5) 0.2) (+ (* (pow (fabs x) 3) 0.6666666666666666) (* (fabs x) 2.0)))) (sqrt (/ 1 PI)))
7.0ms	(* (pow (fabs x) 3) 0.6666666666666666)

simplify68.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5429	3540

prune460.0ms

Filtered

90 candidates to 132 candidates (-46.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	132	5	137

Merged error: 0b

Counts

137 → 5

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* 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 (/ 1.0 (sqrt PI))))
0.3b	(* (sqrt (/ 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)))) (sqrt (/ 1.0 (sqrt PI)))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

92×	`associate-*r/`
72×	`sqrt-prod`
48×	`frac-add`
47×	`add-sqr-sqrt`
45×	`sqrt-div`
41×	`frac-times`
38×	`times-frac`
36×	`flip3-+` `flip-+`
35×	`add-cube-cbrt` `*-un-lft-identity`
28×	`associate-l`
26×	`associate-r`
25×	`associate-*l/`
13×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative` `div-inv`

Counts

4 → 161

Calls

4 calls:

63.0ms	(* (+ (* 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 (/ 1.0 (sqrt PI))))
43.0ms	(* (sqrt (/ 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)))) (sqrt (/ 1.0 (sqrt PI)))))
3.0ms	(sqrt PI)
3.0ms	(sqrt PI)

series155.0ms

Counts

4 → 8

Calls

4 calls:

89.0ms	(* (+ (* 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 (/ 1.0 (sqrt PI))))
66.0ms	(* (sqrt (/ 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)))) (sqrt (/ 1.0 (sqrt PI)))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify137.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5029	12208

prune1.0s

Filtered

133 candidates to 169 candidates (-27.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	169	5	174

Merged error: 0b

Counts

174 → 5

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (/ 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)))) (sqrt 1.0)))
0.3b	(/ (* (sqrt (/ 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)))) (sqrt 1.0))) (sqrt (sqrt PI)))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

64×	`associate-*r/`
55×	`sqrt-prod`
34×	`associate-*l/`
32×	`frac-add`
28×	`add-sqr-sqrt`
27×	`times-frac`
26×	`add-cube-cbrt` `*-un-lft-identity`
25×	`associate-l`
24×	`flip3-+` `flip-+`
18×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
17×	`associate-/l/`
16×	`frac-times`
11×	`pow1`
9×	`associate-/r*`
6×	`prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp` `pow-prod-down`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv`
1×	`frac-2neg` `associate-r` `clear-num` `-commutative` `associate-/l`

Counts

4 → 135

Calls

4 calls:

51.0ms	(* (sqrt (/ 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)))) (sqrt 1.0)))
68.0ms	(/ (* (sqrt (/ 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)))) (sqrt 1.0))) (sqrt (sqrt PI)))
3.0ms	(sqrt PI)
3.0ms	(sqrt PI)

series196.0ms

Counts

4 → 8

Calls

4 calls:

121.0ms	(* (sqrt (/ 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)))) (sqrt 1.0)))
75.0ms	(/ (* (sqrt (/ 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)))) (sqrt 1.0))) (sqrt (sqrt PI)))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify109.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5015	8798

prune726.0ms

Filtered

105 candidates to 143 candidates (-36.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	143	5	148

Merged error: 0b

Counts

148 → 5

regimes130.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	53
1	38	53

end0.0ms

sample1.2s

Algorithm

intervals

Results

970.0ms	8000×	body	80	valid
104.0ms	8001×	pre	80	true
0.0ms	1×	body	80	invalid

Details

analyze5.0ms

sample34.0ms

simplify62.0ms

prune9.0ms

localize27.0ms

rewrite74.0ms

series76.0ms

simplify150.0ms

prune758.0ms

localize39.0ms

rewrite50.0ms

series125.0ms

simplify68.0ms

prune460.0ms

localize38.0ms

rewrite121.0ms

series155.0ms

simplify137.0ms

prune1.0s

localize36.0ms

rewrite133.0ms

series196.0ms

simplify109.0ms

prune726.0ms

regimes130.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample1.2s

Profiling