Details

sample359.0ms

Algorithm

intervals

Results

47.0ms	57×	body	1280	valid
19.0ms	153×	body	80	valid
19.0ms	36×	body	640	valid
10.0ms	26×	body	320	valid
5.0ms	53×	body	80	nan
3.0ms	10×	body	160	valid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	43	15
1	91	14
2	169	14
3	378	14
4	1100	14
5	5001	14

prune30.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 11.6b

Counts

2 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
5.6b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
16.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
37×	`times-frac`
30×	`pow-unpow`
14×	`associate-r`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`distribute-lft-out`
9×	`unpow-prod-down` `associate-*r/`
8×	`associate-l`
7×	`pow1` `associate-/l*`
6×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`clear-num`
2×	`tan-quot` `cbrt-undiv` `frac-2neg` `div-exp` `prod-exp` `associate-/r/` `un-div-inv` `cbrt-unprod` `unswap-sqr`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `pow-prod-down` `pow-exp` `*-commutative` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 139

Calls

4 calls:

4.0ms	(/ 1.0 (tan B))
8.0ms	(* x (/ 1.0 (tan B)))
1.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
19.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1.0 (tan B))
112.0ms	(* x (/ 1.0 (tan B)))
242.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
175.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify69.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	642	1090
1	2605	1002
2	5001	999

prune493.0ms

Filtered

151 candidates to 118 candidates (78.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	140	11	151
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	142	11	153

Merged error: 0.0b

Counts

153 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.1b	(/ x (/ (tan B) 1.0))
5.6b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ x (/ (tan B) 1.0))))
16.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
88×	`*-un-lft-identity`
72×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`pow-unpow`
19×	`associate-/r*`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`associate-/r/` `distribute-lft-out`
9×	`unpow-prod-down` `associate-/l*`
8×	`div-inv`
5×	`pow1` `associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`tan-quot` `neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `pow-exp` `fma-udef` `associate-/l/` `pow-sub` `sqr-pow`

Counts

4 → 174

Calls

4 calls:

3.0ms	(/ F (sin B))
7.0ms	(/ x (/ (tan B) 1.0))
1.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ x (/ (tan B) 1.0))))
16.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series544.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ F (sin B))
110.0ms	(/ x (/ (tan B) 1.0))
229.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ x (/ (tan B) 1.0))))
153.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	831	1479
1	3489	1384
2	5002	1381

prune582.0ms

Filtered

186 candidates to 146 candidates (78.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	183	3	186
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	189	8	197

Merged error: 0.0b

Counts

197 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (/ (tan B) 1.0))
0.3b	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
5.6b	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (/ x (/ (tan B) 1.0))))
16.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

165×	`*-un-lft-identity`
132×	`times-frac`
85×	`add-sqr-sqrt` `add-cube-cbrt`
50×	`distribute-lft-out`
45×	`unpow-prod-down`
29×	`associate-/r*`
26×	`pow-unpow`
25×	`associate-l`
19×	`add-exp-log`
16×	`pow-flip`
11×	`add-cbrt-cube`
10×	`associate-/r/`
9×	`div-exp` `associate-/l*`
8×	`div-inv`
7×	`pow1`
5×	`sqr-pow`
4×	`cbrt-undiv` `expm1-log1p-u` `pow-to-exp` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
2×	`pow-pow`
1×	`tan-quot` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 220

Calls

4 calls:

7.0ms	(/ x (/ (tan B) 1.0))
20.0ms	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
1.0ms	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (/ x (/ (tan B) 1.0))))
15.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ x (/ (tan B) 1.0))
714.0ms	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
239.0ms	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (/ x (/ (tan B) 1.0))))
138.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify95.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	921	2057
1	3801	1903
2	5001	1830

prune601.0ms

Filtered

232 candidates to 147 candidates (63.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	229	3	232
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	233	7	240

Merged error: 0.0b

Counts

240 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sin B)) (cos B))
0.2b	(* x (* (/ 1.0 (sin B)) (cos B)))
5.6b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (* (/ 1.0 (sin B)) (cos B)))))
16.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
42×	`add-cube-cbrt`
39×	`times-frac`
34×	`associate-l`
30×	`pow-unpow`
29×	`associate-r`
19×	`add-exp-log`
18×	`associate-*l/` `add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`pow1`
10×	`distribute-lft-out`
9×	`unpow-prod-down` `associate-*r/` `unswap-sqr`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`*-commutative`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `pow-exp` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 162

Calls

4 calls:

8.0ms	(* (/ 1.0 (sin B)) (cos B))
19.0ms	(* x (* (/ 1.0 (sin B)) (cos B)))
1.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (* (/ 1.0 (sin B)) (cos B)))))
16.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series545.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (/ 1.0 (sin B)) (cos B))
115.0ms	(* x (* (/ 1.0 (sin B)) (cos B)))
231.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (* (/ 1.0 (sin B)) (cos B)))))
161.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify96.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	793	1383
1	3747	1251
2	5002	1248

prune516.0ms

Filtered

174 candidates to 132 candidates (75.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	174	7	181

Merged error: 0.0b

Counts

181 → 7

regimes143.0ms

Accuracy

97.8% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 13.9b

bsearch299.0ms

Steps

Iters	Range		Point
9	6.0279012577515685e+54	7.154941822740013e+59	6.831721935628722e+54
10	-1556119314.230081	-0.16456746602421737	-195461829.27451754

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	42
1	63	42
2	64	42
3	64	42

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	1579×	body	1280	valid
736.0ms	1357×	body	640	valid
577.0ms	4864×	body	80	valid
266.0ms	714×	body	320	valid
138.0ms	1606×	body	80	nan
87.0ms	349×	body	160	valid