Details

sample365.0ms

Algorithm

intervals

Results

33.0ms	38×	body	1280	valid
24.0ms	40×	body	640	valid
20.0ms	164×	body	80	valid
10.0ms	25×	body	320	valid
6.0ms	58×	body	80	nan
4.0ms	15×	body	160	valid

simplify47.0ms

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

prune25.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 14.3b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.5b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
18.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

4.0ms	(/ 1.0 (tan B))
7.0ms	(* 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)))))
12.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1.0 (tan B))
106.0ms	(* x (/ 1.0 (tan B)))
220.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
156.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	628	1028
1	2518	940
2	5001	937

prune572.0ms

Filtered

135 candidates to 112 candidates (83.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	122	13	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	13	136

Merged error: 0.0b

Counts

136 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.1b	(/ (* x 1.0) (tan B))
6.5b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
18.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

3.0ms	(/ F (sin B))
5.0ms	(/ (* 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))))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series508.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ F (sin B))
104.0ms	(/ (* x 1.0) (tan B))
212.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
141.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	616	964
1	2352	876
2	5001	873

prune456.0ms

Filtered

123 candidates to 99 candidates (80.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	126	10	136

Merged error: 0.0b

Counts

136 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ (* x (cos B)) (sin B))
6.5b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
18.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

4.0ms	(/ F (sin B))
5.0ms	(/ (* x (cos B)) (sin B))
1.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series493.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ F (sin B))
95.0ms	(/ (* x (cos B)) (sin B))
212.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
140.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	600	1011
1	2303	913
2	5001	910

prune446.0ms

Filtered

122 candidates to 98 candidates (80.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	122	10	132

Merged error: 0.0b

Counts

132 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (tan B) (* x 1.0))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))
6.5b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ 1 (/ (tan B) (* x 1.0)))))
18.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
38×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log`
30×	`pow-unpow`
18×	`add-cbrt-cube`
14×	`div-exp`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`associate-/r*` `div-inv`
7×	`cbrt-undiv`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `rec-exp` `1-exp`
2×	`frac-2neg` `clear-num` `cbrt-unprod`
1×	`tan-quot` `neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-flip` `pow-pow` `pow-exp` `associate-/r/` `fma-udef` `associate-/l/` `inv-pow` `pow-sub` `sqr-pow`

Counts

4 → 140

Calls

4 calls:

5.0ms	(/ (tan B) (* x 1.0))
6.0ms	(/ 1 (/ (tan B) (* x 1.0)))
1.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ 1 (/ (tan B) (* x 1.0)))))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (tan B) (* x 1.0))
82.0ms	(/ 1 (/ (tan B) (* x 1.0)))
213.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ 1 (/ (tan B) (* x 1.0)))))
136.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	734	1253
1	3195	1115
2	5002	1068

prune435.0ms

Filtered

152 candidates to 103 candidates (67.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	152	10	162

Merged error: 0.0b

Counts

162 → 10

regimes173.0ms

Accuracy

98.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 14.1b

bsearch300.0ms

Steps

Iters	Range		Point
10	860.9547529914067	6244423733497697.0	141103877.76016736
9	-2.300964657700246e+24	-4.351120538970112e+16	-4.1641400348628416e+17

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	42
1	55	42
2	61	42
3	61	42

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	1579×	body	1280	valid
726.0ms	1358×	body	640	valid
580.0ms	4885×	body	80	valid
259.0ms	692×	body	320	valid
146.0ms	1684×	body	80	nan
84.0ms	337×	body	160	valid