Details

sample479.0ms

Algorithm

intervals

Results

69.0ms	66×	body	1280	valid
53.0ms	53×	body	640	valid
20.0ms	146×	body	80	valid
5.0ms	46×	body	80	nan
4.0ms	10×	body	320	valid
3.0ms	9×	body	160	valid

simplify43.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
7.7b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
19.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite91.0ms

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×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`tan-quot` `neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `associate-/r/` `-commutative` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 122

Calls

4 calls:

7.0ms	(/ F (sin B))
18.0ms	(* x (/ 1.0 (tan B)))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
60.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ F (sin B))
117.0ms	(* x (/ 1.0 (tan B)))
234.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
159.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify65.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	666	1019
1	2629	931
2	5001	928

prune581.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (sin B))
7.7b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
19.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite70.0ms

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:

10.0ms	(/ (* x 1.0) (tan B))
6.0ms	(/ F (sin B))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
50.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (* x 1.0) (tan B))
54.0ms	(/ F (sin B))
233.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
147.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify54.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (45.0ms)

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

prune503.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
7.7b	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
19.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

39×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
15×	`unpow-prod-down`
13×	`pow-unpow`
10×	`associate-/r*`
8×	`add-cbrt-cube`
7×	`div-exp`
6×	`associate-/l*`
5×	`pow1` `sqr-pow`
4×	`expm1-log1p-u` `pow-to-exp` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `fma-udef` `inv-pow`

Counts

4 → 123

Calls

4 calls:

5.0ms	(/ F (sin B))
81.0ms	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.0ms	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
46.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ F (sin B))
682.0ms	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
253.0ms	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
135.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	645	1355
1	2296	1230
2	5002	1182

prune473.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(* (/ (* x 1.0) (sin B)) (cos B))
7.7b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (/ (* x 1.0) (sin B)) (cos B))))
19.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

5.0ms	(/ F (sin B))
24.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (/ (* x 1.0) (sin B)) (cos B))))
50.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ F (sin B))
108.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
228.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (/ (* x 1.0) (sin B)) (cos B))))
147.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify61.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	670	1083
1	2594	968
2	5002	965

prune485.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes221.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 13.7b

bsearch317.0ms

Steps

Iters	Range		Point
9	2700937.8939785375	817490739025870.2	118194348.126507
10	-5.344867609840325e+23	-62409.316276319805	-173479323.4816099

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	42
1	59	42
2	64	42
3	64	42

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	1641×	body	1280	valid
868.0ms	1389×	body	640	valid
650.0ms	4805×	body	80	valid
307.0ms	702×	body	320	valid
157.0ms	1578×	body	80	nan
111.0ms	363×	body	160	valid