Details

sample367.0ms

Algorithm

intervals

Results

39.0ms	48×	body	1280	valid
28.0ms	52×	body	640	valid
18.0ms	151×	body	80	valid
7.0ms	20×	body	320	valid
5.0ms	47×	body	80	nan
2.0ms	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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin 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)))))
17.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite28.0ms

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:

3.0ms	(/ F (sin 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)))

series566.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ F (sin B))
113.0ms	(* x (/ 1.0 (tan B)))
233.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
165.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify69.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (57.0ms)

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

prune594.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ (* 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))))
17.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite22.0ms

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)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ F (sin B))
115.0ms	(/ (* x 1.0) (tan B))
229.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
153.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (47.0ms)

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

prune521.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.4b	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
6.5b	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
17.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
9.0ms	(/ 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 1.0) (tan B))))
8.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (* x 1.0) (tan B))
717.0ms	(/ 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 1.0) (tan B))))
137.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	676	1344
1	2598	1208
2	5003	1160

prune459.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* x 1.0) (sin B)) (cos B))
0.4b	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
6.5b	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (* (/ (* x 1.0) (sin B)) (cos B))))
17.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

7.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
9.0ms	(/ 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 1.0) (sin B)) (cos B))))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
726.0ms	(/ 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 1.0) (sin B)) (cos B))))
135.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	737	1463
1	2836	1300
2	5001	1251

prune438.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes198.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 13.3b

bsearch280.0ms

Steps

Iters	Range		Point
9	498514027.71492976	1134421401047092.0	504058493.67471987
9	-2.0168541015731498e+34	-1.0296308640320476e+26	-2.731983010624295e+27

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	42
1	58	42
2	63	42
3	63	42

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1726×	body	1280	valid
773.0ms	1421×	body	640	valid
553.0ms	4727×	body	80	valid
263.0ms	671×	body	320	valid
139.0ms	1626×	body	80	nan
82.0ms	334×	body	160	valid