Details

sample473.0ms

Algorithm

intervals

Results

83.0ms	59×	body	1280	valid
38.0ms	60×	body	640	valid
19.0ms	129×	body	80	valid
11.0ms	26×	body	320	valid
5.0ms	48×	body	80	nan
2.0ms	8×	body	160	valid

simplify44.0ms

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: 13.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
4.7b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite92.0ms

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:

6.0ms	(/ 1.0 (tan B))
20.0ms	(* 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)))))
60.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1.0 (tan B))
104.0ms	(* x (/ 1.0 (tan B)))
207.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
143.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify65.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (53.0ms)

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

prune602.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(/ (* x 1.0) (tan B))
4.7b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite72.0ms

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:

5.0ms	(/ F (sin B))
11.0ms	(/ (* 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))))
52.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ F (sin B))
99.0ms	(/ (* x 1.0) (tan B))
202.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
132.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (46.0ms)

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

prune524.0ms

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	(/ (tan B) (* x 1.0))
0.2b	(/ 1 (/ (tan B) (* x 1.0)))
4.7b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ 1 (/ (tan B) (* x 1.0)))))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite83.0ms

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:

10.0ms	(/ (tan B) (* x 1.0))
16.0ms	(/ 1 (/ (tan B) (* x 1.0)))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ 1 (/ (tan B) (* x 1.0)))))
52.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (tan B) (* x 1.0))
78.0ms	(/ 1 (/ (tan B) (* x 1.0)))
199.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ 1 (/ (tan B) (* x 1.0)))))
129.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify72.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (59.0ms)

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

prune542.0ms

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	(* x (cos B))
0.2b	(/ (* x (cos B)) (sin B))
4.7b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow-unpow`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
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` `add-log-exp`
3×	`unpow-prod-down` `associate-r` `associate-l` `associate-/r*` `div-inv`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `fma-udef` `associate-/l` `pow-sub` `unswap-sqr` `sqr-pow`

Counts

4 → 101

Calls

4 calls:

9.0ms	(* x (cos B))
12.0ms	(/ (* x (cos B)) (sin B))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
51.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* x (cos B))
87.0ms	(/ (* x (cos B)) (sin B))
196.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
130.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	553	942
1	2192	844
2	5001	841

prune442.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes199.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 14.0b

bsearch258.0ms

Steps

Iters	Range		Point
8	154062.39550417996	463191646.4289385	150840120.32874382
8	-32473325542171.44	-31516633232.63976	-86718073306.1841

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

sample4.2s

Algorithm

intervals

Results

1.7s	1695×	body	1280	valid
890.0ms	1391×	body	640	valid
655.0ms	4743×	body	80	valid
320.0ms	721×	body	320	valid
168.0ms	1648×	body	80	nan
106.0ms	366×	body	160	valid