Details

sample453.0ms

Algorithm

intervals

Results

54.0ms	54×	body	1280	valid
42.0ms	148×	body	80	valid
28.0ms	46×	body	640	valid
9.0ms	21×	body	320	valid
4.0ms	44×	body	80	nan
3.0ms	11×	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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.2b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
15.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
49×	`times-frac`
45×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`associate-l` `add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
7×	`pow1`
5×	`div-exp` `div-inv`
4×	`expm1-log1p-u` `pow-neg` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `associate-r/` `pow-exp` `associate-/r` `associate-/l*` `pow-sub`
2×	`tan-quot` `frac-times` `associate-/r/` `*-commutative`
1×	`neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `un-div-inv`

Counts

4 → 163

Calls

4 calls:

6.0ms	(/ 1.0 (tan B))
18.0ms	(* x (/ 1.0 (tan B)))
173.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
59.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series599.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1.0 (tan B))
113.0ms	(* x (/ 1.0 (tan B)))
290.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
157.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	784	1475
1	3245	1361
2	5001	1358

prune685.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
15.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 143

Calls

4 calls:

6.0ms	(/ 1.0 (tan B))
18.0ms	(* x (/ 1.0 (tan B)))
157.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
52.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1.0 (tan B))
110.0ms	(* x (/ 1.0 (tan B)))
200.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
139.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	653	1120
1	2699	1029
2	5001	1027

prune597.0ms

Pruning

15 alts after pruning (15 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))
0.2b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
15.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

12.0ms	(/ (* x 1.0) (tan B))
67.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
159.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
51.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series783.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (* x 1.0) (tan B))
337.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
198.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
139.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify78.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	692	1304
1	2969	1166
2	5001	1157

prune555.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (/ 1 (sin B)))
0.2b	(/ (* x 1.0) (tan B))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
15.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite425.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log`
37×	`add-sqr-sqrt`
32×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp`
30×	`pow-unpow` `times-frac`
23×	`add-cbrt-cube`
20×	`associate-r`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`div-exp`
8×	`cbrt-unprod`
7×	`pow1` `pow-neg` `unpow-prod-down` `associate-*r/`
6×	`pow-to-exp` `pow-exp`
4×	`cbrt-undiv` `neg-sub0` `expm1-log1p-u` `rec-exp` `1-exp` `associate-l` `un-div-inv` `log1p-expm1-u` `div-inv` `pow-sub` `add-log-exp`
3×	`frac-times` `associate-l/` `associate-/r` `unswap-sqr` `sqr-pow`
2×	`*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 155

Calls

4 calls:

196.0ms	(* (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (/ 1 (sin B)))
11.0ms	(/ (* x 1.0) (tan B))
159.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
53.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series813.0ms

Counts

4 → 12

Calls

4 calls:

352.0ms	(* (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (/ 1 (sin B)))
111.0ms	(/ (* x 1.0) (tan B))
204.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
146.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify89.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	854	1620
1	3904	1414
2	5002	1381

prune535.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes206.0ms

Accuracy

98% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.2b

bsearch274.0ms

Steps

Iters	Range		Point
8	1.350953981158519e+19	8.171756335825397e+21	1.634712104582305e+19
9	-2.1635908418835426e+55	-6.652785550494656e+49	-2.3932939828235706e+51

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	42
1	77	42
2	82	42
3	82	42

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	1659×	body	1280	valid
871.0ms	1421×	body	640	valid
628.0ms	4772×	body	80	valid
289.0ms	697×	body	320	valid
158.0ms	1628×	body	80	nan
94.0ms	339×	body	160	valid