Details

sample452.0ms

Algorithm

intervals

Results

76.0ms	53×	body	1280	valid
42.0ms	159×	body	80	valid
33.0ms	37×	body	640	valid
12.0ms	20×	body	320	valid
11.0ms	63×	body	80	nan
5.0ms	11×	body	160	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	42	15
1	83	14
2	151	14
3	356	14
4	1063	14
5	5002	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.9b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite129.0ms

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×	`pow-neg` `cbrt-unprod` `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 → 155

Calls

4 calls:

2.0ms	(/ 1.0 (tan B))
8.0ms	(* x (/ 1.0 (tan B)))
79.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
32.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series602.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1.0 (tan B))
113.0ms	(* x (/ 1.0 (tan B)))
296.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
158.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	767	1428
1	3183	1338
2	5001	1337

prune651.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (/ 1.0 (tan B)))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
0.7b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
18.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

8.0ms	(* x (/ 1.0 (tan B)))
73.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
28.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series840.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* x (/ 1.0 (tan B)))
220.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
361.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
147.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify82.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	721	1300
1	3143	1182
2	5002	1182

prune535.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
0.7b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
18.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite132.0ms

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` `associate-*r/` `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 → 122

Calls

4 calls:

3.0ms	(/ (* x 1.0) (tan B))
71.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
28.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
26.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series828.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (* x 1.0) (tan B))
210.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
357.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
149.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	674	1245
1	2898	1127
2	5001	1127

prune496.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.1b	(/ (* x 1.0) (tan B))
0.7b	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
18.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

192×	`times-frac`
112×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
51×	`unpow-prod-down`
29×	`associate-/l*`
25×	`add-exp-log`
17×	`sqr-pow`
16×	`add-cbrt-cube`
13×	`pow-unpow` `associate-/r*`
12×	`div-exp`
8×	`div-inv`
6×	`cbrt-undiv`
5×	`pow1`
4×	`add-log-exp`
3×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`tan-quot` `pow-pow` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`

Counts

4 → 214

Calls

4 calls:

35.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
3.0ms	(/ (* x 1.0) (tan B))
57.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series863.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
110.0ms	(/ (* x 1.0) (tan B))
369.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
140.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify101.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	990	3237
1	4176	3123
2	5001	3123

prune834.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes206.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.7b

bsearch410.0ms

Steps

Iters	Range		Point
10	2.0114125408603258e-10	8982319.97820102	7212012.336046098
10	-8.932761495434891e+18	-62103362.424651496	-752955800017062.8

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	35
1	49	35

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.1s	1696×	body	1280	valid
1.2s	4781×	body	80	valid
1.2s	1396×	body	640	valid
414.0ms	671×	body	320	valid
287.0ms	1623×	body	80	nan
157.0ms	354×	body	160	valid