Details

sample412.0ms

Algorithm

intervals

Results

52.0ms	47×	body	1280	valid
47.0ms	171×	body	80	valid
28.0ms	39×	body	640	valid
13.0ms	20×	body	320	valid
8.0ms	48×	body	80	nan
6.0ms	15×	body	160	valid

simplify44.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
8.8b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite136.0ms

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))
9.0ms	(* x (/ 1.0 (tan B)))
89.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
27.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1.0 (tan B))
114.0ms	(* x (/ 1.0 (tan B)))
304.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
161.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (69.0ms)

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

prune680.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite143.0ms

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:

9.0ms	(* x (/ 1.0 (tan B)))
76.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
30.0ms	(/ (* 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)))

series840.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* x (/ 1.0 (tan B)))
213.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
360.0ms	(/ (* 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)))

simplify78.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	721	1300
1	3143	1182
2	5001	1182

prune543.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 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))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite138.0ms

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))
74.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
32.0ms	(/ (* 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)))

series827.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (* x 1.0) (tan B))
216.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
356.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
145.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 1 (15.0ms)

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

prune516.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ 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))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite135.0ms

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:

4.0ms	(/ (* x 1.0) (tan B))
37.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
63.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
22.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series882.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (* x 1.0) (tan B))
250.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
380.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
137.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify107.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 1 (20.0ms)

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

prune882.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes181.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.9b

bsearch354.0ms

Steps

Iters	Range		Point
10	0.817620533678417	5.496318983503676e+17	760094393.573885
8	-2.3306471377965617e+111	-6.497766399924529e+107	-1.40065760476294e+108

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	46
1	84	46
2	89	46
3	89	46

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.9s	1706×	body	1280	valid
1.1s	4706×	body	80	valid
1.0s	1391×	body	640	valid
366.0ms	690×	body	320	valid
270.0ms	1617×	body	80	nan
132.0ms	353×	body	160	valid