Details

sample402.0ms

Algorithm

intervals

Results

66.0ms	65×	body	1280	valid
28.0ms	44×	body	640	valid
20.0ms	141×	body	80	valid
11.0ms	26×	body	320	valid
7.0ms	47×	body	80	nan
4.0ms	14×	body	160	valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (16.0ms)

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

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(* x (/ 1.0 (tan B)))
5.8b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
19.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite132.0ms

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×	`frac-times` `*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `associate-/r/` `un-div-inv`

Counts

4 → 154

Calls

4 calls:

2.0ms	(/ F (sin B))
9.0ms	(* x (/ 1.0 (tan B)))
87.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
26.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series638.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ F (sin B))
117.0ms	(* x (/ 1.0 (tan B)))
304.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
167.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify82.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	765	1418
1	3213	1329
2	5001	1328

prune672.0ms

Filtered

166 candidates to 127 candidates (76.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

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))
0.2b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
19.0b	(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:

8.0ms	(* x (/ 1.0 (tan B)))
29.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
77.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series876.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* x (/ 1.0 (tan B)))
380.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
225.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
155.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify80.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (16.0ms)

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

prune557.0ms

Filtered

145 candidates to 108 candidates (74.5%)

Pruning

12 alts after pruning (12 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))
0.2b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
19.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite139.0ms

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:

4.0ms	(/ (* x 1.0) (tan B))
29.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
75.0ms	(* F (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)))

series851.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (* x 1.0) (tan B))
365.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
220.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
155.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify76.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 1 (15.0ms)

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

prune506.0ms

Filtered

134 candidates to 101 candidates (75.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b	(/ (* x 1.0) (tan B))
0.2b	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
19.0b	(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:

37.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
4.0ms	(/ (* x 1.0) (tan B))
60.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
25.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series894.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
113.0ms	(/ (* x 1.0) (tan B))
388.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
141.0ms	(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

prune881.0ms

Filtered

226 candidates to 179 candidates (79.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes171.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 11.1b

bsearch257.0ms

Steps

Iters	Range		Point
6	7.709245479379255e+52	8.503002622430935e+53	2.6571035656186667e+53
9	-8.056251097937594e+129	-5.005393495068343e+122	-9.690791470079618e+125

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	35
1	57	35
2	57	35

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	1679×	body	1280	valid
878.0ms	1361×	body	640	valid
648.0ms	4742×	body	80	valid
299.0ms	698×	body	320	valid
173.0ms	1703×	body	80	nan
104.0ms	362×	body	160	valid