Details

sample385.0ms

Algorithm

intervals

Results

41.0ms	45×	body	1280	valid
28.0ms	46×	body	640	valid
23.0ms	168×	body	80	valid
8.0ms	20×	body	320	valid
8.0ms	59×	body	80	nan
3.0ms	9×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	43	15
1	91	14
2	169	14
3	378	14
4	1100	14
5	5001	14

prune28.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 13.3b

Counts

2 → 2

localize25.0ms

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))))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite43.0ms

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:

4.0ms	(/ 1.0 (tan B))
7.0ms	(* x (/ 1.0 (tan B)))
13.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
13.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series588.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1.0 (tan B))
111.0ms	(* x (/ 1.0 (tan B)))
284.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
159.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (72.0ms)

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

prune672.0ms

Filtered

175 candidates to 138 candidates (78.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	160	15	175
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	162	15	177

Merged error: 0.0b

Counts

177 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
0.3b	(* x (/ 1.0 (tan B)))
0.4b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite44.0ms

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×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `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 → 141

Calls

4 calls:

11.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
7.0ms	(* x (/ 1.0 (tan B)))
11.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series806.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
107.0ms	(* x (/ 1.0 (tan B)))
343.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
144.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	739	1359
1	3214	1221
2	5001	1213

prune524.0ms

Filtered

153 candidates to 118 candidates (77.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	149	4	153
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	154	14	168

Merged error: 0.0b

Counts

168 → 14

localize23.0ms

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))))
0.4b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite40.0ms

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:

5.0ms	(/ (* x 1.0) (tan B))
10.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
11.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series791.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (* x 1.0) (tan B))
203.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
341.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
143.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (61.0ms)

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

prune490.0ms

Filtered

142 candidates to 112 candidates (78.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	142	14	156

Merged error: 0.0b

Counts

156 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* x 1.0) (sin B)) (cos B))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
0.4b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

7.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
10.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
11.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series794.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
201.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
344.0ms	(/ (* 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)))

simplify81.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	743	1399
1	3192	1238
2	5001	1230

prune452.0ms

Filtered

147 candidates to 112 candidates (76.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	147	14	161

Merged error: 0.0b

Counts

161 → 14

regimes218.0ms

Accuracy

97.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.7b

bsearch303.0ms

Steps

Iters	Range		Point
11	2.034228214667056e-17	57946.35045805707	47108.36037005531
8	-15369046078.029392	-18062256.86705318	-3207980569.070885

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	37
1	69	37
2	73	37
3	73	37

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.4s	1651×	body	1280	valid
799.0ms	1366×	body	640	valid
626.0ms	4756×	body	80	valid
296.0ms	725×	body	320	valid
158.0ms	1630×	body	80	nan
95.0ms	342×	body	160	valid