Details

sample374.0ms

Algorithm

intervals

Results

42.0ms	47×	body	1280	valid
27.0ms	51×	body	640	valid
17.0ms	145×	body	80	valid
13.0ms	35×	body	320	valid
6.0ms	61×	body	80	nan
2.0ms	7×	body	160	valid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	42	15
1	83	14
2	151	14
3	356	14
4	1063	14
5	5001	14

prune23.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 11.8b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
5.6b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

6×	`frac-times` `pow-neg` `clear-num`
5×	`neg-sub0` `frac-2neg` `associate-*r/` `div-inv` `pow-sub`
3×	`pow-unpow` `associate-r` `associate-*l/`
2×	`tan-quot` `associate-/r/` `un-div-inv` `*-commutative` `sqr-pow`
1×	`distribute-lft-neg-in` `pow-to-exp` `neg-mul-1` `distribute-rgt-neg-in` `associate-l`

Counts

4 → 33

Calls

4 calls:

2.0ms	(/ 1.0 (tan B))
3.0ms	(* x (/ 1.0 (tan B)))
7.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
8.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series600.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (tan B))
112.0ms	(* x (/ 1.0 (tan B)))
291.0ms	(* (/ 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)))

simplify131.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	284	261
1	1015	258
2	4775	258
3	5002	258

prune180.0ms

Filtered

45 candidates to 36 candidates (80.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	37	8	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	8	46

Merged error: 0.0b

Counts

46 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 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))
16.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

7×	`associate-*r/`
5×	`pow-neg`
4×	`associate-r` `div-inv`
3×	`neg-sub0` `pow-unpow` `clear-num` `un-div-inv` `-commutative` `associate-/l/` `associate-/l` `pow-sub` `sqr-pow`
2×	`frac-2neg`
1×	`tan-quot` `distribute-lft-neg-in` `pow-to-exp` `neg-mul-1` `distribute-rgt-neg-in` `associate-/r/`

Counts

4 → 28

Calls

4 calls:

3.0ms	(* x (/ 1.0 (tan B)))
6.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
8.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
5.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series828.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* x (/ 1.0 (tan B)))
207.0ms	(* 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))
150.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify132.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	261	238
1	966	230
2	4551	230
3	5002	230

prune154.0ms

Filtered

40 candidates to 32 candidates (80.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	34	6	40
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	41	7	48

Merged error: 0.0b

Counts

48 → 7

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))
16.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow-neg` `associate-/l*`
4×	`associate-*r/` `div-inv`
3×	`neg-sub0` `pow-unpow` `*-commutative` `associate-/l/` `pow-sub` `sqr-pow`
2×	`frac-2neg` `associate-r` `clear-num` `un-div-inv`
1×	`tan-quot` `distribute-lft-neg-in` `pow-to-exp` `neg-mul-1` `distribute-rgt-neg-in` `associate-/r/`

Counts

4 → 27

Calls

4 calls:

4.0ms	(/ (* x 1.0) (tan B))
6.0ms	(* 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))
5.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series815.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (* x 1.0) (tan B))
213.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
351.0ms	(/ (* 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)))

simplify119.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	266	247
1	873	239
2	3988	239
3	5001	239

prune165.0ms

Filtered

39 candidates to 35 candidates (89.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	34	5	39
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	39	7	46

Merged error: 0.0b

Counts

46 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.3b	(/ (* F 1) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
16.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-commutative`
6×	`times-frac`
5×	`sqr-pow`
4×	`associate-r` `associate-/l*`
3×	`associate-/r*` `div-inv`
2×	`frac-2neg` `clear-num`
1×	`tan-quot` `pow-to-exp` `pow-unpow` `associate-/r/`

Counts

4 → 25

Calls

4 calls:

3.0ms	(/ (* x 1.0) (tan B))
8.0ms	(/ (* F 1) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
7.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
5.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series797.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (* x 1.0) (tan B))
300.0ms	(/ (* F 1) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
249.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
136.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify136.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	320	306
1	1011	300
2	4983	293
3	5002	293

prune150.0ms

Filtered

37 candidates to 34 candidates (91.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	32	5	37
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	36	8	44

Merged error: 0.0b

Counts

44 → 8

regimes141.0ms

Accuracy

98.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.8b

bsearch311.0ms

Steps

Iters	Range		Point
11	790.7798925822519	8.057486284669742e+26	192622.2736792481
9	-251622.495232721	-0.6319501064166059	-158492.60646815697

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	46
1	46	46

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1646×	body	1280	valid
778.0ms	1429×	body	640	valid
575.0ms	4754×	body	80	valid
269.0ms	712×	body	320	valid
152.0ms	1714×	body	80	nan
86.0ms	330×	body	160	valid