Details

sample376.0ms

Algorithm

intervals

Results

49.0ms	57×	body	1280	valid
20.0ms	153×	body	80	valid
20.0ms	36×	body	640	valid
10.0ms	26×	body	320	valid
5.0ms	53×	body	80	nan
3.0ms	10×	body	160	valid

simplify48.0ms

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	5001	14

prune26.0ms

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: 11.6b

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)))
5.8b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
71×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
49×	`times-frac`
30×	`pow-unpow`
27×	`associate-r`
26×	`associate-l`
25×	`add-exp-log`
20×	`unpow-prod-down` `distribute-lft-out`
18×	`frac-times`
16×	`add-cbrt-cube` `associate-/l*`
15×	`associate-/r*`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`pow-neg`
11×	`neg-sub0` `associate-*r/` `pow-sub`
9×	`pow1` `associate-*l/`
8×	`prod-exp` `unswap-sqr`
6×	`clear-num`
5×	`frac-2neg` `div-exp` `div-inv`
4×	`cbrt-unprod` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `un-div-inv`
2×	`tan-quot` `pow-prod-down` `associate-/r/` `*-commutative`
1×	`neg-mul-1` `pow-pow`

Counts

4 → 202

Calls

4 calls:

4.0ms	(/ 1.0 (tan B))
9.0ms	(* x (/ 1.0 (tan B)))
40.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
19.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 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))))
167.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify100.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	861	1762
1	3768	1671
2	5001	1671

prune570.0ms

Filtered

214 candidates to 147 candidates (68.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	201	13	214
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	202	13	215

Merged error: 0.0b

Counts

215 → 13

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))))
0.9b	(/ (* (- F) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (- (sin B)))
16.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

406×	`*-un-lft-identity`
338×	`times-frac`
262×	`add-sqr-sqrt`
197×	`add-cube-cbrt`
188×	`associate-l`
170×	`associate-r`
145×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
130×	`distribute-lft-out`
129×	`unpow-prod-down`
45×	`neg-mul-1`
38×	`unswap-sqr`
35×	`associate-/l*`
30×	`pow-unpow`
25×	`add-exp-log` `sqr-pow`
16×	`add-cbrt-cube`
13×	`associate-r/` `associate-/r` `*-commutative`
9×	`pow1`
8×	`prod-exp`
5×	`pow-neg` `div-exp`
4×	`un-div-inv` `cbrt-unprod` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `pow-exp` `clear-num` `associate-/l/` `pow-sub`
2×	`distribute-lft-neg-out` `frac-2neg` `pow-prod-down`
1×	`tan-quot` `pow-pow` `distribute-frac-neg` `associate-/r/`

Counts

4 → 509

Calls

4 calls:

8.0ms	(* x (/ 1.0 (tan B)))
28.0ms	(* (- F) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
44.0ms	(/ (* (- F) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (- (sin B)))
17.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series839.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* x (/ 1.0 (tan B)))
221.0ms	(* (- 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)))
152.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify110.0ms

Algorithm

egg-herbie

Counts

521 → 521

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1698	8208
1	5001	8056

prune1.3s

Filtered

521 candidates to 334 candidates (64.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	513	8	521
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	523	11	534

Merged error: 0.0b

Counts

534 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 1.0 x) (tan B))
0.3b	(* (- F) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
0.9b	(/ (* (- F) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (- (sin B)))
16.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

420×	`*-un-lft-identity`
364×	`times-frac`
280×	`add-sqr-sqrt`
212×	`add-cube-cbrt`
197×	`associate-l`
168×	`associate-r`
145×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
130×	`distribute-lft-out`
129×	`unpow-prod-down`
45×	`neg-mul-1`
43×	`associate-/l*`
40×	`unswap-sqr`
30×	`pow-unpow`
25×	`add-exp-log` `sqr-pow`
16×	`*-commutative` `add-cbrt-cube`
13×	`associate-/r*`
7×	`pow1` `prod-exp`
6×	`div-exp`
5×	`pow-neg`
4×	`cbrt-undiv` `associate-*r/` `div-inv` `add-log-exp`
3×	`neg-sub0` `pow-to-exp` `pow-exp` `cbrt-unprod` `associate-/l/` `pow-sub`
2×	`distribute-lft-neg-out` `frac-2neg` `clear-num` `un-div-inv`
1×	`tan-quot` `pow-pow` `distribute-frac-neg` `pow-prod-down` `associate-/r/`

Counts

4 → 532

Calls

4 calls:

7.0ms	(/ (* 1.0 x) (tan B))
29.0ms	(* (- F) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
44.0ms	(/ (* (- F) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (- (sin B)))
17.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series835.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (* 1.0 x) (tan B))
223.0ms	(* (- F) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
352.0ms	(/ (* (- F) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (- (sin B)))
151.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify115.0ms

Algorithm

egg-herbie

Counts

544 → 544

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1773	8458
1	5001	8310

prune1.4s

Filtered

544 candidates to 355 candidates (65.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	537	7	544
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	546	9	555

Merged error: 0.0b

Counts

555 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- F) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.9b	(/ (* (- F) (/ 1 (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))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

1258×	`*-un-lft-identity`
1247×	`times-frac`
712×	`add-sqr-sqrt`
532×	`add-cube-cbrt`
516×	`associate-r`
430×	`distribute-lft-out`
411×	`unpow-prod-down`
335×	`associate-l`
234×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
84×	`unswap-sqr`
78×	`neg-mul-1`
76×	`associate-/l*`
67×	`sqr-pow`
66×	`add-exp-log`
49×	`associate-/r*`
38×	`associate-*r/`
29×	`div-exp`
26×	`pow-unpow`
22×	`associate-/l/`
20×	`prod-exp` `add-cbrt-cube`
16×	`pow-flip` `div-inv`
12×	`*-commutative`
10×	`pow-to-exp` `pow-exp`
9×	`pow1` `rec-exp` `1-exp`
6×	`cbrt-undiv` `clear-num` `un-div-inv`
4×	`frac-2neg` `cbrt-unprod` `add-log-exp`
2×	`distribute-lft-neg-out` `pow-pow`
1×	`distribute-frac-neg` `pow-prod-down` `inv-pow`

Counts

4 → 1001

Calls

4 calls:

40.0ms	(* (- F) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
24.0ms	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
62.0ms	(/ (* (- F) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))) (- (sin B)))
19.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

256.0ms	(* (- F) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
704.0ms	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
372.0ms	(/ (* (- F) (/ 1 (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))

simplify226.0ms

Algorithm

egg-herbie

Counts

1013 → 1013

Iterations

Useful iterations: 1 (57.0ms)

Iter	Nodes	Cost
0	2996	18014
1	5001	17303

prune2.1s

Filtered

1013 candidates to 459 candidates (45.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1012	1	1013
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	1013	9	1022

Merged error: 0.0b

Counts

1022 → 9

regimes158.0ms

Accuracy

97.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.5b

bsearch251.0ms

Steps

Iters	Range		Point
7	4.70109762468519e+27	1.360790827813975e+29	4.7477022110331865e+27
10	-1556119314.230081	-0.16456746602421737	-598092.347711255

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	35
1	46	35

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.3s	1579×	body	1280	valid
738.0ms	1357×	body	640	valid
600.0ms	4864×	body	80	valid
273.0ms	714×	body	320	valid
140.0ms	1606×	body	80	nan
95.0ms	349×	body	160	valid