Details

sample375.0ms

Algorithm

intervals

Results

44.0ms	49×	body	1280	valid
29.0ms	52×	body	640	valid
17.0ms	146×	body	80	valid
9.0ms	23×	body	320	valid
4.0ms	48×	body	80	nan
2.0ms	9×	body	160	valid

simplify50.0ms

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

prune24.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 11.6b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(* x (/ 1.0 (tan B)))
4.5b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite79.0ms

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×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `un-div-inv`
2×	`pow-prod-down` `*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `associate-/r/`

Counts

4 → 209

Calls

4 calls:

4.0ms	(/ F (sin B))
9.0ms	(* x (/ 1.0 (tan B)))
38.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series629.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ F (sin B))
116.0ms	(* x (/ 1.0 (tan B)))
295.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
165.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify109.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	870	1801
1	3912	1685
2	5002	1683

prune620.0ms

Filtered

221 candidates to 154 candidates (30.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	211	10	221
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	212	10	222

Merged error: 0.0b

Counts

222 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1.0 (tan B)))
0.2b	(/ (- F) (* (- (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)))
16.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

398×	`*-un-lft-identity`
329×	`times-frac`
254×	`add-sqr-sqrt`
189×	`add-cube-cbrt`
188×	`associate-l`
170×	`associate-r`
132×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
130×	`distribute-lft-out`
129×	`unpow-prod-down`
44×	`neg-mul-1`
38×	`unswap-sqr`
34×	`associate-/r*`
25×	`add-exp-log` `sqr-pow`
16×	`add-cbrt-cube`
14×	`associate-/l*`
13×	`pow-unpow` `*-commutative`
9×	`pow1` `associate-*r/`
8×	`prod-exp`
5×	`div-exp`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `clear-num` `div-inv`
2×	`frac-2neg` `pow-prod-down` `un-div-inv`
1×	`tan-quot` `distribute-lft-neg-out` `neg-sub0` `pow-pow` `div-sub` `distribute-frac-neg` `associate-/r/`

Counts

4 → 493

Calls

4 calls:

8.0ms	(* x (/ 1.0 (tan B)))
37.0ms	(/ (- F) (* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
24.0ms	(* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
16.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series838.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* x (/ 1.0 (tan B)))
311.0ms	(/ (- F) (* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
271.0ms	(* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
143.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify111.0ms

Algorithm

egg-herbie

Counts

505 → 505

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1679	7420
1	5002	7288

prune1.3s

Filtered

505 candidates to 322 candidates (36.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	499	6	505
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	505	10	515

Merged error: 0.0b

Counts

515 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (/ (tan B) 1.0))
0.2b	(/ (- F) (* (- (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)))
16.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

431×	`*-un-lft-identity`
394×	`times-frac`
283×	`add-sqr-sqrt`
223×	`add-cube-cbrt`
185×	`associate-l`
156×	`associate-r`
132×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
130×	`distribute-lft-out`
129×	`unpow-prod-down`
47×	`associate-/r*`
44×	`neg-mul-1`
36×	`unswap-sqr`
25×	`add-exp-log` `sqr-pow`
16×	`add-cbrt-cube` `associate-/l*`
13×	`pow-unpow`
12×	`*-commutative`
10×	`associate-/r/`
7×	`pow1` `div-exp` `div-inv`
6×	`prod-exp`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
2×	`cbrt-unprod`
1×	`tan-quot` `distribute-lft-neg-out` `neg-sub0` `pow-pow` `div-sub` `distribute-frac-neg` `pow-prod-down` `associate-/l/`

Counts

4 → 529

Calls

4 calls:

7.0ms	(/ x (/ (tan B) 1.0))
34.0ms	(/ (- F) (* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
26.0ms	(* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
15.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series824.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ x (/ (tan B) 1.0))
301.0ms	(/ (- F) (* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
271.0ms	(* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
138.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify115.0ms

Algorithm

egg-herbie

Counts

541 → 541

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1826	7817
1	5001	7684

prune1.5s

Filtered

541 candidates to 359 candidates (33.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	536	5	541
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	542	9	551

Merged error: 0.0b

Counts

551 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (* (- (sin B)) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))) (/ (- F) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))))
0.4b	(/ (- F) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
16.9b	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
16.9b	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

rewrite556.0ms

Algorithm

rewrite-expression-head

Rules

2313×	`*-un-lft-identity`
1738×	`associate-/r*`
1260×	`unpow-prod-down`
1189×	`frac-times`
1159×	`add-sqr-sqrt`
980×	`distribute-lft-out`
936×	`sqrt-prod`
929×	`associate-l`
718×	`add-cube-cbrt`
692×	`associate-r`
522×	`associate-/l*`
519×	`times-frac`
325×	`distribute-rgt-neg-in`
324×	`distribute-lft-neg-in`
229×	`unswap-sqr`
179×	`add-exp-log`
150×	`sqr-pow`
108×	`neg-mul-1`
88×	`prod-exp`
74×	`div-exp` `clear-num`
73×	`frac-2neg`
41×	`associate-*l/`
34×	`*-commutative`
29×	`associate-*r/`
27×	`add-cbrt-cube`
26×	`pow-to-exp` `pow-exp`
16×	`rec-exp` `1-exp`
8×	`pow1` `cbrt-undiv` `cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-div` `hypot-def` `log1p-expm1-u` `add-log-exp`
3×	`un-div-inv` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `distribute-frac-neg` `flip-+`
1×	`neg-sub0` `div-sub` `pow-prod-down` `distribute-rgt-neg-out`

Counts

4 → 1914

Calls

4 calls:

282.0ms	(* (/ 1 (* (- (sin B)) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))) (/ (- F) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))))
23.0ms	(/ (- F) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
16.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
15.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

series784.0ms

Counts

4 → 12

Calls

4 calls:

373.0ms	(* (/ 1 (* (- (sin B)) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))) (/ (- F) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))))
286.0ms	(/ (- F) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
59.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
66.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

simplify616.0ms

Algorithm

egg-herbie

Counts

1926 → 1926

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5001	47099

prune4.1s

Filtered

1926 candidates to 800 candidates (58.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1926	0	1926
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	1926	9	1935

Merged error: 0.0b

Counts

1935 → 9

regimes155.0ms

Accuracy

98.1% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.4b

bsearch227.0ms

Steps

Iters	Range		Point
7	3.934319081849634e+93	9.936034952497785e+95	3.9992969853246413e+93
7	-5154421704.732712	-46881322.55292306	-99771073.77480982

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	52
1	67	52
2	79	52
3	81	52
4	81	52

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1678×	body	1280	valid
783.0ms	1460×	body	640	valid
552.0ms	4623×	body	80	valid
258.0ms	701×	body	320	valid
149.0ms	1550×	body	80	nan
88.0ms	357×	body	160	valid