Details

sample385.0ms

Algorithm

intervals

Results

54.0ms	60×	body	1280	valid
29.0ms	44×	body	640	valid
23.0ms	164×	body	80	valid
7.0ms	18×	body	320	valid
7.0ms	64×	body	80	nan
2.0ms	7×	body	160	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (16.0ms)

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

prune12.0ms

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: 14.8b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
6.6b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
19.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
37×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
14×	`associate-r`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unpow-prod-down` `associate-l` `associate-/r` `associate-/l`
2×	`tan-quot` `cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 123

Calls

4 calls:

4.0ms	(/ 1.0 (tan B))
7.0ms	(* x (/ 1.0 (tan B)))
1.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
12.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1.0 (tan B))
113.0ms	(* x (/ 1.0 (tan B)))
228.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
162.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify69.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	628	1028
1	2518	940
2	5001	937

prune566.0ms

Filtered

135 candidates to 112 candidates (83.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	123	12	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	12	136

Merged error: 0.0b

Counts

136 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ (* x 1.0) (tan B))
6.6b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
19.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity` `times-frac`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`add-exp-log`
11×	`add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `unpow-prod-down` `div-exp`
2×	`frac-2neg` `clear-num`
1×	`tan-quot` `neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 111

Calls

4 calls:

4.0ms	(/ F (sin B))
5.0ms	(/ (* x 1.0) (tan B))
1.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series531.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ F (sin B))
109.0ms	(/ (* x 1.0) (tan B))
223.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
147.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	616	964
1	2352	876
2	5001	873

prune480.0ms

Filtered

123 candidates to 100 candidates (81.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	123	12	135

Merged error: 0.0b

Counts

135 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1.0 (tan B)))
0.3b	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
6.6b	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
19.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
40×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log`
15×	`unpow-prod-down`
14×	`associate-r`
13×	`pow-unpow`
11×	`add-cbrt-cube`
7×	`pow1` `div-exp` `associate-/r*`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-to-exp` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-l` `div-inv` `associate-/l*`
2×	`cbrt-undiv` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`tan-quot` `pow-flip` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r/` `-commutative` `fma-udef` `inv-pow`

Counts

4 → 129

Calls

4 calls:

7.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
1.0ms	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

117.0ms	(* x (/ 1.0 (tan B)))
708.0ms	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
242.0ms	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
135.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify73.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	726	1399
1	2881	1263
2	5001	1214

prune473.0ms

Filtered

141 candidates to 94 candidates (66.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	142	11	153

Merged error: 0.0b

Counts

153 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
6.7b	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
19.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

191×	`times-frac`
117×	`add-sqr-sqrt`
112×	`add-cube-cbrt` `*-un-lft-identity`
45×	`unpow-prod-down`
25×	`add-exp-log`
16×	`add-cbrt-cube` `associate-/l*`
15×	`sqr-pow`
14×	`associate-r`
13×	`pow-unpow`
12×	`div-inv`
11×	`div-exp`
10×	`associate-/r*`
7×	`pow1`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `associate-l` `pow-exp`
2×	`tan-quot` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`pow-pow` `associate-r/` `pow-prod-down` `-commutative` `associate-/l/`

Counts

4 → 226

Calls

4 calls:

4.0ms	(/ 1.0 (tan B))
7.0ms	(* x (/ 1.0 (tan B)))
14.0ms	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series601.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1.0 (tan B))
113.0ms	(* x (/ 1.0 (tan B)))
306.0ms	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
141.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify117.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	1027	3151
1	4540	3045
2	5001	3036

prune821.0ms

Filtered

238 candidates to 186 candidates (78.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	234	4	238
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	237	12	249

Merged error: 0.0b

Counts

249 → 12

regimes202.0ms

Accuracy

97.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 11.0b

bsearch298.0ms

Steps

Iters	Range		Point
9	4.0033008338845853e+65	7.402926812642739e+71	4.0460331114730965e+65
9	-1.9873362550655262e+49	-1.019819475951661e+43	-1.0311824715820677e+43

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	40
1	61	40
2	61	40

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	1731×	body	1280	valid
811.0ms	1380×	body	640	valid
638.0ms	4769×	body	80	valid
273.0ms	672×	body	320	valid
165.0ms	1675×	body	80	nan
90.0ms	332×	body	160	valid