Details

sample388.0ms

Algorithm

intervals

Results

55.0ms	58×	body	1280	valid
28.0ms	47×	body	640	valid
21.0ms	149×	body	80	valid
11.0ms	25×	body	320	valid
7.0ms	47×	body	80	nan
4.0ms	11×	body	160	valid

simplify61.0ms

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

prune13.0ms

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: 12.2b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
5.8b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite31.0ms

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)))))
13.0ms	(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))
112.0ms	(* 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)))

simplify68.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (55.0ms)

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

prune580.0ms

Filtered

135 candidates to 112 candidates (83.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	125	10	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	10	136

Merged error: 0.0b

Counts

136 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(/ (* x 1.0) (tan B))
5.8b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite26.0ms

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:

3.0ms	(/ 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))))
13.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ F (sin B))
109.0ms	(/ (* x 1.0) (tan B))
225.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
143.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (48.0ms)

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

prune457.0ms

Filtered

123 candidates to 100 candidates (81.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	123	10	133

Merged error: 0.0b

Counts

133 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (/ 1.0 (sin B))) (cos B))
0.3b	(* x (/ 1.0 (sin B)))
5.8b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (* x (/ 1.0 (sin B))) (cos B))))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`pow-unpow`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
19×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`associate-r`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `div-inv`
2×	`cbrt-undiv` `associate-r/` `div-exp` `-commutative` `unswap-sqr`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `associate-*l/` `pow-exp` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 115

Calls

4 calls:

8.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
7.0ms	(* x (/ 1.0 (sin B)))
1.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (* x (/ 1.0 (sin B))) (cos B))))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series504.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
55.0ms	(* x (/ 1.0 (sin B)))
208.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (* x (/ 1.0 (sin B))) (cos B))))
142.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify76.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	666	1079
1	2913	953
2	5001	950

prune440.0ms

Filtered

127 candidates to 96 candidates (75.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	127	10	137

Merged error: 0.0b

Counts

137 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)))
5.8b	(fma (/ F (sin B)) (* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))) (- (* x (/ 1.0 (tan B)))))
17.8b	(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))
17.8b	(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
188×	`pow-unpow`
178×	`add-sqr-sqrt`
166×	`add-cube-cbrt` `*-un-lft-identity`
78×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
24×	`unpow-prod-down`
18×	`add-exp-log`
14×	`div-inv`
12×	`sqr-pow`
9×	`pow-neg` `distribute-frac-neg` `prod-exp` `unswap-sqr`
8×	`neg-sub0` `pow-to-exp` `div-sub` `pow-exp` `pow-sub`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`pow1` `neg-mul-1` `add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
2×	`pow-pow` `associate-r/` `associate-l/`
1×	`pow2` `pow-prod-down` `pow-sqr` `un-div-inv` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef`

Counts

4 → 297

Calls

4 calls:

8.0ms	(* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)))
1.0ms	(fma (/ F (sin B)) (* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))) (- (* x (/ 1.0 (tan B)))))
11.0ms	(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))
11.0ms	(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))

series1.7s

Counts

4 → 12

Calls

4 calls:

844.0ms	(* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)))
246.0ms	(fma (/ F (sin B)) (* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))) (- (* x (/ 1.0 (tan B)))))
305.0ms	(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))
303.0ms	(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))

simplify122.0ms

Algorithm

egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	1237	3275
1	4476	3077
2	5001	3052

prune1.4s

Filtered

309 candidates to 244 candidates (79.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	308	1	309
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	308	11	319

Merged error: 0.0b

Counts

319 → 11

regimes189.0ms

Accuracy

91.3% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 10.3b

bsearch251.0ms

Steps

Iters	Range		Point
8	4268475410697743.5	1.3727849185068273e+18	4304957722136079.5
7	-1.0920372133005971e+148	-8.280020211587743e+145	-8.417579212684862e+145

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	40
1	57	40
2	57	40

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	1686×	body	1280	valid
823.0ms	1406×	body	640	valid
628.0ms	4682×	body	80	valid
296.0ms	722×	body	320	valid
158.0ms	1597×	body	80	nan
99.0ms	357×	body	160	valid

Details

sample388.0ms

simplify61.0ms

prune13.0ms

localize27.0ms

rewrite31.0ms

series539.0ms

simplify68.0ms

prune580.0ms

localize23.0ms

rewrite26.0ms

series529.0ms

simplify59.0ms

prune457.0ms

localize27.0ms

rewrite30.0ms

series504.0ms

simplify76.0ms

prune440.0ms

localize25.0ms

rewrite54.0ms

series1.7s

simplify122.0ms

prune1.4s

regimes189.0ms

bsearch251.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling