Details

sample375.0ms

Algorithm

intervals

Results

49.0ms	55×	body	1280	valid
22.0ms	38×	body	640	valid
21.0ms	139×	body	80	valid
9.0ms	22×	body	320	valid
5.0ms	18×	body	160	valid
4.0ms	43×	body	80	nan

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune29.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 13.5b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
5.7b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
17.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite30.0ms

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)))

series540.0ms

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)))))
163.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (56.0ms)

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

prune576.0ms

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	1	0	1
Picked	1	0	1
Done	0	0	0
Total	125	12	137

Merged error: 0.0b

Counts

137 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ (* x 1.0) (tan B))
5.7b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
17.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite22.0ms

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))))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ F (sin B))
111.0ms	(/ (* x 1.0) (tan B))
220.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
148.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (48.0ms)

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

prune477.0ms

Filtered

123 candidates to 100 candidates (81.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	124	11	135

Merged error: 0.0b

Counts

135 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(* F (/ 1 (sin B)))
5.7b	(fma (* F (/ 1 (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
17.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
8.0ms	(* F (/ 1 (sin B)))
1.0ms	(fma (* F (/ 1 (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)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (* x 1.0) (tan B))
46.0ms	(* F (/ 1 (sin B)))
220.0ms	(fma (* F (/ 1 (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
141.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	710	1020
1	2989	910
2	5003	890

prune467.0ms

Filtered

132 candidates to 103 candidates (78.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	132	11	143

Merged error: 0.0b

Counts

143 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(/ 1 (/ (sin B) F))
5.7b	(fma (/ 1 (/ (sin B) F)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
17.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 160

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
6.0ms	(/ 1 (/ (sin B) F))
1.0ms	(fma (/ 1 (/ (sin B) F)) (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)))

series604.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (* x 1.0) (tan B))
41.0ms	(/ 1 (/ (sin B) F))
314.0ms	(fma (/ 1 (/ (sin B) F)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
138.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify80.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	834	1412
1	3667	1255
2	5001	1180

prune487.0ms

Filtered

172 candidates to 113 candidates (65.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	172	11	183

Merged error: 0.0b

Counts

183 → 11

regimes185.0ms

Accuracy

97.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.5b

bsearch276.0ms

Steps

Iters	Range		Point
10	255.34126550931038	3002406562115.273	510104655.9351056
7	-3.5424501143714747e+70	-3.8889969902603776e+68	-4.052779556219714e+68

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	41
1	58	41
2	58	41

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.5s	1713×	body	1280	valid
787.0ms	1368×	body	640	valid
623.0ms	4676×	body	80	valid
280.0ms	697×	body	320	valid
164.0ms	1652×	body	80	nan
101.0ms	354×	body	160	valid