Details

sample361.0ms

Algorithm

intervals

Results

39.0ms	46×	body	1280	valid
22.0ms	40×	body	640	valid
20.0ms	149×	body	80	valid
13.0ms	34×	body	320	valid
5.0ms	58×	body	80	nan
3.0ms	13×	body	160	valid

simplify48.0ms

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

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: 12.4b

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)))
5.1b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
18.1b	(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))
8.0ms	(* 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)))

series545.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1.0 (tan B))
112.0ms	(* x (/ 1.0 (tan B)))
230.0ms	(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)))

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

prune612.0ms

Filtered

135 candidates to 112 candidates (83.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	122	13	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	13	136

Merged error: 0.0b

Counts

136 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ (* x 1.0) (tan B))
5.1b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
18.1b	(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:

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)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ F (sin B))
111.0ms	(/ (* 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))))
146.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify64.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (49.0ms)

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

prune524.0ms

Filtered

123 candidates to 97 candidates (78.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	125	11	136

Merged error: 0.0b

Counts

136 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (cos B))
0.2b	(/ (* x (cos B)) (sin B))
5.1b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
18.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow-unpow`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
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` `add-log-exp`
3×	`unpow-prod-down` `associate-r` `associate-l` `associate-/r*` `div-inv`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `fma-udef` `associate-/l` `pow-sub` `unswap-sqr` `sqr-pow`

Counts

4 → 101

Calls

4 calls:

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

series515.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* x (cos B))
103.0ms	(/ (* x (cos B)) (sin B))
223.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
153.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	553	942
1	2192	844
2	5001	841

prune486.0ms

Filtered

113 candidates to 89 candidates (78.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	114	10	124

Merged error: 0.0b

Counts

124 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.3b	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
5.1b	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
18.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
30×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log`
15×	`unpow-prod-down`
13×	`pow-unpow`
11×	`add-cbrt-cube`
10×	`associate-/r*`
8×	`div-exp`
5×	`pow1` `sqr-pow`
4×	`expm1-log1p-u` `pow-to-exp` `pow-exp` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `1-exp` `div-inv`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `prod-exp` `cbrt-unprod` `fma-udef` `inv-pow`

Counts

4 → 117

Calls

4 calls:

5.0ms	(/ (* x (cos B)) (sin 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))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (* x (cos B)) (sin B))
708.0ms	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
237.0ms	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
137.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify70.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	669	1391
1	2562	1245
2	5002	1196

prune432.0ms

Filtered

129 candidates to 84 candidates (65.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	129	10	139

Merged error: 0.0b

Counts

139 → 10

regimes202.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 13.7b

bsearch263.0ms

Steps

Iters	Range		Point
8	4436625.583370406	92957968930.74826	194118726.978796
8	-1.306740821185158e+22	-4.7666883365959066e+19	-4.824994114943747e+19

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	44
1	58	44
2	64	44
3	64	44

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1671×	body	1280	valid
757.0ms	1392×	body	640	valid
563.0ms	4736×	body	80	valid
269.0ms	719×	body	320	valid
153.0ms	1591×	body	80	nan
92.0ms	356×	body	160	valid