Details

sample462.0ms

Algorithm

intervals

Results

49.0ms	51×	body	1280	valid
43.0ms	145×	body	80	valid
37.0ms	59×	body	640	valid
7.0ms	50×	body	80	nan
6.0ms	15×	body	320	valid
4.0ms	14×	body	160	valid

simplify46.0ms

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.1b	(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)))

rewrite90.0ms

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:

8.0ms	(/ 1.0 (tan B))
17.0ms	(* x (/ 1.0 (tan B)))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
59.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1.0 (tan B))
106.0ms	(* x (/ 1.0 (tan B)))
211.0ms	(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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (54.0ms)

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

prune596.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (/ 1.0 (tan B)))
0.4b	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
7.1b	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
17.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite151.0ms

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:

18.0ms	(* x (/ 1.0 (tan B)))
80.0ms	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.0ms	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
48.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

105.0ms	(* x (/ 1.0 (tan B)))
698.0ms	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
221.0ms	(fma (/ F (sin B)) (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
127.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	726	1399
1	2785	1263
2	5002	1214

prune511.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ (* x (cos B)) (sin B))
7.1b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
17.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite73.0ms

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×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `pow-exp` `prod-exp` `cbrt-unprod` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 110

Calls

4 calls:

6.0ms	(/ F (sin B))
12.0ms	(/ (* x (cos B)) (sin B))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
52.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series475.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ F (sin B))
89.0ms	(/ (* x (cos B)) (sin B))
204.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
133.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify54.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	600	1011
1	2303	913
2	5001	910

prune528.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (/ (sin B) (cos B)))
0.2b	(/ (sin B) (cos B))
7.1b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ x (/ (sin B) (cos B))))))
17.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 160

Calls

4 calls:

10.0ms	(/ x (/ (sin B) (cos B)))
11.0ms	(/ (sin B) (cos B))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ x (/ (sin B) (cos B))))))
49.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ x (/ (sin B) (cos B)))
18.0ms	(/ (sin B) (cos B))
209.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* 1.0 (/ x (/ (sin B) (cos B))))))
134.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	774	1590
1	3177	1481
2	5001	1478

prune744.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes209.0ms

Accuracy

98% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 13.4b

bsearch276.0ms

Steps

Iters	Range		Point
8	19335.207415959976	8405677.530639332	8324873.69956413
9	-1557293340.659962	-7.429186107752767	-128874030.50003308

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	41
1	59	41
2	59	41

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	1626×	body	1280	valid
897.0ms	1419×	body	640	valid
641.0ms	4741×	body	80	valid
295.0ms	703×	body	320	valid
180.0ms	1688×	body	80	nan
98.0ms	347×	body	160	valid