Details

sample401.0ms

Algorithm

intervals

Results

49.0ms	45×	body	1280	valid
32.0ms	47×	body	640	valid
22.0ms	152×	body	80	valid
10.0ms	22×	body	320	valid
5.0ms	47×	body	80	nan
5.0ms	15×	body	160	valid

simplify45.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

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)))))
19.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite87.0ms

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:

5.0ms	(/ 1.0 (tan B))
18.0ms	(* 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)))))
58.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1.0 (tan B))
102.0ms	(* x (/ 1.0 (tan B)))
208.0ms	(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)))

simplify67.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (55.0ms)

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

prune850.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.1b	(/ (* 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))))
19.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite71.0ms

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:

6.0ms	(/ F (sin B))
10.0ms	(/ (* 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))))
51.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ F (sin B))
103.0ms	(/ (* x 1.0) (tan B))
209.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
137.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (47.0ms)

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

prune744.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 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))))
19.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite143.0ms

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×	`tan-quot` `pow-flip` `pow-pow` `prod-exp` `associate-/r/` `cbrt-unprod` `fma-udef` `inv-pow`

Counts

4 → 118

Calls

4 calls:

10.0ms	(/ (* x 1.0) (tan B))
79.0ms	(/ 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))))
49.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (* x 1.0) (tan B))
685.0ms	(/ 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))))
126.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	676	1344
1	2598	1208
2	5003	1160

prune675.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ 1 (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
6.6b	(fma (/ F (sin B)) (/ (/ 1 (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
19.5b	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
19.5b	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

rewrite327.0ms

Algorithm

rewrite-expression-head

Rules

670×	`times-frac`
408×	`unpow-prod-down`
333×	`add-sqr-sqrt`
331×	`add-cube-cbrt` `*-un-lft-identity`
210×	`sqrt-prod`
68×	`sqr-pow`
54×	`add-exp-log`
48×	`div-exp`
34×	`associate-/l*`
19×	`pow-to-exp` `pow-exp`
12×	`div-inv`
10×	`associate-/r*`
9×	`rec-exp` `1-exp` `add-cbrt-cube`
6×	`pow1`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-flip` `frac-2neg` `clear-num` `fma-udef` `associate-/l/` `pow-div`

Counts

4 → 474

Calls

4 calls:

208.0ms	(/ (/ 1 (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
0.0ms	(fma (/ F (sin B)) (/ (/ 1 (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
40.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
42.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

696.0ms	(/ (/ 1 (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
224.0ms	(fma (/ F (sin B)) (/ (/ 1 (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
54.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
48.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

simplify142.0ms

Algorithm

egg-herbie

Counts

486 → 486

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1625	14494
1	5001	12857

prune2.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes253.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 13.9b

bsearch404.0ms

Steps

Iters	Range		Point
10	0.6595217963696074	11346062936.778234	131675528.13994873
8	-2.9553247459863325e+35	-8.124316099194928e+31	-8.31093442491394e+31

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	49
1	58	49
2	58	49

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.8s	1676×	body	1280	valid
983.0ms	1436×	body	640	valid
712.0ms	4772×	body	80	valid
335.0ms	695×	body	320	valid
199.0ms	1645×	body	80	nan
112.0ms	331×	body	160	valid