Details

sample393.0ms

Algorithm

intervals

Results

57.0ms	58×	body	1280	valid
25.0ms	40×	body	640	valid
23.0ms	159×	body	80	valid
9.0ms	20×	body	320	valid
6.0ms	55×	body	80	nan
3.0ms	11×	body	160	valid

simplify47.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.5b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
17.0b	(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))
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)))))
13.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (tan B))
108.0ms	(* x (/ 1.0 (tan B)))
224.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
160.0ms	(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

prune599.0ms

Pruning

14 alts after pruning (14 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))
0.2b	(/ F (sin B))
6.5b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
17.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite25.0ms

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:

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

series533.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (* x 1.0) (tan B))
48.0ms	(/ F (sin B))
229.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
142.0ms	(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

prune516.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.3b	(* F (/ 1 (sin B)))
6.5b	(fma (* F (/ 1 (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
17.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite31.0ms

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))))
14.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (* x 1.0) (tan B))
48.0ms	(* F (/ 1 (sin B)))
228.0ms	(fma (* F (/ 1 (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
145.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (58.0ms)

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

prune540.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* x 1.0) (sin B)) (cos B))
0.3b	(* F (/ 1 (sin B)))
6.5b	(fma (* F (/ 1 (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (/ (* x 1.0) (sin B)) (cos B))))
17.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `times-frac`
31×	`add-cube-cbrt`
30×	`pow-unpow`
23×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`associate-r`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-l`
9×	`pow1`
8×	`prod-exp`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `unpow-prod-down`
2×	`pow-prod-down` `*-commutative`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `rec-exp` `pow-pow` `1-exp` `associate-r/` `associate-l/` `pow-exp` `un-div-inv` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 125

Calls

4 calls:

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

series515.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
48.0ms	(* 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) (sin B)) (cos B))))
143.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify82.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	764	1139
1	3236	1002
2	5002	982

prune520.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes240.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 13.8b

bsearch298.0ms

Steps

Iters	Range		Point
9	873466466.9378852	81094817210814.34	261935352784.4859
8	-7.40032466583203e+30	-7.814960403485421e+27	-7.910525873650278e+27

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

sample4.1s

Algorithm

intervals

Results

1.7s	1706×	body	1280	valid
905.0ms	1395×	body	640	valid
644.0ms	4758×	body	80	valid
281.0ms	643×	body	320	valid
172.0ms	1641×	body	80	nan
109.0ms	346×	body	160	valid