Details

sample428.0ms

Algorithm

intervals

Results

59.0ms	48×	body	1280	valid
44.0ms	47×	body	640	valid
30.0ms	141×	body	80	valid
13.0ms	23×	body	320	valid
8.0ms	19×	body	160	valid
7.0ms	48×	body	80	nan

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
6.2b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite50.0ms

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×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`tan-quot` `neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `associate-/r/` `-commutative` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 122

Calls

4 calls:

2.0ms	(/ F (sin B))
9.0ms	(* 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)))))
27.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ F (sin B))
105.0ms	(* x (/ 1.0 (tan B)))
223.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
152.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify72.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	666	1019
1	2629	931
2	5001	928

prune580.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ (* x 1.0) (tan B))
6.2b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite34.0ms

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:

2.0ms	(/ F (sin B))
4.0ms	(/ (* 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))))
25.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ F (sin B))
107.0ms	(/ (* x 1.0) (tan B))
215.0ms	(fma (/ F (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)))

simplify56.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (46.0ms)

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

prune500.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (tan B) (* x 1.0))
0.2b	(/ 1 (/ (tan B) (* x 1.0)))
6.2b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ 1 (/ (tan B) (* x 1.0)))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

3.0ms	(/ (tan B) (* x 1.0))
6.0ms	(/ 1 (/ (tan B) (* x 1.0)))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ 1 (/ (tan B) (* x 1.0)))))
25.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (tan B) (* x 1.0))
83.0ms	(/ 1 (/ (tan B) (* x 1.0)))
215.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ 1 (/ (tan B) (* x 1.0)))))
141.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	734	1253
1	3195	1115
2	5002	1068

prune520.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (sin B))
0.2b	(* (/ (* x 1.0) (sin B)) (cos B))
6.2b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (/ (* x 1.0) (sin B)) (cos B))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

3.0ms	(/ (* x 1.0) (sin B))
10.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (/ (* x 1.0) (sin B)) (cos B))))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (* x 1.0) (sin B))
98.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
205.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (/ (* x 1.0) (sin B)) (cos B))))
139.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	634	1064
1	2689	938
2	5002	935

prune434.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes223.0ms

Accuracy

98.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 13.7b

bsearch322.0ms

Steps

Iters	Range		Point
9	181026.7805503304	1564200866895.669	91215186.09641933
8	-3.361850782781731e+33	-6.5768074190538535e+28	-1.1279187237830132e+29

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	42
1	59	42
2	64	42
3	64	42

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.0s	1682×	body	1280	valid
1.1s	1402×	body	640	valid
957.0ms	4773×	body	80	valid
383.0ms	684×	body	320	valid
225.0ms	1574×	body	80	nan
135.0ms	341×	body	160	valid