Details

sample43.0ms

Algorithm

intervals

Results

21.0ms	262×	body	80	valid
1.0ms	4×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	1×	body	2560	valid
0.0ms	1×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	15
5	5001	15

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ m n) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
34.7b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
81×	`add-sqr-sqrt`
69×	`add-cube-cbrt` `prod-diff`
59×	`times-frac`
23×	`cos-sum`
16×	`fma-neg`
13×	`distribute-lft-out`
7×	`pow1` `add-exp-log` `div-inv`
6×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `difference-of-squares`
3×	`pow-unpow` `associate-l`
2×	`sub-neg` `associate-*r/` `distribute-lft-out--`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr` `sqr-pow`

Counts

4 → 161

Calls

4 calls:

59.0ms	(- (/ (+ m n) 2.0) M)
54.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
18.0ms	(* K (+ m n))
36.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series344.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(- (/ (+ m n) 2.0) M)
244.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
22.0ms	(* K (+ m n))
53.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify68.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	728	2114
1	2226	1561
2	5001	1545

prune539.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ (+ m n) 2.0) M)
0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

233×	`add-sqr-sqrt`
223×	`*-un-lft-identity`
177×	`prod-diff`
113×	`add-cube-cbrt`
78×	`unpow-prod-down`
62×	`distribute-rgt-neg-in` `times-frac`
60×	`distribute-lft-neg-in`
53×	`difference-of-squares`
44×	`distribute-lft-out--`
40×	`fma-neg`
15×	`add-log-exp`
13×	`sqr-pow`
12×	`distribute-lft-out`
11×	`associate--r+`
7×	`diff-log`
6×	`neg-mul-1`
4×	`pow1` `add-exp-log` `div-inv`
3×	`expm1-log1p-u` `sub-neg` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `neg-log` `flip--`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `pow-exp` `associate--r-`

Counts

3 → 282

Calls

3 calls:

59.0ms	(- (/ (+ m n) 2.0) M)
1.1s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
55.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series433.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(- (/ (+ m n) 2.0) M)
162.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
243.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify102.0ms

Algorithm

egg-herbie

Counts

291 → 291

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	819	5976
1	2514	4207
2	5002	4120

prune591.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ K (sqrt 2.0))
0.5b	(/ K (sqrt 2.0))
34.9b	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
34.9b	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`sqrt-prod`
12×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`
1×	`cos-sum` `sin-sum`

Counts

4 → 102

Calls

4 calls:

6.0ms	(/ K (sqrt 2.0))
8.0ms	(/ K (sqrt 2.0))
2.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
2.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

series495.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ K (sqrt 2.0))
52.0ms	(/ K (sqrt 2.0))
191.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
198.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

simplify62.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	196	770
1	549	706
2	2117	685
3	5002	684

prune745.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (* -1 M))) 3))
0.6b	(pow (cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (* -1 M))) 3)
34.9b	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
34.9b	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (* -1 M)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `fma-udef` `sqr-pow`
1×	`pow-to-exp` `cos-sum` `pow-pow` `sin-sum` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

2.0ms	(cbrt (pow (cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (* -1 M))) 3))
3.0ms	(pow (cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (* -1 M))) 3)
2.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
2.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (* -1 M)))

series949.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt (pow (cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (* -1 M))) 3))
374.0ms	(pow (cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (* -1 M))) 3)
191.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
193.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (* -1 M)))

simplify138.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (128.0ms)

Iter	Nodes	Cost
0	179	968
1	590	897
2	3401	888
3	5001	887

prune525.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

regimes231.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	23	10
2	23	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

594.0ms	8120×	body	80	valid
51.0ms	115×	body	1280	valid
44.0ms	144×	body	640	valid
25.0ms	112×	body	320	valid
10.0ms	68×	body	160	valid
2.0ms	3×	body	2560	valid