Details

sample41.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
1.0ms	2×	body	640	valid
1.0ms	1×	body	1280	valid
0.0ms	7×	body	80	overflowed
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	50	16
1	93	16
2	200	16
3	517	15
4	1893	15
5	5001	15

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
32.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite430.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
9×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log`
6×	`unpow-prod-down` `add-cbrt-cube`
4×	`associate-r`
3×	`pow-unpow` `associate-l` `distribute-lft-out`
2×	`sub-neg` `cos-sum` `associate-+r+` `flip3-+` `associate-*r/` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `distribute-rgt-in` `cos-diff` `pow-to-exp` `associate-+r-` `pow-pow` `distribute-lft-in` `times-frac` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

327.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
18.0ms	(* K (+ m n))
55.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
28.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series605.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
28.0ms	(* K (+ m n))
237.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
53.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	411	566
1	1369	528
2	5001	523

prune302.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
8×	`add-log-exp`
6×	`unpow-prod-down` `pow-flip`
5×	`pow1` `add-exp-log` `exp-prod` `add-cbrt-cube`
4×	`exp-sum` `associate-/r*` `distribute-lft-out`
3×	`pow-unpow` `associate-/l*` `distribute-lft-out--`
2×	`associate-+r-` `associate-+r+` `div-exp` `sum-log` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `rec-exp` `pow-pow` `frac-2neg` `flip3-+` `exp-diff` `diff-log` `1-exp` `pow-exp` `clear-num` `associate-/r/` `flip-+` `div-inv` `inv-pow` `sqr-pow`

Counts

3 → 78

Calls

3 calls:

326.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
1.7s	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
55.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series542.0ms

Counts

3 → 9

Calls

3 calls:

158.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
150.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
234.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	412	1005
1	1568	934
2	5001	910

prune253.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
32.9b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt K)
1.0ms	(cbrt K)
1.0ms	(cbrt K)
82.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series606.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt K)
170.0ms	(cbrt K)
169.0ms	(cbrt K)
93.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify97.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	111	309
1	265	279
2	681	273
3	3070	273
4	5001	273

prune285.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
32.9b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt K)
1.0ms	(cbrt K)
1.0ms	(cbrt K)
82.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series612.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt K)
172.0ms	(cbrt K)
169.0ms	(cbrt K)
93.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify98.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	111	309
1	265	279
2	681	273
3	3070	273
4	5001	273

prune310.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.3b

regimes207.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

634.0ms	8121×	body	80	valid
29.0ms	85×	body	640	valid
19.0ms	255×	body	80	overflowed
17.0ms	33×	body	1280	valid
10.0ms	42×	body	320	valid
3.0ms	16×	body	160	valid