Details

sample48.0ms

Algorithm

intervals

Results

25.0ms	260×	body	80	valid
2.0ms	7×	body	640	valid
2.0ms	5×	body	1280	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify49.0ms

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
36.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite272.0ms

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:

10.0ms	(* K (+ m n))
34.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
211.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
15.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series526.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* K (+ m n))
266.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
172.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify41.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (34.0ms)

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

prune353.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.4b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite1.3s

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:

1.1s	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
33.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
212.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

series738.0ms

Counts

3 → 9

Calls

3 calls:

161.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
399.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
178.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

simplify49.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (36.0ms)

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

prune270.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.4b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

33.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
213.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

series439.0ms

Counts

2 → 6

Calls

2 calls:

264.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
174.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

simplify73.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	253	368
1	720	351
2	2937	346
3	5002	343

prune174.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
36.3b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite53.0ms

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:

0.0ms	(cbrt K)
0.0ms	(cbrt K)
1.0ms	(cbrt K)
51.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series629.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt K)
175.0ms	(cbrt K)
181.0ms	(cbrt K)
101.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify96.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (8.0ms)

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

prune298.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.4b

regimes232.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	11
1	27	11
2	27	11

end0.0ms

sample1.1s

Algorithm

intervals

Results

664.0ms	8075×	body	80	valid
65.0ms	129×	body	1280	valid
56.0ms	157×	body	640	valid
24.0ms	95×	body	320	valid
14.0ms	62×	body	160	valid
3.0ms	4×	body	2560	valid