Details

sample40.0ms

Algorithm

intervals

Results

20.0ms	258×	body	80	valid
2.0ms	5×	body	640	valid
1.0ms	2×	body	1280	valid
0.0ms	1×	body	320	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

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (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)
34.3b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite3.3s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

3.2s	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
9.0ms	(* K (+ m n))
30.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
14.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series696.0ms

Counts

4 → 12

Calls

4 calls:

355.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
25.0ms	(* K (+ m n))
260.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify48.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	489	871
1	1795	780
2	5001	777

prune561.0ms

Filtered

87 candidates to 62 candidates (71.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize19.0ms

Local error

Found 1 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`add-cube-cbrt` `pow-unpow`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 20

Calls

1 calls:

30.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

series258.0ms

Counts

1 → 3

Calls

1 calls:

258.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	156	164
1	433	159
2	1446	158
3	5001	155

prune93.0ms

Filtered

23 candidates to 17 candidates (73.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
33.7b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite49.0ms

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)
0.0ms	(cbrt K)
47.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series624.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt K)
176.0ms	(cbrt K)
178.0ms	(cbrt K)
101.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify93.0ms

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

prune297.0ms

Filtered

55 candidates to 46 candidates (83.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(pow (cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M)) 3)
33.7b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
2×	`cos-sum` `pow1/3`
1×	`cos-diff` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

0.0ms	(cbrt K)
0.0ms	(cbrt K)
2.0ms	(pow (cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M)) 3)
46.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series609.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt K)
167.0ms	(cbrt K)
171.0ms	(pow (cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M)) 3)
101.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify136.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	178	625
1	591	554
2	3445	546
3	5003	546

prune316.0ms

Filtered

67 candidates to 48 candidates (71.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

regimes227.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify1.0ms

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

620.0ms	8080×	body	80	valid
55.0ms	117×	body	1280	valid
50.0ms	146×	body	640	valid
23.0ms	101×	body	320	valid
7.0ms	47×	body	160	valid
1.0ms	2×	body	2560	valid