Details

sample51.0ms

Algorithm

intervals

Results

25.0ms	259×	body	80	valid
3.0ms	6×	body	1280	valid
2.0ms	6×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

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

prune13.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 16.9b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
35.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

8.0ms	(- (/ (* K (+ m n)) 2.0) M)
6.0ms	(* K (+ m n))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series401.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (/ (* K (+ m n)) 2.0) M)
25.0ms	(* K (+ m n))
261.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify43.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	378	485
1	1267	447
2	5002	443

prune284.0ms

Filtered

79 candidates to 56 candidates (70.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	4	80

Merged error: 1.2b

Counts

80 → 4

localize17.0ms

Local error

Found 2 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)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 61

Calls

2 calls:

22.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series434.0ms

Counts

2 → 6

Calls

2 calls:

166.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
268.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	352	801
1	1279	742
2	5001	721

prune171.0ms

Filtered

67 candidates to 41 candidates (61.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	67	4	71

Merged error: 1.2b

Counts

71 → 4

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

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:

11.0ms

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

series268.0ms

Counts

1 → 3

Calls

1 calls:

268.0ms

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

simplify48.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 3 (44.0ms)

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

prune79.0ms

Filtered

23 candidates to 17 candidates (73.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	23	4	27

Merged error: 1.2b

Counts

27 → 4

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
35.9b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite20.0ms

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)
15.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series634.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt K)
178.0ms	(cbrt K)
178.0ms	(cbrt K)
103.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify104.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (10.0ms)

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

prune247.0ms

Filtered

55 candidates to 47 candidates (85.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	52	3	55
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	53	6	59

Merged error: 1.2b

Counts

59 → 6

regimes222.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.0b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	23	10
2	23	10

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.1s	8111×	body	80	valid
89.0ms	164×	body	640	valid
88.0ms	109×	body	1280	valid
40.0ms	99×	body	320	valid
17.0ms	59×	body	160	valid
3.0ms	3×	body	2560	valid