Details

sample53.0ms

Algorithm

intervals

Results

25.0ms	258×	body	80	valid
5.0ms	7×	body	1280	valid
1.0ms	4×	body	320	valid
1.0ms	2×	body	640	valid
1.0ms	1×	body	2560	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

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

prune8.0ms

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: 16.4b

Counts

2 → 1

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
35.9b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`prod-diff`
29×	`add-cube-cbrt`
23×	`cos-sum`
12×	`unpow-prod-down`
11×	`associate-+r+` `times-frac`
10×	`fma-def`
9×	`add-log-exp`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `difference-of-squares`
3×	`pow-unpow` `associate-l` `div-inv` `distribute-lft-out` `distribute-lft-out--`
2×	`sub-neg` `flip3-+` `associate-*r/` `sum-log` `flip-+` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `cos-diff` `pow-to-exp` `associate-+r-` `pow-pow` `distribute-lft-in` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

19.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
10.0ms	(* K (+ m n))
19.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series504.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
252.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
24.0ms	(* K (+ m n))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify63.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	709	1542
1	2139	1259
2	5001	1252

prune505.0ms

Filtered

130 candidates to 88 candidates (67.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	124	6	130
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	125	6	131

Merged error: 1.0b

Counts

131 → 6

localize14.0ms

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`times-frac`
12×	`unpow-prod-down`
11×	`associate-+r+`
10×	`fma-def`
9×	`prod-diff`
8×	`add-log-exp`
6×	`pow-flip`
5×	`pow1` `add-exp-log` `exp-prod` `add-cbrt-cube`
4×	`exp-sum` `associate-/r*` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `associate-/l*`
2×	`associate-+r-` `div-exp` `sum-log` `sqr-pow`
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`

Counts

3 → 103

Calls

3 calls:

20.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
19.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series584.0ms

Counts

3 → 9

Calls

3 calls:

158.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
170.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
255.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	490	1187
1	1842	1061
2	5001	1034

prune350.0ms

Filtered

112 candidates to 76 candidates (67.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	113	5	118

Merged error: 1.0b

Counts

118 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.1b	(pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)
13.8b	(cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

72×	`unpow-prod-down`
63×	`add-sqr-sqrt`
52×	`cbrt-prod`
47×	`*-un-lft-identity`
30×	`cube-prod`
29×	`fma-def`
28×	`add-cube-cbrt`
14×	`difference-of-squares`
11×	`associate-+r+`
10×	`sqr-pow`
9×	`prod-diff` `add-log-exp`
8×	`distribute-lft-out--`
7×	`add-exp-log` `times-frac`
6×	`pow-unpow`
5×	`pow1` `pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cube-mult` `pow-to-exp` `unpow3`
2×	`pow-pow` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `pow1/3` `diff-log` `rem-cbrt-cube` `flip-+` `rem-cube-cbrt`

Counts

4 → 157

Calls

4 calls:

27.0ms	(+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
12.0ms	(pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)
13.0ms	(cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3))

series1.3s

Counts

4 → 12

Calls

4 calls:

180.0ms	(+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n))))
262.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
544.0ms	(pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)
309.0ms	(cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3))

simplify60.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	529	1277
1	1999	1176
2	5002	1165

prune515.0ms

Filtered

169 candidates to 102 candidates (60.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	169	5	174

Merged error: 1.0b

Counts

174 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

13.8b	(cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3))
40.6b	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))
40.6b	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))
40.6b	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

41×	`cbrt-prod`
31×	`*-un-lft-identity`
22×	`add-sqr-sqrt` `unpow-prod-down`
12×	`add-cube-cbrt`
10×	`cube-prod`
6×	`cbrt-div` `distribute-lft-out`
5×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`flip3-+` `flip-+` `sqr-pow`
2×	`times-frac`
1×	`cube-mult` `unpow3` `rem-cbrt-cube`

Counts

4 → 88

Calls

4 calls:

13.0ms	(cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3))
27.0ms	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))
24.0ms	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))
24.0ms	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

302.0ms	(cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3))
410.0ms	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))
396.0ms	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))
389.0ms	(cbrt (+ (cbrt (pow (pow (- (/ (+ m n) 2.0) M) 2.0) 3)) (- l (fabs (- m n)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	408	1490
1	1322	1415
2	5002	1402

prune470.0ms

Filtered

100 candidates to 73 candidates (73.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	100	5	105

Merged error: 1.0b

Counts

105 → 5

regimes192.0ms

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	27	37
1	27	37

end0.0ms

sample1.1s

Algorithm

intervals

Results

670.0ms	8071×	body	80	valid
68.0ms	127×	body	1280	valid
56.0ms	153×	body	640	valid
30.0ms	118×	body	320	valid
7.0ms	41×	body	160	valid
4.0ms	5×	body	2560	valid