Details

sample40.0ms

Algorithm

intervals

Results

20.0ms	257×	body	80	valid
2.0ms	5×	body	640	valid
1.0ms	3×	body	1280	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	320	valid

simplify52.0ms

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

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* K (+ m n)) 2.0)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
34.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

176×	`add-sqr-sqrt`
151×	`*-un-lft-identity`
141×	`prod-diff`
123×	`exp-sum`
71×	`add-cube-cbrt`
66×	`unpow-prod-down`
52×	`distribute-rgt-neg-in`
50×	`distribute-lft-neg-in`
47×	`difference-of-squares`
41×	`distribute-lft-out--`
23×	`cos-sum` `times-frac`
15×	`add-log-exp`
11×	`sqr-pow`
10×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`exp-prod`
6×	`diff-log`
5×	`pow1` `neg-mul-1` `rem-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`pow-unpow` `associate-/r*`
2×	`cbrt-undiv` `sub-neg` `associate-*r/` `div-exp` `neg-log` `associate-/l/`
1×	`cos-diff` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `exp-diff` `pow-exp` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `associate-/l*` `associate--r-`

Counts

4 → 226

Calls

4 calls:

6.0ms	(/ (* K (+ m n)) 2.0)
31.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.1s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
23.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series484.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (* K (+ m n)) 2.0)
265.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
119.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify105.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	1030	6048
1	3034	4879
2	5001	4389

prune575.0ms

Filtered

238 candidates to 91 candidates (38.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.2b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

330×	`add-sqr-sqrt`
277×	`*-un-lft-identity`
249×	`prod-diff`
138×	`unpow-prod-down`
123×	`exp-sum`
115×	`add-cube-cbrt`
114×	`distribute-rgt-neg-in`
110×	`distribute-lft-neg-in`
96×	`difference-of-squares`
83×	`distribute-lft-out--`
24×	`fma-neg` `add-log-exp`
23×	`times-frac` `sqr-pow`
12×	`diff-log`
11×	`neg-mul-1` `associate--r+`
8×	`exp-prod`
5×	`rem-exp-log`
4×	`pow1` `add-exp-log` `neg-log`
3×	`expm1-log1p-u` `sub-neg` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u`
2×	`associate--r-`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `exp-diff` `pow-exp` `flip--`

Counts

3 → 347

Calls

3 calls:

671.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
34.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.1s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

series562.0ms

Counts

3 → 9

Calls

3 calls:

183.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
260.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
118.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

simplify117.0ms

Algorithm

egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	783	9869
1	2227	7499
2	5001	5146

prune497.0ms

Filtered

356 candidates to 98 candidates (27.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
34.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cos-sum`
63×	`prod-diff`
44×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`div-inv`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 112

Calls

4 calls:

1.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
23.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series324.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
51.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify87.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 4 (67.0ms)

Iter	Nodes	Cost
0	313	2908
1	519	2268
2	1140	2266
3	3283	2085
4	5002	2049

prune430.0ms

Filtered

124 candidates to 58 candidates (46.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

localize36.0ms

Local error

Found 4 expressions with local error:

34.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

92×	`cos-sum`
84×	`prod-diff`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`times-frac`
12×	`div-inv`
4×	`pow1` `add-exp-log` `cos-diff` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 132

Calls

4 calls:

23.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series220.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
58.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
53.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify91.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 4 (63.0ms)

Iter	Nodes	Cost
0	294	3688
1	495	2852
2	1095	2852
3	3121	2612
4	5002	2564

prune470.0ms

Filtered

144 candidates to 60 candidates (41.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

regimes260.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.0b 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

636.0ms	8137×	body	80	valid
57.0ms	164×	body	640	valid
53.0ms	111×	body	1280	valid
25.0ms	104×	body	320	valid
9.0ms	55×	body	160	valid
1.0ms	1×	body	2560	valid