Details

sample63.0ms

Algorithm

intervals

Results

36.0ms	261×	body	80	valid
2.0ms	4×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid
1.0ms	1×	body	1280	valid

simplify50.0ms

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

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.2b	(/ (* K (+ m n)) 2.0)
36.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
42×	`prod-diff`
40×	`*-un-lft-identity`
36×	`add-cube-cbrt`
25×	`times-frac`
23×	`cos-sum`
10×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-inv`
7×	`fma-neg`
6×	`unpow-prod-down` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-/r*` `difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `associate-*r/` `div-exp` `associate-/l/` `distribute-lft-out--`
1×	`cos-diff` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `pow-exp` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `flip-+` `associate-/l*` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

11.0ms	(- (/ (* K (+ m n)) 2.0) M)
35.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
5.0ms	(/ (* K (+ m n)) 2.0)
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series91.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (/ (* K (+ m n)) 2.0) M)
45.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
9.0ms	(/ (* K (+ m n)) 2.0)
23.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify61.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	622	1697
1	2068	1299
2	5002	1294

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite34.0ms

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×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 22

Calls

1 calls:

33.0ms

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

series44.0ms

Counts

1 → 3

Calls

1 calls:

43.0ms

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

simplify44.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	159	174
1	445	168
2	1492	167
3	5001	162

prune292.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
36.0b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 49

Calls

4 calls:

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

series41.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
40.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

simplify100.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (28.0ms)

Iter	Nodes	Cost
0	77	281
1	144	253
2	316	247
3	854	247
4	3641	244
5	5002	244

prune864.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
36.0b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 49

Calls

4 calls:

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

series40.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
40.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

simplify98.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (28.0ms)

Iter	Nodes	Cost
0	77	311
1	144	283
2	316	277
3	854	277
4	3641	274
5	5002	274

prune865.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.8b

regimes531.0ms

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	20	10
1	20	10

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.1s	8076×	body	80	valid
99.0ms	126×	body	1280	valid
89.0ms	144×	body	640	valid
47.0ms	103×	body	320	valid
12.0ms	43×	body	160	valid
7.0ms	6×	body	2560	valid