Details

sample48.0ms

Algorithm

intervals

Results

25.0ms	259×	body	80	valid
3.0ms	5×	body	1280	valid
1.0ms	4×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.7b

localize22.0ms

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	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
33.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
144×	`*-un-lft-identity`
141×	`prod-diff`
130×	`associate-r`
123×	`exp-sum`
72×	`add-cube-cbrt`
66×	`unpow-prod-down`
50×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
46×	`difference-of-squares`
35×	`distribute-lft-out--`
23×	`cos-sum`
20×	`times-frac`
11×	`sqr-pow`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l`
5×	`neg-mul-1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-*r/` `div-inv`
2×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `exp-diff` `pow-exp` `flip-+` `distribute-lft-out` `associate--r-`

Counts

4 → 224

Calls

4 calls:

64.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
7.0ms	(* K (+ m n))
12.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series690.0ms

Counts

4 → 12

Calls

4 calls:

345.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
264.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
28.0ms	(* K (+ m n))
53.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify109.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	1228	4982
1	3736	4262
2	5002	4261

prune714.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.6b

localize15.0ms

Local error

Found 2 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)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
148×	`*-un-lft-identity`
129×	`prod-diff`
78×	`unpow-prod-down`
64×	`add-cube-cbrt`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
51×	`difference-of-squares`
43×	`distribute-lft-out--`
24×	`fma-neg`
13×	`times-frac` `sqr-pow`
12×	`add-log-exp`
11×	`associate--r+`
6×	`neg-mul-1` `diff-log`
3×	`pow1` `add-exp-log` `pow-unpow`
2×	`expm1-log1p-u` `sub-neg` `neg-log` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `flip--` `associate--r-`

Counts

2 → 201

Calls

2 calls:

31.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series462.0ms

Counts

2 → 6

Calls

2 calls:

188.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
273.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify74.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	608	5050
1	1693	3609
2	5001	3001

prune379.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.6b

localize26.0ms

Local error

Found 4 expressions with local error:

12.0b	(cbrt (* K (+ m n)))
12.0b	(cbrt (* K (+ m n)))
12.0b	(cbrt (* K (+ m n)))
33.6b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cos-sum`
21×	`prod-diff`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`cbrt-div` `associate-*r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+` `div-inv`
1×	`cos-diff` `sub-neg`

Counts

4 → 72

Calls

4 calls:

5.0ms	(cbrt (* K (+ m n)))
5.0ms	(cbrt (* K (+ m n)))
5.0ms	(cbrt (* K (+ m n)))
18.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series383.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (* K (+ m n)))
109.0ms	(cbrt (* K (+ m n)))
111.0ms	(cbrt (* K (+ m n)))
54.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify60.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	426	1888
1	786	1586
2	1878	1562
3	5002	1391

prune413.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.5b

localize31.0ms

Local error

Found 4 expressions with local error:

12.0b	(cbrt (* K (+ m n)))
12.0b	(cbrt (* K (+ m n)))
12.0b	(cbrt (* K (+ m n)))
33.7b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n)))))) 2.0) M))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cos-sum`
21×	`prod-diff`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`cbrt-div` `associate-*r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+` `div-inv`
1×	`cos-diff` `sub-neg`

Counts

4 → 72

Calls

4 calls:

5.0ms	(cbrt (* K (+ m n)))
5.0ms	(cbrt (* K (+ m n)))
5.0ms	(cbrt (* K (+ m n)))
29.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n)))))) 2.0) M))

series379.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (* K (+ m n)))
112.0ms	(cbrt (* K (+ m n)))
106.0ms	(cbrt (* K (+ m n)))
54.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n)))))) 2.0) M))

simplify73.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	441	2746
1	865	2356
2	2322	2332
3	5001	2029

prune446.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.5b

regimes302.0ms

Accuracy

0% (0.3b remaining)

Error of 1.6b against oracle of 1.3b and baseline of 1.6b

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

675.0ms	8063×	body	80	valid
67.0ms	124×	body	1280	valid
62.0ms	164×	body	640	valid
30.0ms	117×	body	320	valid
13.0ms	55×	body	160	valid
4.0ms	5×	body	2560	valid