Details

sample41.0ms

Algorithm

intervals

Results

22.0ms	261×	body	80	valid
1.0ms	3×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	1×	body	1280	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
35.3b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
8×	`add-log-exp`
6×	`unpow-prod-down`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log`
3×	`pow-unpow` `add-cbrt-cube`
2×	`sub-neg` `cos-sum` `associate-+r+` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `cos-diff` `pow-to-exp` `associate-+r-` `pow-pow` `flip3-+` `times-frac` `diff-log` `pow-exp` `flip-+` `sqr-pow`

Counts

3 → 47

Calls

3 calls:

33.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
206.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
15.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series499.0ms

Counts

3 → 9

Calls

3 calls:

268.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
176.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
54.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify80.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	308	480
1	821	452
2	3239	447
3	5002	444

prune242.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.1b

localize14.0ms

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)

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
7×	`add-log-exp`
6×	`unpow-prod-down`
4×	`add-cube-cbrt`
3×	`pow1` `add-exp-log` `pow-unpow`
2×	`associate-+r+` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `sub-neg` `pow-pow` `flip3-+` `times-frac` `diff-log` `pow-exp` `flip-+` `sqr-pow`

Counts

2 → 37

Calls

2 calls:

206.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
31.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series444.0ms

Counts

2 → 6

Calls

2 calls:

180.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
264.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify78.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	253	368
1	720	351
2	2937	346
3	5002	343

prune157.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* (cos (/ (* K (+ m n)) 2.0)) (cos M)) (* (sin (/ (* K (+ m n)) 2.0)) (sin M)))
0.3b	(* (sin (/ (* K (+ m n)) 2.0)) (sin M))
40.4b	(cos (/ (* K (+ m n)) 2.0))
40.6b	(sin (/ (* K (+ m n)) 2.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`sin-mult`
1×	`+-commutative` `flip3-+` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `cos-mult` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 45

Calls

4 calls:

4.0ms	(+ (* (cos (/ (* K (+ m n)) 2.0)) (cos M)) (* (sin (/ (* K (+ m n)) 2.0)) (sin M)))
6.0ms	(* (sin (/ (* K (+ m n)) 2.0)) (sin M))
1.0ms	(cos (/ (* K (+ m n)) 2.0))
2.0ms	(sin (/ (* K (+ m n)) 2.0))

series217.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(+ (* (cos (/ (* K (+ m n)) 2.0)) (cos M)) (* (sin (/ (* K (+ m n)) 2.0)) (sin M)))
50.0ms	(* (sin (/ (* K (+ m n)) 2.0)) (sin M))
15.0ms	(cos (/ (* K (+ m n)) 2.0))
24.0ms	(sin (/ (* K (+ m n)) 2.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	207	584
1	625	524
2	1844	524
3	5001	524

prune315.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.1b

localize40.0ms

Local error

Found 4 expressions with local error:

40.4b	(cos (/ (* K (+ m n)) 2.0))
40.4b	(cos (/ (* K (+ m n)) 2.0))
40.4b	(cos (/ (* K (+ m n)) 2.0))
40.6b	(sin (/ (* K (+ m n)) 2.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

1.0ms	(cos (/ (* K (+ m n)) 2.0))
1.0ms	(cos (/ (* K (+ m n)) 2.0))
1.0ms	(cos (/ (* K (+ m n)) 2.0))
2.0ms	(sin (/ (* K (+ m n)) 2.0))

series71.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cos (/ (* K (+ m n)) 2.0))
16.0ms	(cos (/ (* K (+ m n)) 2.0))
15.0ms	(cos (/ (* K (+ m n)) 2.0))
25.0ms	(sin (/ (* K (+ m n)) 2.0))

simplify109.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	56	236
1	88	199
2	113	199
3	124	199
4	158	199
5	236	199
6	761	199
7	2328	199
8	5001	199

prune285.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.1b

regimes204.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

628.0ms	8086×	body	80	valid
56.0ms	115×	body	1280	valid
54.0ms	161×	body	640	valid
26.0ms	107×	body	320	valid
6.0ms	38×	body	160	valid
2.0ms	3×	body	2560	valid