Details

sample69.0ms

Algorithm

intervals

Results

45.0ms	258×	body	80	valid
3.0ms	4×	body	1280	valid
3.0ms	5×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify49.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ 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)
34.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite616.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`unpow-prod-down` `diff-log` `add-cbrt-cube`
4×	`associate-r`
3×	`sub-neg` `pow-unpow` `associate-l` `difference-of-squares`
2×	`cos-sum` `distribute-rgt-neg-in` `associate-*r/` `neg-log` `associate--r+`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

9.0ms	(* K (+ m n))
560.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
31.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
14.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series513.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* K (+ m n))
180.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
254.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify49.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	435	667
1	1447	621
2	5002	620

prune347.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

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)

rewrite592.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`add-log-exp`
11×	`add-sqr-sqrt`
7×	`distribute-lft-out--`
6×	`unpow-prod-down` `diff-log`
4×	`add-cube-cbrt`
3×	`pow1` `add-exp-log` `pow-unpow` `difference-of-squares`
2×	`sub-neg` `distribute-rgt-neg-in` `neg-log` `add-cbrt-cube` `associate--r+`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `times-frac` `pow-exp` `flip--` `associate--r-` `sqr-pow`

Counts

2 → 44

Calls

2 calls:

559.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
31.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series448.0ms

Counts

2 → 6

Calls

2 calls:

183.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
264.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify83.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	277	469
1	798	444
2	3368	435
3	5001	432

prune180.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
34.0b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 43

Calls

4 calls:

0.0ms	(cbrt K)
0.0ms	(cbrt K)
0.0ms	(cbrt K)
44.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series646.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt K)
178.0ms	(cbrt K)
176.0ms	(cbrt K)
106.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify100.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	111	309
1	265	279
2	681	273
3	3070	273
4	5001	273

prune309.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(log (exp (cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))))
34.0b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cos-sum` `log-prod` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`exp-prod`
2×	`cos-diff` `sub-neg` `log-div` `exp-diff` `pow1/3`
1×	`rem-log-exp` `exp-sum`

Counts

4 → 50

Calls

4 calls:

0.0ms	(cbrt K)
1.0ms	(cbrt K)
89.0ms	(log (exp (cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))))
48.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series559.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt K)
183.0ms	(cbrt K)
99.0ms	(log (exp (cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))))
100.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify104.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	151	582
1	333	521
2	811	517
3	3357	517
4	5001	517

prune333.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.3b

regimes268.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	23	10
2	23	10

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.4s	8116×	body	80	valid
103.0ms	124×	body	1280	valid
98.0ms	162×	body	640	valid
43.0ms	93×	body	320	valid
21.0ms	66×	body	160	valid