Details

sample42.0ms

Algorithm

intervals

Results

24.0ms	260×	body	80	valid
1.0ms	10×	body	80	overflowed
1.0ms	1×	body	1280	valid
0.0ms	1×	body	640	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	15
5	5001	15

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`cos-sum`
21×	`prod-diff`
20×	`add-cube-cbrt`
10×	`times-frac`
6×	`pow1` `add-exp-log` `unpow-prod-down`
5×	`add-cbrt-cube`
4×	`associate-r`
3×	`expm1-log1p-u` `pow-unpow` `associate-l` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`associate-*r/` `difference-of-squares`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `flip3-+` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr` `sqr-pow`

Counts

3 → 80

Calls

3 calls:

9.0ms	(* K (+ m n))
35.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series350.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(* K (+ m n))
269.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify55.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	547	1188
1	1611	963
2	5002	962

prune339.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite36.0ms

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:

35.0ms

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

series272.0ms

Counts

1 → 3

Calls

1 calls:

272.0ms

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

simplify50.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 3 (45.0ms)

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

prune99.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (* K (+ m n))) (sqrt (* K (+ m n))))
8.5b	(sqrt (* K (+ m n)))
8.5b	(sqrt (* K (+ m n)))
15.0b	(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

59×	`pow1`
32×	`sqrt-pow1`
23×	`add-sqr-sqrt` `cos-sum`
22×	`pow-prod-down`
21×	`add-cube-cbrt` `*-un-lft-identity` `prod-diff`
18×	`associate-*r/`
16×	`sqrt-div`
12×	`pow1/2`
10×	`pow-prod-up`
9×	`times-frac`
8×	`flip3-+` `flip-+`
6×	`add-exp-log` `sqrt-prod` `pow-sqr` `add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `swap-sqr` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`associate-*l/`
1×	`pow2` `cos-diff` `sub-neg` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 122

Calls

4 calls:

30.0ms	(* (sqrt (* K (+ m n))) (sqrt (* K (+ m n))))
4.0ms	(sqrt (* K (+ m n)))
4.0ms	(sqrt (* K (+ m n)))
55.0ms	(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

series186.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (sqrt (* K (+ m n))) (sqrt (* K (+ m n))))
54.0ms	(sqrt (* K (+ m n)))
50.0ms	(sqrt (* K (+ m n)))
58.0ms	(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

simplify68.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	491	1808
1	1474	1498
2	5001	1478

prune464.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M)))
8.5b	(sqrt (* K (+ m n)))
8.5b	(sqrt (* K (+ m n)))
15.0b	(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cos-sum`
21×	`prod-diff`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`times-frac`
5×	`log1p-expm1-u`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `sqrt-div` `associate-*r/` `add-cbrt-cube` `add-log-exp`
3×	`div-inv`
2×	`flip3-+` `pow1/2` `pow-prod-down` `sqrt-prod` `flip-+`
1×	`cos-diff` `sub-neg` `expm1-log1p` `expm1-udef`

Counts

4 → 74

Calls

4 calls:

0.0ms	(expm1 (cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M)))
4.0ms	(sqrt (* K (+ m n)))
4.0ms	(sqrt (* K (+ m n)))
60.0ms	(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

series272.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(expm1 (cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M)))
49.0ms	(sqrt (* K (+ m n)))
53.0ms	(sqrt (* K (+ m n)))
54.0ms	(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

simplify67.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	426	1664
1	824	1374
2	1925	1364
3	5001	1240

prune573.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

regimes133.0ms

Accuracy

0% (0.1b remaining)

Error of 1.2b against oracle of 1.1b and baseline of 1.2b

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

sample986.0ms

Algorithm

intervals

Results

632.0ms	8139×	body	80	valid
22.0ms	44×	body	1280	valid
21.0ms	62×	body	640	valid
20.0ms	273×	body	80	overflowed
9.0ms	39×	body	320	valid
3.0ms	21×	body	160	valid