Details

sample42.0ms

Algorithm

intervals

Results

19.0ms	259×	body	80	valid
3.0ms	5×	body	1280	valid
2.0ms	5×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

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

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
32.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite584.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

9.0ms	(* K (+ m n))
515.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
32.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
24.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series454.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* K (+ m n))
113.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
256.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify60.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	661	1406
1	2052	1163
2	5002	1159

prune420.0ms

Filtered

111 candidates to 73 candidates (65.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
35×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
15×	`add-log-exp`
14×	`times-frac`
12×	`unpow-prod-down`
11×	`associate-+r+`
10×	`exp-prod` `fma-def`
9×	`prod-diff`
6×	`pow1` `add-exp-log` `pow-flip` `add-cbrt-cube` `distribute-lft-out`
5×	`exp-sum` `distribute-lft-out--`
4×	`expm1-log1p-u` `associate-/r*` `sum-log` `log1p-expm1-u` `difference-of-squares`
3×	`associate-+r-` `pow-unpow` `rem-exp-log` `associate-/l*`
2×	`exp-diff` `diff-log` `div-exp` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `rec-exp` `pow-pow` `frac-2neg` `flip3-+` `1-exp` `pow-exp` `clear-num` `associate-/r/` `flip-+` `div-inv` `inv-pow`

Counts

4 → 122

Calls

4 calls:

1.0s	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
224.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
512.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
34.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series718.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
177.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
110.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
271.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	514	1402
1	1946	1261
2	5002	1231

prune433.0ms

Filtered

134 candidates to 92 candidates (68.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
32.5b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

0.0ms	(cbrt K)
0.0ms	(cbrt K)
1.0ms	(cbrt K)
55.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series627.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt K)
175.0ms	(cbrt K)
180.0ms	(cbrt K)
98.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify86.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	356	1441
1	740	1183
2	2530	1177
3	5002	1054

prune379.0ms

Filtered

84 candidates to 57 candidates (67.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
32.5b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

0.0ms	(cbrt K)
0.0ms	(cbrt K)
1.0ms	(cbrt K)
54.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series630.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt K)
174.0ms	(cbrt K)
181.0ms	(cbrt K)
100.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify79.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	356	1441
1	740	1183
2	2530	1177
3	5002	1054

prune393.0ms

Filtered

84 candidates to 58 candidates (69.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.5b

regimes308.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

sample1.0s

Algorithm

intervals

Results

616.0ms	8079×	body	80	valid
53.0ms	163×	body	640	valid
51.0ms	109×	body	1280	valid
30.0ms	113×	body	320	valid
8.0ms	50×	body	160	valid
4.0ms	2×	body	2560	valid