Details

sample46.0ms

Algorithm

intervals

Results

24.0ms	265×	body	80	valid
2.0ms	8×	body	320	valid
1.0ms	3×	body	640	valid
1.0ms	2×	body	1280	valid
0.0ms	1×	body	160	valid

simplify51.0ms

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

prune12.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 16.8b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- l (fabs (- m n)))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.2b	(/ (* K (+ m n)) 2.0)
35.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
40×	`times-frac`
32×	`add-cube-cbrt`
16×	`associate-r`
13×	`associate-/l*`
12×	`associate-l`
10×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`unpow-prod-down` `add-log-exp`
5×	`pow1`
4×	`*-commutative` `distribute-lft-out` `unswap-sqr`
3×	`pow-unpow` `associate-/r*` `difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `cos-sum` `associate-*r/` `div-exp` `associate-/l/` `distribute-lft-out--`
1×	`cos-diff` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `pow-exp` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 115

Calls

4 calls:

3.0ms	(- l (fabs (- m n)))
12.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
12.0ms	(/ (* K (+ m n)) 2.0)
23.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series365.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- l (fabs (- m n)))
257.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
44.0ms	(/ (* K (+ m n)) 2.0)
53.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify60.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	564	828
1	2363	781
2	5001	781

prune506.0ms

Filtered

127 candidates to 93 candidates (73.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	125	4	129

Merged error: 0.8b

Counts

129 → 4

localize18.0ms

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
22×	`times-frac`
20×	`add-cube-cbrt` `exp-sum`
12×	`add-log-exp`
10×	`add-exp-log` `associate-+r+` `exp-prod`
7×	`associate-/r*`
6×	`pow1` `sub-neg` `unpow-prod-down` `pow-flip` `add-cbrt-cube`
5×	`+-commutative`
4×	`div-exp` `distribute-lft-out` `distribute-lft-out--`
3×	`pow-unpow` `rem-exp-log` `associate-/l*` `difference-of-squares`
2×	`associate-+r-` `rec-exp` `exp-diff` `diff-log` `1-exp` `sum-log`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `pow-exp` `clear-num` `associate-/r/` `flip--` `div-inv` `inv-pow` `sqr-pow`

Counts

4 → 110

Calls

4 calls:

24.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
21.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
3.0ms	(- l (fabs (- m n)))
12.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series543.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
113.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
12.0ms	(- l (fabs (- m n)))
258.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	433	1296
1	1496	1201
2	5002	1160

prune328.0ms

Filtered

122 candidates to 71 candidates (58.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	122	4	126

Merged error: 0.8b

Counts

126 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`unpow-prod-down`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `add-exp-log` `pow-unpow` `difference-of-squares`
4×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `times-frac` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

3.0ms	(- l (fabs (- m n)))
3.0ms	(- l (fabs (- m n)))
12.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
13.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series550.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- l (fabs (- m n)))
15.0ms	(- l (fabs (- m n)))
261.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
261.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	214	518
1	546	494
2	1696	492
3	5002	486

prune353.0ms

Filtered

80 candidates to 56 candidates (70.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	80	4	84

Merged error: 0.8b

Counts

84 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
1.0b	(/ 2.0 (* (cbrt K) (+ m n)))
34.8b	(cos (- (/ (* (cbrt K) (cbrt K)) (/ 2.0 (* (cbrt K) (+ m n)))) M))

rewrite418.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
51×	`times-frac`
48×	`*-un-lft-identity`
40×	`add-cube-cbrt`
24×	`associate-l`
22×	`cbrt-prod`
17×	`associate-/r*`
16×	`associate-r`
11×	`add-cbrt-cube`
9×	`add-exp-log`
8×	`unswap-sqr`
4×	`pow1` `*-commutative` `distribute-lft-out` `add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`cos-sum` `pow1/3` `associate-*r/` `div-exp` `associate-/r/` `cbrt-unprod`
1×	`cos-diff` `sub-neg` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 120

Calls

4 calls:

1.0ms	(cbrt K)
1.0ms	(cbrt K)
11.0ms	(/ 2.0 (* (cbrt K) (+ m n)))
400.0ms	(cos (- (/ (* (cbrt K) (cbrt K)) (/ 2.0 (* (cbrt K) (+ m n)))) M))

series569.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt K)
172.0ms	(cbrt K)
123.0ms	(/ 2.0 (* (cbrt K) (+ m n)))
101.0ms	(cos (- (/ (* (cbrt K) (cbrt K)) (/ 2.0 (* (cbrt K) (+ m n)))) M))

simplify54.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	465	980
1	1833	922
2	5001	918

prune614.0ms

Filtered

132 candidates to 104 candidates (78.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	131	5	136

Merged error: 0.8b

Counts

136 → 5

regimes197.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	23
1	22	23

end0.0ms

sample1.2s

Algorithm

intervals

Results

684.0ms	8160×	body	80	valid
60.0ms	117×	body	1280	valid
60.0ms	157×	body	640	valid
32.0ms	108×	body	320	valid
9.0ms	49×	body	160	valid
4.0ms	4×	body	2560	valid