Details

sample42.0ms

Algorithm

intervals

Results

21.0ms	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	95	16
2	211	16
3	553	15
4	1974	15
5	5001	15

prune15.0ms

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

localize21.0ms

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))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
30×	`prod-diff`
28×	`add-cube-cbrt`
23×	`cos-sum`
13×	`times-frac`
10×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`unpow-prod-down` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`pow-unpow` `fma-neg` `associate-/r*` `difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `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-+` `associate-/l*` `sqr-pow`

Counts

4 → 108

Calls

4 calls:

4.0ms	(- l (fabs (- m n)))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
7.0ms	(/ (* K (+ m n)) 2.0)
11.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series376.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- l (fabs (- m n)))
267.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
42.0ms	(/ (* K (+ m n)) 2.0)
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify63.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	673	1539
1	2157	1180
2	5002	1179

prune410.0ms

Filtered

120 candidates to 75 candidates (62.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	118	4	122

Merged error: 0.8b

Counts

122 → 4

localize16.0ms

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)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

20.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
17.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
4.0ms	(- l (fabs (- m n)))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series549.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
115.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
12.0ms	(- l (fabs (- m n)))
263.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify60.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	486	1358
1	1760	1156
2	5001	1132

prune370.0ms

Filtered

124 candidates to 79 candidates (63.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	124	4	128

Merged error: 0.8b

Counts

128 → 4

localize19.0ms

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)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff`
12×	`unpow-prod-down`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `pow-unpow` `fma-neg` `difference-of-squares`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `times-frac` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

4 → 100

Calls

4 calls:

4.0ms	(- l (fabs (- m n)))
4.0ms	(- l (fabs (- m n)))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series563.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- l (fabs (- m n)))
12.0ms	(- l (fabs (- m n)))
267.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
272.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify83.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	271	968
1	778	718
2	3111	716
3	5002	676

prune462.0ms

Filtered

112 candidates to 72 candidates (64.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	112	4	116

Merged error: 0.8b

Counts

116 → 4

localize42.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
35.0b	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
35.1b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`
1×	`cos-sum` `sin-sum`

Counts

4 → 46

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
2.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
2.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

series422.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
211.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
211.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify117.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	162	536
1	394	479
2	986	470
3	2961	468
4	5003	468

prune430.0ms

Filtered

54 candidates to 47 candidates (87.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	54	4	58

Merged error: 0.8b

Counts

58 → 4

regimes208.0ms

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

sample1.1s

Algorithm

intervals

Results

661.0ms	8160×	body	80	valid
57.0ms	117×	body	1280	valid
54.0ms	157×	body	640	valid
26.0ms	108×	body	320	valid
8.0ms	49×	body	160	valid
3.0ms	4×	body	2560	valid