Details

sample71.0ms

Algorithm

intervals

Results

21.0ms	273×	body	80	valid
15.0ms	45×	body	640	valid
10.0ms	22×	body	1280	valid
4.0ms	16×	body	320	valid
1.0ms	9×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	8
1	78	8
2	261	8
3	834	8
4	2600	8
5	5001	8

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 3.1b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.9b	(cos (/ (+ phi1 phi2) 2.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 63

Calls

4 calls:

1.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
3.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
6.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series954.0ms

Counts

4 → 12

Calls

4 calls:

378.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
456.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
92.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	328	677
1	1130	579
2	5001	569

prune260.0ms

Filtered

75 candidates to 62 candidates (82.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	64	11	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	11	76

Merged error: 3.0b

Counts

76 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
0.3b	(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.5b	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
3.9b	(cos (/ (+ phi1 phi2) 2.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`associate-l` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`associate-r`
2×	`associate-*l/`
1×	`log1p-udef` `expm1-log1p` `flip3--` `log1p-expm1` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `expm1-udef` `difference-of-squares` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

6.0ms	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
1.0ms	(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
1.0ms	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series273.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
58.0ms	(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
65.0ms	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	206	431
1	601	364
2	2665	364
3	5001	364

prune237.0ms

Filtered

67 candidates to 53 candidates (79.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	66	12	78

Merged error: 3.0b

Counts

78 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
0.5b	(+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.5b	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
3.9b	(cos (/ (+ phi1 phi2) 2.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
6×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
5×	`pow1` `add-exp-log` `log1p-expm1-u`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube`
3×	`fma-def`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out` `expm1-udef`
1×	`+-commutative` `associate-+r-` `expm1-log1p` `log1p-def` `rem-log-exp` `sum-log` `log-pow`

Counts

4 → 56

Calls

4 calls:

3.0ms	(log (+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
3.0ms	(+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
1.0ms	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series216.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(log (+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
67.0ms	(+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
68.0ms	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	187	406
1	628	368
2	1866	365
3	5002	365

prune248.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	68	12	80

Merged error: 3.0b

Counts

80 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
3.9b	(cos (/ (+ phi1 phi2) 2.0))
3.9b	(cos (/ (+ phi1 phi2) 2.0))
3.9b	(cos (/ (+ phi1 phi2) 2.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series204.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (cos (/ (+ phi1 phi2) 2.0)))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify183.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (54.0ms)

Iter	Nodes	Cost
0	88	284
1	165	254
2	433	252
3	1255	252
4	4860	243
5	5001	243

prune196.0ms

Filtered

52 candidates to 46 candidates (88.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	9	9
Picked	1	0	1
Done	0	2	2
Total	51	13	64

Merged error: 3.0b

Counts

64 → 13

regimes377.0ms

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.5b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms

sample2.1s

Algorithm

intervals

Results

654.0ms	8459×	body	80	valid
430.0ms	1276×	body	640	valid
357.0ms	754×	body	1280	valid
194.0ms	796×	body	320	valid
69.0ms	400×	body	160	valid