Details

sample66.0ms

Algorithm

intervals

Results

22.0ms	293×	body	80	valid
11.0ms	35×	body	640	valid
8.0ms	18×	body	1280	valid
4.0ms	15×	body	320	valid
2.0ms	11×	body	160	valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune8.0ms

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: 3.4b

Counts

2 → 1

localize13.0ms

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))

rewrite20.0ms

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)
7.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))

series985.0ms

Counts

4 → 12

Calls

4 calls:

393.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
474.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
91.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (32.0ms)

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

prune271.0ms

Filtered

75 candidates to 62 candidates (82.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	63	12	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	12	76

Merged error: 3.3b

Counts

76 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
0.3b	(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.5b	(log1p (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×	`expm1-log1p-u` `associate-l`
4×	`log1p-expm1-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) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
1.0ms	(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
1.0ms	(log1p (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series269.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
54.0ms	(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
61.0ms	(log1p (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	191	432
1	547	363
2	2476	363
3	5001	363

prune242.0ms

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	2	9	11
Picked	0	1	1
Done	0	0	0
Total	67	12	79

Merged error: 3.3b

Counts

79 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(log1p (cos (/ (+ phi1 phi2) 2.0)))
0.7b	(cbrt (pow (log1p (cos (/ (+ phi1 phi2) 2.0))) 3))
0.8b	(pow (log1p (cos (/ (+ phi1 phi2) 2.0))) 3)
3.9b	(cos (/ (+ phi1 phi2) 2.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube`
4×	`log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `log1p-udef` `pow-pow` `pow1/3` `log1p-expm1` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

1.0ms	(log1p (cos (/ (+ phi1 phi2) 2.0)))
4.0ms	(cbrt (pow (log1p (cos (/ (+ phi1 phi2) 2.0))) 3))
4.0ms	(pow (log1p (cos (/ (+ phi1 phi2) 2.0))) 3)
10.0ms	(cos (/ (+ phi1 phi2) 2.0))

series280.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(log1p (cos (/ (+ phi1 phi2) 2.0)))
61.0ms	(cbrt (pow (log1p (cos (/ (+ phi1 phi2) 2.0))) 3))
126.0ms	(pow (log1p (cos (/ (+ phi1 phi2) 2.0))) 3)
32.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify145.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (138.0ms)

Iter	Nodes	Cost
0	207	531
1	690	492
2	3784	484
3	5002	483

prune263.0ms

Filtered

80 candidates to 49 candidates (61.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	80	12	92

Merged error: 3.3b

Counts

92 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- lambda1 lambda2))
0.5b	(cbrt (- lambda1 lambda2))
0.5b	(cbrt (- lambda1 lambda2))
3.9b	(cos (/ (+ phi1 phi2) 2.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

3.0ms	(cbrt (- lambda1 lambda2))
3.0ms	(cbrt (- lambda1 lambda2))
3.0ms	(cbrt (- lambda1 lambda2))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series506.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (- lambda1 lambda2))
161.0ms	(cbrt (- lambda1 lambda2))
161.0ms	(cbrt (- lambda1 lambda2))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify129.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 4 (116.0ms)

Iter	Nodes	Cost
0	199	399
1	419	377
2	1147	368
3	3713	347
4	5001	342

prune284.0ms

Filtered

72 candidates to 65 candidates (90.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	70	14	84

Merged error: 3.3b

Counts

84 → 14

regimes423.0ms

Accuracy

0% (0.1b remaining)

Error of 3.7b against oracle of 3.6b 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

647.0ms	8387×	body	80	valid
442.0ms	1292×	body	640	valid
372.0ms	785×	body	1280	valid
165.0ms	688×	body	320	valid
63.0ms	380×	body	160	valid