Details

sample59.0ms

Algorithm

intervals

Results

15.0ms	257×	body	80	valid
10.0ms	37×	body	640	valid
8.0ms	22×	body	1280	valid
4.0ms	21×	body	320	valid
2.0ms	13×	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: 3.1b

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)))
3.0b	(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))

series963.0ms

Counts

4 → 12

Calls

4 calls:

380.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
463.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
92.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify37.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (30.0ms)

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

prune246.0ms

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

localize17.0ms

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)))
3.0b	(cos (/ (+ phi1 phi2) 2.0))

rewrite17.0ms

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)))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))

series276.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
54.0ms	(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
67.0ms	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify62.0ms

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

prune226.0ms

Filtered

67 candidates to 52 candidates (77.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

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

Merged error: 3.0b

Counts

78 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
0.4b	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
0.4b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
3.0b	(cos (/ (+ phi1 phi2) 2.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
26×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `associate-r`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3`
2×	`associate-*l/`
1×	`pow-to-exp` `flip3--` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 97

Calls

4 calls:

13.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
2.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
2.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series198.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
32.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
48.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify43.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	273	715
1	1100	668
2	5002	655

prune277.0ms

Filtered

109 candidates to 67 candidates (61.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	109	12	121

Merged error: 3.0b

Counts

121 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ phi1 phi2) 2.0)))
0.2b	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.4b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
3.0b	(cos (/ (+ phi1 phi2) 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

5.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
12.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
6.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))

series198.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
91.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
27.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	224	596
1	703	507
2	3169	501
3	5002	501

prune242.0ms

Filtered

85 candidates to 65 candidates (76.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	9	9
Picked	1	0	1
Done	0	2	2
Total	85	12	97

Merged error: 3.0b

Counts

97 → 12

regimes333.0ms

Accuracy

0% (0.2b remaining)

Error of 3.6b against oracle of 3.5b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

511.0ms	8406×	body	80	valid
376.0ms	1357×	body	640	valid
297.0ms	750×	body	1280	valid
138.0ms	709×	body	320	valid
51.0ms	367×	body	160	valid

Details

sample59.0ms

simplify56.0ms

prune8.0ms

localize13.0ms

rewrite20.0ms

series963.0ms

simplify37.0ms

prune246.0ms

localize17.0ms

rewrite17.0ms

series276.0ms

simplify62.0ms

prune226.0ms

localize15.0ms

rewrite25.0ms

series198.0ms

simplify43.0ms

prune277.0ms

localize17.0ms

rewrite32.0ms

series198.0ms

simplify69.0ms

prune242.0ms

regimes333.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.8s

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