Details

sample81.0ms

Algorithm

intervals

Results

20.0ms	268×	body	80	valid
18.0ms	39×	body	1280	valid
13.0ms	42×	body	640	valid
6.0ms	26×	body	320	valid
2.0ms	13×	body	160	valid

simplify60.0ms

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

prune12.0ms

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: 4.6b

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)))
3.1b	(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)
7.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series911.0ms

Counts

4 → 12

Calls

4 calls:

357.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
441.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
87.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (31.0ms)

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

prune255.0ms

Filtered

75 candidates to 62 candidates (82.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	61	14	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	14	76

Merged error: 4.4b

Counts

76 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
0.2b	(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.3b	(log1p (cos (/ (+ phi1 phi2) 2.0)))
3.1b	(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))

series246.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
54.0ms	(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
52.0ms	(log1p (cos (/ (+ phi1 phi2) 2.0)))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify58.0ms

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

prune226.0ms

Filtered

67 candidates to 53 candidates (79.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	67	14	81

Merged error: 4.4b

Counts

81 → 14

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)))))
0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
3.1b	(cos (/ (+ phi1 phi2) 2.0))

rewrite30.0ms

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

series190.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
86.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
26.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify68.0ms

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

prune270.0ms

Filtered

85 candidates to 65 candidates (76.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	86	13	99

Merged error: 4.4b

Counts

99 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow E (cos (/ (+ phi1 phi2) 2.0)))
0.2b	(* (- lambda1 lambda2) (log (pow E (cos (/ (+ phi1 phi2) 2.0)))))
0.5b	(log (pow E (cos (/ (+ phi1 phi2) 2.0))))
3.1b	(cos (/ (+ phi1 phi2) 2.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

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

series274.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow E (cos (/ (+ phi1 phi2) 2.0)))
116.0ms	(* (- lambda1 lambda2) (log (pow E (cos (/ (+ phi1 phi2) 2.0)))))
62.0ms	(log (pow E (cos (/ (+ phi1 phi2) 2.0))))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify43.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	275	777
1	1058	671
2	5002	647

prune268.0ms

Filtered

101 candidates to 70 candidates (69.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	101	13	114

Merged error: 4.4b

Counts

114 → 13

regimes354.0ms

Accuracy

0% (0.2b remaining)

Error of 4.0b against oracle of 3.8b and baseline of 4.0b

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

642.0ms	8329×	body	80	valid
436.0ms	1292×	body	640	valid
363.0ms	791×	body	1280	valid
187.0ms	788×	body	320	valid
59.0ms	363×	body	160	valid