Details

sample62.0ms

Algorithm

intervals

Results

17.0ms	271×	body	80	valid
11.0ms	39×	body	640	valid
10.0ms	25×	body	1280	valid
4.0ms	19×	body	320	valid
2.0ms	14×	body	160	valid

simplify58.0ms

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

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

localize18.0ms

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)))
2.5b	(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))
4.0ms	(* (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))

series938.0ms

Counts

4 → 12

Calls

4 calls:

369.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
453.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
90.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (29.0ms)

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

prune283.0ms

Filtered

75 candidates to 62 candidates (82.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	60	15	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	15	76

Merged error: 3.2b

Counts

76 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
0.2b	(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.4b	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
2.5b	(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))

series269.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
52.0ms	(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
65.0ms	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify61.0ms

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

prune307.0ms

Filtered

67 candidates to 53 candidates (79.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	60	7	67
Fresh	5	9	14
Picked	0	1	1
Done	0	0	0
Total	65	17	82

Merged error: 3.2b

Counts

82 → 17

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* 1 (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))) (- phi1 phi2))
0.1b	(* (hypot (* 1 (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))) (- phi1 phi2)) R)
0.2b	(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
2.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`pow1` `add-exp-log` `associate-r` `add-cbrt-cube`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

1.0ms	(hypot (* 1 (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))) (- phi1 phi2))
4.0ms	(* (hypot (* 1 (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))) (- phi1 phi2)) R)
8.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

589.0ms	(hypot (* 1 (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))) (- phi1 phi2))
421.0ms	(* (hypot (* 1 (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))) (- phi1 phi2)) R)
124.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	377	1101
1	1406	881
2	5002	873

prune321.0ms

Filtered

97 candidates to 64 candidates (66.0%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	89	8	97
Fresh	7	8	15
Picked	0	1	1
Done	0	1	1
Total	96	18	114

Merged error: 3.2b

Counts

114 → 18

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
0.5b	(cbrt (pow (expm1 (cos (/ (+ phi1 phi2) 2.0))) 3))
0.8b	(pow (expm1 (cos (/ (+ phi1 phi2) 2.0))) 3)
2.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite12.0ms

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` `add-cbrt-cube` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `expm1-log1p` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `expm1-udef` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

1.0ms	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
2.0ms	(cbrt (pow (expm1 (cos (/ (+ phi1 phi2) 2.0))) 3))
2.0ms	(pow (expm1 (cos (/ (+ phi1 phi2) 2.0))) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series308.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
64.0ms	(cbrt (pow (expm1 (cos (/ (+ phi1 phi2) 2.0))) 3))
153.0ms	(pow (expm1 (cos (/ (+ phi1 phi2) 2.0))) 3)
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify43.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	281	549
1	1091	511
2	5002	502

prune279.0ms

Filtered

80 candidates to 49 candidates (61.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	1	14	15
Picked	1	0	1
Done	1	1	2
Total	81	17	98

Merged error: 3.2b

Counts

98 → 17

regimes631.0ms

Accuracy

0% (0.2b remaining)

Error of 3.8b against oracle of 3.6b and baseline of 3.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	9
1	24	9
2	24	9

end0.0ms

sample1.8s

Algorithm

intervals

Results

538.0ms	8407×	body	80	valid
363.0ms	1308×	body	640	valid
315.0ms	781×	body	1280	valid
146.0ms	735×	body	320	valid
48.0ms	332×	body	160	valid