Details

sample66.0ms

Algorithm

intervals

Results

19.0ms	257×	body	80	valid
12.0ms	37×	body	640	valid
10.0ms	22×	body	1280	valid
5.0ms	21×	body	320	valid
2.0ms	13×	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

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

localize17.0ms

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))

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))

series1.1s

Counts

4 → 12

Calls

4 calls:

359.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
634.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
88.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (31.0ms)

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

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

localize21.0ms

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))

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))

series262.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
52.0ms	(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
63.0ms	(expm1 (cos (/ (+ phi1 phi2) 2.0)))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify60.0ms

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

prune217.0ms

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

localize16.0ms

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))

rewrite24.0ms

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:

10.0ms	(* (- 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)
7.0ms	(cos (/ (+ phi1 phi2) 2.0))

series195.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
27.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
52.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (37.0ms)

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

prune267.0ms

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

localize20.0ms

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))

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))

series185.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(exp (cos (/ (+ phi1 phi2) 2.0)))
84.0ms	(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
30.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (19.0ms)

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

prune226.0ms

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

regimes322.0ms

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

sample2.3s

Algorithm

intervals

Results

718.0ms	8406×	body	80	valid
507.0ms	1357×	body	640	valid
386.0ms	750×	body	1280	valid
190.0ms	709×	body	320	valid
72.0ms	367×	body	160	valid