Details

sample62.0ms

Algorithm

intervals

Results

17.0ms	269×	body	80	valid
10.0ms	26×	body	1280	valid
9.0ms	34×	body	640	valid
5.0ms	25×	body	320	valid
2.0ms	12×	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: 3.8b

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)))
4.1b	(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))

series919.0ms

Counts

4 → 12

Calls

4 calls:

370.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
437.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
86.0ms	(* (- 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

prune270.0ms

Filtered

75 candidates to 62 candidates (82.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	62	13	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	14	76

Merged error: 3.6b

Counts

76 → 14

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))
0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
4.1b	(cos (/ (+ phi1 phi2) 2.0))

rewrite22.0ms

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

series197.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
27.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
49.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
33.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (34.0ms)

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

prune289.0ms

Filtered

109 candidates to 68 candidates (62.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	110	13	123

Merged error: 3.6b

Counts

123 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3))
0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
0.5b	(pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3)
4.1b	(cos (/ (+ phi1 phi2) 2.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

6.0ms	(cbrt (pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3))
3.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
9.0ms	(pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series158.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3))
48.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
56.0ms	(pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3)
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify223.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	281	941
1	707	869
2	4409	847
3	5001	847

prune287.0ms

Filtered

143 candidates to 60 candidates (42.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	0	11	11
Picked	1	0	1
Done	0	1	1
Total	143	13	156

Merged error: 3.6b

Counts

156 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
0.5b	(pow (cbrt (pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3)) 3)
0.5b	(pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3)
4.1b	(cos (/ (+ phi1 phi2) 2.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

144×	`cbrt-prod`
105×	`unpow-prod-down` `cube-prod`
37×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`cube-mult` `unpow3` `sqr-pow`
9×	`pow-unpow`
7×	`pow1` `add-exp-log`
5×	`pow-pow` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `rem-cube-cbrt`
2×	`pow1/3`

Counts

4 → 182

Calls

4 calls:

3.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
11.0ms	(pow (cbrt (pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3)) 3)
9.0ms	(pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series186.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
49.0ms	(pow (cbrt (pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3)) 3)
56.0ms	(pow (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)) 3)
27.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify221.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	413	1326
1	829	1145
2	4529	1101
3	5001	1101

prune317.0ms

Filtered

194 candidates to 66 candidates (34.0%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	194	13	207

Merged error: 3.6b

Counts

207 → 13

regimes365.0ms

Accuracy

0% (0.2b remaining)

Error of 3.6b against oracle of 3.4b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	8
1	17	8

end0.0ms

sample1.8s

Algorithm

intervals

Results

530.0ms	8354×	body	80	valid
367.0ms	1302×	body	640	valid
313.0ms	772×	body	1280	valid
143.0ms	695×	body	320	valid
55.0ms	380×	body	160	valid