Details

sample67.0ms

Algorithm

intervals

Results

22.0ms	278×	body	80	valid
12.0ms	40×	body	640	valid
10.0ms	24×	body	1280	valid
3.0ms	14×	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

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.7b

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

rewrite21.0ms

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:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
3.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
10.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series924.0ms

Counts

4 → 12

Calls

4 calls:

367.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
441.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
86.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
30.0ms	(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

prune273.0ms

Filtered

75 candidates to 62 candidates (82.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
0.5b	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.0b	(cos (/ (+ phi1 phi2) 2.0))

rewrite28.0ms

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:

17.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
1.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
1.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series194.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
30.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
46.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (36.0ms)

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

prune358.0ms

Filtered

109 candidates to 69 candidates (63.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))
0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
1.2b	(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
2.0b	(cos (/ (+ phi1 phi2) 2.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

26×	`log-pow`
24×	`exp-prod`
16×	`cbrt-prod`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down` `cube-prod`
7×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-mult` `pow-unpow` `log-prod` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `rem-log-exp` `pow-exp` `rem-cube-cbrt`

Counts

4 → 86

Calls

4 calls:

4.0ms	(cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))
1.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms	(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))

series154.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))
51.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
47.0ms	(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify141.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	207	563
1	609	507
2	3490	499
3	5001	499

prune363.0ms

Filtered

98 candidates to 63 candidates (64.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.5b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

1.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series133.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
25.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify135.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	139	317
1	487	294
2	3179	290
3	5001	290

prune289.0ms

Filtered

64 candidates to 48 candidates (75.0%)

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.5b

regimes641.0ms

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	12
1	22	12

end0.0ms

sample1.9s

Algorithm

intervals

Results

576.0ms	8380×	body	80	valid
396.0ms	1292×	body	640	valid
342.0ms	781×	body	1280	valid
161.0ms	762×	body	320	valid
52.0ms	343×	body	160	valid