Details

sample60.0ms

Algorithm

intervals

Results

17.0ms	269×	body	80	valid
12.0ms	33×	body	640	valid
8.0ms	20×	body	1280	valid
4.0ms	20×	body	320	valid
1.0ms	8×	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

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.5b

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)))
3.9b	(cos (/ (+ phi1 phi2) 2.0))

rewrite20.0ms

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))

series923.0ms

Counts

4 → 12

Calls

4 calls:

367.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
440.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
87.0ms	(* (- 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

prune270.0ms

Filtered

75 candidates to 62 candidates (82.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
0.1b	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
3.9b	(cos (* 0.5 (+ phi2 phi1)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
12×	`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` `cos-sum` `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 → 87

Calls

4 calls:

0.0ms	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
3.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
15.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
3.0ms	(cos (* 0.5 (+ phi2 phi1)))

series1.3s

Counts

4 → 12

Calls

4 calls:

520.0ms	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
594.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
122.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
30.0ms	(cos (* 0.5 (+ phi2 phi1)))

simplify52.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	395	1071
1	1515	866
2	5001	851

prune276.0ms

Filtered

99 candidates to 63 candidates (63.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
0.1b	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
0.2b	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
0.2b	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`flip3--` `associate-l` `cos-mult` `flip--` `sin-mult`
8×	`frac-times`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-*l/` `frac-sub` `log1p-expm1-u` `sub-div`
3×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-*r/`
1×	`fma-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 118

Calls

4 calls:

7.0ms	(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
13.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
46.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
7.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
103.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
303.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
66.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

simplify86.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	622	2233
1	2632	2015
2	5001	2014

prune551.0ms

Filtered

130 candidates to 92 candidates (70.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* (cos (* 0.5 phi1)) (cos (* 0.5 phi2))) lambda1 (- (* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1)))) (fma (cos (* 0.5 phi2)) (* (cos (* 0.5 phi1)) lambda2) (* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1)))))
0.1b	(* (cos (* 0.5 phi1)) lambda2)
0.2b	(* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1))
0.2b	(* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`associate-l`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`fma-udef` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

0.0ms	(fma (* (cos (* 0.5 phi1)) (cos (* 0.5 phi2))) lambda1 (- (* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1)))) (fma (cos (* 0.5 phi2)) (* (cos (* 0.5 phi1)) lambda2) (* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1)))))
5.0ms	(* (cos (* 0.5 phi1)) lambda2)
12.0ms	(* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1))
11.0ms	(* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1))))

series673.0ms

Counts

4 → 12

Calls

4 calls:

466.0ms	(fma (* (cos (* 0.5 phi1)) (cos (* 0.5 phi2))) lambda1 (- (* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1)))) (fma (cos (* 0.5 phi2)) (* (cos (* 0.5 phi1)) lambda2) (* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1)))))
47.0ms	(* (cos (* 0.5 phi1)) lambda2)
87.0ms	(* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1))
73.0ms	(* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1))))

simplify111.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	311	850
1	1150	707
2	4694	699
3	5001	697

prune395.0ms

Filtered

82 candidates to 62 candidates (75.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes410.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	28
1	33	28

end0.0ms

sample1.8s

Algorithm

intervals

Results

560.0ms	8254×	body	80	valid
385.0ms	1316×	body	640	valid
319.0ms	767×	body	1280	valid
159.0ms	721×	body	320	valid
48.0ms	351×	body	160	valid