Details

Time bar (total: 8.9s)

sample161.0ms

Algorithm
intervals
Results
93.0ms108×body1280valid
35.0ms72×body640valid
9.0ms28×body320valid
8.0ms24×body160valid
2.0ms24×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12312
22312

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.8b

Counts
2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.5b
(cos (- lambda1 lambda2))
2.5b
(sin (- lambda1 lambda2))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×cos-sum sin-sum
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cos-diff fma-def
2×sub-neg associate-+r+
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-diff flip-+
Counts
4 → 69
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
6.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

series150.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
100.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))
21.0ms
(sin (- lambda1 lambda2))

simplify70.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune318.0ms

Filtered
81 candidates to 55 candidates (67.9%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New661581
Fresh000
Picked101
Done000
Total671582

Merged error: 0.5b

Counts
82 → 15

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.5b
(cos (- lambda1 lambda2))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×cos-sum
9×prod-diff
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cos-diff fma-def associate-*r* associate-*l*
2×distribute-rgt-in associate-+r+ distribute-lft-in flip3-+ associate-*r/ flip-+
1×+-commutative sub-neg pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
4 → 72
Calls
4 calls:
9.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
1.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
6.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))

series271.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
13.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
100.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))

simplify52.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04581104
11634916
25001912

prune416.0ms

Filtered
84 candidates to 65 candidates (77.4%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New82284
Fresh11314
Picked101
Done000
Total841599

Merged error: 0.1b

Counts
99 → 15

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×fma-udef
1×+-commutative associate-+l+ flip3-+ pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
4.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series385.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
45.0ms
(* (sin lambda1) (sin lambda2))
17.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
126.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify151.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0284848
1949757
24930751
35001751

prune388.0ms

Filtered
69 candidates to 57 candidates (82.6%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New69069
Fresh01414
Picked011
Done000
Total691584

Merged error: 0.1b

Counts
84 → 15

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(fma (cos (- lambda1 lambda2)) (cos phi2) (cos phi1))
0.7b
(pow (fma (cos (- lambda1 lambda2)) (cos phi2) (cos phi1)) 3)
2.5b
(cos (- lambda1 lambda2))
2.5b
(sin (- lambda1 lambda2))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×prod-diff
11×cos-sum sin-sum
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
2×sub-neg
1×cos-diff cube-mult pow-to-exp pow-pow unpow3 pow-exp sin-diff fma-udef rem-cube-cbrt sqr-pow
Counts
4 → 77
Calls
4 calls:
1.0ms
(fma (cos (- lambda1 lambda2)) (cos phi2) (cos phi1))
2.0ms
(pow (fma (cos (- lambda1 lambda2)) (cos phi2) (cos phi1)) 3)
5.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

series322.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(fma (cos (- lambda1 lambda2)) (cos phi2) (cos phi1))
179.0ms
(pow (fma (cos (- lambda1 lambda2)) (cos phi2) (cos phi1)) 3)
17.0ms
(cos (- lambda1 lambda2))
21.0ms
(sin (- lambda1 lambda2))

simplify41.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0342979
1891770
25002762

prune280.0ms

Filtered
89 candidates to 54 candidates (60.7%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New87289
Fresh21113
Picked011
Done011
Total8915104

Merged error: 0.1b

Counts
104 → 15

regimes490.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03224
13224

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3538×body1280valid
1.2s2355×body640valid
354.0ms957×body320valid
94.0ms429×body160valid
82.0ms721×body80valid