Details

Time bar (total: 8.9s)

sample178.0ms

Algorithm
intervals
Results
111.0ms121×body1280valid
34.0ms67×body640valid
12.0ms34×body320valid
4.0ms17×body160valid
2.0ms17×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12312
22312

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize22.0ms

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))))
3.4b
(cos (- lambda1 lambda2))
3.6b
(sin (- lambda1 lambda2))

rewrite24.0ms

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)))))
10.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

series146.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
99.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))
21.0ms
(sin (- lambda1 lambda2))

simplify66.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune299.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* (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))))
3.4b
(cos (- lambda1 lambda2))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt cos-sum *-un-lft-identity
10×prod-diff
8×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 flip3-- distribute-lft-in flip3-+ fma-neg diff-log sum-log flip-- flip-+
Counts
4 → 64
Calls
4 calls:
6.0ms
(- (* (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)))))
5.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))

series222.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
12.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
102.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))

simplify88.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 3 (80.0ms)

IterNodesCost
0404948
11086785
23778782
35001781

prune403.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-log-exp
7×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×associate-+r+
1×+-commutative distribute-rgt-in sub-neg flip3-- distribute-lft-in flip3-+ fma-neg diff-log prod-diff pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 64
Calls
4 calls:
5.0ms
(- (* (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) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms
(* (sin lambda1) (sin lambda2))
5.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series382.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
17.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
50.0ms
(* (sin lambda1) (sin lambda2))
220.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0351910
11215792
25001784

prune422.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×associate-*r* associate-*l*
1×sub-neg flip3-- fma-neg diff-log prod-diff pow-prod-down prod-exp *-commutative flip-- cbrt-unprod fma-udef sin-mult unswap-sqr
Counts
4 → 56
Calls
4 calls:
5.0ms
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
3.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))

series365.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
14.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
47.0ms
(* (sin lambda1) (sin lambda2))
210.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify83.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0268760
1840665
23241663
35001657

prune312.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes380.0ms

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
02420
12420

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.3s3581×body1280valid
1.2s2314×body640valid
342.0ms961×body320valid
94.0ms423×body160valid
72.0ms721×body80valid