Details

Time bar (total: 11.0s)

sample176.0ms

Algorithm
intervals
Results
114.0ms124×body1280valid
35.0ms71×body640valid
8.0ms26×body320valid
2.0ms11×body160valid
2.0ms24×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12312
22312

prune3.0ms

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: 1.3b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
1.6b
(cos (- lambda1 lambda2))
1.9b
(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)))))
5.0ms
(+ (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:
9.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
99.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(cos (- lambda1 lambda2))
21.0ms
(sin (- lambda1 lambda2))

simplify68.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (59.0ms)

IterNodesCost
03651011
1800787
22597784
35001735

prune320.0ms

Filtered
81 candidates to 55 candidates (67.9%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New641781
Fresh000
Picked101
Done000
Total651782

Merged error: 1.0b

Counts
82 → 17

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)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
1.6b
(cos (- lambda1 lambda2))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×cos-sum prod-diff
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×distribute-rgt-in expm1-log1p-u distribute-lft-in log1p-expm1-u
3×cos-diff sub-neg fma-def associate-*r* associate-*l*
2×associate-+r+ associate-*r/
1×+-commutative flip3-- flip3-+ pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
4 → 76
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)))))
5.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))

series268.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(* (cos phi2) (- (* (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))

simplify46.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04271128
11340942
25001940

prune466.0ms

Filtered
88 candidates to 66 candidates (75.0%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New83588
Fresh7916
Picked101
Done000
Total9114105

Merged error: 0.1b

Counts
105 → 14

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube
6×distribute-rgt-in associate-+r+ distribute-lft-in associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u sub-neg prod-diff log1p-expm1-u
3×fma-def
2×associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-- flip3-+ sin-neg sum-log distribute-rgt-neg-out flip-- flip-+ sin-mult
Counts
4 → 81
Calls
4 calls:
8.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
5.0ms
(* (sin 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
(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

series440.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
53.0ms
(* (sin lambda1) (sin (- lambda2)))
20.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
226.0ms
(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify48.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04071197
115721056
250011041

prune548.0ms

Filtered
93 candidates to 74 candidates (79.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New811293
Fresh12113
Picked101
Done000
Total9413107

Merged error: 0.1b

Counts
107 → 13

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
0.4b
(pow (cos phi1) 3)
0.6b
(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
1.1b
(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt fma-def
8×pow1 add-exp-log add-cbrt-cube add-log-exp
7×unpow-prod-down cube-prod
6×pow-unpow associate--l+
5×prod-diff
4×cube-div expm1-log1p-u associate-*r/ log1p-expm1-u
3×distribute-rgt-in cube-mult sub-neg pow-pow distribute-lft-in unpow3 pow-exp rem-cube-cbrt sqr-pow
2×pow-to-exp flip3-- cos-mult flip-- sin-mult
1×+-commutative flip3-+ fma-neg diff-log pow-prod-down prod-exp sum-log sum-cubes frac-sub cbrt-unprod flip-+ distribute-lft-out sub-div
Counts
4 → 104
Calls
4 calls:
10.0ms
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
3.0ms
(pow (cos phi1) 3)
9.0ms
(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
11.0ms
(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

series1.6s

Counts
4 → 12
Calls
4 calls:
1.1s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
28.0ms
(pow (cos phi1) 3)
205.0ms
(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
216.0ms
(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

simplify121.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
07511337
136961192
250011185

prune721.0ms

Filtered
116 candidates to 80 candidates (69.0%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1106116
Fresh3912
Picked101
Done000
Total11415129

Merged error: 0.1b

Counts
129 → 15

regimes695.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03952
13952

end0.0ms

sample5.1s

Algorithm
intervals
Results
3.2s3653×body1280valid
1.2s2318×body640valid
299.0ms903×body320valid
91.0ms406×body160valid
75.0ms720×body80valid