Details

Time bar (total: 8.4s)

sample184.0ms

Algorithm
intervals
Results
108.0ms113×body1280valid
41.0ms77×body640valid
12.0ms28×body320valid
4.0ms16×body160valid
2.0ms22×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: 0.6b

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)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.1b
(cos (- lambda1 lambda2))
4.4b
(sin (- lambda1 lambda2))

rewrite20.0ms

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))))
6.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

series151.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
102.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))
22.0ms
(sin (- lambda1 lambda2))

simplify74.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune297.0ms

Filtered
81 candidates to 55 candidates (67.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New691281
Fresh000
Picked101
Done000
Total701282

Merged error: 0.4b

Counts
82 → 12

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (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))))
4.1b
(cos (- lambda1 lambda2))

rewrite18.0ms

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×associate-+r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 68
Calls
4 calls:
5.0ms
(* (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))

series177.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (cos lambda1) (sin lambda2))
12.0ms
(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))))
17.0ms
(cos (- lambda1 lambda2))

simplify104.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
0381864
11081704
24187702
35001701

prune359.0ms

Filtered
80 candidates to 59 candidates (73.8%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New79180
Fresh01111
Picked101
Done000
Total801292

Merged error: 0.1b

Counts
92 → 12

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (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)))))

rewrite16.0ms

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×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-def
2×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log flip-+ sin-mult
Counts
4 → 68
Calls
4 calls:
5.0ms
(* (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)))))

series331.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (cos lambda1) (sin lambda2))
49.0ms
(* (sin lambda1) (sin lambda2))
18.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
221.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0327826
11159712
25002704

prune352.0ms

Filtered
80 candidates to 61 candidates (76.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New79180
Fresh11011
Picked101
Done000
Total811192

Merged error: 0.1b

Counts
92 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×fma-udef sin-mult
Counts
4 → 60
Calls
4 calls:
5.0ms
(* (cos lambda1) (sin lambda2))
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(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)))
1.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))

series312.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (cos lambda1) (sin lambda2))
46.0ms
(* (sin 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)))
205.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify64.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0241676
1756585
22691584
35002584

prune278.0ms

Filtered
72 candidates to 53 candidates (73.6%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New72072
Fresh01010
Picked011
Done000
Total721183

Merged error: 0.1b

Counts
83 → 11

regimes375.0ms

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

sample5.1s

Algorithm
intervals
Results
3.1s3499×body1280valid
1.2s2357×body640valid
305.0ms947×body320valid
99.0ms450×body160valid
73.0ms747×body80valid