Details

Time bar (total: 8.7s)

sample165.0ms

Algorithm
intervals
Results
98.0ms107×body1280valid
36.0ms74×body640valid
10.0ms33×body320valid
3.0ms16×body160valid
3.0ms26×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: 0.6b

Counts
2 → 1

localize20.0ms

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))))
2.4b
(sin (- lambda1 lambda2))
2.5b
(cos (- lambda1 lambda2))

rewrite18.0ms

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

series153.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
101.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms
(sin (- lambda1 lambda2))
18.0ms
(cos (- lambda1 lambda2))

simplify72.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune290.0ms

Filtered
81 candidates to 55 candidates (67.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New711081
Fresh000
Picked101
Done000
Total721082

Merged error: 0.4b

Counts
82 → 10

localize29.0ms

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))

rewrite21.0ms

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:
8.0ms
(* (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))

series266.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
15.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
98.0ms
(+ (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

prune389.0ms

Filtered
88 candidates to 66 candidates (75.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New85388
Fresh279
Picked101
Done000
Total881098

Merged error: 0.1b

Counts
98 → 10

localize33.0ms

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) (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)))))

rewrite20.0ms

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×distribute-rgt-in expm1-log1p-u distribute-lft-in log1p-expm1-u
3×fma-def
2×sub-neg associate-+r+ associate-*r/ prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-- flip3-+ sum-log flip-- flip-+ sin-mult
Counts
4 → 76
Calls
4 calls:
8.0ms
(* (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) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series420.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(* (cos phi2) (- (* (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))))))
49.0ms
(* (sin lambda1) (sin lambda2))
216.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify53.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03741090
11513949
25002941

prune386.0ms

Filtered
88 candidates to 68 candidates (77.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New86288
Fresh279
Picked101
Done000
Total89998

Merged error: 0.1b

Counts
98 → 9

localize27.0ms

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)))) (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
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
3×distribute-rgt-in distribute-lft-in
2×sub-neg associate-*r/ prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- flip-- fma-udef sin-mult
Counts
4 → 68
Calls
4 calls:
8.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos 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)))
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))

series402.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(* (cos phi2) (- (* (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)))
48.0ms
(* (sin lambda1) (sin lambda2))
200.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify118.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0294940
11086822
24885821
35001821

prune315.0ms

Filtered
80 candidates to 60 candidates (75.0%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New78280
Fresh178
Picked011
Done000
Total791089

Merged error: 0.1b

Counts
89 → 10

regimes356.0ms

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
3.1s3582×body1280valid
1.2s2356×body640valid
326.0ms961×body320valid
88.0ms414×body160valid
69.0ms687×body80valid

Profiling

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