Details

Time bar (total: 8.4s)

sample174.0ms

Algorithm
intervals
Results
110.0ms124×body1280valid
38.0ms79×body640valid
8.0ms27×body320valid
2.0ms9×body160valid
2.0ms17×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

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)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.8b
(sin (- lambda1 lambda2))
3.9b
(cos (- 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
(sin (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

series152.0ms

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))))
21.0ms
(sin (- lambda1 lambda2))
20.0ms
(cos (- lambda1 lambda2))

simplify72.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune295.0ms

Filtered
81 candidates to 55 candidates (67.9%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New681381
Fresh000
Picked101
Done000
Total691382

Merged error: 0.6b

Counts
82 → 13

localize32.0ms

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))))
3.9b
(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))

series262.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(* (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)))))
98.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04271128
11340942
25001940

prune370.0ms

Filtered
88 candidates to 66 candidates (75.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New87188
Fresh21012
Picked101
Done000
Total9011101

Merged error: 0.1b

Counts
101 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

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×distribute-rgt-in fma-def distribute-lft-in associate-*r* associate-*l*
2×sub-neg associate-*r/ prod-diff fma-udef
1×+-commutative associate-+l+ flip3-- flip3-+ pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
4 → 64
Calls
4 calls:
8.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
4.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (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))

series461.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
189.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
16.0ms
(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)))))
120.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify44.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03231098
11294982
25002978

prune372.0ms

Filtered
76 candidates to 63 candidates (82.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New75176
Fresh3710
Picked011
Done000
Total78987

Merged error: 0.1b

Counts
87 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(expm1 (cos (- lambda1 lambda2)))
0.6b
(+ (cos phi1) (* (cos phi2) (log1p (expm1 (cos (- lambda1 lambda2))))))
3.8b
(sin (- lambda1 lambda2))
3.9b
(cos (- lambda1 lambda2))

rewrite17.0ms

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
5×log1p-expm1-u
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube
3×fma-def
2×sub-neg
1×+-commutative cos-diff expm1-log1p flip3-+ sum-log sin-diff flip-+ expm1-udef
Counts
4 → 69
Calls
4 calls:
1.0ms
(expm1 (cos (- lambda1 lambda2)))
4.0ms
(+ (cos phi1) (* (cos phi2) (log1p (expm1 (cos (- lambda1 lambda2))))))
5.0ms
(sin (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

series212.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(expm1 (cos (- lambda1 lambda2)))
131.0ms
(+ (cos phi1) (* (cos phi2) (log1p (expm1 (cos (- lambda1 lambda2))))))
20.0ms
(sin (- lambda1 lambda2))
17.0ms
(cos (- lambda1 lambda2))

simplify83.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0380917
1921694
23160688
35001638

prune231.0ms

Filtered
81 candidates to 52 candidates (64.2%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New80181
Fresh077
Picked011
Done011
Total801090

Merged error: 0.1b

Counts
90 → 10

regimes342.0ms

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
02923
12923

end0.0ms

sample5.1s

Algorithm
intervals
Results
3.1s3570×body1280valid
1.2s2345×body640valid
344.0ms964×body320valid
88.0ms417×body160valid
69.0ms704×body80valid