Details

Time bar (total: 9.3s)

sample168.0ms

Algorithm
intervals
Results
100.0ms111×body1280valid
38.0ms74×body640valid
10.0ms30×body320valid
3.0ms15×body160valid
3.0ms26×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b
(sin (- lambda1 lambda2))
4.2b
(cos (- lambda1 lambda2))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity sin-sum add-cbrt-cube add-log-exp
4×sub-neg
3×distribute-rgt-in cos-diff distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+
1×+-commutative flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 55
Calls
4 calls:
11.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
3.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(sin (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

series190.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
97.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
23.0ms
(sin (- lambda1 lambda2))
16.0ms
(cos (- lambda1 lambda2))

simplify75.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0249435
1795394
22920393
35001393

prune267.0ms

Filtered
67 candidates to 49 candidates (73.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
0.5b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
4.0b
(sin (- lambda1 lambda2))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×sum-log
3×flip3-+ associate-*r* associate-*l* flip-+ sin-mult
2×+-commutative sin-sum associate-*r/ frac-add
1×sub-neg associate-+l+ pow-prod-down prod-exp sin-diff *-commutative cbrt-unprod unswap-sqr
Counts
4 → 55
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
12.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
3.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
5.0ms
(sin (- lambda1 lambda2))

series390.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin lambda1) (sin lambda2))
205.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
122.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
21.0ms
(sin (- lambda1 lambda2))

simplify46.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0339703
11406645
25001628

prune366.0ms

Filtered
67 candidates to 52 candidates (77.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
0.5b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×sum-log
3×flip3-+ associate-*r* associate-*l* flip-+ sin-mult
2×+-commutative associate-*r/ frac-add
1×associate-+l+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 52
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
12.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
3.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (sin lambda1) (sin lambda2))
22.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
210.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
120.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify49.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0347967
11389865
25001848

prune379.0ms

Filtered
64 candidates to 50 candidates (78.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
0.2b
(+ (log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
0.5b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.7b
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×add-sqr-sqrt add-cube-cbrt log-prod *-un-lft-identity
6×exp-prod
5×pow1
4×add-exp-log associate-+l+ log-pow add-cbrt-cube
3×exp-sum sum-log
2×+-commutative flip3-+ flip-+ rem-exp-log
1×rem-log-exp
Counts
4 → 55
Calls
4 calls:
6.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
29.0ms
(+ (log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
3.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
7.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

series618.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
216.0ms
(+ (log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
123.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
122.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0278836
11119754
25002745

prune365.0ms

Filtered
67 candidates to 51 candidates (76.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes454.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04545
14545

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3550×body1280valid
1.2s2343×body640valid
338.0ms982×body320valid
88.0ms409×body160valid
69.0ms716×body80valid