Details

Time bar (total: 8.8s)

sample172.0ms

Algorithm
intervals
Results
103.0ms109×body1280valid
40.0ms80×body640valid
9.0ms28×body320valid
3.0ms28×body80valid
2.0ms11×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.9b

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))))
3.4b
(sin (- lambda1 lambda2))
3.5b
(cos (- lambda1 lambda2))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt add-cbrt-cube
3×cos-diff
2×sub-neg cos-sum associate-+r+ sin-sum distribute-lft-out
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ associate-*l* sum-log sin-diff flip-+
Counts
4 → 42
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
8.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

series165.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
109.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
26.0ms
(sin (- lambda1 lambda2))
19.0ms
(cos (- lambda1 lambda2))

simplify122.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0199433
1483387
21249386
33510386
45002386

prune205.0ms

Filtered
54 candidates to 43 candidates (20.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New431154
Fresh000
Picked101
Done000
Total441155

Merged error: 0.7b

Counts
55 → 11

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos 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))))
3.5b
(cos (- lambda1 lambda2))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube add-log-exp
4×associate-*l*
3×cos-diff associate-*r*
2×cos-sum associate-+r+ distribute-lft-out
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log *-commutative sin-cos-mult cbrt-unprod flip-+ unswap-sqr
Counts
4 → 51
Calls
4 calls:
5.0ms
(* (sin lambda1) (cos lambda2))
1.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
8.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

series190.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin lambda1) (cos lambda2))
13.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
112.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))

simplify67.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0278562
1791495
22394494
35001494

prune282.0ms

Filtered
63 candidates to 47 candidates (25.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New57663
Fresh7310
Picked101
Done000
Total65974

Merged error: 0.1b

Counts
74 → 9

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos 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))))))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
7×associate-*l*
6×associate-*r* add-log-exp
4×associate-+r+
3×+-commutative
2×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out unswap-sqr
1×flip3-+ sum-log sin-cos-mult flip-+ sin-mult
Counts
4 → 62
Calls
4 calls:
5.0ms
(* (sin lambda1) (cos 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))))))
21.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series349.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin lambda1) (cos lambda2))
51.0ms
(* (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))))))
235.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify123.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0333790
11046694
24819693
35003693

prune335.0ms

Filtered
74 candidates to 52 candidates (29.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New66874
Fresh628
Picked101
Done000
Total731083

Merged error: 0.1b

Counts
83 → 10

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (sin lambda1) (sin lambda2)) (cos phi2))) (* (cos phi2) (* (cos lambda1) (cos lambda2)))))
0.6b
(+ (+ (cos phi1) (* (* (sin lambda1) (sin lambda2)) (cos phi2))) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity
28×associate-*l*
19×add-sqr-sqrt
14×distribute-lft-out
11×pow1 add-exp-log add-cbrt-cube
10×add-cube-cbrt
9×associate-*r* add-log-exp
5×unswap-sqr
4×pow-prod-down prod-exp cbrt-unprod
3×sum-log *-commutative
2×+-commutative associate-+l+ flip3-+ associate-*r/ frac-add cos-mult flip-+ sin-mult
1×associate-*l/
Counts
4 → 82
Calls
4 calls:
9.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (sin lambda1) (sin lambda2)) (cos phi2))) (* (cos phi2) (* (cos lambda1) (cos lambda2)))))
27.0ms
(+ (+ (cos phi1) (* (* (sin lambda1) (sin lambda2)) (cos phi2))) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series379.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
47.0ms
(* (sin lambda1) (sin lambda2))
17.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (sin lambda1) (sin lambda2)) (cos phi2))) (* (cos phi2) (* (cos lambda1) (cos lambda2)))))
232.0ms
(+ (+ (cos phi1) (* (* (sin lambda1) (sin lambda2)) (cos phi2))) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify56.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04061166
116451026
250021004

prune369.0ms

Filtered
94 candidates to 67 candidates (28.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New89594
Fresh459
Picked101
Done000
Total9410104

Merged error: 0.1b

Counts
104 → 10

regimes455.0ms

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
03525
13525

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.3s3567×body1280valid
1.2s2377×body640valid
330.0ms953×body320valid
93.0ms399×body160valid
78.0ms704×body80valid