Details

Time bar (total: 12.1s)

analyze2.0s

Algorithm
search

sample191.0ms

Algorithm
intervals
Results
114.0ms110×body1280valid
46.0ms82×body640valid
10.0ms26×body320valid
4.0ms17×body160valid
3.0ms21×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune5.0ms

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))))
3.0b
(cos (- lambda1 lambda2))
3.0b
(sin (- lambda1 lambda2))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×cos-diff
2×sub-neg cos-sum associate-+r+ sin-sum
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-diff flip-+
Counts
4 → 40
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series44.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
28.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

simplify120.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0205421
1508374
21327374
33685374
45001374

prune161.0ms

Filtered
42 candidates to 52 candidates (-23.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New381452
Fresh000
Picked101
Done000
Total391453

Merged error: 0.6b

Counts
53 → 14

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (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))))
3.0b
(cos (- lambda1 lambda2))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×distribute-rgt-in cos-diff sub-neg distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+ associate-*r/
1×+-commutative flip3-- flip3-+ pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
4 → 54
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)))))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

series67.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
9.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
23.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

simplify116.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0289748
11037658
24438658
35002658

prune147.0ms

Filtered
48 candidates to 66 candidates (-37.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New65166
Fresh11213
Picked101
Done000
Total671380

Merged error: 0.1b

Counts
80 → 13

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*l* add-log-exp
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×*-commutative sin-mult
1×+-commutative flip3-+ associate-*r/ sum-log flip-+ unswap-sqr
Counts
4 → 56
Calls
4 calls:
6.0ms
(* (cos phi2) (* (sin lambda1) (sin lambda2)))
1.0ms
(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)))))
4.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series65.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (cos phi2) (* (sin lambda1) (sin lambda2)))
13.0ms
(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)))))
9.0ms
(* (sin lambda1) (sin lambda2))
27.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify40.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0283721
11122611
25001611

prune147.0ms

Filtered
51 candidates to 68 candidates (-33.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New65368
Fresh3912
Picked101
Done000
Total691281

Merged error: 0.1b

Counts
81 → 12

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×+-commutative cbrt-prod sum-log
2×cbrt-div
1×pow1/3
Counts
4 → 46
Calls
4 calls:
2.0ms
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series139.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
27.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
27.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
29.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify92.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0172697
1706604
22906602
35002602

prune94.0ms

Filtered
50 candidates to 58 candidates (-16.0%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New57158
Fresh01111
Picked011
Done000
Total571370

Merged error: 0.1b

Counts
70 → 13

regimes719.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04645
14645

end0.0ms

analyze2.0s

Algorithm
search

sample5.8s

Algorithm
intervals
Results
3.6s3580×body1280valid
1.4s2378×body640valid
376.0ms969×body320valid
113.0ms414×body160valid
81.0ms659×body80valid

Profiling

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