Details

Time bar (total: 9.9s)

analyze2.0s

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
9.4%90.4%0.2%9
9.4%90.4%0.2%10
10.9%88.9%0.2%11
10.9%88.9%0.2%12
10.9%88.9%0.2%13
10.9%88.9%0.2%14

sample191.0ms

Algorithm
intervals
Results
111.0ms108×body1280valid
49.0ms85×body640valid
9.0ms23×body320valid
3.0ms29×body80valid
3.0ms11×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (13.0ms)

IterNodesCost
027020
127020

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.6b

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))))
4.2b
(cos (- lambda1 lambda2))
4.3b
(sin (- lambda1 lambda2))

rewrite13.0ms

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 associate-+r+
1×+-commutative distribute-rgt-in cos-sum distribute-lft-in flip3-+ sin-sum sum-log sin-diff flip-+
Counts
4 → 38
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))

series45.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
27.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
6.0ms
(sin (- lambda1 lambda2))

simplify42.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
04947591
14947591

prune150.0ms

Filtered
42 candidates to 50 candidates (-19.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New381250
Fresh000
Picked101
Done000
Total391251

Merged error: 0.4b

Counts
51 → 12

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.2b
(cos (- lambda1 lambda2))

rewrite14.0ms

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×cos-diff associate-*r* associate-*l*
2×associate-+r+
1×+-commutative distribute-rgt-in sub-neg cos-sum distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 47
Calls
4 calls:
4.0ms
(* (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))

series45.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (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))

simplify71.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
05109730

prune137.0ms

Filtered
46 candidates to 59 candidates (-28.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New58159
Fresh11011
Picked101
Done000
Total601171

Merged error: 0.1b

Counts
71 → 11

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

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* add-log-exp
2×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log flip-+ sin-mult
Counts
4 → 57
Calls
4 calls:
4.0ms
(* (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)))))

series82.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (cos lambda1) (sin lambda2))
13.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
9.0ms
(* (sin lambda1) (sin lambda2))
51.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify45.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
04961985
14961985

prune136.0ms

Filtered
50 candidates to 69 candidates (-38.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New68169
Fresh1910
Picked101
Done000
Total701080

Merged error: 0.1b

Counts
80 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(log (exp (cos (- lambda1 lambda2))))
0.5b
(+ (cos phi1) (* (cos phi2) (log (exp (cos (- lambda1 lambda2))))))
4.2b
(cos (- lambda1 lambda2))
4.3b
(sin (- lambda1 lambda2))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
12×log-prod
8×add-sqr-sqrt add-cube-cbrt associate-+r+ *-un-lft-identity
6×add-log-exp
5×pow1
4×add-exp-log distribute-rgt-in cos-diff distribute-lft-in log-pow add-cbrt-cube
3×sub-neg exp-prod exp-sum
2×cos-sum
1×+-commutative log-div flip3-+ exp-diff sin-sum rem-log-exp sum-log sin-diff flip-+
Counts
4 → 54
Calls
4 calls:
6.0ms
(log (exp (cos (- lambda1 lambda2))))
7.0ms
(+ (cos phi1) (* (cos phi2) (log (exp (cos (- lambda1 lambda2))))))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series36.0ms

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

simplify55.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
04894592
14894592

prune83.0ms

Filtered
52 candidates to 66 candidates (-26.9%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New65166
Fresh099
Picked011
Done000
Total651176

Merged error: 0.1b

Counts
76 → 11

regimes674.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03022
13022

end0.0ms

sample5.9s

Algorithm
intervals
Results
3.6s3585×body1280valid
1.4s2368×body640valid
383.0ms933×body320valid
110.0ms415×body160valid
92.0ms699×body80valid

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