Details

Time bar (total: 9.6s)

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

sample196.0ms

Algorithm
intervals
Results
120.0ms111×body1280valid
43.0ms75×body640valid
12.0ms33×body320valid
3.0ms27×body80valid
3.0ms10×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (14.0ms)

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))))
3.8b
(sin (- lambda1 lambda2))
3.8b
(cos (- 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 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
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

series47.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
25.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(sin (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

simplify43.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
04947591
14947591

prune133.0ms

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

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New41950
Fresh000
Picked101
Done000
Total42951

Merged error: 0.4b

Counts
51 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.8b
(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) (- (* (cos lambda2) (sin lambda1)) (* (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))

series49.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (cos lambda1) (sin lambda2))
10.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
26.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

simplify71.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
05109730

prune119.0ms

Filtered
45 candidates to 59 candidates (-31.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New58159
Fresh178
Picked101
Done000
Total60868

Merged error: 0.1b

Counts
68 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

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

series84.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (cos lambda1) (sin lambda2))
13.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
9.0ms
(* (sin lambda1) (sin lambda2))
52.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify47.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
04961985
14961985

prune112.0ms

Filtered
49 candidates to 69 candidates (-40.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New69069
Fresh077
Picked011
Done000
Total69877

Merged error: 0.1b

Counts
77 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))
0.7b
(log (exp (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))))
3.8b
(sin (- lambda1 lambda2))
3.8b
(cos (- lambda1 lambda2))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
5×pow1
4×add-exp-log log-prod log-pow add-cbrt-cube
3×exp-prod
2×sub-neg
1×+-commutative cos-diff cos-sum flip3-+ sin-sum rem-log-exp exp-sum sum-log sin-diff flip-+
Counts
4 → 45
Calls
4 calls:
4.0ms
(+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))
4.0ms
(log (exp (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))))
4.0ms
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

series57.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))
24.0ms
(log (exp (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))))
4.0ms
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

simplify57.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
04892602
14892602

prune74.0ms

Filtered
42 candidates to 57 candidates (-35.7%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New57057
Fresh066
Picked011
Done011
Total57865

Merged error: 0.1b

Counts
65 → 8

regimes515.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05634
15634

end0.0ms

sample5.9s

Algorithm
intervals
Results
3.6s3591×body1280valid
1.4s2355×body640valid
368.0ms947×body320valid
113.0ms421×body160valid
92.0ms685×body80valid
2.0ms1×body2560valid

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