Details

Time bar (total: 9.2s)

sample185.0ms

Algorithm
intervals
Results
101.0ms102×body1280valid
43.0ms83×body640valid
10.0ms29×body320valid
4.0ms30×body80valid
3.0ms12×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune6.0ms

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: 1.1b

Counts
2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.5b
(cos (- lambda1 lambda2))
4.6b
(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 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))

series48.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
29.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
6.0ms
(sin (- lambda1 lambda2))

simplify125.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0205421
1508374
21327374
33685374
45001374

prune340.0ms

Filtered
52 candidates to 42 candidates (19.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New411152
Fresh000
Picked101
Done000
Total421153

Merged error: 0.8b

Counts
53 → 11

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (cos (- lambda1 lambda2)))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.5b
(cos (- lambda1 lambda2))

rewrite16.0ms

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
5×cos-diff
3×associate-*r* associate-*l*
2×distribute-rgt-in cos-sum associate-+r+ distribute-lft-in
1×+-commutative sub-neg flip3-+ pow-prod-down prod-exp sum-log cos-mult *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 51
Calls
4 calls:
5.0ms
(* (cos phi2) (cos (- lambda1 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))))
6.0ms
(cos (- lambda1 lambda2))

series50.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* (cos phi2) (cos (- lambda1 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))

simplify72.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0242574
1728512
22584512
35002512

prune578.0ms

Filtered
63 candidates to 46 candidates (27.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New61263
Fresh2810
Picked101
Done000
Total641074

Merged error: 0.1b

Counts
74 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos lambda1) (cos lambda2)) (cos phi2))
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-*r* add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×*-commutative
1×+-commutative flip3-+ associate-*l/ sum-log cos-mult flip-+ sin-mult unswap-sqr
Counts
4 → 56
Calls
4 calls:
6.0ms
(* (* (cos lambda1) (cos lambda2)) (cos phi2))
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)))

series68.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (* (cos lambda1) (cos lambda2)) (cos phi2))
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))
29.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify43.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0322717
11273617
25001617

prune450.0ms

Filtered
68 candidates to 50 candidates (26.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New68068
Fresh099
Picked011
Done000
Total681078

Merged error: 0.1b

Counts
78 → 10

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (pow (* (cos phi2) (cos (- lambda1 lambda2))) 3))
0.6b
(pow (* (cos phi2) (cos (- lambda1 lambda2))) 3)
0.7b
(+ (cos phi1) (cbrt (pow (* (cos phi2) (cos (- lambda1 lambda2))) 3)))
4.5b
(cos (- lambda1 lambda2))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-prod *-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube
6×add-sqr-sqrt add-cube-cbrt add-log-exp
3×pow-unpow
2×cube-div cube-mult unpow-prod-down cos-sum pow-pow unpow3 cube-prod pow-exp cos-mult rem-cube-cbrt sqr-pow
1×+-commutative cos-diff pow-to-exp sub-neg cbrt-div flip3-+ pow1/3 pow-prod-down prod-exp sum-log rem-cbrt-cube cbrt-unprod flip-+ distribute-lft-out
Counts
4 → 63
Calls
4 calls:
3.0ms
(cbrt (pow (* (cos phi2) (cos (- lambda1 lambda2))) 3))
5.0ms
(pow (* (cos phi2) (cos (- lambda1 lambda2))) 3)
5.0ms
(+ (cos phi1) (cbrt (pow (* (cos phi2) (cos (- lambda1 lambda2))) 3)))
4.0ms
(cos (- lambda1 lambda2))

series67.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(cbrt (pow (* (cos phi2) (cos (- lambda1 lambda2))) 3))
24.0ms
(pow (* (cos phi2) (cos (- lambda1 lambda2))) 3)
25.0ms
(+ (cos phi1) (cbrt (pow (* (cos phi2) (cos (- lambda1 lambda2))) 3)))
4.0ms
(cos (- lambda1 lambda2))

simplify168.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0261526
1951468
24496467
35001467

prune491.0ms

Filtered
75 candidates to 54 candidates (28.0%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New74175
Fresh088
Picked011
Done011
Total741185

Merged error: 0.1b

Counts
85 → 11

regimes737.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03224
13224

end0.0ms

sample5.6s

Algorithm
intervals
Results
3.4s3620×body1280valid
1.3s2316×body640valid
328.0ms933×body320valid
93.0ms412×body160valid
80.0ms718×body80valid
2.0ms1×body2560valid

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