Details

Time bar (total: 7.6s)

sample199.0ms

Algorithm
intervals
Results
105.0ms115×body1280valid
39.0ms77×body640valid
13.0ms37×body320valid
8.0ms12×body160valid
1.0ms15×body80valid

simplify4.0ms

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

localize20.0ms

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))))
2.6b
(sin (- lambda1 lambda2))
2.7b
(cos (- 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
(sin (- lambda1 lambda2))
4.0ms
(cos (- 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)))))
26.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(sin (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

simplify117.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0205421
1508374
21327374
33684374
45001374

prune145.0ms

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

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New391352
Fresh000
Picked101
Done000
Total401353

Merged error: 0.6b

Counts
53 → 13

localize30.0ms

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)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.7b
(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
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))))
4.0ms
(cos (- lambda1 lambda2))

series67.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (cos phi2) (cos (- lambda1 lambda2)))
17.0ms
(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))

simplify80.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0242574
1728512
22584512
35002512

prune134.0ms

Filtered
46 candidates to 63 candidates (-37.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New61263
Fresh3912
Picked101
Done000
Total651176

Merged error: 0.1b

Counts
76 → 11

localize29.0ms

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)))))
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series66.0ms

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))
29.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify39.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0283721
11122611
25001611

prune128.0ms

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

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New67168
Fresh1910
Picked011
Done000
Total681179

Merged error: 0.1b

Counts
79 → 11

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.3b
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.8b
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity add-log-exp
7×pow1
6×add-exp-log exp-prod add-cbrt-cube
4×log-prod log-pow
3×associate-*r* associate-*l*
2×exp-sum sum-log rem-exp-log
1×+-commutative flip3-+ rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 59
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
5.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
5.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

series106.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin lambda1) (sin lambda2))
43.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
26.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
27.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

simplify99.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0248604
1925531
23624531
35001531

prune90.0ms

Filtered
50 candidates to 71 candidates (-42.0%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New69271
Fresh099
Picked101
Done011
Total701282

Merged error: 0.1b

Counts
82 → 12

regimes636.0ms

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

sample5.5s

Algorithm
intervals
Results
3.3s3503×body1280valid
1.3s2385×body640valid
341.0ms950×body320valid
102.0ms420×body160valid
84.0ms742×body80valid

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