Details

Time bar (total: 9.0s)

sample176.0ms

Algorithm
intervals
Results
107.0ms124×body1280valid
42.0ms79×body640valid
8.0ms27×body320valid
2.0ms9×body160valid
2.0ms17×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
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))))
3.8b
(sin (- lambda1 lambda2))
3.9b
(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))

series150.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
97.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(sin (- lambda1 lambda2))
22.0ms
(cos (- lambda1 lambda2))

simplify116.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0205421
1508375
21327374
33684374
45001374

prune242.0ms

Filtered
52 candidates to 42 candidates (80.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New411152
Fresh000
Picked101
Done000
Total421153

Merged error: 0.6b

Counts
53 → 11

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (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))))
3.9b
(cos (- lambda1 lambda2))

rewrite18.0ms

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))

series262.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
13.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
97.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))

simplify115.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0289748
11037659
24438658
35002658

prune296.0ms

Filtered
66 candidates to 48 candidates (72.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New65166
Fresh2810
Picked101
Done000
Total68977

Merged error: 0.1b

Counts
77 → 9

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×associate-*r/ sum-log
3×flip3-+ associate-*r* associate-*l* flip-+
2×+-commutative distribute-rgt-in sub-neg distribute-lft-in frac-add sin-mult
1×associate-+l+ flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod unswap-sqr
Counts
4 → 57
Calls
4 calls:
9.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
8.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (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
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series493.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
216.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
18.0ms
(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)))))
125.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify56.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
03801171
117381047
250021030

prune327.0ms

Filtered
69 candidates to 52 candidates (75.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New66369
Fresh358
Picked101
Done000
Total70878

Merged error: 0.1b

Counts
78 → 8

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos phi1) 3)
0.4b
(+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3))
0.7b
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
0.9b
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
10×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt add-log-exp
6×pow-unpow
4×unpow-prod-down pow-pow cube-prod pow-exp rem-cube-cbrt
3×pow-prod-down prod-exp cbrt-unprod
2×cube-mult pow-to-exp unpow3 sqr-pow
1×+-commutative cube-div sub-neg flip3-- flip3-+ diff-log associate-*l/ sum-log cos-mult sum-cubes flip-- flip-+ distribute-lft-out
Counts
4 → 74
Calls
4 calls:
3.0ms
(pow (cos phi1) 3)
9.0ms
(+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3))
7.0ms
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
7.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

series457.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (cos phi1) 3)
179.0ms
(+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3))
114.0ms
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
136.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

simplify72.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
0373641
11761565
25001561

prune393.0ms

Filtered
86 candidates to 54 candidates (62.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New83386
Fresh077
Picked101
Done000
Total841094

Merged error: 0.1b

Counts
94 → 10

regimes426.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04546
14546

end0.0ms

sample5.1s

Algorithm
intervals
Results
3.2s3570×body1280valid
1.2s2345×body640valid
320.0ms964×body320valid
95.0ms417×body160valid
75.0ms704×body80valid