Details

Time bar (total: 7.9s)

sample197.0ms

Algorithm
intervals
Results
100.0ms106×body1280valid
53.0ms94×body640valid
16.0ms30×body320valid
2.0ms18×body80valid
2.0ms8×body160valid

simplify5.0ms

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: 0.5b

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)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.7b
(cos (- lambda1 lambda2))
2.7b
(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))

series44.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
24.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

simplify128.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0205421
1508374
21327374
33685374
45001374

prune155.0ms

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

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New381452
Fresh000
Picked101
Done000
Total391453

Merged error: 0.3b

Counts
53 → 14

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.5b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
2.7b
(sin (- 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×associate-*r* associate-*l*
2×associate-+r+ sin-sum
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 49
Calls
4 calls:
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
4.0ms
(sin (- lambda1 lambda2))

series79.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin lambda1) (sin lambda2))
15.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
51.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
5.0ms
(sin (- lambda1 lambda2))

simplify106.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0266635
1830549
23809549
35002549

prune137.0ms

Filtered
45 candidates to 61 candidates (-35.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New60161
Fresh11213
Picked101
Done000
Total621375

Merged error: 0.1b

Counts
75 → 13

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

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
3×distribute-rgt-in distribute-lft-in
2×sub-neg associate-+r+ associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-- flip3-+ sum-log flip-- flip-+ sin-mult
Counts
4 → 63
Calls
4 calls:
5.0ms
(* (sin 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))))))
9.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series108.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin lambda1) (sin lambda2))
15.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
31.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
53.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify44.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0345962
11380833
25001833

prune153.0ms

Filtered
52 candidates to 75 candidates (-44.2%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New72375
Fresh21012
Picked101
Done000
Total751388

Merged error: 0.1b

Counts
88 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (pow (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) 3))
0.7b
(pow (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) 3)
2.7b
(cos (- lambda1 lambda2))
2.7b
(sin (- lambda1 lambda2))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod
5×pow1 add-exp-log add-cbrt-cube
4×cube-div add-log-exp
3×pow-unpow
2×cube-mult sub-neg cbrt-div cos-sum flip3-+ sin-sum unpow3 flip-+ sqr-pow
1×cos-diff pow-to-exp pow-pow pow1/3 pow-exp sin-diff rem-cbrt-cube rem-cube-cbrt
Counts
4 → 68
Calls
4 calls:
4.0ms
(cbrt (pow (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) 3))
4.0ms
(pow (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) 3)
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series83.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(cbrt (pow (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) 3))
48.0ms
(pow (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) 3)
4.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

simplify39.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0279725
11021667
25001659

prune108.0ms

Filtered
49 candidates to 80 candidates (-63.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New75580
Fresh6612
Picked101
Done000
Total821193

Merged error: 0.1b

Counts
93 → 11

regimes636.0ms

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 (0.0ms)

IterNodesCost
02014
12014

end0.0ms

sample5.7s

Algorithm
intervals
Results
3.4s3583×body1280valid
1.3s2360×body640valid
355.0ms965×body320valid
111.0ms410×body160valid
86.0ms681×body80valid
3.0ms1×body2560valid

Profiling

Loading profile data...