Details

Time bar (total: 12.3s)

analyze1.9s

Algorithm
search

sample182.0ms

Algorithm
intervals
Results
95.0ms98×body1280valid
53.0ms85×body640valid
12.0ms32×body320valid
3.0ms29×body80valid
3.0ms12×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.1b

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))))
4.1b
(sin (- lambda1 lambda2))
4.2b
(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))

series41.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
24.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

simplify120.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0205421
1508374
21327374
33684374
45001374

prune132.0ms

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

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New43952
Fresh000
Picked101
Done000
Total44953

Merged error: 0.9b

Counts
53 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (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)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.2b
(cos (- lambda1 lambda2))

rewrite17.0ms

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))

series68.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
9.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
25.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

simplify117.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0289748
11037658
24438658
35002658

prune130.0ms

Filtered
48 candidates to 66 candidates (-37.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New63366
Fresh178
Picked101
Done000
Total651075

Merged error: 0.1b

Counts
75 → 10

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

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

series68.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(* (sin lambda1) (sin lambda2))
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)))))
27.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify38.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0283721
11122611
25001611

prune124.0ms

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

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New67168
Fresh189
Picked011
Done000
Total681078

Merged error: 0.1b

Counts
78 → 10

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))
0.5b
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
0.5b
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
0.5b
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
9.0ms
(* (cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))
2.0ms
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
2.0ms
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
3.0ms
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))

series237.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* (cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))
54.0ms
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
56.0ms
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
57.0ms
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))

simplify45.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02411791
110171622
250011554

prune119.0ms

Filtered
70 candidates to 99 candidates (-41.4%)
Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New95499
Fresh088
Picked011
Done011
Total9514109

Merged error: 0.1b

Counts
109 → 14

regimes784.0ms

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 (0.0ms)

IterNodesCost
03224
13224

end0.0ms

analyze1.9s

Algorithm
search

sample6.0s

Algorithm
intervals
Results
3.8s3562×body1280valid
1.4s2365×body640valid
369.0ms975×body320valid
114.0ms440×body160valid
78.0ms658×body80valid

Profiling

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