Details

Time bar (total: 8.0s)

sample190.0ms

Algorithm
intervals
Results
109.0ms113×body1280valid
43.0ms80×body640valid
13.0ms35×body320valid
3.0ms13×body160valid
2.0ms15×body80valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02120
12120

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.0b

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)))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.1b
(sin (- lambda1 lambda2))
4.1b
(cos (- lambda1 lambda2))

rewrite17.0ms

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)))))
8.0ms
(+ (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)))))
23.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(sin (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

simplify37.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
05049613

prune147.0ms

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: 0.8b

Counts
53 → 14

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
0.2b
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.1b
(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
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:
6.0ms
(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
1.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (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:
29.0ms
(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
9.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (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))

simplify36.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
050051030

prune140.0ms

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

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New60666
Fresh7613
Picked101
Done000
Total681280

Merged error: 0.2b

Counts
80 → 12

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

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:
6.0ms
(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin 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)))))

series104.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
9.0ms
(* (sin lambda1) (sin lambda2))
13.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
52.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify50.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
049451274
149451274

prune135.0ms

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

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New74175
Fresh11011
Picked011
Done000
Total751287

Merged error: 0.2b

Counts
87 → 12

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.7b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
0.7b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
0.7b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
6×associate-+r+
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×+-commutative cbrt-prod distribute-rgt-in distribute-lft-in sum-log
2×cbrt-div
1×pow1/3
Counts
4 → 52
Calls
4 calls:
2.0ms
(cbrt (+ (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
(+ (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)))))

series249.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(cbrt (+ (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)))))
49.0ms
(+ (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)))))

simplify29.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
056751386

prune90.0ms

Filtered
52 candidates to 64 candidates (-23.1%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New61364
Fresh1910
Picked101
Done011
Total631376

Merged error: 0.1b

Counts
76 → 13

regimes695.0ms

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
03034
13034

end0.0ms

sample5.8s

Algorithm
intervals
Results
3.5s3609×body1280valid
1.3s2360×body640valid
340.0ms879×body320valid
103.0ms428×body160valid
82.0ms724×body80valid

Profiling

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