Details

Time bar (total: 8.5s)

sample179.0ms

Algorithm
intervals
Results
108.0ms119×body1280valid
43.0ms72×body640valid
7.0ms22×body320valid
3.0ms15×body160valid
3.0ms28×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune4.0ms

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: 0.9b

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)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b
(cos (- lambda1 lambda2))
3.2b
(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))

series152.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
103.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))
22.0ms
(sin (- lambda1 lambda2))

simplify120.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0205421
1508374
21327374
33685374
45001374

prune233.0ms

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: 0.7b

Counts
53 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b
(* (sin lambda1) (cos lambda2))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b
(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
3×cos-diff associate-*r* associate-*l*
2×cos-sum associate-+r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log *-commutative sin-cos-mult cbrt-unprod flip-+ unswap-sqr
Counts
4 → 49
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
5.0ms
(* (sin lambda1) (cos lambda2))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

series170.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
43.0ms
(* (sin lambda1) (cos lambda2))
97.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))

simplify61.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0264537
1790471
22426471
35001471

prune307.0ms

Filtered
61 candidates to 46 candidates (75.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New58361
Fresh4610
Picked101
Done000
Total63972

Merged error: 0.0b

Counts
72 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(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
(* (sin lambda1) (cos lambda2))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite16.0ms

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
2×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-cos-mult flip-+ sin-mult
Counts
4 → 58
Calls
4 calls:
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))))))
5.0ms
(* (sin lambda1) (cos lambda2))
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series314.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
40.0ms
(* (sin lambda1) (cos lambda2))
45.0ms
(* (sin lambda1) (sin lambda2))
211.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify111.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0311751
11012646
24556646
35001646

prune280.0ms

Filtered
70 candidates to 50 candidates (71.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New70070
Fresh088
Picked011
Done000
Total70979

Merged error: 0.0b

Counts
79 → 9

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))
0.6b
(cbrt (pow (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) 3))
0.7b
(pow (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) 3)
3.1b
(cos (- lambda1 lambda2))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod add-log-exp
5×pow1 add-exp-log add-cbrt-cube
4×cube-div
3×pow-unpow flip3-+ flip-+
2×cube-mult cbrt-div cos-sum unpow3 sqr-pow
1×+-commutative cos-diff pow-to-exp sub-neg pow-pow pow1/3 pow-exp sum-log rem-cbrt-cube rem-cube-cbrt
Counts
4 → 69
Calls
4 calls:
4.0ms
(+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))
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))

series388.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))
106.0ms
(cbrt (pow (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) 3))
160.0ms
(pow (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) 3)
20.0ms
(cos (- lambda1 lambda2))

simplify39.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0261784
11057734
25001728

prune321.0ms

Filtered
81 candidates to 50 candidates (61.7%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New80181
Fresh167
Picked011
Done011
Total81990

Merged error: 0.0b

Counts
90 → 9

regimes341.0ms

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
03022
13022

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.3s3550×body1280valid
1.2s2332×body640valid
316.0ms908×body320valid
96.0ms428×body160valid
88.0ms782×body80valid

Profiling

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