Details

Time bar (total: 7.9s)

sample185.0ms

Algorithm
intervals
Results
104.0ms111×body1280valid
43.0ms73×body640valid
11.0ms33×body320valid
3.0ms12×body160valid
3.0ms27×body80valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02120
12120

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.4b

Counts
2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.2b
(sin (- lambda1 lambda2))
2.3b
(cos (- lambda1 lambda2))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity sin-sum add-cbrt-cube add-log-exp
4×sub-neg
3×distribute-rgt-in cos-diff distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+
1×+-commutative flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 55
Calls
4 calls:
6.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
8.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

series45.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
23.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

simplify50.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
05096645

prune153.0ms

Filtered
51 candidates to 67 candidates (-31.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New561167
Fresh000
Picked101
Done000
Total571168

Merged error: 1.1b

Counts
68 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.2b
(* (sin lambda1) (sin lambda2))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
2.2b
(sin (- lambda1 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×sin-sum associate-*r* associate-*l* add-log-exp
3×distribute-rgt-in sub-neg distribute-lft-in
2×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-+ sum-log sin-diff flip-+ sin-mult
Counts
4 → 64
Calls
4 calls:
7.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
4.0ms
(sin (- lambda1 lambda2))

series77.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
9.0ms
(* (sin lambda1) (sin lambda2))
50.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
4.0ms
(sin (- lambda1 lambda2))

simplify31.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
04993812
14993812

prune136.0ms

Filtered
56 candidates to 76 candidates (-35.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New75176
Fresh1910
Picked101
Done000
Total771087

Merged error: 0.2b

Counts
87 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

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 flip-+ sin-mult
Counts
4 → 57
Calls
4 calls:
4.0ms
(* (cos 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))))))
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series102.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (cos lambda1) (sin lambda2))
27.0ms
(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
(* (sin lambda1) (sin lambda2))
50.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify41.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
04979985
14979985

prune152.0ms

Filtered
50 candidates to 69 candidates (-38.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New64569
Fresh279
Picked101
Done000
Total671279

Merged error: 0.2b

Counts
79 → 12

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2)))))))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2))))))
4.5b
(log (pow (exp (sin lambda1)) (sin lambda2)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×add-exp-log log-prod
6×pow1 add-cbrt-cube add-log-exp
3×unpow-prod-down rem-log-exp associate-*r* associate-*l*
2×associate-+r+
1×+-commutative distribute-rgt-in pow-to-exp distribute-lft-in flip3-+ pow-prod-down pow-exp prod-exp sum-log log-pow *-commutative cbrt-unprod flip-+ unswap-sqr sqr-pow
Counts
4 → 56
Calls
4 calls:
5.0ms
(* (cos lambda1) (sin lambda2))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2)))))))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2))))))
4.0ms
(log (pow (exp (sin lambda1)) (sin lambda2)))

series110.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (cos lambda1) (sin lambda2))
15.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2)))))))
63.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2))))))
23.0ms
(log (pow (exp (sin lambda1)) (sin lambda2)))

simplify45.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
049801016
149801016

prune80.0ms

Filtered
53 candidates to 68 candidates (-28.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New68068
Fresh01111
Picked011
Done000
Total681280

Merged error: 0.2b

Counts
80 → 12

regimes679.0ms

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
03136
13136

end0.0ms

sample5.8s

Algorithm
intervals
Results
3.4s3514×body1280valid
1.3s2371×body640valid
344.0ms945×body320valid
107.0ms430×body160valid
84.0ms739×body80valid
3.0ms1×body2560valid

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