Details

Time bar (total: 9.2s)

sample176.0ms

Algorithm
intervals
Results
107.0ms112×body1280valid
36.0ms69×body640valid
14.0ms37×body320valid
4.0ms17×body160valid
2.0ms21×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune3.0ms

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: 1.2b

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)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.3b
(sin (- lambda1 lambda2))
5.3b
(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))

series150.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
98.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms
(sin (- lambda1 lambda2))
17.0ms
(cos (- lambda1 lambda2))

simplify122.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0205421
1508375
21327374
33684374
45001374

prune249.0ms

Filtered
52 candidates to 42 candidates (80.8%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New371552
Fresh000
Picked101
Done000
Total381553

Merged error: 1.0b

Counts
53 → 15

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b
(* (sin lambda1) (sin lambda2))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
5.3b
(sin (- 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×associate-*r* associate-*l*
2×sin-sum
1×+-commutative sub-neg flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 47
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
4.0ms
(sin (- lambda1 lambda2))

series201.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
47.0ms
(* (sin lambda1) (sin lambda2))
119.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
21.0ms
(sin (- lambda1 lambda2))

simplify101.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0260561
1912490
23390489
35001489

prune281.0ms

Filtered
59 candidates to 45 candidates (76.3%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New58159
Fresh21214
Picked101
Done000
Total611374

Merged error: 0.1b

Counts
74 → 13

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×sum-log
3×flip3-+ associate-*r* associate-*l* flip-+ sin-mult
2×+-commutative associate-*r/ frac-add
1×associate-+l+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 52
Calls
4 calls:
8.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (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)))))
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
17.0ms
(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)))))
47.0ms
(* (sin lambda1) (sin lambda2))
121.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify45.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0325954
11363854
25001837

prune313.0ms

Filtered
64 candidates to 50 candidates (78.1%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New62264
Fresh11112
Picked011
Done000
Total631477

Merged error: 0.1b

Counts
77 → 14

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.7b
(pow (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) 3)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube
4×flip3-+ flip-+
3×+-commutative unpow-prod-down pow-unpow cube-prod sum-log
2×cube-div
1×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 58
Calls
4 calls:
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
4.0ms
(pow (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) 3)

series546.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
126.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
122.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
176.0ms
(pow (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) 3)

simplify46.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0226767
11125716
25001708

prune355.0ms

Filtered
70 candidates to 48 candidates (68.6%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New66470
Fresh5712
Picked101
Done011
Total721284

Merged error: 0.1b

Counts
84 → 12

regimes474.0ms

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
03224
13224

end0.0ms

sample5.5s

Algorithm
intervals
Results
3.4s3547×body1280valid
1.3s2372×body640valid
340.0ms944×body320valid
100.0ms417×body160valid
92.0ms720×body80valid