Details

Time bar (total: 9.3s)

sample181.0ms

Algorithm
intervals
Results
113.0ms131×body1280valid
33.0ms67×body640valid
11.0ms22×body320valid
3.0ms12×body160valid
2.0ms24×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

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)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.9b
(cos (- lambda1 lambda2))
4.9b
(sin (- lambda1 lambda2))

rewrite40.0ms

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:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
10.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))
12.0ms
(sin (- lambda1 lambda2))

series165.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
109.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
18.0ms
(cos (- lambda1 lambda2))
24.0ms
(sin (- lambda1 lambda2))

simplify130.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0205421
1508375
21327374
33685374
45002374

prune251.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

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))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.9b
(cos (- lambda1 lambda2))

rewrite35.0ms

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:
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
13.0ms
(* (sin lambda1) (cos lambda2))
10.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
11.0ms
(cos (- lambda1 lambda2))

series190.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
45.0ms
(* (sin lambda1) (cos lambda2))
110.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(cos (- lambda1 lambda2))

simplify65.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0264537
1790472
22426471
35001471

prune337.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos lambda2))
0.3b
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.3b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×add-log-exp
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
4×sum-log
3×flip3-+ flip-+ sin-mult
2×+-commutative pow-prod-down associate-*l/ frac-add prod-exp *-commutative cbrt-unprod unswap-sqr
1×associate-+l+ sin-cos-mult
Counts
4 → 64
Calls
4 calls:
12.0ms
(* (sin lambda1) (cos lambda2))
38.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
15.0ms
(* (sin lambda1) (sin lambda2))
10.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin lambda1) (cos lambda2))
234.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
47.0ms
(* (sin lambda1) (sin lambda2))
138.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify53.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0379746
11673679
25002664

prune401.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.3b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.7b
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
8×log-prod
7×pow1 add-log-exp
6×add-exp-log add-cbrt-cube
4×associate-+l+ log-pow
3×exp-prod associate-*r* associate-*l*
2×+-commutative flip3-+ exp-sum sum-log flip-+
1×rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
Counts
4 → 61
Calls
4 calls:
75.0ms
(+ (log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
16.0ms
(* (sin lambda1) (sin lambda2))
10.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
20.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

series582.0ms

Counts
4 → 12
Calls
4 calls:
236.0ms
(+ (log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
51.0ms
(* (sin lambda1) (sin lambda2))
149.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
145.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

simplify46.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0309790
11388710
25001701

prune371.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes409.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03324
13324

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3573×body1280valid
1.2s2341×body640valid
326.0ms968×body320valid
88.0ms416×body160valid
66.0ms702×body80valid