Details

Time bar (total: 9.1s)

sample224.0ms

Algorithm
intervals
Results
138.0ms116×body1280valid
50.0ms79×body640valid
11.0ms25×body320valid
4.0ms13×body160valid
3.0ms23×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.9b
(sin (- lambda1 lambda2))
2.9b
(cos (- lambda1 lambda2))

rewrite27.0ms

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:
13.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(sin (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

series201.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
100.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(sin (- lambda1 lambda2))
23.0ms
(cos (- lambda1 lambda2))

simplify76.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0249435
1795394
22920393
35001393

prune263.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (sin (- lambda2)))
0.2b
(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.9b
(cos (- lambda1 lambda2))

rewrite15.0ms

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 sin-neg sum-log *-commutative distribute-rgt-neg-out cbrt-unprod flip-+ unswap-sqr
Counts
4 → 49
Calls
4 calls:
6.0ms
(* (cos lambda1) (sin (- lambda2)))
0.0ms
(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
3.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))

series188.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (cos lambda1) (sin (- lambda2)))
15.0ms
(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
102.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))

simplify65.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0286599
1859524
22708523
35001523

prune353.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.2b
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

rewrite23.0ms

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-*l/ frac-add
1×associate-+l+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 52
Calls
4 calls:
0.0ms
(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
15.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
4.0ms
(* (sin lambda1) (sin lambda2))
3.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
222.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
44.0ms
(* (sin lambda1) (sin lambda2))
125.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify50.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0352985
11515879
25001864

prune370.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3))
0.4b
(pow (cos phi1) 3)
0.6b
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
0.8b
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
10×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt add-log-exp
6×pow-unpow
4×unpow-prod-down pow-pow cube-prod pow-exp rem-cube-cbrt
3×pow-prod-down prod-exp cbrt-unprod
2×cube-mult pow-to-exp unpow3 sqr-pow
1×+-commutative cube-div sub-neg flip3-- flip3-+ diff-log associate-*l/ sum-log cos-mult sum-cubes flip-- flip-+ distribute-lft-out
Counts
4 → 74
Calls
4 calls:
13.0ms
(+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3))
1.0ms
(pow (cos phi1) 3)
8.0ms
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
10.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

series466.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3))
28.0ms
(pow (cos phi1) 3)
112.0ms
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
136.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

simplify69.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0373645
11745565
25002561

prune472.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes326.0ms

Accuracy

0% (0.1b 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
04747
14747

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.3s3575×body1280valid
1.3s2393×body640valid
325.0ms925×body320valid
100.0ms432×body160valid
74.0ms675×body80valid