Details

Time bar (total: 13.3s)

sample163.0ms

Algorithm
intervals
Results
93.0ms109×body1280valid
35.0ms71×body640valid
15.0ms33×body320valid
3.0ms16×body160valid
3.0ms27×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: 1.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b
(sin (- lambda1 lambda2))
3.2b
(cos (- lambda1 lambda2))

rewrite19.0ms

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:
7.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

series189.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
96.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms
(sin (- lambda1 lambda2))
16.0ms
(cos (- lambda1 lambda2))

simplify74.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0249435
1795394
22920393
35001393

prune272.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.2b

localize35.0ms

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 phi2) (cos (- lambda1 lambda2)))))
0.2b
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.2b
(cos (- lambda1 lambda2))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log add-cbrt-cube
6×add-log-exp
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
3×cos-diff associate-*l* pow-prod-down prod-exp cbrt-unprod
2×cos-sum associate-+r+ distribute-rgt-neg-out
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ associate-*r* sin-neg sum-log *-commutative flip-+
Counts
4 → 49
Calls
4 calls:
1.0ms
(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
7.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

series212.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
82.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
99.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))

simplify81.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0288644
1866548
23228547
35002547

prune351.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
0.5b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*l* add-log-exp
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×associate-+r+ *-commutative distribute-rgt-neg-out
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sin-neg sum-log flip-+ sin-mult unswap-sqr
Counts
4 → 58
Calls
4 calls:
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
6.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series359.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin lambda1) (sin lambda2))
19.0ms
(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
80.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
214.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify38.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0343858
11180723
25002722

prune406.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos phi1) 3)
0.4b
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)) (+ (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
0.7b
(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
1.2b
(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
18×add-sqr-sqrt add-cube-cbrt
15×times-frac frac-add cos-mult
14×associate-*r/
13×associate-/r/
10×add-exp-log add-cbrt-cube
8×pow1
6×frac-times pow-unpow flip3-+ flip-+ add-log-exp
5×flip3-- flip-- associate-/l*
4×unpow-prod-down cube-prod sum-cubes sin-mult distribute-lft-out
3×cube-div pow-pow associate-*l/ pow-exp associate-/r* rem-cube-cbrt
2×cube-mult pow-to-exp unpow3 associate--l+ associate-/l/ sqr-pow
1×cbrt-undiv distribute-rgt-in sub-neg frac-2neg distribute-lft-in diff-log div-exp pow-prod-down prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 112
Calls
4 calls:
4.0ms
(pow (cos phi1) 3)
54.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)) (+ (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
15.0ms
(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
15.0ms
(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

series4.1s

Counts
4 → 12
Calls
4 calls:
29.0ms
(pow (cos phi1) 3)
3.7s
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)) (+ (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
177.0ms
(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
242.0ms
(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

simplify61.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010824127
150023885

prune856.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes547.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04954
14954

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3565×body1280valid
1.2s2349×body640valid
313.0ms939×body320valid
90.0ms416×body160valid
80.0ms730×body80valid
2.0ms1×body2560valid