Details

Time bar (total: 10.1s)

sample173.0ms

Algorithm
intervals
Results
101.0ms115×body1280valid
32.0ms64×body640valid
19.0ms36×body320valid
4.0ms17×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: 1.4b

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))))
3.2b
(sin (- lambda1 lambda2))
3.3b
(cos (- lambda1 lambda2))

rewrite14.0ms

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)))))
3.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(sin (- lambda1 lambda2))
5.0ms
(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)))))
102.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(sin (- lambda1 lambda2))
17.0ms
(cos (- lambda1 lambda2))

simplify125.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0205421
1508375
21327374
33684374
45001374

prune255.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
3.2b
(sin (- 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×associate-*r* associate-*l*
2×associate-+r+ sin-sum
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 49
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
3.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
5.0ms
(sin (- lambda1 lambda2))

series295.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin lambda1) (sin lambda2))
14.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
213.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
21.0ms
(sin (- lambda1 lambda2))

simplify103.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0266635
1830550
23809549
35002549

prune327.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×associate-*r* associate-*l*
2×+-commutative associate-+r+ flip3-+ sum-log flip-+ sin-mult
1×distribute-rgt-in distribute-lft-in pow-prod-down frac-add prod-exp cos-mult *-commutative cbrt-unprod unswap-sqr
Counts
4 → 51
Calls
4 calls:
4.0ms
(+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
3.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series360.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))
47.0ms
(* (sin lambda1) (sin lambda2))
17.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
218.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify42.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0351818
11147717
25001716

prune371.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.3b
(/ (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.6b
(+ (cos phi1) (* (cos phi2) (/ (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
82×pow1
34×pow-prod-down
30×add-exp-log add-cbrt-cube
24×cos-mult sin-mult
16×prod-exp cbrt-unprod associate-/l/
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×times-frac associate-*r/ associate-*l/
10×frac-times frac-sub
8×pow-sqr pow-prod-up
6×sub-div add-log-exp
4×pow-plus associate-/r/ associate-/l* difference-of-squares
3×associate-/r*
2×pow2 flip3-- swap-sqr associate-*r* associate-*l* *-commutative flip--
1×cbrt-undiv +-commutative frac-2neg flip3-+ div-sub div-exp clear-num sum-log flip-+ div-inv
Counts
4 → 137
Calls
4 calls:
14.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
48.0ms
(/ (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
16.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
3.0ms
(+ (cos phi1) (* (cos phi2) (/ (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series944.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
214.0ms
(/ (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
52.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
627.0ms
(+ (cos phi1) (* (cos phi2) (/ (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify107.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
06652340
133901969
250011933

prune737.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

regimes555.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04645
14645

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.3s3608×body1280valid
1.2s2271×body640valid
344.0ms976×body320valid
107.0ms459×body160valid
74.0ms686×body80valid