Details

Time bar (total: 9.0s)

sample179.0ms

Algorithm
intervals
Results
112.0ms121×body1280valid
35.0ms67×body640valid
12.0ms34×body320valid
4.0ms17×body160valid
2.0ms17×body80valid

simplify6.0ms

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: 0.8b

localize22.0ms

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))))
3.4b
(cos (- lambda1 lambda2))
3.6b
(sin (- 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:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series151.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
97.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))
27.0ms
(sin (- lambda1 lambda2))

simplify121.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0205421
1508375
21327374
33685374
45001374

prune248.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.4b
(cos (- lambda1 lambda2))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×cos-diff
2×+-commutative cos-sum associate-+r+ flip3-+ sin-neg sum-log distribute-rgt-neg-out flip-+
1×distribute-rgt-in sub-neg distribute-lft-in unsub-neg
Counts
4 → 43
Calls
4 calls:
6.0ms
(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
1.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

series215.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
13.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
97.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))

simplify78.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0299616
1945545
22802540
35002539

prune327.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

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

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-*r* add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×*-commutative sin-mult
1×+-commutative flip3-+ associate-*l/ sum-log flip-+ unswap-sqr
Counts
4 → 56
Calls
4 calls:
6.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
1.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
18.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
43.0ms
(* (sin lambda1) (sin lambda2))
120.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify43.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0309736
11280625
25002624

prune390.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
0.5b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.6b
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity add-log-exp
7×pow1
6×add-exp-log exp-prod add-cbrt-cube
4×log-prod log-pow
3×associate-*r* associate-*l*
2×exp-sum sum-log rem-exp-log
1×+-commutative flip3-+ rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 59
Calls
4 calls:
5.0ms
(* (sin lambda1) (sin lambda2))
5.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
5.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

series448.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin lambda1) (sin lambda2))
161.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
121.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
122.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

simplify103.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0248604
1925534
23624532
35001532

prune373.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes505.0ms

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
03727
13727

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.3s3581×body1280valid
1.2s2314×body640valid
333.0ms961×body320valid
101.0ms423×body160valid
74.0ms721×body80valid