Details

Time bar (total: 9.2s)

sample175.0ms

Algorithm
intervals
Results
103.0ms113×body1280valid
40.0ms69×body640valid
12.0ms35×body320valid
3.0ms13×body160valid
3.0ms26×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: 0.7b

localize30.0ms

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))))
3.6b
(cos (- lambda1 lambda2))
3.6b
(sin (- lambda1 lambda2))

rewrite15.0ms

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
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

series154.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
103.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))
23.0ms
(sin (- lambda1 lambda2))

simplify126.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0205421
1508375
21327374
33685374
45002374

prune253.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.2b
(* (sin lambda1) (sin lambda2))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
3.6b
(sin (- lambda1 lambda2))

rewrite13.0ms

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×sin-sum
1×+-commutative sub-neg flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 47
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (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)))
5.0ms
(sin (- lambda1 lambda2))

series205.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
43.0ms
(* (sin lambda1) (sin lambda2))
126.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
21.0ms
(sin (- lambda1 lambda2))

simplify101.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0259561
1901490
23361489
35002489

prune339.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-+ sum-log flip-+ sin-mult
Counts
4 → 55
Calls
4 calls:
0.0ms
(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))))
4.0ms
(* (cos lambda1) (sin lambda2))
4.0ms
(* (sin lambda1) (sin lambda2))
3.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
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))))
44.0ms
(* (cos lambda1) (sin lambda2))
43.0ms
(* (sin lambda1) (sin lambda2))
124.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify137.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0299672
11115582
24883581
35002581

prune364.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (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)
0.9b
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

rewrite35.0ms

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:
12.0ms
(+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3))
3.0ms
(pow (cos phi1) 3)
8.0ms
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
10.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

series455.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3))
30.0ms
(pow (cos phi1) 3)
112.0ms
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
132.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

simplify71.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
0373641
11761565
25001561

prune451.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes540.0ms

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
04854
14854

end0.0ms

sample5.4s

Algorithm
intervals
Results
3.3s3559×body1280valid
1.3s2334×body640valid
364.0ms984×body320valid
101.0ms410×body160valid
75.0ms713×body80valid