Details

Time bar (total: 9.4s)

sample209.0ms

Algorithm
intervals
Results
121.0ms111×body1280valid
47.0ms74×body640valid
15.0ms30×body320valid
5.0ms15×body160valid
4.0ms26×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: 1.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b
(sin (- lambda1 lambda2))
4.2b
(cos (- lambda1 lambda2))

rewrite20.0ms

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))

series201.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
102.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(sin (- lambda1 lambda2))
18.0ms
(cos (- lambda1 lambda2))

simplify72.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0249435
1795394
22920393
35001393

prune283.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.5b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
4.0b
(sin (- lambda1 lambda2))

rewrite22.0ms

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 sin-sum associate-*l/ frac-add
1×sub-neg associate-+l+ pow-prod-down prod-exp sin-diff *-commutative cbrt-unprod unswap-sqr
Counts
4 → 55
Calls
4 calls:
5.0ms
(* (sin lambda1) (sin lambda2))
8.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
4.0ms
(sin (- lambda1 lambda2))

series414.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (sin lambda1) (sin lambda2))
218.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
123.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
25.0ms
(sin (- lambda1 lambda2))

simplify48.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0339695
11511637
25001622

prune362.0ms

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

rewrite19.0ms

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:
5.0ms
(* (sin lambda1) (sin lambda2))
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))))
8.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series533.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin lambda1) (sin lambda2))
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))))
347.0ms
(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
124.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify48.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0325946
11473846
25001831

prune338.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
0.2b
(+ (log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.5b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.7b
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×add-sqr-sqrt add-cube-cbrt log-prod *-un-lft-identity
6×exp-prod
5×pow1
4×add-exp-log associate-+l+ log-pow add-cbrt-cube
3×exp-sum sum-log
2×+-commutative flip3-+ flip-+ rem-exp-log
1×rem-log-exp
Counts
4 → 55
Calls
4 calls:
5.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
8.0ms
(+ (log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))) (* (* (sin lambda1) (sin 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)))))

series620.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
212.0ms
(+ (log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
124.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
124.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

simplify41.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0277836
11287754
25002745

prune332.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes435.0ms

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
04244
14244

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3550×body1280valid
1.2s2343×body640valid
353.0ms982×body320valid
95.0ms409×body160valid
71.0ms716×body80valid