Details

Time bar (total: 9.1s)

sample189.0ms

Algorithm
intervals
Results
111.0ms114×body1280valid
40.0ms70×body640valid
18.0ms33×body320valid
4.0ms15×body160valid
3.0ms24×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: 1.3b

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))))
1.8b
(sin (- lambda1 lambda2))
1.9b
(cos (- lambda1 lambda2))

rewrite13.0ms

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))))
4.0ms
(sin (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

series296.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
105.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
162.0ms
(sin (- lambda1 lambda2))
19.0ms
(cos (- lambda1 lambda2))

simplify123.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0205421
1508375
21327374
33684374
45001374

prune231.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
1.8b
(sin (- lambda1 lambda2))

rewrite24.0ms

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×sin-sum *-commutative sin-mult
1×+-commutative sub-neg flip3-+ associate-*l/ sum-log sin-diff flip-+ unswap-sqr
Counts
4 → 59
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
3.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
5.0ms
(sin (- lambda1 lambda2))

series270.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin lambda1) (sin lambda2))
78.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
123.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
21.0ms
(sin (- lambda1 lambda2))

simplify39.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0289472
11273405
25001404

prune343.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

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

rewrite17.0ms

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:
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
(* (sin lambda1) (sin lambda2))
9.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
3.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(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))))
48.0ms
(* (sin lambda1) (sin lambda2))
76.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
126.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify42.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0288723
11255614
25001613

prune342.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

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))) (* (log (exp (* (sin lambda1) (sin lambda2)))) (cos phi2))))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
4.4b
(log (exp (* (sin lambda1) (sin lambda2))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×pow1 add-cube-cbrt *-un-lft-identity add-log-exp
6×add-exp-log add-cbrt-cube
3×log-prod associate-*r* associate-*l* log-pow
1×+-commutative exp-prod exp-to-pow flip3-+ rem-log-exp pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 51
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (log (exp (* (sin lambda1) (sin lambda2)))) (cos phi2))))
3.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
1.0ms
(log (exp (* (sin lambda1) (sin lambda2))))

series233.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (sin lambda1) (sin lambda2))
17.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (log (exp (* (sin lambda1) (sin lambda2)))) (cos phi2))))
126.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
45.0ms
(log (exp (* (sin lambda1) (sin lambda2))))

simplify98.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0249674
1867581
23262578
35003578

prune305.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes392.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03426
13426

end0.0ms

sample5.7s

Algorithm
intervals
Results
3.5s3638×body1280valid
1.4s2339×body640valid
359.0ms908×body320valid
112.0ms420×body160valid
85.0ms695×body80valid