Details

Time bar (total: 9.4s)

sample174.0ms

Algorithm
intervals
Results
100.0ms114×body1280valid
38.0ms76×body640valid
10.0ms17×body160valid
7.0ms23×body320valid
3.0ms26×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12312
22312

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

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)))))
0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.6b
(cos (- lambda1 lambda2))
2.7b
(sin (- lambda1 lambda2))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×cos-sum sin-sum
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cos-diff fma-def
2×sub-neg associate-+r+
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-diff flip-+
Counts
4 → 69
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
16.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.0ms
(cos (- lambda1 lambda2))
13.0ms
(sin (- lambda1 lambda2))

series135.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
91.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
15.0ms
(cos (- lambda1 lambda2))
20.0ms
(sin (- lambda1 lambda2))

simplify69.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune313.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (+ (* (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)))))
0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.6b
(cos (- lambda1 lambda2))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×cos-sum
9×prod-diff
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cos-diff fma-def associate-*r* associate-*l*
2×distribute-rgt-in associate-+r+ distribute-lft-in flip3-+ associate-*r/ flip-+
1×+-commutative sub-neg pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
4 → 72
Calls
4 calls:
41.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
13.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.0ms
(cos (- lambda1 lambda2))

series258.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
12.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
89.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
15.0ms
(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04581104
11634916
25001912

prune455.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
0.2b
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b
(* (sin lambda1) (sin lambda2))
0.4b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r*
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative
2×associate-*r/ sin-mult unswap-sqr
1×distribute-rgt-in distribute-lft-in flip3-+ associate-*l/ flip-+ fma-udef
Counts
4 → 76
Calls
4 calls:
26.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
40.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
12.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series370.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
128.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
40.0ms
(* (sin lambda1) (sin lambda2))
122.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify49.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0361722
11769620
25001617

prune502.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b
(* (sin lambda1) (sin lambda2))
0.4b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.6b
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log-prod log-pow log1p-expm1-u add-log-exp
3×exp-prod
2×associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
1×distribute-rgt-in distribute-lft-in flip3-+ rem-log-exp exp-sum flip-+ sin-mult
Counts
4 → 73
Calls
4 calls:
49.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
17.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
3.0ms
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

series398.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
40.0ms
(* (sin lambda1) (sin lambda2))
112.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
114.0ms
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

simplify43.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0333743
11356651
25002647

prune477.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes430.0ms

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
03526
13526

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.2s3598×body1280valid
1.2s2345×body640valid
325.0ms950×body320valid
91.0ms417×body160valid
65.0ms690×body80valid