Details

Time bar (total: 9.4s)

sample176.0ms

Algorithm
intervals
Results
114.0ms131×body1280valid
34.0ms67×body640valid
7.0ms22×body320valid
3.0ms12×body160valid
2.0ms24×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02012
12312
22312

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize21.0ms

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))))
4.9b
(cos (- lambda1 lambda2))
4.9b
(sin (- lambda1 lambda2))

rewrite42.0ms

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)))))
13.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.0ms
(cos (- lambda1 lambda2))
13.0ms
(sin (- lambda1 lambda2))

series162.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
105.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
18.0ms
(cos (- lambda1 lambda2))
27.0ms
(sin (- lambda1 lambda2))

simplify69.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune312.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b
(* (sin lambda1) (cos lambda2))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.9b
(cos (- lambda1 lambda2))

rewrite43.0ms

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×associate-+r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log *-commutative sin-cos-mult cbrt-unprod flip-+ unswap-sqr
Counts
4 → 69
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
13.0ms
(* (sin lambda1) (cos lambda2))
13.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.0ms
(cos (- lambda1 lambda2))

series182.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
43.0ms
(* (sin lambda1) (cos lambda2))
107.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
18.0ms
(cos (- lambda1 lambda2))

simplify94.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0412884
11112723
24144720
35001719

prune420.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos lambda2))
0.3b
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.3b
(* (sin lambda1) (sin lambda2))
0.5b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-def
2×pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
1×+-commutative associate-+l+ flip3-+ sum-log sin-cos-mult flip-+ sin-mult
Counts
4 → 69
Calls
4 calls:
13.0ms
(* (sin lambda1) (cos lambda2))
8.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
12.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series429.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin lambda1) (cos lambda2))
211.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
45.0ms
(* (sin lambda1) (sin lambda2))
130.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify41.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0306607
11230548
25001541

prune465.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.3b
(* (sin lambda1) (sin lambda2))
0.5b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.7b
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
8×pow1 log-prod log-pow
7×fma-def
6×add-exp-log exp-prod add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u associate-+l+ log1p-expm1-u
3×associate-*r* associate-*l* fma-udef
2×exp-sum
1×+-commutative flip3-+ rem-log-exp pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 73
Calls
4 calls:
17.0ms
(+ (log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
12.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
5.0ms
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

series517.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(+ (log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
45.0ms
(* (sin lambda1) (sin lambda2))
133.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
131.0ms
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

simplify38.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0275743
11088667
25002657

prune487.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes448.0ms

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
03426
13426

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3573×body1280valid
1.2s2341×body640valid
326.0ms968×body320valid
92.0ms416×body160valid
66.0ms702×body80valid