Details

Time bar (total: 9.3s)

sample192.0ms

Algorithm
intervals
Results
112.0ms114×body1280valid
40.0ms70×body640valid
18.0ms33×body320valid
4.0ms15×body160valid
3.0ms24×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12312
22312

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

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

rewrite23.0ms

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)))))
6.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms
(sin (- lambda1 lambda2))
7.0ms
(cos (- lambda1 lambda2))

series152.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
100.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(sin (- lambda1 lambda2))
22.0ms
(cos (- lambda1 lambda2))

simplify70.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune325.0ms

Pruning

12 alts after pruning (12 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
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
1.8b
(sin (- lambda1 lambda2))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×pow1 add-exp-log sin-sum add-cbrt-cube
9×prod-diff
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×*-commutative sin-mult
1×sub-neg associate-*l/ sin-diff fma-udef unswap-sqr
Counts
4 → 73
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
9.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
7.0ms
(sin (- lambda1 lambda2))

series273.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin lambda1) (sin lambda2))
79.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
129.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
21.0ms
(sin (- lambda1 lambda2))

simplify40.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0349719
11137569
25001567

prune423.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

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

rewrite15.0ms

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*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×*-commutative sin-mult
1×associate-*l/ fma-udef unswap-sqr
Counts
4 → 61
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
9.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series271.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sin lambda1) (sin lambda2))
16.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
81.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
125.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify105.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0226727
1898621
24339620
35001620

prune394.0ms

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)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (log (exp (* (sin lambda1) (sin lambda2)))) (cos phi2))))
0.2b
(* (sin lambda1) (sin lambda2))
0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
4.4b
(log (exp (* (sin lambda1) (sin lambda2))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×log-prod associate-*r* associate-*l* log-pow
1×exp-prod exp-to-pow rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef sin-mult unswap-sqr
Counts
4 → 56
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (log (exp (* (sin lambda1) (sin lambda2)))) (cos phi2))))
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
2.0ms
(log (exp (* (sin lambda1) (sin lambda2))))

series245.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (log (exp (* (sin lambda1) (sin lambda2)))) (cos phi2))))
49.0ms
(* (sin lambda1) (sin lambda2))
127.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
52.0ms
(log (exp (* (sin lambda1) (sin lambda2))))

simplify46.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0186678
1506588
21639585
35001585

prune363.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes390.0ms

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
03327
13327

end0.0ms

sample5.8s

Algorithm
intervals
Results
3.6s3638×body1280valid
1.4s2339×body640valid
365.0ms908×body320valid
109.0ms420×body160valid
88.0ms695×body80valid