Details

Time bar (total: 9.4s)

sample169.0ms

Algorithm
intervals
Results
109.0ms125×body1280valid
31.0ms64×body640valid
8.0ms26×body320valid
4.0ms27×body80valid
3.0ms14×body160valid

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: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.8b
(sin (- lambda1 lambda2))
2.8b
(cos (- lambda1 lambda2))

rewrite20.0ms

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:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
6.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
6.0ms
(sin (- lambda1 lambda2))
6.0ms
(cos (- lambda1 lambda2))

series157.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
105.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(sin (- lambda1 lambda2))
18.0ms
(cos (- lambda1 lambda2))

simplify70.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune293.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b
(* (cos lambda1) (sin (- lambda2)))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.8b
(cos (- lambda1 lambda2))

rewrite19.0ms

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 sin-neg sum-log *-commutative distribute-rgt-neg-out cbrt-unprod flip-+ unswap-sqr
Counts
4 → 69
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
5.0ms
(* (cos lambda1) (sin (- lambda2)))
5.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))

series188.0ms

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)))))
53.0ms
(* (cos lambda1) (sin (- lambda2)))
102.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(cos (- lambda1 lambda2))

simplify111.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (100.0ms)

IterNodesCost
0404909
11169743
24635741
35001739

prune427.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* add-log-exp
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
3×fma-def
2×*-commutative fma-udef sin-mult
1×+-commutative associate-+l+ flip3-+ associate-*l/ sum-log flip-+ unswap-sqr
Counts
4 → 69
Calls
4 calls:
7.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
4.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series460.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
207.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
46.0ms
(* (sin lambda1) (sin lambda2))
129.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify45.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0282646
11301579
25001573

prune460.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
0.5b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.5b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.7b
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow cube-prod fma-udef
1×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 55
Calls
4 calls:
1.0ms
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
2.0ms
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

series562.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
127.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
127.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
182.0ms
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

simplify181.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0170548
1633507
24290499
35001499

prune440.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes509.0ms

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
3.2s3604×body1280valid
1.2s2297×body640valid
310.0ms935×body320valid
95.0ms442×body160valid
77.0ms722×body80valid