Details

Time bar (total: 9.7s)

sample186.0ms

Algorithm
intervals
Results
103.0ms105×body1280valid
49.0ms89×body640valid
15.0ms28×body320valid
3.0ms24×body80valid
2.0ms10×body160valid

simplify5.0ms

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

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)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.2b
(sin (- lambda1 lambda2))
2.2b
(cos (- lambda1 lambda2))

rewrite27.0ms

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))

series158.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
107.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(sin (- lambda1 lambda2))
19.0ms
(cos (- lambda1 lambda2))

simplify69.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune368.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.2b
(cos (- lambda1 lambda2))

rewrite20.0ms

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:
4.0ms
(* (sin lambda1) (cos lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
7.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms
(cos (- lambda1 lambda2))

series323.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (sin lambda1) (cos lambda2))
12.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
244.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(cos (- lambda1 lambda2))

simplify90.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (82.0ms)

IterNodesCost
0390869
11061710
23925707
35001706

prune430.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-cos-mult fma-udef sin-mult
Counts
4 → 61
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)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
5.0ms
(* (sin lambda1) (cos lambda2))
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series239.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
44.0ms
(* (sin lambda1) (cos lambda2))
49.0ms
(* (sin lambda1) (sin lambda2))
129.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify65.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0240677
1726590
22516588
35002588

prune398.0ms

Pruning

10 alts after pruning (10 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
(exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))
0.5b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.7b
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
7×pow1
6×add-exp-log exp-prod add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u log-prod log-pow log1p-expm1-u
3×associate-*r* associate-*l* fma-udef
2×exp-sum
1×rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log sin-mult unswap-sqr
Counts
4 → 63
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
2.0ms
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

series481.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (sin lambda1) (sin lambda2))
168.0ms
(exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))
134.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
130.0ms
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

simplify52.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (46.0ms)

IterNodesCost
0198556
1560490
21900486
35001485

prune382.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes512.0ms

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
03125
13125

end0.0ms

sample5.7s

Algorithm
intervals
Results
3.5s3603×body1280valid
1.3s2343×body640valid
372.0ms957×body320valid
99.0ms390×body160valid
92.0ms707×body80valid