Details

Time bar (total: 41.7s)

sample445.0ms

Algorithm
intervals
Results
247.0ms122×body1280valid
114.0ms71×body640valid
32.0ms17×body80valid
29.0ms33×body320valid
7.0ms13×body160valid

simplify9.0ms

Counts
1 → 1
Iterations
IterNodes
323
223
120
014

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.5b

localize51.0ms

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))))
4.0b
(cos (- lambda1 lambda2))
4.2b
(sin (- lambda1 lambda2))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×cos-sum sin-sum
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×cos-diff fma-def
2×associate-+r+ sub-neg
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ sin-diff flip-+
Counts
4 → 73
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
11.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
10.0ms
(cos (- lambda1 lambda2))
10.0ms
(sin (- lambda1 lambda2))

series208.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
143.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(cos (- lambda1 lambda2))
29.0ms
(sin (- lambda1 lambda2))

simplify3.4s

Counts
85 → 85
Iterations
IterNodes
45761
31784
2699
1365
0195

prune845.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.3b

localize70.0ms

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)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b
(cos (- lambda1 lambda2))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
11×cos-sum prod-diff
6×pow1 add-cbrt-cube add-exp-log add-log-exp
4×distribute-rgt-in expm1-log1p-u distribute-lft-in insert-posit16 log1p-expm1-u
3×cos-diff sub-neg fma-def associate-*r* associate-*l*
2×associate-+r+ associate-*r/
1×+-commutative sum-log flip3-+ flip3-- pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ flip-- unswap-sqr
Counts
4 → 80
Calls
4 calls:
88.0ms
(* (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)))))
17.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))

series447.0ms

Counts
4 → 12
Calls
4 calls:
239.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
19.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
169.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(cos (- lambda1 lambda2))

simplify2.0s

Counts
92 → 92
Iterations
IterNodes
33377
21169
1451
0212

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

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

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l* add-log-exp
4×distribute-rgt-in expm1-log1p-u distribute-lft-in insert-posit16 log1p-expm1-u
3×fma-def
2×associate-+r+ sub-neg prod-diff pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×+-commutative sum-log flip3-+ flip3-- flip-+ flip-- sin-mult
Counts
4 → 80
Calls
4 calls:
73.0ms
(* (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) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
12.0ms
(* (sin lambda1) (sin lambda2))
17.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series694.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
16.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
90.0ms
(* (sin lambda1) (sin lambda2))
360.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify6.4s

Counts
92 → 92
Iterations
IterNodes
37394
21449
1411
0164

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize99.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(exp (fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.5b
(fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1))
0.6b
(log (exp (fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
7×pow1
6×exp-prod add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u log-prod log-pow insert-posit16 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 sin-mult unswap-sqr rem-exp-log
Counts
4 → 67
Calls
4 calls:
12.0ms
(* (sin lambda1) (sin lambda2))
2.0ms
(exp (fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.0ms
(fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1))
5.0ms
(log (exp (fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1))))

series1.1s

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (sin lambda1) (sin lambda2))
369.0ms
(exp (fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)))
335.0ms
(fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1))
332.0ms
(log (exp (fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1))))

simplify2.4s

Counts
79 → 79
Iterations
IterNodes
44463
31397
2515
1238
0120

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes734.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
230
130
021

end0.0ms

sample17.4s

Algorithm
intervals
Results
9.4s3589×body1280valid
5.4s2325×body640valid
1.5s962×body320valid
392.0ms407×body160valid
279.0ms717×body80valid