Details

Time bar (total: 9.8s)

sample170.0ms

Algorithm
intervals
Results
98.0ms112×body1280valid
40.0ms76×body640valid
10.0ms30×body320valid
3.0ms28×body80valid
2.0ms10×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12312
22312
done2312

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.4b
(sin (- lambda1 lambda2))
3.4b
(cos (- lambda1 lambda2))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
36×prod-diff
33×add-sqr-sqrt sin-sum
31×add-cube-cbrt *-un-lft-identity
12×distribute-rgt-in distribute-lft-in
11×cos-sum
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u sub-neg log1p-expm1-u
3×cos-diff fma-def associate-*r* associate-*l*
2×associate-+r+
1×+-commutative flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 102
Calls
4 calls:
33.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
13.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms
(sin (- lambda1 lambda2))
17.0ms
(cos (- lambda1 lambda2))

series210.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
107.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms
(sin (- lambda1 lambda2))
19.0ms
(cos (- lambda1 lambda2))

simplify110.0ms

Counts
114 → 114
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
05051623
114301236
248731161
350011161
done50011161

prune348.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.3b
(* (sin lambda1) (sin lambda2))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
3.4b
(sin (- lambda1 lambda2))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
33×sin-sum
31×add-sqr-sqrt
27×add-cube-cbrt *-un-lft-identity prod-diff
12×distribute-rgt-in distribute-lft-in
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×sub-neg fma-def
2×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-+ sum-log sin-diff flip-+ sin-mult
Counts
4 → 102
Calls
4 calls:
33.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
12.0ms
(* (sin lambda1) (sin lambda2))
9.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
15.0ms
(sin (- lambda1 lambda2))

series361.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
50.0ms
(* (sin lambda1) (sin lambda2))
231.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
22.0ms
(sin (- lambda1 lambda2))

simplify50.0ms

Counts
114 → 114
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
05331504
117871178
250011097
done50011097

prune451.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
0.3b
(* (sin lambda1) (sin lambda2))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite53.0ms

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-*l* add-log-exp
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
3×fma-def
2×associate-+r+ *-commutative distribute-rgt-neg-out
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sin-neg sum-log flip-+ sin-mult unswap-sqr
Counts
4 → 69
Calls
4 calls:
0.0ms
(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
28.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
11.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series392.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
91.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
46.0ms
(* (sin lambda1) (sin lambda2))
234.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify40.0ms

Counts
81 → 81
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0362950
11266805
25001797
done5001797

prune458.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.3b
(* (sin lambda1) (sin lambda2))
0.6b
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
0.6b
(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))

rewrite22.0ms

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:
2.0ms
(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
12.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
6.0ms
(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))

series752.0ms

Counts
4 → 12
Calls
4 calls:
276.0ms
(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
45.0ms
(* (sin lambda1) (sin lambda2))
213.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
217.0ms
(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))

simplify57.0ms

Counts
75 → 75
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0219746
1602643
22130638
35002638
done5002638

prune412.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes476.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03125
13125
done3125

end0.0ms

sample5.1s

Algorithm
intervals
Results
3.1s3528×body1280valid
1.2s2384×body640valid
321.0ms947×body320valid
88.0ms422×body160valid
70.0ms719×body80valid