Details

Time bar (total: 48.5s)

sample497.0ms

Algorithm
intervals
Results
239.0ms111×body1280valid
178.0ms77×body640valid
32.0ms37×body320valid
7.0ms12×body160valid
5.0ms19×body80valid

simplify21.0ms

Counts
1 → 1
Iterations
IterNodes
done23
223
120
014

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize105.0ms

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
(cos (- lambda1 lambda2))
3.6b
(sin (- lambda1 lambda2))

rewrite161.0ms

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:
71.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
27.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
28.0ms
(cos (- lambda1 lambda2))
28.0ms
(sin (- lambda1 lambda2))

series361.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
177.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
40.0ms
(cos (- lambda1 lambda2))
39.0ms
(sin (- lambda1 lambda2))

simplify4.2s

Counts
114 → 114
Iterations
IterNodes
done5005
33062
21198
1574
0242

prune1.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.7b

localize151.0ms

Local error

Found 4 expressions with local error:

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

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
11×pow1 add-exp-log cos-sum add-cbrt-cube
9×prod-diff
6×associate-*l* add-log-exp
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
3×cos-diff fma-def distribute-rgt-neg-out
2×associate-+r+ sin-neg *-commutative
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ sum-log flip-+ unswap-sqr
Counts
4 → 81
Calls
4 calls:
50.0ms
(* (cos lambda1) (sin (- lambda2)))
61.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
27.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
26.0ms
(cos (- lambda1 lambda2))

series501.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (cos lambda1) (sin (- lambda2)))
152.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
199.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
54.0ms
(cos (- lambda1 lambda2))

simplify5.2s

Counts
93 → 93
Iterations
IterNodes
done5000
34347
21115
1452
0209

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize151.0ms

Local error

Found 4 expressions with local error:

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

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×pow1 add-exp-log add-cbrt-cube
10×add-cube-cbrt associate-+r+ *-un-lft-identity
9×associate-*l*
7×distribute-rgt-in distribute-lft-in associate-*r*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×neg-sub0 cos-diff expm1-log1p-u associate--l+ distribute-rgt-neg-out log1p-expm1-u
3×fma-def sin-neg *-commutative
2×sub-neg prod-diff unswap-sqr
1×+-commutative flip3-+ sum-log flip-+ sin-mult
Counts
4 → 90
Calls
4 calls:
34.0ms
(* (cos lambda1) (sin (- lambda2)))
38.0ms
(* (sin lambda1) (sin (- lambda2)))
66.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
27.0ms
(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos (- lambda2))) (* (sin lambda1) (sin (- lambda2))))))

series832.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (cos lambda1) (sin (- lambda2)))
89.0ms
(* (sin lambda1) (sin (- lambda2)))
169.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
480.0ms
(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos (- lambda2))) (* (sin lambda1) (sin (- lambda2))))))

simplify4.9s

Counts
102 → 102
Iterations
IterNodes
done5000
34195
21299
1452
0185

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize169.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (cos phi1))
0.4b
(cbrt (cos phi1))
0.4b
(cbrt (cos phi1))
0.6b
(fma (* (cbrt (cos phi1)) (cbrt (cos phi1))) (cbrt (cos phi1)) (* (cos phi2) (- (* (cos lambda1) (cos (- lambda2))) (* (sin lambda1) (sin (- lambda2))))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
3.0ms
(cbrt (cos phi1))
3.0ms
(cbrt (cos phi1))
3.0ms
(cbrt (cos phi1))
1.0ms
(fma (* (cbrt (cos phi1)) (cbrt (cos phi1))) (cbrt (cos phi1)) (* (cos phi2) (- (* (cos lambda1) (cos (- lambda2))) (* (sin lambda1) (sin (- lambda2))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
199.0ms
(cbrt (cos phi1))
211.0ms
(cbrt (cos phi1))
197.0ms
(cbrt (cos phi1))
595.0ms
(fma (* (cbrt (cos phi1)) (cbrt (cos phi1))) (cbrt (cos phi1)) (* (cos phi2) (- (* (cos lambda1) (cos (- lambda2))) (* (sin lambda1) (sin (- lambda2))))))

simplify4.1s

Counts
61 → 61
Iterations
IterNodes
done5000
42911
3879
2301
1136
074

prune954.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes1.6s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify19.0ms

Iterations
IterNodes
done34
134
026

end0.0ms

sample17.6s

Algorithm
intervals
Results
10.2s3461×body1280valid
4.7s2422×body640valid
1.6s955×body320valid
254.0ms732×body80valid
232.0ms429×body160valid
2.0ms1×body2560valid