Details

Time bar (total: 29.8s)

sample347.0ms

Algorithm
intervals
Results
155.0ms106×body1280valid
72.0ms67×body640valid
60.0ms30×body80valid
22.0ms39×body320valid
4.0ms14×body160valid

simplify17.0ms

Counts
1 → 1
Iterations
IterNodes
done23
223
120
014

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b
(sin (- lambda1 lambda2))
4.1b
(cos (- lambda1 lambda2))

rewrite84.0ms

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 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 → 69
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
22.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms
(sin (- lambda1 lambda2))
36.0ms
(cos (- lambda1 lambda2))

series244.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
145.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
39.0ms
(sin (- lambda1 lambda2))
39.0ms
(cos (- lambda1 lambda2))

simplify2.2s

Counts
81 → 81
Iterations
IterNodes
done5000
31944
2727
1372
0191

prune862.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.0b

localize104.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (sin lambda1) (sin lambda2))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
4.0b
(sin (- lambda1 lambda2))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
11×sin-sum
9×prod-diff
6×pow1 add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×associate-+r+
1×distribute-rgt-in +-commutative sum-log sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 69
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
18.0ms
(* (sin lambda1) (sin lambda2))
13.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
27.0ms
(sin (- lambda1 lambda2))

series428.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
62.0ms
(* (sin lambda1) (sin lambda2))
305.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
31.0ms
(sin (- lambda1 lambda2))

simplify3.1s

Counts
81 → 81
Iterations
IterNodes
done5000
34362
2965
1404
0196

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize82.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

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×expm1-log1p-u log1p-expm1-u
3×fma-def
2×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ flip-+ sin-mult
Counts
4 → 68
Calls
4 calls:
22.0ms
(* (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))))))
15.0ms
(* (sin lambda1) (sin lambda2))
7.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series502.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (cos lambda1) (sin lambda2))
34.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
75.0ms
(* (sin lambda1) (sin lambda2))
335.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify2.6s

Counts
80 → 80
Iterations
IterNodes
done5000
34091
21021
1346
0141

prune930.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize109.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos lambda1))
0.3b
(cbrt (cos lambda1))
0.3b
(cbrt (cos lambda1))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u
3×fma-def pow1/3
2×associate-+r+
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ flip-+
Counts
4 → 57
Calls
4 calls:
2.0ms
(cbrt (cos lambda1))
10.0ms
(cbrt (cos lambda1))
2.0ms
(cbrt (cos lambda1))
15.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series812.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(cbrt (cos lambda1))
174.0ms
(cbrt (cos lambda1))
135.0ms
(cbrt (cos lambda1))
366.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify2.7s

Counts
69 → 69
Iterations
IterNodes
done5000
33509
2732
1212
083

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes1.2s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations
IterNodes
done39
139
027

end0.0ms

sample10.9s

Algorithm
intervals
Results
6.9s3635×body1280valid
2.5s2270×body640valid
846.0ms1014×body320valid
180.0ms405×body160valid
139.0ms674×body80valid
6.0ms2×body2560valid