Details

Time bar (total: 36.4s)

sample359.0ms

Algorithm
intervals
Results
212.0ms104×body1280valid
90.0ms86×body640valid
12.0ms19×body320valid
9.0ms19×body160valid
6.0ms28×body80valid

simplify11.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
120
014

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize97.0ms

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))))
3.6b
(sin (- lambda1 lambda2))
3.8b
(cos (- lambda1 lambda2))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×cos-diff
2×cos-sum associate-+r+ sub-neg sin-sum
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ sin-diff flip-+
Counts
4 → 40
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
7.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
9.0ms
(sin (- lambda1 lambda2))
16.0ms
(cos (- lambda1 lambda2))

series219.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
145.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
23.0ms
(sin (- lambda1 lambda2))
38.0ms
(cos (- lambda1 lambda2))

simplify1.3s

Counts
52 → 52
Iterations
IterNodes
done5000
31502
2528
1207
097

prune521.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.7b

localize66.0ms

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))))
3.8b
(cos (- lambda1 lambda2))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
3×distribute-rgt-in cos-diff sub-neg distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+ associate-*r/
1×+-commutative sum-log flip3-+ flip3-- pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ flip-- unswap-sqr
Counts
4 → 54
Calls
4 calls:
72.0ms
(* (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)))))
13.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms
(cos (- lambda1 lambda2))

series425.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
18.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
159.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms
(cos (- lambda1 lambda2))

simplify1.4s

Counts
66 → 66
Iterations
IterNodes
done5000
21276
1310
0124

prune874.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize99.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l* add-log-exp
3×distribute-rgt-in distribute-lft-in
2×associate-+r+ sub-neg pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×+-commutative sum-log flip3-+ flip3-- flip-+ flip-- sin-mult
Counts
4 → 63
Calls
4 calls:
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))))))
60.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
10.0ms
(* (sin lambda1) (sin lambda2))
7.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series672.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
226.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
59.0ms
(* (sin lambda1) (sin lambda2))
350.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.8s

Counts
75 → 75
Iterations
IterNodes
done5001
21865
1376
0144

prune947.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize273.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (* (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))) (* (cos phi1) (* (cos phi1) (cos phi1))))
0.4b
(/ (+ (* (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (- (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))) (* (cos phi1) (cos phi1))))
0.5b
(* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))
0.6b
(- (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
381×associate-*l/
244×frac-add cos-mult
177×frac-times
161×associate-*r/
110×flip3-+ flip-+
107×sin-mult
65×associate-/l/
43×pow1
18×add-cbrt-cube add-exp-log
17×pow-prod-down
13×add-sqr-sqrt *-un-lft-identity associate-/r/ add-cube-cbrt
12×times-frac
8×prod-exp cbrt-unprod add-log-exp
5×flip3-- cube-unmult pow3 sum-cubes flip--
4×pow-sqr pow-prod-up associate-/l*
3×associate-/r*
2×sqr-cos associate-+r+ pow-plus
1×pow2 distribute-rgt-in cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg distribute-lft-in diff-log swap-sqr div-exp associate-*r* associate-*l* *-commutative div-inv
Counts
4 → 247
Calls
4 calls:
493.0ms
(+ (* (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))) (* (cos phi1) (* (cos phi1) (cos phi1))))
1.1s
(/ (+ (* (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (- (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))) (* (cos phi1) (cos phi1))))
164.0ms
(* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))
31.0ms
(- (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))

series6.2s

Counts
4 → 12
Calls
4 calls:
1.5s
(+ (* (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))) (* (cos phi1) (* (cos phi1) (cos phi1))))
4.2s
(/ (+ (* (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (- (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))) (* (cos phi1) (cos phi1))))
189.0ms
(* (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))
327.0ms
(- (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))

simplify3.2s

Counts
259 → 259
Iterations
IterNodes
done5001
12546
0702

prune4.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes970.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify15.0ms

Iterations
IterNodes
done45
145
031

end0.0ms

sample10.9s

Algorithm
intervals
Results
6.6s3606×body1280valid
2.3s2359×body640valid
898.0ms900×body320valid
445.0ms429×body160valid
108.0ms706×body80valid