Details

Time bar (total: 39.2s)

sample599.0ms

Algorithm
intervals
Results
364.0ms141×body1280valid
116.0ms68×body640valid
80.0ms16×body320valid
8.0ms26×body80valid
3.0ms5×body160valid

simplify141.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
017744
128744
247744
378744
495744
done95744

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize95.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.6b
(sin (- lambda1 lambda2))
3.8b
(cos (- lambda1 lambda2))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×*-un-lft-identity add-cube-cbrt
18×prod-diff
11×pow1 cos-sum add-cbrt-cube sin-sum add-exp-log
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×cos-diff
2×sub-neg *-commutative sin-cos-mult
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff unswap-sqr
Counts
4 → 86
Calls
4 calls:
29.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
48.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

series327.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
146.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
42.0ms
(sin (- lambda1 lambda2))
29.0ms
(cos (- lambda1 lambda2))

simplify1.5s

Counts
98 → 98
Iterations

Useful iterations: done (1.5s)

IterNodesCost
021040233
143436169
2180232515
done500032250

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.7b

localize88.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (cos phi2))
0.2b
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.8b
(cos (- lambda1 lambda2))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
13×pow1 add-cbrt-cube add-exp-log
11×cos-sum
9×associate-*r* prod-diff
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cos-diff associate-*l/ *-commutative
2×sin-cos-mult unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in flip3-- flip--
Counts
4 → 87
Calls
4 calls:
9.0ms
(* (sin phi1) (cos phi2))
45.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
49.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
12.0ms
(cos (- lambda1 lambda2))

series415.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (sin phi1) (cos phi2))
183.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
137.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
26.0ms
(cos (- lambda1 lambda2))

simplify1.9s

Counts
99 → 99
Iterations

Useful iterations: done (1.8s)

IterNodesCost
020940635
146937703
2206435756
done500035476

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×pow1 add-cbrt-cube add-exp-log
12×associate-*r*
11×*-un-lft-identity add-cube-cbrt
10×associate-*l*
6×pow-prod-down prod-exp cbrt-unprod
5×sin-cos-mult
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp
3×frac-times associate-*l/ associate-*r/ sin-mult unswap-sqr
2×flip3-+ frac-add cos-mult flip-+
1×distribute-rgt-in distribute-lft-in flip3-- flip--
Counts
4 → 93
Calls
4 calls:
9.0ms
(* (sin phi1) (cos phi2))
46.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
10.0ms
(* (sin lambda1) (sin lambda2))
73.0ms
(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series628.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (sin phi1) (cos phi2))
218.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
86.0ms
(* (sin lambda1) (sin lambda2))
270.0ms
(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify2.9s

Counts
105 → 105
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
018944763
155442349
2345042029
done500042109

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize121.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
0.2b
(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.4b
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

rewrite733.0ms

Algorithm
rewrite-expression-head
Rules
87×pow1
78×cos-mult sin-mult
74×associate-*r/
66×frac-times
44×associate-*l/
42×add-cbrt-cube add-exp-log
37×pow-prod-down frac-sub
34×sin-cos-mult
33×associate-/l/
22×prod-exp cbrt-unprod
21×sub-div
8×pow-sqr pow-prod-up
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×associate-*r*
5×flip3-- flip--
4×expm1-log1p-u pow-plus associate-/r/ log1p-expm1-u add-log-exp
3×distribute-rgt-in cbrt-undiv associate-/r* distribute-lft-in times-frac div-exp associate-*l* *-commutative
2×pow2 sub-neg swap-sqr prod-diff
1×clear-num frac-2neg div-inv associate-/l* difference-of-squares
Counts
4 → 200
Calls
4 calls:
329.0ms
(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
269.0ms
(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
69.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
54.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

series1.4s

Counts
4 → 12
Calls
4 calls:
346.0ms
(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
876.0ms
(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
94.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
114.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

simplify1.7s

Counts
212 → 212
Iterations

Useful iterations: done (1.7s)

IterNodesCost
0322121324
11055108097
done5001106397

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes821.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify25.0ms

Iterations

Useful iterations: 0 (12.0ms)

IterNodesCost
0351544
1461544
done461544

end0.0ms

sample19.1s

Algorithm
intervals
Results
14.3s4601×body1280valid
3.6s2007×body640valid
521.0ms542×body320valid
202.0ms650×body80valid
102.0ms200×body160valid