Details

Time bar (total: 59.9s)

sample549.0ms

Algorithm
intervals
Results
364.0ms136×body1280valid
107.0ms83×body640valid
17.0ms22×body320valid
5.0ms1×body2560valid
4.0ms8×body160valid
1.0ms6×body80valid

simplify94.0ms

Calls
1 calls:
Slowest
93.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.0b

localize41.0ms

Local error

Found 4 expressions with local error:

3.3b
(cos (- lambda1 lambda2))
0.9b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b
(* (sin phi1) (sin phi2))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
11×cos-sum
9×prod-diff
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Calls
4 calls:
Slowest
18.0ms
(cos (- lambda1 lambda2))
10.0ms
(* (sin phi1) (sin phi2))
5.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series169.0ms

Calls
4 calls:
Slowest
64.0ms
(* (sin phi1) (sin phi2))
59.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
28.0ms
(cos (- lambda1 lambda2))
17.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify2.0s

Calls
44 calls:
Slowest
375.0ms
(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (* (* R R) R))
311.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
116.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
72.0ms
(* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))))
71.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune2.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.8b

localize72.0ms

Local error

Found 4 expressions with local error:

0.9b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (sin phi1) (sin phi2))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Calls
4 calls:
Slowest
28.0ms
(* (sin phi1) (sin phi2))
22.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
3.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series241.0ms

Calls
4 calls:
Slowest
76.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
72.0ms
(* (sin phi1) (sin phi2))
72.0ms
(* (sin lambda1) (sin lambda2))
21.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify4.9s

Calls
43 calls:
Slowest
362.0ms
(* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2)))
361.0ms
(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (* (* R R) R))
341.0ms
(sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
325.0ms
(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (sqrt R))
325.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))

prune2.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.6b

localize65.0ms

Local error

Found 4 expressions with local error:

31.9b
(cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))
0.9b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))))))
0.2b
(* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1)))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))))))) R)

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
45×pow1
18×add-cbrt-cube pow-prod-down add-exp-log
16×sin-mult
9×prod-exp cbrt-unprod
8×add-sqr-sqrt
7×cbrt-div
6×frac-times *-un-lft-identity associate-*l/ add-cube-cbrt
4×expm1-log1p-u associate-*r* associate-*l* associate-*r/ pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
2×pow-plus *-commutative
1×cbrt-prod pow2 acos-asin pow1/3 swap-sqr pow3 rem-cbrt-cube unswap-sqr
Calls
4 calls:
Slowest
160.0ms
(cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))
57.0ms
(* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1)))
11.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))))))

series280.0ms

Calls
4 calls:
Slowest
94.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))))))) R)
91.0ms
(* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1)))
66.0ms
(cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))
29.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))))))

simplify8.9s

Calls
67 calls:
Slowest
867.0ms
(* (* (* (* (sin lambda2) (sin lambda2)) (sin lambda2)) (* (* (sin lambda1) (sin lambda1)) (sin lambda1))) (* (* (* (sin lambda2) (sin lambda2)) (sin lambda2)) (* (* (sin lambda1) (sin lambda1)) (sin lambda1))))
659.0ms
(* (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))) (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))
442.0ms
(cbrt (* (* (- (cos (- lambda2 lambda1)) (cos (+ lambda2 lambda1))) (- (cos (- lambda2 lambda1)) (cos (+ lambda2 lambda1)))) (- (cos (- lambda2 lambda1)) (cos (+ lambda2 lambda1)))))
355.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))
337.0ms
(* (acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2))))) R)

prune3.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.6b

localize95.0ms

Local error

Found 4 expressions with local error:

31.9b
(cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))
0.9b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))))))
0.6b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))))))))
0.3b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))))))))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
12×sin-mult
7×add-sqr-sqrt cbrt-div *-un-lft-identity add-cube-cbrt
6×exp-prod
5×frac-times pow1 associate-*l/ add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log log-pow insert-posit16 log1p-expm1-u
3×acos-asin log-prod associate-*r/
2×exp-diff
1×cbrt-prod log-div pow1/3 rem-log-exp pow3 rem-cbrt-cube rem-exp-log
Calls
4 calls:
Slowest
159.0ms
(cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))
11.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))))))))
6.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))))))))
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))))))

series162.0ms

Calls
4 calls:
Slowest
66.0ms
(cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))
55.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))))))))
21.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))))))
19.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))))))))

simplify7.3s

Calls
34 calls:
Slowest
600.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
433.0ms
(cbrt (* (* (- (cos (- lambda2 lambda1)) (cos (+ lambda2 lambda1))) (- (cos (- lambda2 lambda1)) (cos (+ lambda2 lambda1)))) (- (cos (- lambda2 lambda1)) (cos (+ lambda2 lambda1)))))
336.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))
329.0ms
(cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (- (cos (- lambda2 lambda1)) (cos (+ lambda2 lambda1)))))
324.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.6b

regimes1.6s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch3.0ms

end0.0ms

sample23.9s

Algorithm
intervals
Results
17.0s4732×body1280valid
5.2s2162×body640valid
910.0ms679×body320valid
355.0ms301×body160valid
46.0ms124×body80valid
42.0ms8×body2560valid