Details

Time bar (total: 43.1s)

sample1.2s

Algorithm
intervals
Results
834.0ms149×body1280valid
128.0ms75×body640valid
26.0ms22×body320valid
5.0ms7×body160valid
1.0ms3×body80valid

simplify41.0ms

Calls
1 calls:
Slowest
41.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize85.0ms

Local error

Found 4 expressions with local error:

4.1b
(cos (- lambda1 lambda2))
0.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.3b
(* (sin phi1) (sin phi2))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube associate-*l* add-exp-log
4×insert-posit16 add-log-exp
3×associate-*r*
2×cos-sum *-commutative
1×acos-asin cos-diff sub-neg pow-prod-down prod-exp cbrt-unprod sin-mult
Calls
4 calls:
Slowest
9.0ms
(* (sin phi1) (sin phi2))
7.0ms
(cos (- lambda1 lambda2))
6.0ms
(* (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)))))

series175.0ms

Calls
4 calls:
Slowest
56.0ms
(* (sin phi1) (sin phi2))
50.0ms
(cos (- lambda1 lambda2))
43.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
21.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify656.0ms

Calls
26 calls:
Slowest
107.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
78.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
54.0ms
(sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))))
54.0ms
(acos (+ (* (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) (* (sin phi1) (sin phi2))))
50.0ms
(* (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)))))))

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.5b

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.3b
(* (sin phi1) (sin phi2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b
(* (sin lambda1) (sin lambda2))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r*
4×insert-posit16 add-log-exp
3×*-commutative
2×pow-prod-down prod-exp cbrt-unprod sin-mult
1×acos-asin
Calls
4 calls:
Slowest
5.0ms
(* (sin lambda1) (sin lambda2))
5.0ms
(* (sin phi1) (sin phi2))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series229.0ms

Calls
4 calls:
Slowest
83.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
72.0ms
(* (sin lambda1) (sin lambda2))
60.0ms
(* (sin phi1) (sin phi2))
15.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.0s

Calls
32 calls:
Slowest
265.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
222.0ms
(sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
218.0ms
(* (acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2))))) R)
206.0ms
(* R (acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
204.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

prune1.6s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.3b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.3b
(* (sin phi1) (sin phi2))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×pow1
6×exp-prod add-cbrt-cube add-exp-log
5×add-log-exp
4×log-pow insert-posit16
3×acos-asin log-prod associate-*r* associate-*l*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult rem-exp-log
Calls
4 calls:
Slowest
6.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
5.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
5.0ms
(* (sin phi1) (sin phi2))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series164.0ms

Calls
4 calls:
Slowest
58.0ms
(* (sin phi1) (sin phi2))
48.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
29.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
29.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify4.2s

Calls
34 calls:
Slowest
256.0ms
(log (sqrt (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
249.0ms
(exp (* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
248.0ms
(sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
247.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
240.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.3b

localize21.0ms

Local error

Found 4 expressions with local error:

2.5b
(log (exp (* (sin lambda1) (sin lambda2))))
0.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
0.3b
(* (sin phi1) (sin phi2))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×pow1
6×add-cbrt-cube associate-*l* add-exp-log
5×add-log-exp
4×insert-posit16
3×log-prod associate-*r* log-pow
2×*-commutative
1×acos-asin exp-prod exp-to-pow rem-log-exp pow-prod-down prod-exp cbrt-unprod sin-mult
Calls
4 calls:
Slowest
9.0ms
(* (sin phi1) (sin phi2))
6.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
5.0ms
(log (exp (* (sin lambda1) (sin lambda2))))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))

series216.0ms

Calls
4 calls:
Slowest
82.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
53.0ms
(log (exp (* (sin lambda1) (sin lambda2))))
51.0ms
(* (sin phi1) (sin phi2))
29.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))

simplify2.0s

Calls
29 calls:
Slowest
275.0ms
(* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))))
235.0ms
(sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))))
233.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
229.0ms
(* R (acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
219.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

prune1.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.3b

regimes1.8s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch5.0ms

end0.0ms

sample23.9s

Algorithm
intervals
Results
17.1s4797×body1280valid
4.7s2096×body640valid
1.4s683×body320valid
257.0ms260×body160valid
82.0ms15×body2560valid
59.0ms154×body80valid