Details

Time bar (total: 59.4s)

sample1.1s

Algorithm
intervals
Results
676.0ms146×body1280valid
282.0ms75×body640valid
34.0ms22×body320valid
7.0ms7×body160valid
3.0ms6×body80valid

simplify51.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
50.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize76.0ms

Local error

Found 4 expressions with local error:

3.7b
(cos (- lambda1 lambda2))
0.5b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

rewrite55.0ms

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*
4×insert-posit16 add-log-exp
2×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Counts
4 → 59
Calls
4 calls:
Slowest
22.0ms
(* (sin phi1) (sin phi2))
19.0ms
(cos (- lambda1 lambda2))
8.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series193.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
74.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
62.0ms
(* (sin phi1) (sin phi2))
32.0ms
(cos (- lambda1 lambda2))
18.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.5s

Counts
35 → 71
Calls
35 calls:
Slowest
360.0ms
(* (* (* (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))
300.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
132.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
66.0ms
(* (acos (+ (* (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) (* (sin phi1) (sin phi2)))) R)
64.0ms
(+ (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (log R))

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.1b

localize84.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity associate-*r* add-cube-cbrt
7×associate-*l*
6×cos-mult
5×pow-prod-down prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×frac-times associate-*r/ *-commutative sin-mult
2×flip3-+ frac-add flip-+ unswap-sqr
1×distribute-rgt-in acos-asin distribute-lft-in associate-*l/
Counts
4 → 76
Calls
4 calls:
Slowest
72.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
11.0ms
(* (sin phi1) (sin phi2))
5.0ms
(* (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))))))

series830.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
474.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
268.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
63.0ms
(* (sin phi1) (sin phi2))
25.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify7.5s

Counts
54 → 88
Calls
54 calls:
Slowest
615.0ms
(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
544.0ms
(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (+ (* (+ (cos (+ lambda1 lambda2)) (cos (- lambda1 lambda2))) 2) (* 2 (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))))))
507.0ms
(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
357.0ms
(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
326.0ms
(+ (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (log R))

prune2.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.0b

localize71.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

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×insert-posit16 add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Counts
4 → 68
Calls
4 calls:
Slowest
22.0ms
(* (sin phi1) (sin phi2))
21.0ms
(* (sin lambda2) (sin lambda1))
5.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))

series227.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
74.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))))) R)
66.0ms
(* (sin phi1) (sin phi2))
65.0ms
(* (sin lambda2) (sin lambda1))
22.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))

simplify4.2s

Counts
43 → 80
Calls
43 calls:
Slowest
384.0ms
(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))) (sqrt R))
368.0ms
(* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))))
359.0ms
(+ (log (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))) (log R))
345.0ms
(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))) (sqrt R))
326.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))

prune2.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.0b

localize119.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))))))
0.3b
(asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))
0.2b
(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))) R)
0.2b
(* (sin phi1) (sin phi2))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
12×*-un-lft-identity
9×associate-*l*
8×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* add-log-exp
4×insert-posit16 difference-of-squares
2×asin-acos times-frac flip3-- pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod flip-- distribute-lft-out-- unswap-sqr
1×sub-neg diff-log sin-mult associate--r-
Counts
4 → 70
Calls
4 calls:
Slowest
58.0ms
(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))) R)
19.0ms
(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))))))
11.0ms
(* (sin phi1) (sin phi2))
4.0ms
(asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))

series391.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
241.0ms
(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))) R)
69.0ms
(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))))))
66.0ms
(* (sin phi1) (sin phi2))
15.0ms
(asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))

simplify8.4s

Counts
43 → 82
Calls
43 calls:
Slowest
406.0ms
(+ (sqrt (/ PI 2)) (sqrt (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))))
394.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))
392.0ms
(+ (sqrt (/ PI 2)) (sqrt (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))))
384.0ms
(sqrt (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))))
372.0ms
(/ (exp (/ PI 2)) (exp (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))))

prune1.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 1.9b

regimes1.2s

Accuracy

0% (0.5b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch7.0ms

end0.0ms

sample25.5s

Algorithm
intervals
Results
18.2s4784×body1280valid
5.5s2135×body640valid
952.0ms677×body320valid
246.0ms260×body160valid
124.0ms13×body2560valid
94.0ms132×body80valid