Details

Time bar (total: 1.4m)

sample801.0ms

Algorithm
intervals
Results
464.0ms160×body1280valid
91.0ms59×body640valid
73.0ms25×body320valid
6.0ms7×body160valid
1.0ms5×body80valid

simplify68.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
67.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize100.0ms

Local error

Found 4 expressions with local error:

2.6b
(cos (- lambda1 lambda2))
0.7b
(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)
0.2b
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×associate-*r*
4×associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 add-log-exp
3×cos-diff
2×cos-sum *-commutative
1×distribute-rgt-in acos-asin sub-neg distribute-lft-in associate-*l/ cos-mult unswap-sqr
Counts
4 → 61
Calls
4 calls:
Slowest
33.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms
(cos (- lambda1 lambda2))
11.0ms
(* (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)))))

series227.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
56.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
32.0ms
(cos (- lambda1 lambda2))
10.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify6.0s

Counts
78 → 73
Calls
78 calls:
Slowest
985.0ms
(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
543.0ms
(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
486.0ms
(* (* (* (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))
339.0ms
(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R) (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)) (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R))
252.0ms
(exp (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 1.8b

localize90.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
0.2b
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-cbrt-cube add-exp-log
12×add-sqr-sqrt
10×pow-prod-down prod-exp cbrt-unprod
8×*-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
4×insert-posit16 add-log-exp
3×*-commutative sin-mult
2×cos-mult unswap-sqr
1×acos-asin frac-times associate-*l/ associate-*r/
Counts
4 → 74
Calls
4 calls:
Slowest
66.0ms
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
22.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series323.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
65.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
64.0ms
(* (sin lambda1) (sin lambda2))
30.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify12.6s

Counts
87 → 86
Calls
87 calls:
Slowest
496.0ms
(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (* (* R R) R))
445.0ms
(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R) (* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)) (* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R))
423.0ms
(exp (* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R))
404.0ms
(* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2)))
317.0ms
(* (* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))

prune2.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 1.7b

localize83.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* R (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))
0.2b
(* (sin phi2) (sin phi1))

rewrite50.0ms

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
21.0ms
(* (sin phi2) (sin phi1))
15.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(* R (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))
2.0ms
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))

series232.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
73.0ms
(* R (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))
64.0ms
(* (sin lambda1) (sin lambda2))
61.0ms
(* (sin phi2) (sin phi1))
34.0ms
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))

simplify13.6s

Counts
81 → 80
Calls
81 calls:
Slowest
643.0ms
(* R (acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
517.0ms
(+ (log R) (log (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))))
498.0ms
(real->posit16 (* R (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))))
487.0ms
(* (cbrt (* R (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))) (cbrt (* R (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))))
476.0ms
(* (cbrt R) (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))

prune2.0s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 1.6b

localize76.0ms

Local error

Found 4 expressions with local error:

25.5b
(cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))
0.7b
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))) (cos phi2)))))
0.3b
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.2b
(* (sin lambda1) (sin lambda2))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
45×pow1
18×add-cbrt-cube pow-prod-down add-exp-log
17×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×associate-*r* associate-*l* associate-*r/ pow-sqr pow-prod-up insert-posit16 add-log-exp
2×pow-plus *-commutative
1×cbrt-prod pow2 acos-asin pow1/3 swap-sqr pow3 rem-cbrt-cube unswap-sqr
Counts
4 → 85
Calls
4 calls:
Slowest
144.0ms
(cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))
87.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
20.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))) (cos phi2)))))

series262.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
91.0ms
(cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))
72.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
69.0ms
(* (sin lambda1) (sin lambda2))
29.0ms
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))) (cos phi2)))))

simplify11.2s

Counts
104 → 97
Calls
104 calls:
Slowest
822.0ms
(* (* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2))) (* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2))))
667.0ms
(* (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))) (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))
399.0ms
(* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2)))
344.0ms
(cbrt (* (* (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))) (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2)))) (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2)))))
338.0ms
(real->posit16 (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2)))))

prune2.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 1.6b

regimes2.7s

Accuracy

0% (0.4b remaining)

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

bsearch6.0ms

end0.0ms

sample24.8s

Algorithm
intervals
Results
18.6s4787×body1280valid
4.2s2059×body640valid
1.1s714×body320valid
258.0ms300×body160valid
59.0ms8×body2560valid
55.0ms134×body80valid