Details

Time bar (total: 1.3m)

sample762.0ms

Algorithm
intervals
Results
447.0ms146×body1280valid
118.0ms72×body640valid
18.0ms20×body320valid
6.0ms10×body160valid
5.0ms1×body2560valid
3.0ms7×body80valid

simplify52.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
52.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize73.0ms

Local error

Found 4 expressions with local error:

4.3b
(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
(* (sin phi1) (sin phi2))

rewrite38.0ms

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
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)
3.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series229.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
89.0ms
(* (sin phi1) (sin phi2))
76.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
45.0ms
(cos (- lambda1 lambda2))
19.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.6s

Counts
35 → 71
Calls
35 calls:
Slowest
448.0ms
(* (* (* (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))
355.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
133.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
76.0ms
(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (sqrt R))
69.0ms
(* (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)))))))

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.8b

localize105.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

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
56.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
17.0ms
(* (sin phi1) (sin phi2))
7.0ms
(* (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))))))

series450.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
290.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
90.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
49.0ms
(* (sin phi1) (sin phi2))
21.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify8.4s

Counts
54 → 88
Calls
54 calls:
Slowest
1.1s
(* (* (* (* (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)))))
694.0ms
(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (+ (* (+ (cos (+ lambda1 lambda2)) (cos (- lambda1 lambda2))) 2) (* 2 (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))))))
436.0ms
(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
422.0ms
(* (* (* (* (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)))))
279.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))

prune2.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.6b

localize126.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.6b
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.3b
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.2b
(* (sin phi1) (sin phi2))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×pow1 associate-*l*
8×add-cbrt-cube add-exp-log
7×log-prod
6×associate-*r*
4×exp-sum insert-posit16 add-log-exp
3×unswap-sqr
2×pow-prod-down prod-exp *-commutative cbrt-unprod
1×acos-asin rem-log-exp log-pow sin-mult
Counts
4 → 65
Calls
4 calls:
Slowest
13.0ms
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
10.0ms
(* (sin phi1) (sin phi2))
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
1.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series219.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
87.0ms
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
56.0ms
(* (sin phi1) (sin phi2))
54.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
21.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify5.9s

Counts
41 → 77
Calls
41 calls:
Slowest
322.0ms
(* (* (* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) (* (* R R) R))
311.0ms
(log (* (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)))))))))
300.0ms
(+ (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (log R))
295.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
269.0ms
(exp (log (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.6b

localize101.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos 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
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.3b
(/ (* (* (cos 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
(* (acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos 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)))))) R)

rewrite440.0ms

Algorithm
rewrite-expression-head
Rules
59×cos-mult
45×pow1
38×sin-mult
37×associate-*r/
33×frac-times associate-/l/
27×add-cbrt-cube add-exp-log
22×associate-*l/
19×frac-sub
18×pow-prod-down
12×prod-exp cbrt-unprod
11×sub-div
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
4×associate-*r* associate-*l* associate-/r/ pow-sqr pow-prod-up insert-posit16 add-log-exp
3×cbrt-undiv associate-/r* times-frac flip3-- div-exp flip--
2×pow-plus *-commutative
1×pow2 acos-asin clear-num frac-2neg swap-sqr div-inv associate-/l* unswap-sqr
Counts
4 → 127
Calls
4 calls:
Slowest
349.0ms
(/ (* (* (cos 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))))
79.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
5.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos 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)))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos 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))))))

series934.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
624.0ms
(/ (* (* (cos 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))))
168.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos 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)))))) R)
97.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
43.0ms
(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos 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))))))

simplify22.7s

Counts
110 → 139
Calls
110 calls:
Slowest
1.6s
(/ (* (* (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))) (* (* (cos 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))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
1.3s
(/ (* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))) (* (* (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
1.3s
(/ (* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))) (* (* (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
801.0ms
(* (* (* (* (cos lambda1) (cos lambda1)) (cos lambda1)) (* (* (cos lambda2) (cos lambda2)) (cos lambda2))) (* (* (* (cos lambda1) (cos lambda1)) (cos lambda1)) (* (* (cos lambda2) (cos lambda2)) (cos lambda2))))
699.0ms
(* (* (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (cos lambda1) (cos lambda2))) (* (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (cos lambda1) (cos lambda2))))

prune3.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.6b

regimes2.5s

Accuracy

0% (0.4b remaining)

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

bsearch7.0ms

end0.0ms

sample24.3s

Algorithm
intervals
Results
17.6s4744×body1280valid
4.9s2087×body640valid
1.1s743×body320valid
290.0ms280×body160valid
57.0ms11×body2560valid
56.0ms144×body80valid