Details

Time bar (total: 40.4s)

sample950.0ms

Algorithm
intervals
Results
556.0ms157×body1280valid
217.0ms62×body640valid
27.0ms25×body320valid
7.0ms9×body160valid
1.0ms3×body80valid

simplify72.0ms

Counts
1 → 1

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize77.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (- lambda1 lambda2))
1.2b
(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
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))

rewrite86.0ms

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
52.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms
(cos (- lambda1 lambda2))
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series273.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
53.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
43.0ms
(cos (- lambda1 lambda2))
19.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.0s

Counts
73 → 73

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.0b

localize89.0ms

Local error

Found 4 expressions with local error:

1.2b
(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
(* (sin lambda1) (sin lambda2))

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×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 phi1) (sin phi2))
21.0ms
(* (sin lambda1) (sin lambda2))
19.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series250.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
93.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
64.0ms
(* (sin phi1) (sin phi2))
62.0ms
(* (sin lambda1) (sin lambda2))
30.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.3s

Counts
80 → 80

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.7b

localize96.0ms

Local error

Found 4 expressions with local error:

25.1b
(cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))
1.2b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))))))
0.3b
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2)))))))) R)

rewrite217.0ms

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×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 → 84
Calls
4 calls:
Slowest
117.0ms
(cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))
83.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
11.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2)))))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))))))

series310.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2)))))))) R)
93.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
72.0ms
(cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))
26.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))))))

simplify1.5s

Counts
96 → 96

prune2.3s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 3.7b

localize62.0ms

Local error

Found 4 expressions with local error:

1.2b
(acos (+ (* (cos phi2) (* (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (sin phi1) (sin phi2))))
0.9b
(log (exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (sin phi1) (sin phi2))))))
0.4b
(exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (sin phi1) (sin phi2)))))
0.2b
(* (log (exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (sin phi1) (sin phi2)))))) R)

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×insert-posit16
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 62
Calls
4 calls:
Slowest
26.0ms
(* (log (exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (sin phi1) (sin phi2)))))) R)
14.0ms
(log (exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (sin phi1) (sin phi2))))))
5.0ms
(exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (sin phi1) (sin phi2)))))
3.0ms
(acos (+ (* (cos phi2) (* (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (sin phi1) (sin phi2))))

series173.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
94.0ms
(* (log (exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (sin phi1) (sin phi2)))))) R)
44.0ms
(exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (sin phi1) (sin phi2)))))
20.0ms
(log (exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (sin phi1) (sin phi2))))))
15.0ms
(acos (+ (* (cos phi2) (* (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (cos phi1))) (* (sin phi1) (sin phi2))))

simplify1.9s

Counts
74 → 74

prune1.5s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 3.7b

regimes1.4s

Accuracy

0% (0.4b remaining)

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

bsearch7.0ms

end0.0ms

sample22.0s

Algorithm
intervals
Results
14.7s4776×body1280valid
5.5s2157×body640valid
787.0ms654×body320valid
367.0ms9×body2560valid
186.0ms285×body160valid
43.0ms122×body80valid