Details

Time bar (total: 1.5m)

sample1.5s

Algorithm
intervals
Results
706.0ms75×body640valid
494.0ms139×body1280valid
42.0ms28×body320valid
10.0ms11×body160valid
1.0ms3×body80valid

simplify56.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
55.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize52.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (- lambda1 lambda2))
1.0b
(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))

rewrite32.0ms

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
11.0ms
(* (sin phi1) (sin phi2))
10.0ms
(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)))))

series219.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
74.0ms
(* (sin phi1) (sin phi2))
72.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
53.0ms
(cos (- lambda1 lambda2))
20.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify4.3s

Counts
75 → 71
Calls
75 calls:
Slowest
570.0ms
(* (* (* (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))
431.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
351.0ms
(* (* (* (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
(* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))
194.0ms
(exp (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R))

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.8b

localize86.0ms

Local error

Found 4 expressions with local error:

1.0b
(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
(* (sin lambda1) (sin lambda2))

rewrite48.0ms

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))
19.0ms
(* (sin lambda1) (sin lambda2))
6.0ms
(* (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))))))

series233.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
89.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
65.0ms
(* (sin lambda1) (sin lambda2))
64.0ms
(* (sin phi1) (sin phi2))
16.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify9.8s

Counts
81 → 80
Calls
81 calls:
Slowest
424.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
412.0ms
(exp (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R))
380.0ms
(* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2)))
358.0ms
(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R) (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)) (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R))
299.0ms
(* (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

prune2.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.7b

localize114.0ms

Local error

Found 4 expressions with local error:

1.0b
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))
0.3b
(* R (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))
0.2b
(* (sin phi2) (sin phi1))
0.2b
(* (sin lambda1) (sin lambda2))

rewrite70.0ms

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 lambda1) (sin lambda2))
22.0ms
(* (sin phi2) (sin phi1))
13.0ms
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))
11.0ms
(* R (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))

series208.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
73.0ms
(* (sin lambda1) (sin lambda2))
59.0ms
(* (sin phi2) (sin phi1))
54.0ms
(* R (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))
22.0ms
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))

simplify12.8s

Counts
81 → 80
Calls
81 calls:
Slowest
500.0ms
(log (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))
488.0ms
(real->posit16 (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))
475.0ms
(real->posit16 (* R (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))))
459.0ms
(* (sqrt R) (sqrt (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))))
444.0ms
(exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.6b

localize89.0ms

Local error

Found 4 expressions with local error:

1.0b
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))
0.7b
(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))))
0.4b
(exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))
0.3b
(* R (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
9×log-prod exp-prod
8×pow1 log-pow
7×associate-*r*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×insert-posit16
3×distribute-rgt-in acos-asin distribute-lft-in associate-*l*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 68
Calls
4 calls:
Slowest
18.0ms
(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))))
12.0ms
(* R (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))))
4.0ms
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))
3.0ms
(exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))

series531.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
441.0ms
(exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))
57.0ms
(* R (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))))
17.0ms
(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))))
15.0ms
(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))

simplify28.5s

Counts
90 → 80
Calls
90 calls:
Slowest
529.0ms
(* R (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))))
491.0ms
(* R (log (cbrt (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))))))
474.0ms
(* R (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2))))))))
473.0ms
(* (log (cbrt (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))))) R)
472.0ms
(asin (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))) (cos phi2)))))

prune2.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.6b

regimes1.2s

Accuracy

0% (0.5b remaining)

Error of 4.0b against oracle of 3.5b and baseline of 4.0b

bsearch8.0ms

end0.0ms

sample24.2s

Algorithm
intervals
Results
17.2s4782×body1280valid
4.9s2151×body640valid
952.0ms660×body320valid
456.0ms135×body80valid
244.0ms270×body160valid
64.0ms9×body2560valid