Details

sample994.0ms

Algorithm

intervals

Results

511.0ms	147×	body	1280	valid
139.0ms	69×	body	640	valid
139.0ms	26×	body	320	valid
7.0ms	8×	body	160	valid
2.0ms	6×	body	80	valid

simplify82.0ms

Counts: 1 → 1

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize97.0ms

Local error

Found 4 expressions with local error:

3.4b	(cos (- lambda1 lambda2))
0.8b	(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	(* (sin phi1) (sin phi2))

rewrite57.0ms

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))
18.0ms	(cos (- lambda1 lambda2))
10.0ms	(* (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)))))

series247.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

90.0ms	(* (sin phi1) (sin phi2))
80.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
56.0ms	(cos (- lambda1 lambda2))
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.5s

Counts: 71 → 71

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.6b

localize78.0ms

Local error

Found 4 expressions with local error:

0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (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))

rewrite64.0ms

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

28.0ms	(* (sin phi1) (sin phi2))
20.0ms	(* (sin lambda1) (sin lambda2))
11.0ms	(* (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))))))

series642.0ms

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)
80.0ms	(* (sin lambda1) (sin lambda2))
59.0ms	(* (sin phi1) (sin phi2))
28.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.1s

Counts: 80 → 80

prune2.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.5b

localize92.0ms

Local error

Found 4 expressions with local error:

0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.5b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.2b	(* (sin lambda1) (sin lambda2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`exp-prod` `add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`log-pow` `insert-posit16`
3×	`acos-asin` `log-prod` `associate-r` `associate-l`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr` `rem-exp-log`

Counts

4 → 59

Calls

4 calls:

Slowest

15.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
3.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series200.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

88.0ms	(* (sin lambda1) (sin lambda2))
74.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
22.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
16.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

simplify2.4s

Counts: 71 → 71

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.4b

localize132.0ms

Local error

Found 4 expressions with local error:

0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2)))))))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3`
1×	`acos-asin`

Counts

4 → 45

Calls

4 calls:

Slowest

4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2)))))))
2.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))
1.0ms	(cbrt (sin lambda2))

series516.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

169.0ms	(cbrt (sin lambda2))
164.0ms	(cbrt (sin lambda2))
157.0ms	(cbrt (sin lambda2))
25.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2)))))))

simplify1.2s

Counts: 57 → 57

prune1.5s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 3.4b

regimes1.1s

Accuracy

0% (0.5b remaining)

Error of 3.8b against oracle of 3.3b and baseline of 3.8b

bsearch15.0ms

end0.0ms

sample22.6s

Algorithm

intervals

Results

17.1s	4798×	body	1280	valid
3.8s	2056×	body	640	valid
977.0ms	712×	body	320	valid
281.0ms	302×	body	160	valid
50.0ms	126×	body	80	valid
50.0ms	9×	body	2560	valid