Details

sample614.0ms

Algorithm

intervals

Results

422.0ms	160×	body	1280	valid
70.0ms	60×	body	640	valid
14.0ms	20×	body	320	valid
6.0ms	12×	body	160	valid
1.0ms	4×	body	80	valid

simplify36.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.0b	(cos (- lambda1 lambda2))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `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 → 57

Calls

4 calls:

42.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(* (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)))))
48.0ms	(cos (- lambda1 lambda2))

series324.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
101.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
39.0ms	(cos (- lambda1 lambda2))

simplify1.8s

Counts: 69 → 69

prune472.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.1b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.4b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`*-commutative` `sin-mult`
2×	`cos-mult` `unswap-sqr`
1×	`acos-asin` `frac-times` `associate-r/` `associate-l/`

Counts

4 → 70

Calls

4 calls:

17.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
67.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series412.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin lambda1) (sin lambda2))
117.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
186.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
42.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify775.0ms

Counts: 82 → 82

prune659.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.3b	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
0.8b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
1.4b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
16×	`add-exp-log` `add-cbrt-cube`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`add-log-exp`
4×	`log-pow`
3×	`acos-asin` `log-prod`
2×	`exp-diff` `cos-mult` `sin-mult`
1×	`frac-times` `log-div` `associate-r/` `rem-log-exp` `associate-r` `associate-l` `associate-l/` `*-commutative` `rem-exp-log`

Counts

4 → 61

Calls

4 calls:

69.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
7.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
11.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
108.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
27.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
21.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify2.4s

Counts: 73 → 73

prune648.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (* (cos phi2) (sin lambda2)))
0.2b	(* (* 1 (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))) R)
0.2b	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2))))
1.4b	(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
23×	`pow1` `add-cbrt-cube`
14×	`prod-exp`
12×	`pow-prod-down` `cbrt-unprod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*`
5×	`associate-r`
4×	`add-log-exp`
3×	`*-commutative`
1×	`acos-asin` `1-exp`

Counts

4 → 66

Calls

4 calls:

37.0ms	(* (cos phi1) (* (cos phi2) (sin lambda2)))
25.0ms	(* (* 1 (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))) R)
90.0ms	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2))))
6.0ms	(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

series447.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (cos phi1) (* (cos phi2) (sin lambda2)))
125.0ms	(* (* 1 (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))) R)
181.0ms	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2))))
33.0ms	(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

simplify2.2s

Counts: 78 → 78

prune582.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.0b

regimes1.9s

Accuracy

0% (0.4b remaining)

Error of 3.6b against oracle of 3.3b and baseline of 3.6b

bsearch0.0ms

simplify1.3s

end0.0ms

sample18.3s

Algorithm

intervals

Results

12.9s	4891×	body	1280	valid
2.8s	2078×	body	640	valid
1.2s	640×	body	320	valid
431.0ms	7×	body	2560	valid
187.0ms	263×	body	160	valid
32.0ms	128×	body	80	valid