Details

sample1.6s

Algorithm

intervals

Results

628.0ms	10×	body	160	valid
568.0ms	145×	body	1280	valid
177.0ms	73×	body	640	valid
29.0ms	23×	body	320	valid
2.0ms	5×	body	80	valid

simplify73.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

72.0ms

(* (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: 16.0b

localize52.0ms

Local error

Found 4 expressions with local error:

4.3b	(cos (- lambda1 lambda2))
1.1b	(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	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))

rewrite43.0ms

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

25.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(cos (- lambda1 lambda2))
5.0ms	(* (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)))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

148.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
72.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
35.0ms	(cos (- lambda1 lambda2))
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify2.9s

Counts

37 → 73

Calls

37 calls:

Slowest

626.0ms	(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
541.0ms	(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
503.0ms	(* (* (* (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))
157.0ms	(- 1 (+ (* 1/2 (pow phi2 2)) (* 1/2 (pow phi1 2))))
86.0ms	(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))

prune1.3s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.8b

localize95.0ms

Local error

Found 4 expressions with local error:

1.1b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
0.2b	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
0.2b	(* (sin phi1) (sin phi2))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
4×	`cos-mult` `insert-posit16` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`acos-asin` `frac-times` `associate-l/` `associate-r/` `sin-mult`

Counts

4 → 74

Calls

4 calls:

Slowest

80.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
12.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

196.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
88.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
84.0ms	(* (sin phi1) (sin phi2))
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify5.7s

Counts

49 → 86

Calls

49 calls:

Slowest

443.0ms	(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (* (* R R) R))
325.0ms	(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
261.0ms	(+ (log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (log R))
256.0ms	(* (* (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))))
255.0ms	(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (sqrt R))

prune2.3s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 3.7b

localize130.0ms

Local error

Found 4 expressions with local error:

1.1b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`*-commutative` `sin-mult`
2×	`cos-mult` `unswap-sqr`
1×	`acos-asin` `frac-times` `associate-l/` `associate-r/`

Counts

4 → 74

Calls

4 calls:

Slowest

55.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
21.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

171.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
81.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
67.0ms	(* (sin phi1) (sin phi2))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify5.6s

Counts

49 → 86

Calls

49 calls:

Slowest

431.0ms	(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (* (* R R) R))
325.0ms	(* (* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2))) (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))))
308.0ms	(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
272.0ms	(* (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))) (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))))
246.0ms	(* (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))) (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))))

prune2.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 3.6b

localize94.0ms

Local error

Found 4 expressions with local error:

1.1b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))
0.8b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))
0.3b	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))) R)

rewrite34.0ms

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

15.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))) R)
10.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))
6.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series188.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

76.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))
74.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))) R)
23.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify7.7s

Counts

37 → 74

Calls

37 calls:

Slowest

663.0ms	(exp (acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
474.0ms	(exp (* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))))
285.0ms	(cbrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))
275.0ms	(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
274.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi1)) (cos phi2)) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

prune1.9s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 3.6b

regimes3.4s

Accuracy

0% (0.5b remaining)

Error of 3.7b against oracle of 3.2b and baseline of 3.7b

bsearch10.0ms

end0.0ms

sample23.9s

Algorithm

intervals

Results

17.9s	4788×	body	1280	valid
4.4s	2073×	body	640	valid
888.0ms	702×	body	320	valid
248.0ms	288×	body	160	valid
84.0ms	143×	body	80	valid
61.0ms	11×	body	2560	valid