Details

sample945.0ms

Algorithm

intervals

Results

515.0ms	153×	body	1280	valid
149.0ms	67×	body	640	valid
79.0ms	25×	body	320	valid
4.0ms	1×	body	2560	valid
4.0ms	7×	body	160	valid
1.0ms	3×	body	80	valid

simplify42.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

41.0ms

(* (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: 18.1b

localize501.0ms

Local error

Found 4 expressions with local error:

4.3b	(cos (- lambda1 lambda2))
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

rewrite72.0ms

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

43.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))
5.0ms	(* (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)))))

series240.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

144.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
51.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
34.0ms	(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

573.0ms	(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
464.0ms	(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
422.0ms	(* (* (* (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))
204.0ms	(- 1 (+ (* 1/2 (pow phi2 2)) (* 1/2 (pow phi1 2))))
101.0ms	(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.0b

localize81.0ms

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))))))
0.2b	(* (* (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 lambda1) (sin lambda2))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
6×	`cos-mult`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-*l/`

Counts

4 → 76

Calls

4 calls:

Slowest

56.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
12.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
10.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series529.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

332.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
121.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
60.0ms	(* (sin lambda1) (sin lambda2))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify7.9s

Counts

54 → 88

Calls

54 calls:

Slowest

652.0ms	(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
554.0ms	(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (+ (* (+ (cos (+ lambda1 lambda2)) (cos (- lambda1 lambda2))) 2) (* 2 (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))))))
483.0ms	(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
393.0ms	(* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2)))
372.0ms	(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))

prune1.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.9b

localize131.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
11×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `cos-mult`
5×	`log-prod` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`frac-times` `associate-*r/` `log-pow`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `exp-sum` `frac-add` `*-commutative` `flip-+` `sin-mult`
1×	`acos-asin` `exp-prod` `exp-to-pow` `rem-log-exp` `associate-*l/` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

Slowest

73.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
14.0ms	(log (exp (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (log (exp (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (log (exp (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

series722.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

322.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
276.0ms	(log (exp (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
109.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (log (exp (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (log (exp (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

simplify9.6s

Counts

51 → 85

Calls

51 calls:

Slowest

615.0ms	(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (+ (* (+ (cos (+ lambda1 lambda2)) (cos (- lambda1 lambda2))) 2) (* 2 (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))))))
531.0ms	(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
445.0ms	(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
405.0ms	(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (log (exp (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) (acos (+ (* (sin phi1) (sin phi2)) (log (exp (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) (acos (+ (* (sin phi1) (sin phi2)) (log (exp (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) (* (* R R) R))
369.0ms	(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))

prune2.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.9b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

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

30.0ms	(* (sin lambda1) (sin lambda2))
21.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))))) R)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))))) R)
78.0ms	(* (sin phi1) (sin phi2))
70.0ms	(* (sin lambda1) (sin lambda2))
29.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))))

simplify5.4s

Counts

43 → 80

Calls

43 calls:

Slowest

676.0ms	(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))))) (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))))) (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))))) (* (* R R) R))
487.0ms	(+ (log (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))))) (log R))
469.0ms	(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))))) (sqrt R))
432.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))))) R)
407.0ms	(sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2))))))

prune1.7s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.8b

regimes1.4s

Accuracy

0% (0.4b remaining)

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

bsearch8.0ms

end0.0ms

sample23.5s

Algorithm

intervals

Results

16.6s	4811×	body	1280	valid
4.8s	2082×	body	640	valid
1.4s	693×	body	320	valid
195.0ms	266×	body	160	valid
87.0ms	140×	body	80	valid
50.0ms	9×	body	2560	valid