Details

sample610.0ms

Algorithm

intervals

Results

335.0ms	140×	body	1280	valid
137.0ms	78×	body	640	valid
23.0ms	27×	body	320	valid
4.0ms	8×	body	160	valid
1.0ms	4×	body	80	valid

simplify85.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

84.0ms

(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize84.0ms

Local error

Found 4 expressions with local error:

4.5b	(cos (- lambda1 lambda2))
0.6b	(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))

rewrite46.0ms

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

20.0ms	(* (sin phi1) (sin phi2))
12.0ms	(cos (- lambda1 lambda2))
10.0ms	(* (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)))))

series178.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

71.0ms	(* (sin phi1) (sin phi2))
59.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
36.0ms	(cos (- lambda1 lambda2))
11.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.6s

Counts

35 → 71

Calls

35 calls:

Slowest

410.0ms	(* (* (* (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))
277.0ms	(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
114.0ms	(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
76.0ms	(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (sqrt R))
69.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.1b

localize81.0ms

Local error

Found 4 expressions with local error:

0.6b	(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))

rewrite38.0ms

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

19.0ms	(* (sin lambda1) (sin lambda2))
11.0ms	(* (sin phi1) (sin phi2))
5.0ms	(* (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))))))

series265.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

115.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
63.0ms	(* (sin phi1) (sin phi2))
59.0ms	(* (sin lambda1) (sin lambda2))
29.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify3.8s

Counts

43 → 80

Calls

43 calls:

Slowest

388.0ms	(* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2)))
338.0ms	(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
286.0ms	(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (sqrt R))
286.0ms	(* (* (* (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))))))) (* (* R R) R))
255.0ms	(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (sqrt R))

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.6b	(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)))))))
0.4b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.3b	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)

rewrite47.0ms

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

26.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
10.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
6.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series186.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

79.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
70.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
23.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify7.8s

Counts

37 → 74

Calls

37 calls:

Slowest

575.0ms	(exp (acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2))))))
389.0ms	(exp (* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
305.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
302.0ms	(* (* (* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) (* (* R R) R))
288.0ms	(sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

prune2.0s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 4.9b

localize101.0ms

Local error

Found 4 expressions with local error:

24.4b	(cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2))))
0.6b	(acos (+ (cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.3b	(* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2)))
0.3b	(* (acos (+ (cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
18×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
16×	`sin-mult`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
7×	`cbrt-div`
6×	`frac-times` `-un-lft-identity` `associate-l/` `add-cube-cbrt`
4×	`associate-r` `associate-l` `associate-*r/` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
2×	`pow-plus` `*-commutative`
1×	`cbrt-prod` `pow2` `acos-asin` `pow1/3` `swap-sqr` `pow3` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

Slowest

142.0ms	(cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2))))
50.0ms	(* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2)))
11.0ms	(* (acos (+ (cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

83.0ms	(cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2))))
79.0ms	(* (acos (+ (cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
74.0ms	(* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2)))
31.0ms	(acos (+ (cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify7.7s

Counts

67 → 96

Calls

67 calls:

Slowest

856.0ms	(* (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2))) (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2))))
715.0ms	(* (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2))) (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2))))
297.0ms	(cbrt (* (* (- (cos (- phi1 phi2)) (cos (+ phi1 phi2))) (- (cos (- phi1 phi2)) (cos (+ phi1 phi2)))) (- (cos (- phi1 phi2)) (cos (+ phi1 phi2)))))
282.0ms	(cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (- (cos (- phi1 phi2)) (cos (+ phi1 phi2)))))
276.0ms	(* (acos (+ (cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)

prune2.4s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 4.9b

regimes1.4s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch11.0ms

end0.0ms

sample24.8s

Algorithm

intervals

Results

18.6s	4699×	body	1280	valid
4.5s	2179×	body	640	valid
1.0s	671×	body	320	valid
296.0ms	301×	body	160	valid
77.0ms	13×	body	2560	valid
54.0ms	140×	body	80	valid