Details

sample969.0ms

Algorithm

intervals

Results

581.0ms	153×	body	1280	valid
230.0ms	71×	body	640	valid
21.0ms	17×	body	320	valid
9.0ms	10×	body	160	valid
2.0ms	5×	body	80	valid

simplify28.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	34
3	34
2	33
1	26
0	17

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize110.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (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)))))
3.8b	(cos (- lambda1 lambda2))

rewrite60.0ms

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:

22.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (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)))))
19.0ms	(cos (- lambda1 lambda2))

series216.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (sin phi1) (sin phi2))
55.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
57.0ms	(cos (- lambda1 lambda2))

simplify3.6s

Counts

71 → 71

Iterations

Iter	Nodes
6	4399
5	1944
4	1234
3	801
2	423
1	211
0	115

prune1.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.8b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

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:

21.0ms	(* (sin phi1) (sin phi2))
14.0ms	(* (sin lambda1) (sin lambda2))
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))))))

series225.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (sin phi1) (sin phi2))
63.0ms	(* (sin lambda1) (sin lambda2))
66.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.5s

Counts

80 → 80

Iterations

Iter	Nodes
4	2588
3	1402
2	628
1	281
0	138

prune2.0s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 2.6b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.3b	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
2.6b	(log (exp (* (sin phi1) (sin phi2))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

11.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
3.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
8.0ms	(log (exp (* (sin phi1) (sin phi2))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (sin lambda1) (sin lambda2))
106.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
29.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
65.0ms	(log (exp (* (sin phi1) (sin phi2))))

simplify1.3s

Counts

75 → 75

Iterations

Iter	Nodes
4	2299
3	1205
2	522
1	236
0	125

prune1.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 2.6b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (acos (+ (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (sin phi2) (sin phi1)))))) R)
0.4b	(exp (acos (+ (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (sin phi2) (sin phi1)))))
0.8b	(log (exp (acos (+ (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (sin phi2) (sin phi1))))))
1.3b	(acos (+ (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (sin phi2) (sin phi1))))

rewrite30.0ms

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:

14.0ms	(* (log (exp (acos (+ (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (sin phi2) (sin phi1)))))) R)
4.0ms	(exp (acos (+ (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (sin phi2) (sin phi1)))))
7.0ms	(log (exp (acos (+ (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (sin phi2) (sin phi1))))))
3.0ms	(acos (+ (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (sin phi2) (sin phi1))))

series183.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (log (exp (acos (+ (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (sin phi2) (sin phi1)))))) R)
51.0ms	(exp (acos (+ (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (sin phi2) (sin phi1)))))
32.0ms	(log (exp (acos (+ (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (sin phi2) (sin phi1))))))
20.0ms	(acos (+ (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (sin phi2) (sin phi1))))

simplify3.0s

Counts

74 → 74

Iterations

Iter	Nodes
6	3654
5	1307
4	796
3	623
2	392
1	193
0	109

prune1.7s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 2.6b

regimes3.0s

Accuracy

0% (0.5b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	34
1	34
0	25

end0.0ms

sample24.8s

Algorithm

intervals

Results

17.8s	4709×	body	1280	valid
5.1s	2157×	body	640	valid
1.1s	697×	body	320	valid
220.0ms	290×	body	160	valid
76.0ms	11×	body	2560	valid
56.0ms	138×	body	80	valid