Details

sample689.0ms

Algorithm

intervals

Results

409.0ms	167×	body	1280	valid
110.0ms	57×	body	640	valid
20.0ms	22×	body	320	valid
3.0ms	6×	body	160	valid
1.0ms	4×	body	80	valid

simplify25.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize92.0ms

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)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.7b	(cos (- lambda1 lambda2))

rewrite50.0ms

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×	`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 → 55

Calls

4 calls:

13.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
21.0ms	(cos (- lambda1 lambda2))

series213.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (sin phi1) (sin phi2))
73.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
24.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
31.0ms	(cos (- lambda1 lambda2))

simplify3.2s

Counts

67 → 67

Iterations

Iter	Nodes
done	5003
4	2877
3	1111
2	460
1	208
0	111

prune709.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.5b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite35.0ms

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×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 64

Calls

4 calls:

10.0ms	(* (sin phi1) (sin phi2))
16.0ms	(* (sin lambda1) (sin lambda2))
6.0ms	(* (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))))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin phi1) (sin phi2))
84.0ms	(* (sin lambda1) (sin lambda2))
111.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify3.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
4	3001
3	1446
2	622
1	277
0	134

prune995.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.4b

localize89.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.7b	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

14.0ms	(* (sin lambda1) (sin lambda2))
34.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
1.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sin lambda1) (sin lambda2))
121.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
92.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify4.2s

Counts

73 → 73

Iterations

Iter	Nodes
done	5011
5	4469
4	2300
3	1157
2	520
1	243
0	124

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.4b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.9b	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
3.6b	(log (exp (* (sin phi1) (sin phi2))))

rewrite55.0ms

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`
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 → 59

Calls

4 calls:

20.0ms	(* (sin lambda1) (sin lambda2))
21.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
5.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
7.0ms	(log (exp (* (sin phi1) (sin phi2))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin lambda1) (sin lambda2))
123.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
33.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
74.0ms	(log (exp (* (sin phi1) (sin phi2))))

simplify3.0s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
4	2857
3	1293
2	526
1	232
0	121

prune719.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.4b

regimes1.8s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample17.4s

Algorithm

intervals

Results

11.6s	4738×	body	1280	valid
4.4s	2174×	body	640	valid
707.0ms	676×	body	320	valid
172.0ms	262×	body	160	valid
52.0ms	12×	body	2560	valid
36.0ms	142×	body	80	valid