Details

sample804.0ms

Algorithm

intervals

Results

420.0ms	144×	body	1280	valid
198.0ms	76×	body	640	valid
16.0ms	19×	body	320	valid
6.0ms	12×	body	160	valid
3.0ms	1×	body	2560	valid
1.0ms	4×	body	80	valid

simplify125.0ms

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize117.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.9b	(cos (- lambda1 lambda2))
2.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

rewrite98.0ms

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:

41.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
20.0ms	(cos (- lambda1 lambda2))
24.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series622.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
269.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
49.0ms	(cos (- lambda1 lambda2))
85.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify6.5s

Counts

73 → 73

Iterations

Iter	Nodes
done	5003
3	3195
2	837
1	281
0	125

prune1.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.1b

localize167.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
0.2b	(* (* (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)
2.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

69.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
66.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
20.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
6.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

300.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
268.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
416.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
104.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify3.5s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1544
1	447
0	172

prune2.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 5.9b

localize185.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (cos lambda1) (cos 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)
2.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (* (sin lambda1) (sin lambda2)) (cos phi1)) (cos phi2)))))

rewrite174.0ms

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:

34.0ms	(* (sin lambda1) (sin lambda2))
108.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
19.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (* (sin lambda1) (sin lambda2)) (cos phi1)) (cos phi2))))) R)
5.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (* (sin lambda1) (sin lambda2)) (cos phi1)) (cos phi2)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (sin lambda1) (sin lambda2))
331.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
439.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (* (sin lambda1) (sin lambda2)) (cos phi1)) (cos phi2))))) R)
113.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (* (sin lambda1) (sin lambda2)) (cos phi1)) (cos phi2)))))

simplify8.7s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
3	4624
2	1183
1	400
0	168

prune2.5s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 5.9b

localize150.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (acos (+ (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))))
0.3b	(* (exp (log (acos (+ (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))) R)
0.7b	(log (acos (+ (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
2.0b	(acos (+ (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`log-prod` `*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
7×	`exp-sum`
6×	`add-cbrt-cube` `associate-l` `add-exp-log`
4×	`exp-prod` `insert-posit16` `add-log-exp`
3×	`associate-r`
2×	`log-pow` `unswap-sqr`
1×	`acos-asin` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log`

Counts

4 → 61

Calls

4 calls:

5.0ms	(exp (log (acos (+ (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))))
38.0ms	(* (exp (log (acos (+ (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))) R)
2.0ms	(log (acos (+ (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
4.0ms	(acos (+ (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))

series1.0s

Counts

4 → 12

Calls

4 calls:

109.0ms	(exp (log (acos (+ (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))))
473.0ms	(* (exp (log (acos (+ (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))) R)
315.0ms	(log (acos (+ (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
110.0ms	(acos (+ (* (cos phi2) (* (cos phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))

simplify8.2s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
5	3349
4	1688
3	898
2	415
1	189
0	105

prune1.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 5.9b

regimes6.9s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify19.0ms

Iterations

Iter	Nodes
done	38
1	38
0	27

end0.0ms

sample19.2s

Algorithm

intervals

Results

13.5s	4823×	body	1280	valid
4.1s	2129×	body	640	valid
633.0ms	633×	body	320	valid
128.0ms	257×	body	160	valid
69.0ms	12×	body	2560	valid
38.0ms	147×	body	80	valid