Details

sample1.2s

Algorithm

intervals

Results

964.0ms	156×	body	1280	valid
119.0ms	64×	body	640	valid
30.0ms	23×	body	320	valid
9.0ms	10×	body	160	valid
1.0ms	3×	body	80	valid

simplify43.0ms

Counts

1 → 1

Iterations

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

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize53.0ms

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)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.8b	(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×	`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:

17.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (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)))))
10.0ms	(cos (- lambda1 lambda2))

series220.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sin phi1) (sin phi2))
77.0ms	(* (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)))))
45.0ms	(cos (- lambda1 lambda2))

simplify1.3s

Counts

71 → 71

Iterations

Iter	Nodes
done	2006
4	2006
3	1060
2	432
1	211
0	115

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.4b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (* (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)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite78.0ms

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:

10.0ms	(* (sin phi1) (sin phi2))
57.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series517.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (sin phi1) (sin phi2))
314.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
88.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
27.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	2035
3	2035
2	1881
1	518
0	187

prune2.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.3b

localize89.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
0.2b	(* (sin phi1) (sin 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)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

rewrite101.0ms

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×	`insert-posit16` `add-log-exp`
3×	`*-commutative` `sin-mult`
2×	`cos-mult` `unswap-sqr`
1×	`acos-asin` `frac-times` `associate-l/` `associate-r/`

Counts

4 → 74

Calls

4 calls:

69.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
17.0ms	(* (sin phi1) (sin phi2))
10.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
67.0ms	(* (sin phi1) (sin phi2))
93.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
31.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify1.3s

Counts

86 → 86

Iterations

Iter	Nodes
done	2000
3	2000
2	1104
1	376
0	161

prune2.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.2b

localize109.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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:

12.0ms	(* (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))))))) R)
3.0ms	(exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))))))
5.0ms	(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))))))
2.0ms	(acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))))

series188.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))))))) R)
50.0ms	(exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))))))
17.0ms	(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))))))
20.0ms	(acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))))

simplify1.8s

Counts

74 → 74

Iterations

Iter	Nodes
done	2000
5	2000
4	1266
3	798
2	413
1	191
0	109

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.2b

regimes1.9s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	42
1	42
0	30

end0.0ms

sample23.9s

Algorithm

intervals

Results

17.1s	4745×	body	1280	valid
4.6s	2109×	body	640	valid
1.5s	722×	body	320	valid
259.0ms	278×	body	160	valid
53.0ms	144×	body	80	valid
33.0ms	7×	body	2560	valid