Details

sample460.0ms

Algorithm

intervals

Results

286.0ms	109×	body	1280	valid
108.0ms	81×	body	640	valid
31.0ms	31×	body	320	valid
7.0ms	26×	body	80	valid
6.0ms	9×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
2	23
1	20
0	14

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.1b	(cos (- lambda1 lambda2))
5.2b	(sin (- lambda1 lambda2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
17×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum` `sin-sum`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`cos-diff` `fma-def`
2×	`associate-+r+` `sub-neg`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `flip3-+` `sin-diff` `flip-+`

Counts

4 → 73

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
13.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
10.0ms	(cos (- lambda1 lambda2))
10.0ms	(sin (- lambda1 lambda2))

series252.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
174.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
29.0ms	(cos (- lambda1 lambda2))
41.0ms	(sin (- lambda1 lambda2))

simplify1.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	2010
4	2010
3	1948
2	723
1	376
0	195

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.5b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
5.2b	(sin (- lambda1 lambda2))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`sin-sum`
9×	`prod-diff`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l`
2×	`associate-+r+`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `sub-neg` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

12.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
26.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
18.0ms	(sin (- lambda1 lambda2))

series451.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (sin lambda1) (sin lambda2))
25.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
315.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
29.0ms	(sin (- lambda1 lambda2))

simplify1.1s

Counts

85 → 85

Iterations

Iter	Nodes
done	2005
3	2005
2	931
1	408
0	200

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos lambda1) (sin lambda2))
0.3b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-def`
2×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `flip3-+` `flip-+` `sin-mult`

Counts

4 → 72

Calls

4 calls:

21.0ms	(* (sin lambda1) (sin lambda2))
16.0ms	(* (cos lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
9.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series600.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (sin lambda1) (sin lambda2))
83.0ms	(* (cos lambda1) (sin lambda2))
33.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
404.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	2010
3	2010
2	1006
1	350
0	145

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize113.0ms

Local error

Found 4 expressions with local error:

0.4b	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))
0.4b	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))
0.5b	(* (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)) (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)))
0.6b	(cbrt (* (* (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)) (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))) (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
1×	`cbrt-prod` `pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow1/3` `pow3` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `cbrt-unprod` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

0.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))
0.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))
11.0ms	(* (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)) (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)))
29.0ms	(cbrt (* (* (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)) (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))) (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))))

series1.2s

Counts

4 → 12

Calls

4 calls:

325.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))
311.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))
318.0ms	(* (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)) (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)))
292.0ms	(cbrt (* (* (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)) (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))) (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))))

simplify1.8s

Counts

77 → 77

Iterations

Iter	Nodes
done	2003
3	2003
2	484
1	183
0	86

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes649.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample15.2s

Algorithm

intervals

Results

9.1s	3428×	body	1280	valid
3.8s	2431×	body	640	valid
1.4s	956×	body	320	valid
316.0ms	454×	body	160	valid
179.0ms	731×	body	80	valid