Details

sample474.0ms

Algorithm

intervals

Results

293.0ms	115×	body	1280	valid
116.0ms	85×	body	640	valid
31.0ms	29×	body	320	valid
6.0ms	11×	body	160	valid
4.0ms	16×	body	80	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
2	23
1	20
0	14

prune418.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.8b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.2b	(cos (- lambda1 lambda2))
2.4b	(sin (- lambda1 lambda2))

rewrite62.0ms

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)))))
28.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
12.0ms	(cos (- lambda1 lambda2))
19.0ms	(sin (- lambda1 lambda2))

series262.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
170.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
34.0ms	(cos (- lambda1 lambda2))
41.0ms	(sin (- lambda1 lambda2))

simplify1.4s

Counts

85 → 85

Iterations

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

prune930.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.6b

localize79.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.8b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.2b	(cos (- lambda1 lambda2))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

107.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
10.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
10.0ms	(cos (- lambda1 lambda2))

series454.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
23.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
165.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
32.0ms	(cos (- lambda1 lambda2))

simplify1.1s

Counts

92 → 92

Iterations

Iter	Nodes
done	2005
3	2005
2	1193
1	461
0	212

prune884.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize82.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.7b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite139.0ms

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×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `insert-posit16` `log1p-expm1-u`
3×	`fma-def`
2×	`associate-+r+` `sub-neg` `prod-diff` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `flip3--` `flip-+` `flip--` `sin-mult`

Counts

4 → 80

Calls

4 calls:

96.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
22.0ms	(* (sin 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))))))
18.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series709.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
58.0ms	(* (sin lambda1) (sin lambda2))
32.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
384.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.3s

Counts

92 → 92

Iterations

Iter	Nodes
done	2000
3	2000
2	1499
1	410
0	164

prune881.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))))
0.7b	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
0.7b	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
0.7b	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 46

Calls

4 calls:

20.0ms	(cbrt (* (* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))))
0.0ms	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
0.0ms	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
1.0ms	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))

series1.1s

Counts

4 → 12

Calls

4 calls:

269.0ms	(cbrt (* (* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))))
281.0ms	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
282.0ms	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
305.0ms	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))

simplify1.1s

Counts

58 → 58

Iterations

Iter	Nodes
done	2010
4	2010
3	729
2	202
1	91
0	53

prune661.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes936.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	31
1	31
0	24

end0.0ms

sample14.7s

Algorithm

intervals

Results

8.4s	3607×	body	1280	valid
3.7s	2345×	body	640	valid
1.2s	937×	body	320	valid
746.0ms	419×	body	160	valid
259.0ms	692×	body	80	valid