Details

sample509.0ms

Algorithm

intervals

Results

306.0ms	114×	body	1280	valid
129.0ms	74×	body	640	valid
40.0ms	38×	body	320	valid
7.0ms	22×	body	80	valid
6.0ms	8×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
2	23
1	20
0	14

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.3b	(cos (- lambda1 lambda2))
4.4b	(sin (- lambda1 lambda2))

rewrite438.0ms

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)))))
14.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
405.0ms	(cos (- lambda1 lambda2))
17.0ms	(sin (- lambda1 lambda2))

series258.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
169.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
30.0ms	(cos (- lambda1 lambda2))
40.0ms	(sin (- lambda1 lambda2))

simplify1.5s

Counts

85 → 85

Iterations

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

prune986.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
4.4b	(sin (- lambda1 lambda2))

rewrite54.0ms

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:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
25.0ms	(* (sin lambda1) (sin lambda2))
14.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
13.0ms	(sin (- lambda1 lambda2))

series469.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
85.0ms	(* (sin lambda1) (sin lambda2))
316.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
40.0ms	(sin (- lambda1 lambda2))

simplify1.1s

Counts

85 → 85

Iterations

Iter	Nodes
done	2002
3	2002
2	957
1	408
0	200

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize111.0ms

Local error

Found 4 expressions with local error:

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

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

126.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
24.0ms	(* (sin lambda1) (cos lambda2))
29.0ms	(* (sin lambda1) (sin lambda2))
28.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series744.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
84.0ms	(* (sin lambda1) (cos lambda2))
89.0ms	(* (sin lambda1) (sin lambda2))
365.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.4s

Counts

104 → 104

Iterations

Iter	Nodes
done	2004
3	2004
2	1574
1	466
0	184

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize106.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(exp (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi1)))
0.6b	(fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi1))
0.6b	(log (exp (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi1))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`exp-prod` `add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-prod` `log-pow` `insert-posit16` `log1p-expm1-u`
3×	`associate-r` `associate-l` `fma-udef`
2×	`exp-sum`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-cos-mult` `unswap-sqr` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

23.0ms	(* (sin lambda1) (cos lambda2))
4.0ms	(exp (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi1)))
0.0ms	(fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi1))
5.0ms	(log (exp (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi1))))

series1.1s

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sin lambda1) (cos lambda2))
419.0ms	(exp (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi1)))
302.0ms	(fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi1))
331.0ms	(log (exp (fma (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi1))))

simplify1.6s

Counts

79 → 79

Iterations

Iter	Nodes
done	2010
4	2010
3	1911
2	583
1	263
0	129

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes867.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample15.1s

Algorithm

intervals

Results

8.0s	3625×	body	1280	valid
4.8s	2310×	body	640	valid
1.6s	976×	body	320	valid
269.0ms	410×	body	160	valid
205.0ms	679×	body	80	valid