Details

sample523.0ms

Algorithm

intervals

Results

306.0ms	115×	body	1280	valid
152.0ms	74×	body	640	valid
23.0ms	21×	body	320	valid
13.0ms	18×	body	160	valid
8.0ms	28×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	23
2	23
1	20
0	14

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.5b	(sin (- lambda1 lambda2))
3.5b	(cos (- lambda1 lambda2))

rewrite38.0ms

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)))))
10.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
9.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

series211.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
131.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
42.0ms	(sin (- lambda1 lambda2))
25.0ms	(cos (- lambda1 lambda2))

simplify4.0s

Counts

85 → 85

Iterations

Iter	Nodes
4	5570
3	1787
2	705
1	365
0	195

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.9b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.5b	(cos (- lambda1 lambda2))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-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×	`cos-diff` `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` `*-commutative` `cbrt-unprod` `flip-+` `sin-cos-mult` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

11.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
16.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms	(cos (- lambda1 lambda2))

series219.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin lambda1) (cos lambda2))
14.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
125.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(cos (- lambda1 lambda2))

simplify960.0ms

Counts

85 → 85

Iterations

Iter	Nodes
3	2348
2	881
1	407
0	203

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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-cos-mult` `sin-mult`

Counts

4 → 73

Calls

4 calls:

16.0ms	(* (sin lambda1) (cos 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))))))
12.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sin lambda1) (cos lambda2))
15.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
87.0ms	(* (sin lambda1) (sin lambda2))
357.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.6s

Counts

85 → 85

Iterations

Iter	Nodes
3	4153
2	1022
1	345
0	148

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi1)))))
0.2b	(exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi1)))
0.6b	(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi1))
0.7b	(log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi1))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube` `add-exp-log` `log-pow` `insert-posit16` `log1p-expm1-u`
3×	`fma-udef`
2×	`exp-sum`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 55

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi1)))))
2.0ms	(exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi1)))
0.0ms	(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi1))
9.0ms	(log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi1))))

series931.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi1)))))
342.0ms	(exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi1)))
256.0ms	(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi1))
320.0ms	(log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi1))))

simplify4.5s

Counts

67 → 67

Iterations

Iter	Nodes
4	9501
3	1572
2	438
1	197
0	107

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes673.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
2	33
1	33
0	26

end0.0ms

sample15.5s

Algorithm

intervals

Results

8.9s	3592×	body	1280	valid
4.8s	2378×	body	640	valid
1.0s	951×	body	320	valid
267.0ms	417×	body	160	valid
173.0ms	662×	body	80	valid