Details

sample457.0ms

Algorithm

intervals

Results

263.0ms	115×	body	1280	valid
110.0ms	74×	body	640	valid
49.0ms	34×	body	320	valid
8.0ms	12×	body	160	valid
6.0ms	21×	body	80	valid

simplify19.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
2	23
1	20
0	14

prune72.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.5b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.1b	(cos (- lambda1 lambda2))
3.2b	(sin (- lambda1 lambda2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
16×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum` `sin-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg`
1×	`cos-diff` `sin-diff` `fma-udef`

Counts

4 → 65

Calls

4 calls:

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

series213.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
148.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
19.0ms	(cos (- lambda1 lambda2))
37.0ms	(sin (- lambda1 lambda2))

simplify1.0s

Counts

77 → 77

Iterations

Iter	Nodes
done	2003
4	2003
3	909
2	445
1	294
0	176

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.1b

localize77.0ms

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)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.5b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.1b	(cos (- lambda1 lambda2))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

22.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
19.0ms	(cos (- lambda1 lambda2))

series278.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin lambda1) (cos lambda2))
11.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
161.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
38.0ms	(cos (- lambda1 lambda2))

simplify1.4s

Counts

77 → 77

Iterations

Iter	Nodes
done	2003
4	2003
3	1534
2	623
1	336
0	184

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

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

rewrite26.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-udef` `sin-cos-mult` `sin-mult`

Counts

4 → 65

Calls

4 calls:

11.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
14.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series508.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin lambda1) (cos lambda2))
25.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
83.0ms	(* (sin lambda1) (sin lambda2))
339.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify1.2s

Counts

77 → 77

Iterations

Iter	Nodes
done	2008
4	2008
3	1730
2	620
1	279
0	136

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize125.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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-mult` `unswap-sqr` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

2.0ms	(exp (fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)))
17.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1))
4.0ms	(log (exp (fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1))))

series1.1s

Counts

4 → 12

Calls

4 calls:

363.0ms	(exp (fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)))
82.0ms	(* (sin lambda1) (sin lambda2))
329.0ms	(fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1))
278.0ms	(log (exp (fma (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1))))

simplify1.3s

Counts

79 → 79

Iterations

Iter	Nodes
done	2006
4	2006
3	1690
2	535
1	239
0	120

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes875.0ms

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

sample15.1s

Algorithm

intervals

Results

8.9s	3598×	body	1280	valid
4.5s	2305×	body	640	valid
938.0ms	939×	body	320	valid
284.0ms	448×	body	160	valid
176.0ms	710×	body	80	valid