Details

sample534.0ms

Algorithm

intervals

Results

290.0ms	109×	body	1280	valid
152.0ms	61×	body	640	valid
45.0ms	39×	body	320	valid
13.0ms	18×	body	160	valid
9.0ms	29×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
2	23
1	20
0	14

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.4b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.3b	(sin (- lambda1 lambda2))
3.4b	(cos (- lambda1 lambda2))

rewrite30.0ms

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))
18.0ms	(sin (- lambda1 lambda2))
9.0ms	(cos (- lambda1 lambda2))

series292.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
193.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
51.0ms	(sin (- lambda1 lambda2))
33.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
3	1619
2	623
1	294
0	176

prune698.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.4b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.4b	(cos (- lambda1 lambda2))

rewrite41.0ms

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` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

20.0ms	(* (cos lambda1) (sin 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))

series231.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (cos lambda1) (sin lambda2))
11.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
140.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
20.0ms	(cos (- lambda1 lambda2))

simplify2.4s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
3	4201
2	882
1	323
0	179

prune895.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin 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))
0.4b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

rewrite29.0ms

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-mult`

Counts

4 → 64

Calls

4 calls:

16.0ms	(* (cos lambda1) (sin 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)))
12.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series440.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos lambda1) (sin lambda2))
15.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
63.0ms	(* (sin lambda1) (sin lambda2))
309.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify886.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
2	949
1	279
0	132

prune676.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize88.0ms

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 lambda1) (cos lambda2))) (cos phi1)))))
0.2b	(exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
0.4b	(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))
0.6b	(log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))))

rewrite11.0ms

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 lambda1) (cos lambda2))) (cos phi1)))))
3.0ms	(exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
0.0ms	(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))
5.0ms	(log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))))

series1.1s

Counts

4 → 12

Calls

4 calls:

23.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
414.0ms	(exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
338.0ms	(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))
295.0ms	(log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))))

simplify2.0s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
3	2367
2	465
1	194
0	104

prune794.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes832.0ms

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

sample16.1s

Algorithm

intervals

Results

9.3s	3530×	body	1280	valid
4.4s	2364×	body	640	valid
1.5s	939×	body	320	valid
278.0ms	440×	body	160	valid
193.0ms	727×	body	80	valid