Details

sample908.0ms

Algorithm

intervals

Results

714.0ms	124×	body	1280	valid
135.0ms	75×	body	640	valid
22.0ms	21×	body	320	valid
11.0ms	18×	body	160	valid
6.0ms	18×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	23
2	23
1	20
0	14

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize99.0ms

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))
2.5b	(cos (- lambda1 lambda2))
2.6b	(sin (- lambda1 lambda2))

rewrite36.0ms

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` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg`
1×	`cos-diff` `sin-diff` `fma-udef`

Counts

4 → 61

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))
17.0ms	(cos (- lambda1 lambda2))
17.0ms	(sin (- lambda1 lambda2))

series261.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
187.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
30.0ms	(cos (- lambda1 lambda2))
35.0ms	(sin (- lambda1 lambda2))

simplify3.0s

Counts

73 → 73

Iterations

Iter	Nodes
5	4278
4	1549
3	738
2	403
1	279
0	172

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.8b

localize109.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.4b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
2.6b	(sin (- lambda1 lambda2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

11.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
1.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
17.0ms	(sin (- lambda1 lambda2))

series425.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin lambda1) (sin lambda2))
11.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
320.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
28.0ms	(sin (- lambda1 lambda2))

simplify3.1s

Counts

73 → 73

Iterations

Iter	Nodes
4	6330
3	1627
2	628
1	329
0	184

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize83.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

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` `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 → 61

Calls

4 calls:

22.0ms	(* (sin lambda1) (cos lambda2))
21.0ms	(* (sin 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)))
0.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series432.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sin lambda1) (cos lambda2))
77.0ms	(* (sin lambda1) (sin lambda2))
14.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
286.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify2.0s

Counts

73 → 73

Iterations

Iter	Nodes
4	4208
3	1485
2	605
1	274
0	132

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log1p (expm1 (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
0.2b	(log1p (expm1 (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))))
0.4b	(expm1 (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))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `fma-udef` `expm1-udef`

Counts

4 → 41

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log1p (expm1 (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
0.0ms	(log1p (expm1 (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))))
0.0ms	(expm1 (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))

series1.2s

Counts

4 → 12

Calls

4 calls:

13.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log1p (expm1 (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
392.0ms	(log1p (expm1 (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))))
455.0ms	(expm1 (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
294.0ms	(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))

simplify2.1s

Counts

53 → 53

Iterations

Iter	Nodes
4	4708
3	1164
2	409
1	183
0	90

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes709.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	28
1	28
0	23

end0.0ms

sample16.9s

Algorithm

intervals

Results

9.9s	3613×	body	1280	valid
5.0s	2397×	body	640	valid
1.1s	915×	body	320	valid
292.0ms	412×	body	160	valid
266.0ms	663×	body	80	valid