Details

sample355.0ms

Algorithm

intervals

Results

229.0ms	120×	body	1280	valid
67.0ms	75×	body	640	valid
18.0ms	29×	body	320	valid
6.0ms	13×	body	160	valid
4.0ms	19×	body	80	valid

simplify17.0ms

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: 0.7b

localize421.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.6b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
2.0b	(cos (- lambda1 lambda2))
2.1b	(sin (- lambda1 lambda2))

rewrite48.0ms

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))
22.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

series252.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
181.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
24.0ms	(cos (- lambda1 lambda2))
27.0ms	(sin (- lambda1 lambda2))

simplify2.4s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
4	2153
3	904
2	441
1	290
0	172

prune890.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.5b

localize79.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (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)))
0.6b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
2.0b	(cos (- lambda1 lambda2))

rewrite49.0ms

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` `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 → 61

Calls

4 calls:

25.0ms	(* (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))
20.0ms	(cos (- lambda1 lambda2))

series297.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin lambda1) (cos lambda2))
28.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
179.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
31.0ms	(cos (- lambda1 lambda2))

simplify2.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
4	3465
3	1518
2	622
1	332
0	180

prune918.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (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)))
0.3b	(* (sin lambda1) (sin lambda2))
0.6b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

rewrite50.0ms

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:

18.0ms	(* (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)))
28.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series507.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin lambda1) (cos lambda2))
35.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
72.0ms	(* (sin lambda1) (sin lambda2))
337.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify2.3s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	1812
2	626
1	275
0	132

prune944.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize129.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (cos phi1)))
0.3b	(* (sin lambda1) (sin lambda2))
0.6b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (cos phi1))
3.9b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (cos phi1)))
20.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (cos phi1))
7.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (cos phi1)))
81.0ms	(* (sin lambda1) (sin lambda2))
320.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (cos phi1))
67.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify2.1s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
3	1567
2	475
1	223
0	117

prune723.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes870.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	26
1	26
0	21

end0.0ms

sample11.8s

Algorithm

intervals

Results

7.2s	3592×	body	1280	valid
3.0s	2352×	body	640	valid
678.0ms	922×	body	320	valid
220.0ms	700×	body	80	valid
177.0ms	433×	body	160	valid
2.0ms	1×	body	2560	valid