Details

sample489.0ms

Algorithm

intervals

Results

290.0ms	128×	body	1280	valid
111.0ms	70×	body	640	valid
56.0ms	28×	body	320	valid
6.0ms	9×	body	160	valid
6.0ms	21×	body	80	valid

simplify38.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
2	23
1	20
0	14

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize70.0ms

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))
2.0b	(sin (- lambda1 lambda2))
2.0b	(cos (- lambda1 lambda2))

rewrite52.0ms

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))
30.0ms	(sin (- lambda1 lambda2))
20.0ms	(cos (- lambda1 lambda2))

series257.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
170.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
39.0ms	(sin (- lambda1 lambda2))
32.0ms	(cos (- lambda1 lambda2))

simplify2.5s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
4	2079
3	918
2	445
1	294
0	176

prune764.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.8b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (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))
2.0b	(cos (- lambda1 lambda2))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum` `prod-diff`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-r` `associate-l`
2×	`associate-*r/`
1×	`cos-diff` `flip3--` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `flip--` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

85.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (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))
27.0ms	(cos (- lambda1 lambda2))

series379.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (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)))
169.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
22.0ms	(cos (- lambda1 lambda2))

simplify2.6s

Counts

84 → 84

Iterations

Iter	Nodes
done	5006
3	2797
2	898
1	375
0	193

prune892.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (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))

rewrite89.0ms

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`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `prod-diff` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `fma-udef` `flip--` `sin-mult`

Counts

4 → 72

Calls

4 calls:

76.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (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)))
11.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series597.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
26.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
57.0ms	(* (sin lambda1) (sin lambda2))
296.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify2.5s

Counts

84 → 84

Iterations

Iter	Nodes
done	5009
3	3934
2	1100
1	352
0	152

prune815.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite144.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `prod-diff` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip3--` `flip-+` `flip--` `sin-mult`

Counts

4 → 76

Calls

4 calls:

89.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1)))
32.0ms	(* (sin lambda2) (sin lambda1))
21.0ms	(+ (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1))

series627.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
13.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1)))
63.0ms	(* (sin lambda2) (sin lambda1))
319.0ms	(+ (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1))

simplify3.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	4982
2	1187
1	406
0	165

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes781.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	33
1	33
0	26

end0.0ms

sample14.3s

Algorithm

intervals

Results

8.4s	3647×	body	1280	valid
4.0s	2303×	body	640	valid
1.3s	976×	body	320	valid
213.0ms	398×	body	160	valid
195.0ms	676×	body	80	valid