Details

sample262.0ms

Algorithm

intervals

Results

187.0ms	160×	body	1280	valid
42.0ms	59×	body	640	valid
9.0ms	22×	body	320	valid
2.0ms	8×	body	160	valid
1.0ms	7×	body	80	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	19
1	27	18
2	38	18
3	43	18
done	43	18

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.9b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.4b	(cos (- lambda1 lambda2))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `add-exp-log` `cos-sum` `add-cbrt-cube`
9×	`prod-diff`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

31.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
16.0ms	(cos (- lambda1 lambda2))

series185.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
45.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
13.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
19.0ms	(cos (- lambda1 lambda2))

simplify5.0s

Counts

86 → 86

Iterations

Useful iterations: done (5.0s)

Iter	Nodes	Cost
0	196	1763
1	377	1589
2	962	1325
3	2320	1281
4	3808	1190
done	5001	1144

prune377.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
0.2b	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.0b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `cos-mult`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
2×	`sub-neg` `flip3--` `prod-diff` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`acos-asin` `associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 87

Calls

4 calls:

16.0ms	(* (sin lambda1) (sin (- lambda2)))
86.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
7.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))

series350.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sin lambda1) (sin (- lambda2)))
221.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
57.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))) R)
14.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))

simplify883.0ms

Counts

99 → 99

Iterations

Useful iterations: done (880.0ms)

Iter	Nodes	Cost
0	205	2400
1	482	2347
2	1724	1919
done	5000	1885

prune605.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))))
0.2b	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))) R)
0.6b	(log (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))
1.0b	(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `log-prod` `*-un-lft-identity`
8×	`pow1`
7×	`exp-sum`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`log-pow` `unswap-sqr`
1×	`acos-asin` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log`

Counts

4 → 65

Calls

4 calls:

3.0ms	(exp (log (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))))
18.0ms	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))) R)
1.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))

series122.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(exp (log (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))))
53.0ms	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))) R)
38.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))
15.0ms	(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))

simplify2.4s

Counts

77 → 77

Iterations

Useful iterations: 4 (301.0ms)

Iter	Nodes	Cost
0	95	2371
1	144	2269
2	278	1957
3	537	1957
4	817	1951
5	1310	1951
6	2784	1951
done	5001	1951

prune502.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))
0.6b	(log (log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))))
0.7b	(log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))))
1.0b	(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`log-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `exp-prod` `*-un-lft-identity` `log-pow`
7×	`pow1`
5×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`acos-asin`
2×	`exp-diff` `rem-log-exp`
1×	`log-div` `rem-exp-log`

Counts

4 → 60

Calls

4 calls:

2.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))
3.0ms	(log (log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))))
3.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))

series100.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))
40.0ms	(log (log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))))
13.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))))
13.0ms	(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))

simplify1.5s

Counts

72 → 72

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	87	2213
1	113	2118
2	151	1872
3	264	1872
4	433	1872
5	639	1872
6	988	1872
7	2338	1872
done	5001	1870

prune417.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.7b

regimes725.0ms

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	30
1	30	30
done	30	30

end0.0ms

sample7.9s

Algorithm

intervals

Results

5.6s	4801×	body	1280	valid
1.4s	2112×	body	640	valid
287.0ms	654×	body	320	valid
79.0ms	298×	body	160	valid
30.0ms	9×	body	2560	valid
18.0ms	128×	body	80	valid