Details

sample623.0ms

Algorithm

intervals

Results

367.0ms	149×	body	1280	valid
116.0ms	66×	body	640	valid
25.0ms	28×	body	320	valid
5.0ms	1×	body	2560	valid
4.0ms	8×	body	160	valid
1.0ms	4×	body	80	valid

simplify40.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	17	19
1	27	18
2	38	18
3	44	18
4	46	18
done	46	18

prune49.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.8b	(cos (- lambda1 lambda2))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum`
9×	`prod-diff`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
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×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 72

Calls

4 calls:

34.0ms	(* (sin phi1) (sin phi2))
14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
31.0ms	(cos (- lambda1 lambda2))

series223.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sin phi1) (sin phi2))
80.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
26.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
45.0ms	(cos (- lambda1 lambda2))

simplify858.0ms

Counts

84 → 84

Iterations

Useful iterations: done (854.0ms)

Iter	Nodes	Cost
0	187	1607
1	335	1399
2	935	1174
done	5000	1127

prune662.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 73

Calls

4 calls:

25.0ms	(* (sin lambda1) (sin (- lambda2)))
17.0ms	(* (sin phi1) (sin phi2))
15.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin lambda1) (sin (- lambda2)))
74.0ms	(* (sin phi1) (sin phi2))
124.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
33.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify966.0ms

Counts

85 → 85

Iterations

Useful iterations: done (963.0ms)

Iter	Nodes	Cost
0	151	1621
1	304	1563
2	1186	1370
done	5000	1254

prune944.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.4b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3)))))) R)
0.3b	(pow (* (sin lambda1) (sin (- lambda2))) 3)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))))
28.6b	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `sin-mult` `rem-cube-cbrt` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `cbrt-div` `pow1/3` `cube-neg` `sin-neg` `*-commutative` `distribute-rgt-neg-out` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

9.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3)))))) R)
29.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))))
10.0ms	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

series323.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3)))))) R)
116.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
27.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))))
79.0ms	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

simplify1.2s

Counts

88 → 88

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	155	1959
1	377	1683
2	1596	1481
done	5001	1377

prune867.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (log1p (expm1 (acos (fma (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))) R)
0.5b	(expm1 (acos (fma (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))
0.6b	(acos (fma (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `expm1-log1p` `sin-mult` `expm1-udef`

Counts

4 → 62

Calls

4 calls:

22.0ms	(* (sin phi1) (sin phi2))
8.0ms	(* (log1p (expm1 (acos (fma (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))) R)
1.0ms	(expm1 (acos (fma (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))
1.0ms	(acos (fma (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin phi1) (sin phi2))
151.0ms	(* (log1p (expm1 (acos (fma (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))) R)
72.0ms	(expm1 (acos (fma (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))
28.0ms	(acos (fma (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2))))

simplify2.4s

Counts

74 → 74

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	111	1676
1	194	1612
2	570	1406
3	3099	1406
done	5001	1406

prune792.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.4b

regimes1.4s

Accuracy

0% (0.3b remaining)

Error of 3.8b against oracle of 3.5b and baseline of 3.8b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	28
1	28	28
done	28	28

end0.0ms

sample17.1s

Algorithm

intervals

Results

12.1s	4860×	body	1280	valid
3.1s	2103×	body	640	valid
1.0s	659×	body	320	valid
199.0ms	255×	body	160	valid
43.0ms	10×	body	2560	valid
25.0ms	115×	body	80	valid