Details

sample701.0ms

Algorithm

intervals

Results

388.0ms	146×	body	1280	valid
157.0ms	71×	body	640	valid
19.0ms	25×	body	320	valid
7.0ms	11×	body	160	valid
1.0ms	3×	body	80	valid

simplify51.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (13.0ms)

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

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.1b	(cos (- lambda1 lambda2))

rewrite61.0ms

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:

28.0ms	(* (sin phi1) (sin phi2))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

series193.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin phi1) (sin phi2))
73.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
37.0ms	(cos (- lambda1 lambda2))

simplify4.4s

Counts

84 → 84

Iterations

Useful iterations: 5 (1.7s)

Iter	Nodes	Cost
0	187	1607
1	316	1393
2	597	1170
3	942	1127
4	1247	1054
5	1907	990
6	3847	990
done	5001	990

prune664.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.0b

localize74.0ms

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)
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite70.0ms

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:

23.0ms	(* (sin lambda1) (sin (- lambda2)))
25.0ms	(* (sin phi1) (sin phi2))
15.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
5.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series326.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (sin lambda1) (sin (- lambda2)))
73.0ms	(* (sin phi1) (sin phi2))
154.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
21.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify6.6s

Counts

85 → 85

Iterations

Useful iterations: 3 (786.0ms)

Iter	Nodes	Cost
0	151	1621
1	281	1563
2	752	1366
3	1626	1254
4	3039	1254
done	5000	1254

prune760.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.8b

localize64.0ms

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)
0.4b	(pow (* (sin lambda1) (sin (- lambda2))) 3)
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))))
26.1b	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

rewrite60.0ms

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:

29.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3)))))) R)
19.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))))
7.0ms	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

series343.0ms

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)
120.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
38.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))))
83.0ms	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

simplify4.3s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	155	1959
1	322	1671
2	950	1479
3	4246	1365
done	5001	1365

prune759.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))
0.4b	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
0.9b	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
1.2b	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

0.0ms	(fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))
2.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
3.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

370.0ms	(fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))
45.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
13.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
14.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

simplify2.2s

Counts

64 → 64

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	90	1821
1	145	1772
2	280	1562
3	733	1561
4	3292	1560
done	5000	1559

prune396.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 4.8b

regimes1.3s

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	30
1	33	30
done	33	30

end0.0ms

sample19.1s

Algorithm

intervals

Results

13.2s	4778×	body	1280	valid
4.3s	2092×	body	640	valid
579.0ms	682×	body	320	valid
186.0ms	301×	body	160	valid
72.0ms	14×	body	2560	valid
37.0ms	135×	body	80	valid