Details

sample755.0ms

Algorithm

intervals

Results

420.0ms	160×	body	1280	valid
143.0ms	57×	body	640	valid
62.0ms	7×	body	160	valid
29.0ms	24×	body	320	valid
11.0ms	2×	body	2560	valid
2.0ms	6×	body	80	valid

simplify94.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (12.0ms)

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.0b	(cos (- lambda1 lambda2))

rewrite133.0ms

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:

81.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(* (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)))))
29.0ms	(cos (- lambda1 lambda2))

series283.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
77.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
23.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
46.0ms	(cos (- lambda1 lambda2))

simplify1.3s

Counts

86 → 86

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	197	1807
1	404	1595
2	1608	1331
done	5001	1299

prune719.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (sin lambda1) (sin lambda2))
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`acos-asin` `frac-times` `associate-r/` `associate-l/` `sin-mult`

Counts

4 → 78

Calls

4 calls:

7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
61.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
20.0ms	(* (sin lambda1) (sin lambda2))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series424.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
190.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
68.0ms	(* (sin lambda1) (sin lambda2))
36.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify1.2s

Counts

90 → 90

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	166	2079
1	397	1783
2	1599	1442
done	5000	1437

prune753.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))) R)
0.3b	(* (sin lambda1) (sin lambda2))
0.6b	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
1.5b	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

49.0ms	(* (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))) R)
14.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))) R)
79.0ms	(* (sin lambda1) (sin lambda2))
40.0ms	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
13.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

simplify4.1s

Counts

81 → 81

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	114	1949
1	202	1882
2	575	1638
3	3839	1634
done	5000	1632

prune876.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(expm1 (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
0.6b	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
1.1b	(log1p (expm1 (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))))
1.5b	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

1.0ms	(expm1 (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
2.0ms	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
0.0ms	(log1p (expm1 (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(expm1 (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
77.0ms	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
162.0ms	(log1p (expm1 (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))))
26.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

simplify4.0s

Counts

58 → 58

Iterations

Useful iterations: 5 (687.0ms)

Iter	Nodes	Cost
0	65	1695
1	92	1662
2	156	1456
3	301	1456
4	725	1454
5	2918	1452
done	5000	1452

prune485.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.5b

regimes954.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	26
1	26	26
done	26	26

end0.0ms

sample17.7s

Algorithm

intervals

Results

12.9s	4733×	body	1280	valid
3.0s	2153×	body	640	valid
536.0ms	659×	body	320	valid
513.0ms	305×	body	160	valid
41.0ms	143×	body	80	valid
32.0ms	7×	body	2560	valid