Details

sample665.0ms

Algorithm

intervals

Results

419.0ms	159×	body	1280	valid
126.0ms	60×	body	640	valid
30.0ms	24×	body	320	valid
4.0ms	8×	body	160	valid
1.0ms	5×	body	80	valid

simplify95.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (14.0ms)

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.4b

localize56.0ms

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)
1.2b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.6b	(cos (- lambda1 lambda2))

rewrite84.0ms

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:

52.0ms	(* (* (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)))))
18.0ms	(cos (- lambda1 lambda2))

series350.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
98.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
21.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
48.0ms	(cos (- lambda1 lambda2))

simplify1.1s

Counts

86 → 86

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	196	1763
1	400	1595
2	1597	1331
done	5000	1299

prune645.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.4b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
0.3b	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.2b	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

51.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
7.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
75.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series626.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
149.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
200.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
32.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify1.5s

Counts

96 → 96

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	166	2336
1	416	2267
2	1822	1682
done	5000	1641

prune940.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.3b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))
0.3b	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))))) R)
0.6b	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))))
1.2b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

32.0ms	(* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))
37.0ms	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))))) R)
1.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

343.0ms	(* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))
88.0ms	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))))) R)
55.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))))
23.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))

simplify1.3s

Counts

83 → 83

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	143	2325
1	311	2252
2	1468	1929
done	5002	1926

prune942.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.3b

localize79.0ms

Local error

Found 4 expressions with local error:

0.3b	(expm1 (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))))
0.6b	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))))
0.8b	(log1p (expm1 (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))))))
1.2b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))

rewrite4.0ms

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

series243.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(expm1 (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))))
44.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))))
115.0ms	(log1p (expm1 (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))))))
15.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))

simplify2.7s

Counts

58 → 58

Iterations

Useful iterations: 5 (640.0ms)

Iter	Nodes	Cost
0	70	1695
1	100	1662
2	172	1456
3	339	1456
4	754	1454
5	2499	1452
done	5002	1452

prune929.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.2b

regimes1.2s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	28
1	30	28
done	30	28

end0.0ms

sample17.7s

Algorithm

intervals

Results

13.4s	4780×	body	1280	valid
2.7s	2104×	body	640	valid
621.0ms	695×	body	320	valid
187.0ms	300×	body	160	valid
65.0ms	12×	body	2560	valid
28.0ms	111×	body	80	valid