Details

sample573.0ms

Algorithm

intervals

Results

446.0ms	150×	body	1280	valid
78.0ms	59×	body	640	valid
14.0ms	15×	body	320	valid
7.0ms	12×	body	160	valid
5.0ms	20×	body	80	valid

simplify76.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	28	24
2	47	24
3	78	24
4	88	24
done	88	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.9b	(cos (- lambda1 lambda2))
4.0b	(sin (- lambda1 lambda2))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
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×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

42.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
34.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))
14.0ms	(sin (- lambda1 lambda2))

series321.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
143.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
30.0ms	(cos (- lambda1 lambda2))
30.0ms	(sin (- lambda1 lambda2))

simplify7.4s

Counts

98 → 98

Iterations

Useful iterations: done (7.4s)

Iter	Nodes	Cost
0	210	1766
1	403	1430
2	995	1144
3	2481	1059
4	4281	878
done	5000	787

prune487.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.9b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.9b	(cos (- lambda1 lambda2))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

12.0ms	(* (sin phi1) (cos phi2))
71.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
60.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))

series352.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (cos phi2))
173.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
113.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify3.2s

Counts

99 → 99

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	207	1587
1	439	1411
2	1282	1175
3	3995	1132
done	5001	1076

prune742.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

34.0ms	(* (sin lambda1) (sin (- lambda2)))
23.0ms	(* (sin phi1) (cos phi2))
85.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
145.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series523.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sin lambda1) (sin (- lambda2)))
54.0ms	(* (sin phi1) (cos phi2))
158.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
252.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify1.3s

Counts

112 → 112

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	209	1870
1	523	1817
2	2016	1545
done	5002	1508

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))
2.5b	(log (exp (* (sin lambda1) (sin (- lambda2)))))

rewrite657.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

21.0ms	(* (sin phi1) (cos phi2))
95.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
517.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))
17.0ms	(log (exp (* (sin lambda1) (sin (- lambda2)))))

series595.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (sin phi1) (cos phi2))
182.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
256.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))
105.0ms	(log (exp (* (sin lambda1) (sin (- lambda2)))))

simplify1.8s

Counts

116 → 116

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	217	2534
1	511	2099
2	1841	1743
done	5000	1586

prune972.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes461.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	41
1	36	41
done	36	41

end0.0ms

sample20.4s

Algorithm

intervals

Results

15.1s	4584×	body	1280	valid
3.4s	1973×	body	640	valid
649.0ms	654×	body	80	valid
601.0ms	593×	body	320	valid
153.0ms	196×	body	160	valid