Details

sample604.0ms

Algorithm

intervals

Results

440.0ms	138×	body	1280	valid
95.0ms	65×	body	640	valid
21.0ms	22×	body	320	valid
6.0ms	23×	body	80	valid
4.0ms	8×	body	160	valid

simplify549.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.2b	(sin (- lambda1 lambda2))
3.4b	(cos (- lambda1 lambda2))

rewrite172.0ms

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:

59.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
69.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(sin (- lambda1 lambda2))
23.0ms	(cos (- lambda1 lambda2))

series309.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
141.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
42.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

simplify8.2s

Counts

98 → 98

Iterations

Useful iterations: done (8.2s)

Iter	Nodes	Cost
0	210	1766
1	403	1430
2	995	1144
3	2466	1059
4	4346	878
done	5001	787

prune667.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.7b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))

rewrite184.0ms

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` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 87

Calls

4 calls:

25.0ms	(* (sin lambda1) (cos lambda2))
85.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
41.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
28.0ms	(cos (- lambda1 lambda2))

series500.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sin lambda1) (cos lambda2))
247.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
136.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
36.0ms	(cos (- lambda1 lambda2))

simplify4.3s

Counts

99 → 99

Iterations

Useful iterations: 3 (2.8s)

Iter	Nodes	Cost
0	230	1618
1	488	1403
2	1517	1159
3	4747	1067
done	5000	1067

prune961.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite261.0ms

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` `distribute-lft-in` `associate-*l/` `unswap-sqr`
2×	`sub-neg` `flip3--` `prod-diff` `frac-sub` `flip--` `sub-div`
1×	`flip3-+` `sin-neg` `distribute-rgt-neg-out` `flip-+`

Counts

4 → 100

Calls

4 calls:

13.0ms	(* (sin lambda1) (cos lambda2))
68.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
22.0ms	(* (sin lambda1) (sin (- lambda2)))
154.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series587.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin lambda1) (cos lambda2))
182.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
71.0ms	(* (sin lambda1) (sin (- lambda2)))
278.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify1.4s

Counts

112 → 112

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	222	1901
1	558	1809
2	2172	1543
done	5000	1509

prune945.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

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

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`expm1-log1p-u` `associate-l/` `-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3-+` `flip-+`

Counts

4 → 97

Calls

4 calls:

46.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
13.0ms	(* (sin lambda1) (sin lambda2))
70.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
45.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
49.0ms	(* (sin lambda1) (sin lambda2))
118.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
128.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.3s

Counts

109 → 109

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	179	1607
1	467	1552
2	2053	1255
done	5001	1254

prune720.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes489.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	42
1	36	42
done	36	42

end0.0ms

sample21.4s

Algorithm

intervals

Results

14.9s	4526×	body	1280	valid
4.2s	1971×	body	640	valid
1.2s	599×	body	320	valid
192.0ms	701×	body	80	valid
174.0ms	203×	body	160	valid