Details

sample469.0ms

Algorithm

intervals

Results

336.0ms	137×	body	1280	valid
75.0ms	59×	body	640	valid
19.0ms	24×	body	320	valid
5.0ms	25×	body	80	valid
5.0ms	11×	body	160	valid

simplify508.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
4	80
3	77
2	47
1	28
0	17

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize75.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b	(sin (- lambda1 lambda2))
4.1b	(cos (- lambda1 lambda2))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

18.0ms	(* (cos phi1) (sin phi2))
48.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms	(sin (- lambda1 lambda2))
13.0ms	(cos (- lambda1 lambda2))

series279.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (cos phi1) (sin phi2))
155.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(sin (- lambda1 lambda2))
24.0ms	(cos (- lambda1 lambda2))

simplify2.8s

Counts

97 → 97

Iterations

Iter	Nodes
done	5004
3	3555
2	1059
1	459
0	222

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.8b

localize68.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.1b	(cos (- lambda1 lambda2))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
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` `*-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-cos-mult`

Counts

4 → 84

Calls

4 calls:

18.0ms	(* (cos lambda1) (sin lambda2))
19.0ms	(* (cos phi1) (sin phi2))
51.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
12.0ms	(cos (- lambda1 lambda2))

series342.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (cos lambda1) (sin lambda2))
74.0ms	(* (cos phi1) (sin phi2))
151.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))

simplify2.6s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
3	4108
2	1164
1	477
0	222

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize138.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

18.0ms	(* (cos phi1) (sin phi2))
17.0ms	(* (cos lambda1) (sin lambda2))
11.0ms	(* (sin lambda1) (sin lambda2))
53.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series426.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (cos phi1) (sin phi2))
60.0ms	(* (cos lambda1) (sin lambda2))
58.0ms	(* (sin lambda1) (sin lambda2))
246.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify1.9s

Counts

102 → 102

Iterations

Iter	Nodes
done	5004
2	2117
1	563
0	197

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize127.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

69.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
2.0ms	(cbrt (cos phi1))
2.0ms	(cbrt (cos phi1))
2.0ms	(cbrt (cos phi1))

series764.0ms

Counts

4 → 12

Calls

4 calls:

324.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
151.0ms	(cbrt (cos phi1))
136.0ms	(cbrt (cos phi1))
153.0ms	(cbrt (cos phi1))

simplify2.1s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1648
1	385
0	124

prune961.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes934.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample19.6s

Algorithm

intervals

Results

14.8s	4650×	body	1280	valid
3.4s	1883×	body	640	valid
647.0ms	619×	body	320	valid
154.0ms	632×	body	80	valid
112.0ms	216×	body	160	valid