Details

sample528.0ms

Algorithm

intervals

Results

379.0ms	142×	body	1280	valid
94.0ms	66×	body	640	valid
17.0ms	21×	body	320	valid
5.0ms	23×	body	80	valid
2.0ms	4×	body	160	valid

simplify85.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	95
4	95
3	78
2	47
1	28
0	17

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.6b	(cos (- lambda1 lambda2))
3.6b	(sin (- lambda1 lambda2))

rewrite91.0ms

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` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

28.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
26.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
18.0ms	(sin (- lambda1 lambda2))

series354.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
180.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
28.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

simplify1.0s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1793
1	434
0	210

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.2b

localize105.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (- (sin lambda2)))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.6b	(cos (- lambda1 lambda2))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

13.0ms	(* (cos lambda1) (- (sin lambda2)))
14.0ms	(* (sin lambda1) (cos lambda2))
25.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(cos (- lambda1 lambda2))

series304.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (cos lambda1) (- (sin lambda2)))
76.0ms	(* (sin lambda1) (cos lambda2))
142.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
2	2246
1	540
0	240

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize112.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

13.0ms	(* (cos lambda1) (- (sin lambda2)))
9.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(* (sin lambda2) (sin lambda1))
72.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cos lambda1) (- (sin lambda2)))
59.0ms	(* (sin lambda1) (cos lambda2))
72.0ms	(* (sin lambda2) (sin lambda1))
242.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

simplify1.7s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
2	3808
1	617
0	216

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize124.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (expm1 (- (* (sin lambda2) (cos lambda1)))))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

rewrite438.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

0.0ms	(log1p (expm1 (- (* (sin lambda2) (cos lambda1)))))
9.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(* (sin lambda2) (sin lambda1))
418.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

series561.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(log1p (expm1 (- (* (sin lambda2) (cos lambda1)))))
81.0ms	(* (sin lambda1) (cos lambda2))
86.0ms	(* (sin lambda2) (sin lambda1))
273.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

simplify1.7s

Counts

94 → 94

Iterations

Iter	Nodes
done	5002
2	3039
1	525
0	186

prune967.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes808.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	45
3	45
2	44
1	40
0	28

end0.0ms

sample17.2s

Algorithm

intervals

Results

12.2s	4571×	body	1280	valid
3.4s	1963×	body	640	valid
596.0ms	535×	body	320	valid
201.0ms	234×	body	160	valid
197.0ms	697×	body	80	valid