Details

sample666.0ms

Algorithm

intervals

Results

491.0ms	150×	body	1280	valid
106.0ms	67×	body	640	valid
21.0ms	20×	body	320	valid
4.0ms	13×	body	80	valid
3.0ms	6×	body	160	valid

simplify169.0ms

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	99	24
5	100	24
done	100	24

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize90.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0b	(sin (- lambda1 lambda2))
3.1b	(cos (- lambda1 lambda2))

rewrite171.0ms

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:

53.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
61.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
28.0ms	(sin (- lambda1 lambda2))
24.0ms	(cos (- lambda1 lambda2))

series346.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
170.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
36.0ms	(sin (- lambda1 lambda2))
29.0ms	(cos (- lambda1 lambda2))

simplify1.7s

Counts

98 → 98

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	210	1766
1	434	1442
2	1770	1146
done	5000	1095

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.4b

localize105.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b	(cos (- lambda1 lambda2))

rewrite179.0ms

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:

77.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
20.0ms	(* (sin lambda1) (cos lambda2))
54.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms	(cos (- lambda1 lambda2))

series480.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
79.0ms	(* (sin lambda1) (cos lambda2))
154.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
28.0ms	(cos (- lambda1 lambda2))

simplify2.0s

Counts

99 → 99

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	230	1618
1	528	1410
2	2336	1178
done	5000	1152

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize131.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 (* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2)) (- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin 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))))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod`
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` `distribute-lft-in` `associate-*l/`

Counts

4 → 80

Calls

4 calls:

1.0ms	(atan2 (* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2)) (- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))))
23.0ms	(* (sin lambda1) (cos lambda2))
25.0ms	(* (sin lambda2) (sin lambda1))
124.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

series572.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(atan2 (* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2)) (- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))))
82.0ms	(* (sin lambda1) (cos lambda2))
87.0ms	(* (sin lambda2) (sin lambda1))
344.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

simplify3.8s

Counts

92 → 92

Iterations

Useful iterations: 2 (720.0ms)

Iter	Nodes	Cost
0	205	1766
1	568	1657
2	3292	1449
done	5001	1449

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize146.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin lambda2) (sin lambda1)) 3))))
0.3b	(pow (* (sin lambda2) (sin lambda1)) 3)
27.2b	(cbrt (pow (* (sin lambda2) (sin lambda1)) 3))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`cbrt-prod`
6×	`associate-r`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
4×	`cube-div` `expm1-log1p-u` `associate-l` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-*r/`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `flip3-+` `unpow3` `cube-prod` `frac-add` `pow-exp` `cos-mult` `*-commutative` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow1/3` `associate-*l/` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

24.0ms	(* (sin lambda2) (sin lambda1))
134.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin lambda2) (sin lambda1)) 3))))
18.0ms	(pow (* (sin lambda2) (sin lambda1)) 3)
10.0ms	(cbrt (pow (* (sin lambda2) (sin lambda1)) 3))

series597.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (sin lambda2) (sin lambda1))
313.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin lambda2) (sin lambda1)) 3))))
113.0ms	(pow (* (sin lambda2) (sin lambda1)) 3)
82.0ms	(cbrt (pow (* (sin lambda2) (sin lambda1)) 3))

simplify4.1s

Counts

107 → 107

Iterations

Useful iterations: 2 (852.0ms)

Iter	Nodes	Cost
0	183	1632
1	567	1313
2	3685	1175
done	5000	1175

prune1.6s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes1.1s

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	29	42
1	39	42
done	39	42

end0.0ms

sample26.1s

Algorithm

intervals

Results

18.6s	4639×	body	1280	valid
4.9s	1928×	body	640	valid
1.2s	576×	body	320	valid
216.0ms	665×	body	80	valid
192.0ms	192×	body	160	valid