Details

sample494.0ms

Algorithm

intervals

Results

298.0ms	128×	body	1280	valid
99.0ms	70×	body	640	valid
41.0ms	9×	body	160	valid
26.0ms	28×	body	320	valid
6.0ms	21×	body	80	valid

simplify19.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	20
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.4b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.0b	(sin (- lambda1 lambda2))
2.0b	(cos (- lambda1 lambda2))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`cos-diff`
2×	`cos-sum` `associate-+r+` `sub-neg` `sin-sum`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `flip3-+` `sin-diff` `flip-+`

Counts

4 → 44

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
8.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
9.0ms	(sin (- lambda1 lambda2))
20.0ms	(cos (- lambda1 lambda2))

series221.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
151.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
36.0ms	(sin (- lambda1 lambda2))
22.0ms	(cos (- lambda1 lambda2))

simplify2.5s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
4	2565
3	1169
2	480
1	211
0	101

prune555.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.8b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.4b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.0b	(cos (- lambda1 lambda2))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
4×	`insert-posit16`
3×	`distribute-rgt-in` `cos-diff` `sub-neg` `distribute-lft-in` `associate-r` `associate-l`
2×	`cos-sum` `associate-+r+` `associate-*r/`
1×	`+-commutative` `sum-log` `flip3-+` `flip3--` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

94.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
17.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
18.0ms	(cos (- lambda1 lambda2))

series404.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
11.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
171.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms	(cos (- lambda1 lambda2))

simplify2.9s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
3	3300
2	917
1	312
0	128

prune642.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`insert-posit16`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`associate-+r+` `sub-neg` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `flip3--` `flip-+` `flip--` `sin-mult`

Counts

4 → 67

Calls

4 calls:

79.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
18.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
16.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
85.0ms	(* (sin lambda1) (sin lambda2))
320.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify2.1s

Counts

79 → 79

Iterations

Iter	Nodes
done	5005
2	1337
1	380
0	148

prune743.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize117.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (- (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
0.3b	(+ (* (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))) (* (cos phi1) (* (cos phi1) (cos phi1))))
0.4b	(* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))
0.5b	(- (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

482×	`associate-*r/`
244×	`frac-add` `cos-mult`
177×	`frac-times`
110×	`flip3-+` `flip-+`
107×	`sin-mult`
65×	`associate-/l/`
60×	`associate-*l/`
43×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down`
13×	`add-sqr-sqrt` `*-un-lft-identity` `associate-/r/` `add-cube-cbrt`
12×	`times-frac`
10×	`distribute-rgt-in` `distribute-lft-in`
8×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`flip3--` `cube-unmult` `pow3` `sum-cubes` `flip--`
4×	`associate-+l+` `pow-sqr` `pow-prod-up` `insert-posit16` `associate-/l*`
3×	`associate-/r*`
2×	`sqr-cos` `associate-+r+` `pow-plus` `associate--l+`
1×	`pow2` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `swap-sqr` `div-exp` `associate-r` `associate-l` `*-commutative` `div-inv`

Counts

4 → 261

Calls

4 calls:

1.2s	(/ (+ (* (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (- (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
522.0ms	(+ (* (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))) (* (cos phi1) (* (cos phi1) (cos phi1))))
196.0ms	(* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))
49.0ms	(- (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))

series5.9s

Counts

4 → 12

Calls

4 calls:

3.8s	(/ (+ (* (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (- (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
1.5s	(+ (* (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))) (* (cos phi1) (* (cos phi1) (cos phi1))))
248.0ms	(* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))
337.0ms	(- (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))

simplify3.6s

Counts

273 → 273

Iterations

Iter	Nodes
done	5000
1	2495
0	728

prune3.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes665.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	46
1	46
0	31

end0.0ms

sample16.2s

Algorithm

intervals

Results

10.1s	3647×	body	1280	valid
4.3s	2303×	body	640	valid
1.0s	976×	body	320	valid
264.0ms	398×	body	160	valid
255.0ms	676×	body	80	valid