Details

sample544.0ms

Algorithm

intervals

Results

404.0ms	137×	body	1280	valid
78.0ms	59×	body	640	valid
24.0ms	24×	body	320	valid
7.0ms	25×	body	80	valid
6.0ms	11×	body	160	valid

simplify43.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	73
4	73
3	69
2	45
1	27
0	17

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize446.0ms

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))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`cos-sum` `sub-neg` `sin-sum` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

14.0ms	(* (cos phi1) (sin phi2))
37.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(sin (- lambda1 lambda2))
8.0ms	(cos (- lambda1 lambda2))

series247.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (cos phi1) (sin phi2))
137.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
27.0ms	(sin (- lambda1 lambda2))
20.0ms	(cos (- lambda1 lambda2))

simplify2.7s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
3	3097
2	833
1	299
0	128

prune668.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize117.0ms

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))

rewrite91.0ms

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`
4×	`add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-cos-mult`

Counts

4 → 67

Calls

4 calls:

17.0ms	(* (cos lambda1) (sin lambda2))
21.0ms	(* (cos phi1) (sin phi2))
41.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))

series282.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (cos lambda1) (sin lambda2))
57.0ms	(* (cos phi1) (sin phi2))
138.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(cos (- lambda1 lambda2))

simplify2.8s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	3545
2	981
1	349
0	146

prune949.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize93.0ms

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))))

rewrite149.0ms

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×	`*-commutative` `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 → 82

Calls

4 calls:

18.0ms	(* (cos phi1) (sin phi2))
19.0ms	(* (cos lambda1) (sin lambda2))
20.0ms	(* (sin lambda1) (sin lambda2))
88.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos phi1) (sin phi2))
54.0ms	(* (cos lambda1) (sin lambda2))
74.0ms	(* (sin lambda1) (sin lambda2))
269.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify2.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	5029
2	2081
1	545
0	189

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize134.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

rewrite427.0ms

Algorithm

rewrite-expression-head

Rules

84×	`pow1`
43×	`sin-mult`
42×	`cos-mult`
39×	`add-cbrt-cube` `add-exp-log`
38×	`associate-*r/`
35×	`pow-prod-down`
34×	`frac-times`
33×	`associate-/l/`
23×	`associate-*l/`
20×	`prod-exp` `cbrt-unprod`
19×	`frac-sub`
17×	`sin-cos-mult`
11×	`sub-div`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `pow-sqr` `pow-prod-up` `add-cube-cbrt`
5×	`associate-r` `associate-l`
4×	`pow-plus` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `times-frac` `flip3--` `div-exp` `-commutative` `flip--`
2×	`pow2` `swap-sqr`
1×	`clear-num` `frac-2neg` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 153

Calls

4 calls:

14.0ms	(* (sin lambda1) (sin lambda2))
278.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
66.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
60.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

series961.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin lambda1) (sin lambda2))
744.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
77.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
67.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

simplify2.3s

Counts

165 → 165

Iterations

Iter	Nodes
done	5002
2	2977
1	739
0	237

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 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

simplify6.0ms

Iterations

Iter	Nodes
done	35
1	35
0	27

end0.0ms

sample17.4s

Algorithm

intervals

Results

12.3s	4650×	body	1280	valid
3.4s	1883×	body	640	valid
917.0ms	619×	body	320	valid
233.0ms	632×	body	80	valid
161.0ms	216×	body	160	valid