Details

sample699.0ms

Algorithm

intervals

Results

434.0ms	147×	body	1280	valid
87.0ms	69×	body	640	valid
21.0ms	25×	body	320	valid
5.0ms	10×	body	160	valid
2.0ms	6×	body	80	valid

simplify37.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	36
3	36
2	33
1	26
0	17

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi2) (sin phi1))
0.2b	(* R (acos (+ (* (cos (- lambda1 lambda2)) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1)))))
0.8b	(acos (+ (* (cos (- lambda1 lambda2)) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1))))
3.0b	(cos (- lambda1 lambda2))

rewrite33.0ms

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`
4×	`add-log-exp`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 55

Calls

4 calls:

10.0ms	(* (sin phi2) (sin phi1))
5.0ms	(* R (acos (+ (* (cos (- lambda1 lambda2)) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1)))))
2.0ms	(acos (+ (* (cos (- lambda1 lambda2)) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1))))
11.0ms	(cos (- lambda1 lambda2))

series186.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (sin phi2) (sin phi1))
40.0ms	(* R (acos (+ (* (cos (- lambda1 lambda2)) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1)))))
20.0ms	(acos (+ (* (cos (- lambda1 lambda2)) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1))))
43.0ms	(cos (- lambda1 lambda2))

simplify3.0s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
3	3988
2	635
1	210
0	111

prune699.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.4b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2)))
0.2b	(* (sin phi2) (sin phi1))
0.2b	(* R (acos (+ (* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1)))))
0.8b	(acos (+ (* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-l*` `cos-mult` `add-cube-cbrt`
7×	`associate-r`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
4×	`frac-times` `associate-*l/` `add-log-exp`
3×	`*-commutative`
2×	`flip3--` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`acos-asin` `associate-*r/`

Counts

4 → 72

Calls

4 calls:

67.0ms	(* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2)))
13.0ms	(* (sin phi2) (sin phi1))
21.0ms	(* R (acos (+ (* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1)))))
2.0ms	(acos (+ (* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2)))
63.0ms	(* (sin phi2) (sin phi1))
59.0ms	(* R (acos (+ (* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1)))))
30.0ms	(acos (+ (* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1))))

simplify909.0ms

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	1953
1	476
0	191

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.2b

localize106.0ms

Local error

Found 4 expressions with local error:

0.2b	(* R (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))))))
0.4b	(exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))))
0.5b	(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))))
0.8b	(acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
3×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-l`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 64

Calls

4 calls:

20.0ms	(* R (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))))))
5.0ms	(exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))))
18.0ms	(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))))
3.0ms	(acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* R (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))))))
101.0ms	(exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))))
27.0ms	(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))))
18.0ms	(acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))

simplify2.6s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
4	3540
3	1650
2	589
1	210
0	113

prune985.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.2b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi2) (sin phi1))
0.2b	(* R (acos (+ (* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2))) (log (exp (* (sin phi2) (sin phi1)))))))
0.8b	(acos (+ (* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2))) (log (exp (* (sin phi2) (sin phi1))))))
5.0b	(log (exp (* (sin phi2) (sin phi1))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`log-prod` `log-pow`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `exp-prod` `exp-to-pow` `rem-log-exp` `sin-mult`

Counts

4 → 59

Calls

4 calls:

9.0ms	(* (sin phi2) (sin phi1))
6.0ms	(* R (acos (+ (* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2))) (log (exp (* (sin phi2) (sin phi1)))))))
2.0ms	(acos (+ (* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2))) (log (exp (* (sin phi2) (sin phi1))))))
8.0ms	(log (exp (* (sin phi2) (sin phi1))))

series243.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin phi2) (sin phi1))
71.0ms	(* R (acos (+ (* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2))) (log (exp (* (sin phi2) (sin phi1)))))))
40.0ms	(acos (+ (* (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))) (* (cos phi1) (cos phi2))) (log (exp (* (sin phi2) (sin phi1))))))
60.0ms	(log (exp (* (sin phi2) (sin phi1))))

simplify1.9s

Counts

71 → 71

Iterations

Iter	Nodes
done	5002
3	3652
2	690
1	229
0	123

prune771.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.2b

regimes1.6s

Accuracy

0% (0.4b remaining)

Error of 3.6b against oracle of 3.2b and baseline of 3.6b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	27

end0.0ms

sample20.1s

Algorithm

intervals

Results

12.8s	4775×	body	1280	valid
5.2s	2113×	body	640	valid
761.0ms	687×	body	320	valid
540.0ms	281×	body	160	valid
52.0ms	12×	body	2560	valid
38.0ms	133×	body	80	valid