Details

sample610.0ms

Algorithm

intervals

Results

398.0ms	149×	body	1280	valid
79.0ms	66×	body	640	valid
20.0ms	28×	body	320	valid
5.0ms	1×	body	2560	valid
4.0ms	8×	body	160	valid
1.0ms	4×	body	80	valid

simplify37.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	17	19
1	26	19
2	33	19
3	36	19
done	36	19

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize97.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.8b	(cos (- lambda1 lambda2))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
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:

28.0ms	(* (sin phi1) (sin phi2))
13.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
29.0ms	(cos (- lambda1 lambda2))

series257.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (sin phi1) (sin phi2))
92.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
24.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
62.0ms	(cos (- lambda1 lambda2))

simplify4.1s

Counts

67 → 67

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	111	1035
1	208	1027
2	712	891
3	4869	887
done	5000	887

prune470.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.5b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 65

Calls

4 calls:

29.0ms	(* (sin lambda1) (sin (- lambda2)))
14.0ms	(* (sin phi1) (sin phi2))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series274.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (sin lambda1) (sin (- lambda2)))
56.0ms	(* (sin phi1) (sin phi2))
107.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
25.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify894.0ms

Counts

77 → 77

Iterations

Useful iterations: done (891.0ms)

Iter	Nodes	Cost
0	143	1487
1	290	1473
2	1133	1274
done	5000	1200

prune717.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.4b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1)))))) R)
0.4b	(exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1)))))
0.5b	(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))))))
0.6b	(acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

32.0ms	(* (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1)))))) R)
5.0ms	(exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1)))))
6.0ms	(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))))))
2.0ms	(acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))))

series249.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1)))))) R)
58.0ms	(exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1)))))
29.0ms	(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))))))
32.0ms	(acos (+ (* (sin phi2) (sin phi1)) (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))))

simplify2.4s

Counts

70 → 70

Iterations

Useful iterations: 3 (512.0ms)

Iter	Nodes	Cost
0	103	2374
1	184	2277
2	493	1931
3	2614	1929
done	5000	1929

prune641.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.6b	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
2.9b	(log (exp (* (sin phi1) (sin phi2))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
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:

12.0ms	(* (sin phi1) (sin phi2))
7.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
4.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
9.0ms	(log (exp (* (sin phi1) (sin phi2))))

series308.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin phi1) (sin phi2))
138.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
25.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
77.0ms	(log (exp (* (sin phi1) (sin phi2))))

simplify1.2s

Counts

71 → 71

Iterations

Useful iterations: done (765.0ms)

Iter	Nodes	Cost
0	124	1515
1	229	1410
2	745	1220
done	5000	1146

prune606.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.4b

regimes1.5s

Accuracy

0% (0.3b remaining)

Error of 3.8b against oracle of 3.5b and baseline of 3.8b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	29
1	31	29
done	31	29

end0.0ms

sample18.1s

Algorithm

intervals

Results

13.1s	4860×	body	1280	valid
3.5s	2103×	body	640	valid
516.0ms	659×	body	320	valid
121.0ms	255×	body	160	valid
76.0ms	115×	body	80	valid
48.0ms	10×	body	2560	valid