Details

sample4.3s

Algorithm

intervals

Results

2.6s	153×	body	1280	valid
890.0ms	62×	body	640	valid
33.0ms	26×	body	320	valid
12.0ms	12×	body	160	valid
1.0ms	3×	body	80	valid

simplify287.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (140.0ms)

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: 18.4b

localize296.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.7b	(cos (- lambda1 lambda2))

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

59.0ms	(* (sin phi1) (sin phi2))
72.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
32.0ms	(cos (- lambda1 lambda2))

series1.1s

Counts

4 → 12

Calls

4 calls:

417.0ms	(* (sin phi1) (sin phi2))
488.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
63.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
73.0ms	(cos (- lambda1 lambda2))

simplify2.9s

Counts

70 → 70

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	125	868
1	281	856
2	1287	740
done	5000	732

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.1b

localize166.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.2b	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite489.0ms

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*` `cos-mult`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
4×	`frac-times` `associate-*r/` `add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`acos-asin` `associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 77

Calls

4 calls:

72.0ms	(* (sin lambda1) (sin (- lambda2)))
31.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))) R)
323.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))

series1.6s

Counts

4 → 12

Calls

4 calls:

223.0ms	(* (sin lambda1) (sin (- lambda2)))
198.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.0s	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
127.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))

simplify6.2s

Counts

89 → 89

Iterations

Useful iterations: done (6.1s)

Iter	Nodes	Cost
0	199	2246
1	501	2198
2	2557	1848
done	5000	1812

prune2.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.9b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (log (exp (* (sin lambda1) (sin (- lambda2))))))))) R)
0.2b	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))))
3.2b	(log (exp (* (sin lambda1) (sin (- lambda2)))))

rewrite617.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
5×	`add-log-exp`
4×	`exp-neg` `associate-l` `pow-prod-down` `prod-exp` `sin-neg` `distribute-rgt-neg-out` `cbrt-unprod`
3×	`distribute-rgt-in` `log-div` `log-prod` `distribute-lft-in` `log-pow` `cos-mult`
2×	`frac-times` `sub-neg` `flip3--` `associate-r/` `-commutative` `flip--` `associate--r-`
1×	`acos-asin` `exp-prod` `exp-to-pow` `rem-log-exp` `log-rec` `associate-*l/` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

25.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (log (exp (* (sin lambda1) (sin (- lambda2))))))))) R)
157.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))
6.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))))
329.0ms	(log (exp (* (sin lambda1) (sin (- lambda2)))))

series991.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (log (exp (* (sin lambda1) (sin (- lambda2))))))))) R)
558.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))
43.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))))
206.0ms	(log (exp (* (sin lambda1) (sin (- lambda2)))))

simplify6.6s

Counts

83 → 83

Iterations

Useful iterations: done (6.6s)

Iter	Nodes	Cost
0	178	2312
1	433	2092
2	2308	1815
done	5000	1712

prune3.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.9b

localize230.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))) R)
0.3b	(exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))
0.7b	(log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))))
0.9b	(acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))

rewrite983.0ms

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:

57.0ms	(* (log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))) R)
725.0ms	(exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))
95.0ms	(log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))))
59.0ms	(acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))

series787.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(* (log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))) R)
445.0ms	(exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))
45.0ms	(log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))))
52.0ms	(acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))

simplify11.7s

Counts

70 → 70

Iterations

Useful iterations: 3 (3.5s)

Iter	Nodes	Cost
0	107	2374
1	190	2277
2	520	1931
3	2864	1929
done	5000	1929

prune2.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.9b

regimes8.3s

Accuracy

0% (0.4b remaining)

Error of 4.1b against oracle of 3.7b and baseline of 4.1b

bsearch2.0ms

simplify81.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	29
1	32	29
done	32	29

end1.0ms

sample2.5m

Algorithm

intervals

Results

1.6m	4834×	body	1280	valid
44.1s	2068×	body	640	valid
7.8s	690×	body	320	valid
1.1s	260×	body	160	valid
172.0ms	11×	body	2560	valid
148.0ms	138×	body	80	valid