Details

sample262.0ms

Algorithm

intervals

Results

186.0ms	153×	body	1280	valid
46.0ms	71×	body	640	valid
10.0ms	23×	body	320	valid
2.0ms	8×	body	160	valid
0.0ms	1×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0b	(cos (- lambda1 lambda2))

rewrite13.0ms

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:

4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms	(cos (- lambda1 lambda2))

series121.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (sin phi2))
43.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms	(cos (- lambda1 lambda2))

simplify1.5s

Counts

67 → 67

Iterations

Useful iterations: 3 (153.0ms)

Iter	Nodes	Cost
0	111	1035
1	199	1027
2	435	889
3	826	887
4	1180	887
5	2201	887
done	5001	887

prune308.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite34.0ms

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/`

Counts

4 → 76

Calls

4 calls:

24.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series341.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
44.0ms	(* (sin phi1) (sin phi2))
73.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify870.0ms

Counts

88 → 88

Iterations

Useful iterations: done (867.0ms)

Iter	Nodes	Cost
0	195	2211
1	489	2178
2	1719	1781
done	5001	1779

prune491.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))) R)
0.4b	(exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))
0.9b	(log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))))
1.2b	(acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))

rewrite13.0ms

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:

6.0ms	(* (log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))) R)
1.0ms	(exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))
2.0ms	(log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))))
1.0ms	(acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))

series146.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))) R)
46.0ms	(exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))
16.0ms	(log (exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))))
16.0ms	(acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))

simplify2.6s

Counts

70 → 70

Iterations

Useful iterations: 5 (428.0ms)

Iter	Nodes	Cost
0	107	2374
1	183	2277
2	355	2025
3	535	2025
4	731	1929
5	1397	1927
6	4428	1927
done	5000	1927

prune393.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (- (/ PI 2) (asin (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))) R)
0.5b	(asin (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))
1.1b	(- (/ PI 2) (asin (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
9×	`associate-l`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
4×	`difference-of-squares`
2×	`asin-acos` `flip3--` `times-frac` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`sub-neg` `diff-log` `sin-mult` `associate--r-`

Counts

4 → 66

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
35.0ms	(* (- (/ PI 2) (asin (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))) R)
1.0ms	(asin (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))
10.0ms	(- (/ PI 2) (asin (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))

series281.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin phi1) (sin phi2))
165.0ms	(* (- (/ PI 2) (asin (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))) R)
16.0ms	(asin (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2))))
53.0ms	(- (/ PI 2) (asin (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))

simplify2.0s

Counts

78 → 78

Iterations

Useful iterations: 3 (306.0ms)

Iter	Nodes	Cost
0	144	2372
1	289	2286
2	697	2036
3	1707	2030
4	3648	2030
done	5001	2030

prune374.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.5b

regimes677.0ms

Accuracy

0% (0.7b remaining)

Error of 3.9b against oracle of 3.2b and baseline of 3.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	86
1	41	86
done	41	86

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.8s	4797×	body	1280	valid
1.5s	2144×	body	640	valid
296.0ms	667×	body	320	valid
79.0ms	264×	body	160	valid
21.0ms	7×	body	2560	valid
19.0ms	123×	body	80	valid