Details

sample249.0ms

Algorithm

intervals

Results

180.0ms	156×	body	1280	valid
40.0ms	64×	body	640	valid
9.0ms	21×	body	320	valid
3.0ms	11×	body	160	valid
1.0ms	4×	body	80	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	19
1	26	19
2	33	19
3	34	19
done	34	19

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.5b	(cos (- lambda1 lambda2))

rewrite14.0ms

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:

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

series118.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
48.0ms	(* (sin phi1) (sin phi2))
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms	(cos (- lambda1 lambda2))

simplify895.0ms

Counts

67 → 67

Iterations

Useful iterations: 3 (190.0ms)

Iter	Nodes	Cost
0	111	1035
1	204	1027
2	503	889
3	1450	887
done	5000	887

prune281.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.2b

localize37.0ms

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 lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite15.0ms

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:

6.0ms	(* (sin lambda1) (sin (- lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
4.0ms	(* (sin phi1) (sin phi2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series187.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (sin lambda1) (sin (- lambda2)))
68.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
48.0ms	(* (sin phi1) (sin phi2))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify1.3s

Counts

77 → 77

Iterations

Useful iterations: 3 (301.0ms)

Iter	Nodes	Cost
0	143	1487
1	288	1473
2	827	1270
3	2162	1200
done	5001	1200

prune450.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.4b	(pow (* (sin lambda1) (sin (- lambda2))) 3)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))))
25.9b	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `cbrt-div` `pow1/3` `cube-neg` `sin-neg` `*-commutative` `distribute-rgt-neg-out` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
4.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))))
2.0ms	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

series324.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(* (sin phi1) (sin phi2))
68.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
21.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))))
51.0ms	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

simplify480.0ms

Counts

81 → 81

Iterations

Useful iterations: done (478.0ms)

Iter	Nodes	Cost
0	154	1148
1	351	992
2	1102	883
done	5000	851

prune459.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (* (sin lambda1) (sin (- lambda2))) 3)
0.7b	(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))))
24.4b	(cbrt (pow (* (sin phi1) (sin phi2)) 3))
25.9b	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
7×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`add-log-exp`
3×	`cube-div` `cube-mult` `unpow-prod-down` `pow-unpow` `unpow3` `cube-prod` `sin-mult` `sqr-pow`
2×	`cbrt-div` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`
1×	`acos-asin` `pow-to-exp` `cube-neg` `pow-prod-down` `prod-exp` `sin-neg` `distribute-rgt-neg-out` `cbrt-unprod`

Counts

4 → 68

Calls

4 calls:

5.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
1.0ms	(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))))
2.0ms	(cbrt (pow (* (sin phi1) (sin phi2)) 3))
2.0ms	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

series191.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
17.0ms	(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))))
47.0ms	(cbrt (pow (* (sin phi1) (sin phi2)) 3))
52.0ms	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

simplify3.2s

Counts

80 → 80

Iterations

Useful iterations: 3 (507.0ms)

Iter	Nodes	Cost
0	151	1269
1	351	1008
2	1081	919
3	4912	887
done	5000	887

prune451.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.1b

regimes463.0ms

Accuracy

0% (0.4b remaining)

Error of 4.1b against oracle of 3.8b and baseline of 4.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	33
1	35	33
done	35	33

end0.0ms

sample7.8s

Algorithm

intervals

Results

5.7s	4828×	body	1280	valid
1.4s	2038×	body	640	valid
313.0ms	708×	body	320	valid
79.0ms	291×	body	160	valid
20.0ms	6×	body	2560	valid
20.0ms	130×	body	80	valid