Details

sample272.0ms

Algorithm

intervals

Results

194.0ms	163×	body	1280	valid
41.0ms	63×	body	640	valid
13.0ms	22×	body	320	valid
2.0ms	6×	body	160	valid
0.0ms	2×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	12
1	34	12
2	36	12
3	36	12
done	36	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.9b	(cos (- lambda1 lambda2))

rewrite50.0ms

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` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

30.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
10.0ms	(cos (- lambda1 lambda2))

series188.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
49.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
11.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

simplify104.0ms

Counts

69 → 69

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	264	773
1	1022	656
2	4705	656
3	5002	656
done	5002	656

prune304.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.3b	(* (sin lambda1) (sin lambda2))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`*-commutative` `sin-mult`
2×	`cos-mult` `unswap-sqr`
1×	`acos-asin` `frac-times` `associate-r/` `associate-l/`

Counts

4 → 70

Calls

4 calls:

6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
43.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
12.0ms	(* (sin lambda1) (sin lambda2))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
118.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
51.0ms	(* (sin lambda1) (sin lambda2))
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify42.0ms

Counts

82 → 82

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	311	1247
1	1196	1031
2	5001	1031
done	5001	1031

prune416.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin lambda1) (sin lambda2))
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
0.6b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

12.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
5.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series141.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin lambda1) (sin lambda2))
49.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
19.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
21.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify95.0ms

Counts

67 → 67

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	190	1274
1	476	1113
2	1023	1113
3	1631	1113
4	3400	1113
5	5002	1113
done	5002	1113

prune438.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.8b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))) (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
7.1b	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
7.1b	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
7.1b	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-div`
6×	`cos-mult` `sin-mult`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `frac-times` `pow1/3` `associate-r/` `associate-l/`
1×	`acos-asin`

Counts

4 → 44

Calls

4 calls:

2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))) (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
29.0ms	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
29.0ms	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
32.0ms	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

series685.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))) (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
220.0ms	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
223.0ms	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
221.0ms	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

simplify43.0ms

Counts

56 → 56

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	183	1016
1	420	886
2	1147	868
3	5002	840
done	5002	840

prune379.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.7b

regimes883.0ms

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	34
1	38	34
done	38	34

end0.0ms

sample8.2s

Algorithm

intervals

Results

5.9s	4752×	body	1280	valid
1.4s	2141×	body	640	valid
289.0ms	667×	body	320	valid
84.0ms	286×	body	160	valid
51.0ms	16×	body	2560	valid
26.0ms	141×	body	80	valid