Details

sample762.0ms

Algorithm

intervals

Results

468.0ms	160×	body	1280	valid
91.0ms	24×	body	320	valid
79.0ms	57×	body	640	valid
11.0ms	2×	body	2560	valid
4.0ms	7×	body	160	valid
2.0ms	6×	body	80	valid

simplify26.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.0b	(cos (- lambda1 lambda2))

rewrite76.0ms

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:

49.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(* (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)))))
13.0ms	(cos (- lambda1 lambda2))

series317.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
102.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
23.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
46.0ms	(cos (- lambda1 lambda2))

simplify971.0ms

Counts

69 → 69

Iterations

Useful iterations: done (967.0ms)

Iter	Nodes	Cost
0	121	1225
1	275	1213
2	1275	1037
done	5000	1033

prune426.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.6b

localize88.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
0.2b	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
0.3b	(* (sin lambda1) (sin lambda2))
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

rewrite106.0ms

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×	`cos-mult` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`acos-asin` `frac-times` `associate-r/` `associate-l/` `sin-mult`

Counts

4 → 70

Calls

4 calls:

14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
70.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
14.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
240.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
86.0ms	(* (sin lambda1) (sin lambda2))
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify1.1s

Counts

82 → 82

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	162	1915
1	386	1693
2	1580	1377
done	5001	1375

prune736.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.5b

localize92.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b	(* (sin lambda1) (sin lambda2))
0.6b	(log (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
1.5b	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

91.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
25.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(log (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
19.0ms	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

series476.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
73.0ms	(* (sin lambda1) (sin lambda2))
58.0ms	(log (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
19.0ms	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

simplify1.9s

Counts

78 → 78

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	170	1830
1	464	1797
2	2551	1529
done	5001	1523

prune760.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.5b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin lambda1) (sin lambda2))
0.4b	(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
1.2b	(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
1.5b	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

rewrite57.0ms

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))
6.0ms	(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
17.0ms	(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
19.0ms	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

series212.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin lambda1) (sin lambda2))
90.0ms	(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
24.0ms	(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
28.0ms	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

simplify3.5s

Counts

67 → 67

Iterations

Useful iterations: 3 (670.0ms)

Iter	Nodes	Cost
0	110	1654
1	199	1611
2	548	1369
3	3065	1367
done	5001	1367

prune540.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.4b

regimes1.3s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	41
1	36	41
done	36	41

end0.0ms

sample15.9s

Algorithm

intervals

Results

9.7s	4733×	body	1280	valid
4.1s	2153×	body	640	valid
1.3s	659×	body	320	valid
135.0ms	305×	body	160	valid
37.0ms	143×	body	80	valid
29.0ms	7×	body	2560	valid