Details

sample624.0ms

Algorithm

intervals

Results

335.0ms	147×	body	1280	valid
88.0ms	79×	body	640	valid
14.0ms	20×	body	320	valid
3.0ms	7×	body	160	valid
1.0ms	4×	body	80	valid

simplify32.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	17	635
1	26	635
2	33	635
3	36	635
done	36	635

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize64.0ms

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))
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.6b	(cos (- lambda1 lambda2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
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:

10.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
13.0ms	(* (sin phi1) (sin phi2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
10.0ms	(cos (- lambda1 lambda2))

series206.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
69.0ms	(* (sin phi1) (sin phi2))
12.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
35.0ms	(cos (- lambda1 lambda2))

simplify4.6s

Counts

67 → 67

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	111	29295
1	207	28822
2	654	28662
3	4255	28622
done	5001	28622

prune842.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize119.0ms

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
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`

Counts

4 → 64

Calls

4 calls:

11.0ms	(* (sin lambda1) (sin lambda2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
18.0ms	(* (sin phi1) (sin phi2))
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series226.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sin lambda1) (sin lambda2))
78.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
63.0ms	(* (sin phi1) (sin phi2))
22.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.6s

Counts

76 → 76

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	134	39874
1	277	39541
2	1001	39061
done	5000	38821

prune841.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.3b

localize110.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.8b	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
3.4b	(log (exp (* (sin phi1) (sin phi2))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

10.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
18.0ms	(* (sin phi1) (sin phi2))
5.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
6.0ms	(log (exp (* (sin phi1) (sin phi2))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
87.0ms	(* (sin phi1) (sin phi2))
37.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
78.0ms	(log (exp (* (sin phi1) (sin phi2))))

simplify4.8s

Counts

71 → 71

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	119	44355
1	228	38723
2	730	38323
3	4382	38243
done	5000	38243

prune979.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.2b

localize104.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.5b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`exp-prod` `add-cbrt-cube` `add-exp-log`
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` `sin-mult` `unswap-sqr` `rem-exp-log`

Counts

4 → 55

Calls

4 calls:

19.0ms	(* (sin phi1) (sin phi2))
5.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
8.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sin phi1) (sin phi2))
97.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
42.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
46.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.8s

Counts

67 → 67

Iterations

Useful iterations: 3 (711.0ms)

Iter	Nodes	Cost
0	107	48060
1	196	45468
2	542	44988
3	2671	44869
done	5001	44869

prune730.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 3.2b

regimes2.0s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	24	1035
1	32	1035
done	32	1035

end0.0ms

sample16.8s

Algorithm

intervals

Results

11.7s	4851×	body	1280	valid
3.1s	2089×	body	640	valid
1.0s	678×	body	320	valid
464.0ms	246×	body	160	valid
31.0ms	133×	body	80	valid
29.0ms	7×	body	2560	valid