Details

sample972.0ms

Algorithm

intervals

Results

621.0ms	166×	body	1280	valid
180.0ms	59×	body	640	valid
29.0ms	20×	body	320	valid
7.0ms	8×	body	160	valid
1.0ms	3×	body	80	valid

simplify36.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	34
3	34
2	33
1	26
0	17

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize110.0ms

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)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.2b	(cos (- lambda1 lambda2))

rewrite30.0ms

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×	`insert-posit16` `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 → 59

Calls

4 calls:

11.0ms	(* (sin phi1) (sin phi2))
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))

series175.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (sin phi1) (sin phi2))
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)))))
40.0ms	(cos (- lambda1 lambda2))

simplify1.6s

Counts

71 → 71

Iterations

Iter	Nodes
5	2416
4	1509
3	872
2	439
1	209
0	115

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.9b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite68.0ms

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×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 68

Calls

4 calls:

30.0ms	(* (sin lambda1) (sin lambda2))
22.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series278.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin lambda1) (sin lambda2))
68.0ms	(* (sin phi1) (sin phi2))
126.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
31.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.5s

Counts

80 → 80

Iterations

Iter	Nodes
4	2887
3	1440
2	639
1	279
0	138

prune1.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.8b

localize130.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.7b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`acos-asin` `log-prod` `associate-r`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 62

Calls

4 calls:

33.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
6.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
10.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series209.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
62.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
29.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
26.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify5.2s

Counts

74 → 74

Iterations

Iter	Nodes
6	4942
5	1438
4	813
3	613
2	383
1	189
0	107

prune1.7s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 2.7b

localize117.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))))))
29.8b	(cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
18×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
16×	`sin-mult`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
7×	`cbrt-div`
6×	`frac-times` `-un-lft-identity` `associate-r/` `add-cube-cbrt`
4×	`associate-r` `associate-l` `associate-*l/` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
2×	`pow-plus` `*-commutative`
1×	`cbrt-prod` `pow2` `acos-asin` `pow1/3` `cube-unmult` `swap-sqr` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
79.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))))))
176.0ms	(cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
98.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
28.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))))))
82.0ms	(cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify2.8s

Counts

96 → 96

Iterations

Iter	Nodes
3	4560
2	1080
1	346
0	159

prune1.5s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 2.7b

regimes2.4s

Accuracy

0% (0.5b remaining)

Error of 4.0b against oracle of 3.5b and baseline of 4.0b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	34
1	34
0	25

end0.0ms

sample24.2s

Algorithm

intervals

Results

18.0s	4811×	body	1280	valid
4.2s	2047×	body	640	valid
1.1s	685×	body	320	valid
268.0ms	323×	body	160	valid
66.0ms	11×	body	2560	valid
49.0ms	123×	body	80	valid