Details

sample817.0ms

Algorithm

intervals

Results

517.0ms	161×	body	1280	valid
176.0ms	70×	body	640	valid
24.0ms	21×	body	320	valid
1.0ms	2×	body	160	valid
1.0ms	2×	body	80	valid

simplify24.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.4b

localize473.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (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)))))
5.0b	(cos (- lambda1 lambda2))

rewrite59.0ms

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:

23.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

series226.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sin phi1) (sin phi2))
77.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
59.0ms	(cos (- lambda1 lambda2))

simplify2.9s

Counts

71 → 71

Iterations

Iter	Nodes
6	4399
5	1944
4	1234
3	801
2	423
1	211
0	115

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.6b

localize77.0ms

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))))))

rewrite37.0ms

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:

18.0ms	(* (sin lambda1) (sin lambda2))
10.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series274.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sin lambda1) (sin lambda2))
81.0ms	(* (sin phi1) (sin phi2))
92.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
29.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.5s

Counts

80 → 80

Iterations

Iter	Nodes
4	2527
3	1401
2	628
1	281
0	138

prune1.7s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.6b

localize93.0ms

Local error

Found 4 expressions with local error:

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

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

Counts

4 → 65

Calls

4 calls:

21.0ms	(* (sin phi1) (sin phi2))
27.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
2.0ms	(log (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))))))

series232.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (sin phi1) (sin phi2))
71.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
52.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
29.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.0s

Counts

77 → 77

Iterations

Iter	Nodes
5	2662
4	1684
3	1022
2	530
1	245
0	128

prune2.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.5b

localize110.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b	(* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2)))
1.1b	(acos (+ (cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
23.7b	(cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2))))

rewrite215.0ms

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-l/` `add-cube-cbrt`
4×	`associate-r` `associate-l` `associate-*r/` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
2×	`pow-plus` `*-commutative`
1×	`cbrt-prod` `pow2` `acos-asin` `pow1/3` `swap-sqr` `pow3` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

12.0ms	(* (acos (+ (cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
81.0ms	(* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2)))
1.0ms	(acos (+ (cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
118.0ms	(cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2))))

series280.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (acos (+ (cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
88.0ms	(* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2)))
30.0ms	(acos (+ (cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
89.0ms	(cbrt (* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2))))

simplify1.9s

Counts

96 → 96

Iterations

Iter	Nodes
3	3934
2	1001
1	336
0	157

prune2.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.5b

regimes1.8s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.3b and baseline of 3.8b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	34
1	34
0	25

end0.0ms

sample22.0s

Algorithm

intervals

Results

16.1s	4735×	body	1280	valid
4.3s	2152×	body	640	valid
870.0ms	696×	body	320	valid
253.0ms	268×	body	160	valid
56.0ms	9×	body	2560	valid
51.0ms	141×	body	80	valid