Details

sample881.0ms

Algorithm

intervals

Results

479.0ms	145×	body	1280	valid
145.0ms	75×	body	640	valid
33.0ms	23×	body	320	valid
12.0ms	1×	body	2560	valid
8.0ms	10×	body	160	valid
1.0ms	2×	body	80	valid

simplify29.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	39
3	39
2	38
1	27
0	17

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize54.0ms

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)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.8b	(cos (- lambda1 lambda2))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum`
9×	`prod-diff`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 76

Calls

4 calls:

20.0ms	(* (sin phi1) (sin phi2))
10.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
14.0ms	(cos (- lambda1 lambda2))

series166.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin phi1) (sin phi2))
44.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
35.0ms	(cos (- lambda1 lambda2))

simplify1.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	2006
4	2006
3	1335
2	624
1	339
0	191

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.4b

localize73.0ms

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)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite71.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 76

Calls

4 calls:

32.0ms	(* (sin lambda1) (sin lambda2))
22.0ms	(* (sin phi1) (sin phi2))
12.0ms	(* (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))))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sin lambda1) (sin lambda2))
80.0ms	(* (sin phi1) (sin phi2))
122.0ms	(* (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))))))

simplify1.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	2036
4	2036
3	1611
2	696
1	295
0	146

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.3b

localize96.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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 → 70

Calls

4 calls:

11.0ms	(* (log (exp (acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1)))))) R)
3.0ms	(log (exp (acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1))))))
2.0ms	(exp (acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1)))))
1.0ms	(acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1))))

series111.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (log (exp (acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1)))))) R)
10.0ms	(log (exp (acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1))))))
28.0ms	(exp (acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1)))))
16.0ms	(acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1))))

simplify1.5s

Counts

82 → 82

Iterations

Iter	Nodes
done	2001
5	2001
4	1833
3	1072
2	378
1	171
0	109

prune1.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 3.2b

localize103.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2)))) (cbrt (* (sin lambda1) (sin lambda2))))))))
9.6b	(cbrt (* (sin lambda1) (sin lambda2)))
9.6b	(cbrt (* (sin lambda1) (sin lambda2)))
9.6b	(cbrt (* (sin lambda1) (sin lambda2)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-mult`
1×	`acos-asin`

Counts

4 → 50

Calls

4 calls:

2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2)))) (cbrt (* (sin lambda1) (sin lambda2))))))))
10.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
10.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
10.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2)))) (cbrt (* (sin lambda1) (sin lambda2))))))))
148.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
122.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
143.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

simplify1.1s

Counts

62 → 62

Iterations

Iter	Nodes
done	2001
4	2001
3	1060
2	406
1	174
0	84

prune821.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 3.2b

regimes2.7s

Accuracy

0% (0.5b remaining)

Error of 4.1b against oracle of 3.6b and baseline of 4.1b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	25

end0.0ms

sample22.2s

Algorithm

intervals

Results

15.0s	4797×	body	1280	valid
5.5s	2117×	body	640	valid
822.0ms	647×	body	320	valid
297.0ms	308×	body	160	valid
74.0ms	12×	body	2560	valid
73.0ms	120×	body	80	valid