Details

sample955.0ms

Algorithm

intervals

Results

496.0ms	146×	body	1280	valid
283.0ms	68×	body	640	valid
38.0ms	28×	body	320	valid
36.0ms	8×	body	160	valid
3.0ms	6×	body	80	valid

simplify40.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	39
3	39
2	38
1	27
0	17

prune45.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.6b	(cos (- lambda1 lambda2))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1` `cos-sum` `add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

32.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(* (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)))))
19.0ms	(cos (- lambda1 lambda2))

series258.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
66.0ms	(* (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)))))
42.0ms	(cos (- lambda1 lambda2))

simplify1.6s

Counts

86 → 86

Iterations

Iter	Nodes
3	3080
2	934
1	393
0	197

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.5b

localize110.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
6×	`cos-mult`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-*l/`

Counts

4 → 80

Calls

4 calls:

94.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
19.0ms	(* (sin lambda1) (sin lambda2))
10.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series524.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
70.0ms	(* (sin lambda1) (sin lambda2))
109.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
27.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify10.4s

Counts

92 → 92

Iterations

Iter	Nodes
3	9428
2	1967
1	520
0	189

prune2.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.4b

localize86.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`acos-asin` `frac-times` `associate-l/` `associate-r/` `sin-mult`

Counts

4 → 78

Calls

4 calls:

41.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
18.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series418.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
85.0ms	(* (sin lambda1) (sin lambda2))
92.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
27.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify2.2s

Counts

90 → 90

Iterations

Iter	Nodes
3	4354
2	1185
1	405
0	170

prune2.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (sin phi2) (sin phi1)))))) R)
0.4b	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (sin phi2) (sin phi1)))))
0.5b	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (sin phi2) (sin phi1))))))
0.9b	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (sin phi2) (sin phi1))))

rewrite27.0ms

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` `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 → 66

Calls

4 calls:

17.0ms	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (sin phi2) (sin phi1)))))) R)
3.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (sin phi2) (sin phi1)))))
5.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (sin phi2) (sin phi1))))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (sin phi2) (sin phi1))))

series169.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (sin phi2) (sin phi1)))))) R)
49.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (sin phi2) (sin phi1)))))
28.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (sin phi2) (sin phi1))))))
17.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (sin phi2) (sin phi1))))

simplify3.9s

Counts

78 → 78

Iterations

Iter	Nodes
6	5037
5	1637
4	861
3	533
2	299
1	153
0	99

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

regimes1.3s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	30
1	30
0	26

end0.0ms

sample24.9s

Algorithm

intervals

Results

17.2s	4801×	body	1280	valid
5.3s	2135×	body	640	valid
954.0ms	682×	body	320	valid
778.0ms	250×	body	160	valid
56.0ms	9×	body	2560	valid
51.0ms	126×	body	80	valid