Details

sample1.5s

Algorithm

intervals

Results

898.0ms	146×	body	1280	valid
176.0ms	66×	body	640	valid
78.0ms	29×	body	320	valid
42.0ms	11×	body	160	valid
7.0ms	1×	body	2560	valid
1.0ms	3×	body	80	valid

simplify102.0ms

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize61.0ms

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)
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.8b	(cos (- lambda1 lambda2))

rewrite33.0ms

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:

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)))))
11.0ms	(cos (- lambda1 lambda2))

series232.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (sin phi1) (sin phi2))
81.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
29.0ms	(cos (- lambda1 lambda2))

simplify878.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	2000
3	1335
2	624
1	339
0	191

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.9b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.8b	(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×	`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:

16.0ms	(* (sin lambda1) (sin lambda2))
23.0ms	(* (sin phi1) (sin phi2))
12.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series551.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin lambda1) (sin lambda2))
60.0ms	(* (sin phi1) (sin phi2))
404.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	2000
3	1611
2	696
1	295
0	146

prune998.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.8b

localize82.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1)))))) R)
0.4b	(exp (acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1)))))
0.5b	(log (exp (acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1))))))
0.8b	(acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1))))

rewrite23.0ms

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:

17.0ms	(* (log (exp (acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1)))))) R)
2.0ms	(exp (acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1)))))
3.0ms	(log (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))))

series143.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (log (exp (acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1)))))) R)
51.0ms	(exp (acos (fma (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (* (sin phi2) (sin phi1)))))
18.0ms	(log (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))))

simplify1.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	2001
4	1772
3	1053
2	381
1	170
0	109

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 5.7b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.8b	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
2.9b	(log (exp (* (sin phi1) (sin phi2))))

rewrite33.0ms

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`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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 → 71

Calls

4 calls:

11.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
3.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms	(log (exp (* (sin phi1) (sin phi2))))

series257.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (sin phi1) (sin phi2))
95.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
29.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
58.0ms	(log (exp (* (sin phi1) (sin phi2))))

simplify1.0s

Counts

83 → 83

Iterations

Iter	Nodes
done	2002
3	1230
2	551
1	244
0	131

prune707.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 5.7b

regimes1.4s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample23.7s

Algorithm

intervals

Results

17.2s	4749×	body	1280	valid
4.5s	2096×	body	640	valid
1.0s	710×	body	320	valid
276.0ms	280×	body	160	valid
115.0ms	14×	body	2560	valid
59.0ms	153×	body	80	valid