Details

sample751.0ms

Algorithm

intervals

Results

423.0ms	156×	body	1280	valid
102.0ms	64×	body	640	valid
63.0ms	23×	body	320	valid
6.0ms	10×	body	160	valid
1.0ms	3×	body	80	valid

simplify50.0ms

Counts

1 → 1

Iterations

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

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.5b

localize68.0ms

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)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.8b	(cos (- lambda1 lambda2))

rewrite48.0ms

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:

21.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (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))

series175.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin phi1) (sin phi2))
57.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
40.0ms	(cos (- lambda1 lambda2))

simplify1.5s

Counts

88 → 88

Iterations

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

prune2.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.4b

localize99.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite103.0ms

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` `insert-posit16` `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 → 84

Calls

4 calls:

23.0ms	(* (sin phi1) (sin phi2))
71.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
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))))))

series493.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (sin phi1) (sin phi2))
294.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
108.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.7s

Counts

96 → 96

Iterations

Iter	Nodes
done	2001
3	2001
2	1996
1	536
0	195

prune2.6s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.3b

localize180.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.4b	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (fma (* (cos lambda2) (cos lambda1)) (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda2) (sin lambda1)) (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))))) (* (cos phi1) (cos phi2))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

121×	`pow1`
51×	`pow-prod-down`
40×	`add-cbrt-cube` `add-exp-log`
24×	`prod-exp` `cbrt-unprod`
12×	`pow-sqr` `pow-prod-up`
8×	`cos-mult`
6×	`pow-plus`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `sin-mult` `add-log-exp`
3×	`pow2` `frac-times` `swap-sqr` `associate-r` `associate-l` `associate-l/` `associate-r/` `*-commutative`
1×	`acos-asin`

Counts

4 → 131

Calls

4 calls:

89.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
63.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
71.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (fma (* (cos lambda2) (cos lambda1)) (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda2) (sin lambda1)) (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))))) (* (cos phi1) (cos phi2))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

series323.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
96.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
94.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
39.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (fma (* (cos lambda2) (cos lambda1)) (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda2) (sin lambda1)) (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))))) (* (cos phi1) (cos phi2))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

simplify1.1s

Counts

143 → 143

Iterations

Iter	Nodes
done	2004
2	2004
1	530
0	203

prune4.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.3b

localize73.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))) R)
0.3b	(fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))
0.3b	(asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))
0.6b	(- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
39×	`prod-diff`
38×	`times-frac`
13×	`fma-neg`
6×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `difference-of-squares`
3×	`associate-r`
2×	`asin-acos` `flip3--` `associate-*l/` `flip--` `distribute-lft-out--`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `associate--r-` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

63.0ms	(* (- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))) R)
0.0ms	(fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))
1.0ms	(asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))
15.0ms	(- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))

series583.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))) R)
348.0ms	(fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))
18.0ms	(asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))
54.0ms	(- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))

simplify1.2s

Counts

131 → 131

Iterations

Iter	Nodes
done	2002
3	2002
2	976
1	438
0	208

prune2.8s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 3.0b

regimes2.1s

Accuracy

0% (0.6b remaining)

Error of 3.8b against oracle of 3.1b and baseline of 3.8b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	30
1	30
0	26

end0.0ms

sample23.1s

Algorithm

intervals

Results

15.4s	4745×	body	1280	valid
5.4s	2109×	body	640	valid
1.5s	722×	body	320	valid
232.0ms	278×	body	160	valid
55.0ms	144×	body	80	valid
38.0ms	7×	body	2560	valid