Details

sample820.0ms

Algorithm

intervals

Results

478.0ms	161×	body	1280	valid
108.0ms	62×	body	640	valid
87.0ms	18×	body	320	valid
8.0ms	10×	body	160	valid
1.0ms	5×	body	80	valid

simplify42.0ms

Counts

1 → 1

Iterations

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

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.5b	(cos (- lambda1 lambda2))

rewrite45.0ms

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)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
22.0ms	(cos (- lambda1 lambda2))

series674.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (sin phi1) (sin phi2))
80.0ms	(* (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)))))
477.0ms	(cos (- lambda1 lambda2))

simplify1.5s

Counts

88 → 88

Iterations

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

prune970.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.6b

localize71.0ms

Local error

Found 4 expressions with local error:

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)
0.2b	(* (sin lambda1) (sin lambda2))
1.0b	(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:

23.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
33.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series286.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (sin phi1) (sin phi2))
116.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
67.0ms	(* (sin lambda1) (sin lambda2))
24.0ms	(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	2031
4	2031
3	1600
2	676
1	295
0	146

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.5b

localize99.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))))) R)
0.4b	(exp (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))))
0.7b	(log (exp (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2))))))
1.0b	(acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2))))

rewrite31.0ms

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:

19.0ms	(* (log (exp (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))))) R)
4.0ms	(exp (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))))
5.0ms	(log (exp (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2))))))
1.0ms	(acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2))))

series142.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (log (exp (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))))) R)
28.0ms	(exp (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))))
19.0ms	(log (exp (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2))))))
18.0ms	(acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2))))

simplify1.7s

Counts

82 → 82

Iterations

Iter	Nodes
done	2003
5	2003
4	1302
3	766
2	337
1	168
0	108

prune1.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 2.5b

localize129.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))
0.2b	(* (- (/ PI 2) (asin (fma (sin phi2) (sin phi1) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (cos phi1))))) R)
0.5b	(asin (fma (sin phi2) (sin phi1) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (cos phi1))))
0.8b	(- (/ PI 2) (asin (fma (sin phi2) (sin phi1) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (cos phi1)))))

rewrite94.0ms

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:

0.0ms	(fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))
62.0ms	(* (- (/ PI 2) (asin (fma (sin phi2) (sin phi1) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (cos phi1))))) R)
1.0ms	(asin (fma (sin phi2) (sin phi1) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (cos phi1))))
26.0ms	(- (/ PI 2) (asin (fma (sin phi2) (sin phi1) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (cos phi1)))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))
218.0ms	(* (- (/ PI 2) (asin (fma (sin phi2) (sin phi1) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (cos phi1))))) R)
18.0ms	(asin (fma (sin phi2) (sin phi1) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (cos phi1))))
84.0ms	(- (/ PI 2) (asin (fma (sin phi2) (sin phi1) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (cos phi1)))))

simplify1.4s

Counts

131 → 131

Iterations

Iter	Nodes
done	2006
3	2006
2	906
1	413
0	203

prune2.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.3b

regimes1.6s

Accuracy

0% (0.7b remaining)

Error of 4.0b against oracle of 3.3b and baseline of 4.0b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	30
1	30
0	26

end0.0ms

sample24.3s

Algorithm

intervals

Results

17.8s	4866×	body	1280	valid
4.3s	2065×	body	640	valid
973.0ms	646×	body	320	valid
516.0ms	124×	body	80	valid
302.0ms	289×	body	160	valid
74.0ms	13×	body	2560	valid