Details

sample851.0ms

Algorithm

intervals

Results

528.0ms	156×	body	1280	valid
129.0ms	64×	body	640	valid
28.0ms	23×	body	320	valid
8.0ms	10×	body	160	valid
1.0ms	3×	body	80	valid

simplify56.0ms

Counts

1 → 1

Iterations

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

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.5b

localize97.0ms

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))

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:

12.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (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)))))
21.0ms	(cos (- lambda1 lambda2))

series208.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sin phi1) (sin phi2))
72.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
39.0ms	(cos (- lambda1 lambda2))

simplify2.4s

Counts

88 → 88

Iterations

Iter	Nodes
5	2884
4	1839
3	1055
2	591
1	329
0	191

prune789.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.4b

localize85.0ms

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))))))

rewrite101.0ms

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:

11.0ms	(* (sin phi1) (sin phi2))
74.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
11.0ms	(* (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))))))

series476.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sin phi1) (sin phi2))
324.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
74.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify8.4s

Counts

96 → 96

Iterations

Iter	Nodes
3	9895
2	1960
1	534
0	195

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.3b

localize71.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))
0.4b	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
0.4b	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
0.6b	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log-pow` `insert-posit16` `log1p-expm1-u`
3×	`acos-asin` `log-prod`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `fma-udef` `rem-exp-log`

Counts

4 → 56

Calls

4 calls:

0.0ms	(fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))
4.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
5.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

328.0ms	(fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))
33.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
25.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
16.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

simplify1.4s

Counts

68 → 68

Iterations

Iter	Nodes
4	3101
3	761
2	317
1	166
0	100

prune863.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.3b

localize139.0ms

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 lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2)))) (* (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))))))))

rewrite230.0ms

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:

69.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
78.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
76.0ms	(* (* (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 lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2)))) (* (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))))))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
88.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
91.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
59.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (fma (* (cos lambda2) (cos lambda1)) (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2)))) (* (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))))))))

simplify6.0s

Counts

143 → 143

Iterations

Iter	Nodes
3	9563
2	1857
1	486
0	197

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.2b

regimes1.6s

Accuracy

0% (0.5b remaining)

Error of 3.8b against oracle of 3.3b and baseline of 3.8b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	30
1	30
0	26

end0.0ms

sample23.4s

Algorithm

intervals

Results

15.6s	4745×	body	1280	valid
6.0s	2109×	body	640	valid
938.0ms	722×	body	320	valid
315.0ms	278×	body	160	valid
82.0ms	144×	body	80	valid
34.0ms	7×	body	2560	valid