Details

sample791.0ms

Algorithm

intervals

Results

468.0ms	151×	body	1280	valid
177.0ms	62×	body	640	valid
32.0ms	27×	body	320	valid
5.0ms	8×	body	160	valid
3.0ms	8×	body	80	valid

simplify48.0ms

Counts

1 → 1

Iterations

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

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.2b

localize102.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
0.2b	(* (sin phi2) (sin phi1))
1.3b	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
3.4b	(cos (- lambda1 lambda2))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum`
9×	`prod-diff`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`acos-asin` `cos-diff` `sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `sin-mult` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

0.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
21.0ms	(* (sin phi2) (sin phi1))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
21.0ms	(cos (- lambda1 lambda2))

series416.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
85.0ms	(* (sin phi2) (sin phi1))
17.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
47.0ms	(cos (- lambda1 lambda2))

simplify2.2s

Counts

78 → 78

Iterations

Iter	Nodes
done	5004
4	2358
3	1156
2	533
1	310
0	180

prune771.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
0.2b	(* (sin phi2) (sin phi1))
0.2b	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
1.3b	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
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` `fma-udef` `sin-mult`

Counts

4 → 65

Calls

4 calls:

0.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
23.0ms	(* (sin phi2) (sin phi1))
9.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

series552.0ms

Counts

4 → 12

Calls

4 calls:

418.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
86.0ms	(* (sin phi2) (sin phi1))
35.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
13.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify2.7s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
3	1755
2	575
1	258
0	130

prune751.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.9b

localize122.0ms

Local error

Found 4 expressions with local error:

0.2b	(* R (log (exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))
0.3b	(exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))
0.9b	(log (exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))))
1.3b	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-l`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 76

Calls

4 calls:

20.0ms	(* R (log (exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))
4.0ms	(exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))
5.0ms	(log (exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))))
2.0ms	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))

series119.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* R (log (exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))
39.0ms	(exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))
19.0ms	(log (exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))))
19.0ms	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))

simplify7.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
5	4491
4	1862
3	743
2	310
1	181
0	116

prune1.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 3.8b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)))
0.2b	(* R (- (/ PI 2) (asin (fma (sin phi2) (sin phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)))))))
0.6b	(asin (fma (sin phi2) (sin phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)))))
1.0b	(- (/ PI 2) (asin (fma (sin phi2) (sin phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1))))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

128×	`add-sqr-sqrt`
120×	`*-un-lft-identity`
117×	`prod-diff`
116×	`add-cube-cbrt`
92×	`times-frac`
42×	`distribute-rgt-in` `distribute-lft-in`
13×	`fma-neg`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`div-inv`
7×	`associate-r`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `asin-acos` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `associate-*r/` `associate--r-`
2×	`flip3--` `*-commutative` `flip--` `distribute-lft-out--`
1×	`diff-log` `cos-mult` `unswap-sqr`

Counts

4 → 214

Calls

4 calls:

21.0ms	(* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)))
33.0ms	(* R (- (/ PI 2) (asin (fma (sin phi2) (sin phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)))))))
1.0ms	(asin (fma (sin phi2) (sin phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)))))
12.0ms	(- (/ PI 2) (asin (fma (sin phi2) (sin phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1))))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)))
118.0ms	(* R (- (/ PI 2) (asin (fma (sin phi2) (sin phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)))))))
10.0ms	(asin (fma (sin phi2) (sin phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)))))
52.0ms	(- (/ PI 2) (asin (fma (sin phi2) (sin phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1))))))

simplify2.4s

Counts

226 → 226

Iterations

Iter	Nodes
done	5000
2	1529
1	701
0	319

prune2.6s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 3.6b

regimes1.5s

Accuracy

0% (0.6b remaining)

Error of 4.2b against oracle of 3.5b and baseline of 4.2b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	29
1	29
0	24

end0.0ms

sample23.6s

Algorithm

intervals

Results

15.7s	4727×	body	1280	valid
5.5s	2132×	body	640	valid
1.4s	705×	body	320	valid
400.0ms	291×	body	160	valid
66.0ms	11×	body	2560	valid
51.0ms	139×	body	80	valid