Details

sample733.0ms

Algorithm

intervals

Results

375.0ms	155×	body	1280	valid
113.0ms	64×	body	640	valid
18.0ms	22×	body	320	valid
6.0ms	10×	body	160	valid
1.0ms	5×	body	80	valid

simplify28.0ms

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize99.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
0.3b	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
0.7b	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
2.2b	(cos (- lambda1 lambda2))

rewrite20.0ms

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` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

0.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
6.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
11.0ms	(cos (- lambda1 lambda2))

series786.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
43.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
18.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
489.0ms	(cos (- lambda1 lambda2))

simplify1.7s

Counts

77 → 77

Iterations

Iter	Nodes
4	3214
3	1115
2	482
1	288
0	172

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.3b

localize110.0ms

Local error

Found 4 expressions with local error:

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)))))
0.3b	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
0.7b	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite38.0ms

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:

23.0ms	(* (sin phi2) (sin phi1))
12.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
0.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
2.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

series523.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin phi2) (sin phi1))
29.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
413.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
20.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify2.0s

Counts

77 → 77

Iterations

Iter	Nodes
4	4361
3	1333
2	541
1	252
0	130

prune1.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.2b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b	(* R (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))
0.3b	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))
0.5b	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))))
0.7b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))

rewrite20.0ms

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:

13.0ms	(* R (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))
2.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))
3.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))

series154.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* R (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))
62.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))
20.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))))
20.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))

simplify1.5s

Counts

88 → 88

Iterations

Iter	Nodes
5	2272
4	1141
3	581
2	279
1	177
0	116

prune2.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.1b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b	(* R (- (/ PI 2) (asin (fma (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi2) (sin phi1))))))
0.3b	(fma (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi2) (sin phi1)))
0.4b	(asin (fma (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi2) (sin phi1))))
0.6b	(- (/ PI 2) (asin (fma (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi2) (sin phi1)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 203

Calls

4 calls:

28.0ms	(* R (- (/ PI 2) (asin (fma (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi2) (sin phi1))))))
0.0ms	(fma (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi2) (sin phi1)))
1.0ms	(asin (fma (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi2) (sin phi1))))
13.0ms	(- (/ PI 2) (asin (fma (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi2) (sin phi1)))))

series589.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* R (- (/ PI 2) (asin (fma (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi2) (sin phi1))))))
395.0ms	(fma (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi2) (sin phi1)))
15.0ms	(asin (fma (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi2) (sin phi1))))
76.0ms	(- (/ PI 2) (asin (fma (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi2) (sin phi1)))))

simplify1.3s

Counts

215 → 215

Iterations

Iter	Nodes
3	2500
2	1041
1	557
0	295

prune5.7s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 2.9b

regimes1.6s

Accuracy

0% (0.7b remaining)

Error of 3.7b against oracle of 3.1b and baseline of 3.7b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
4	39
3	39
2	38
1	34
0	26

end0.0ms

sample24.2s

Algorithm

intervals

Results

17.4s	4817×	body	1280	valid
4.8s	2075×	body	640	valid
1.3s	687×	body	320	valid
256.0ms	296×	body	160	valid
54.0ms	9×	body	2560	valid
45.0ms	117×	body	80	valid