Details

sample755.0ms

Algorithm

intervals

Results

422.0ms	151×	body	1280	valid
192.0ms	62×	body	640	valid
27.0ms	27×	body	320	valid
6.0ms	8×	body	160	valid
3.0ms	8×	body	80	valid

simplify52.0ms

Counts

1 → 1

Iterations

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

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.2b

localize97.0ms

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))

rewrite42.0ms

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)))
13.0ms	(* (sin phi2) (sin phi1))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
17.0ms	(cos (- lambda1 lambda2))

series344.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
61.0ms	(* (sin phi2) (sin phi1))
16.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
43.0ms	(cos (- lambda1 lambda2))

simplify2.3s

Counts

78 → 78

Iterations

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

prune911.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.0b

localize75.0ms

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))))

rewrite46.0ms

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:

1.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
27.0ms	(* (sin phi2) (sin phi1))
15.0ms	(* R (acos (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))))

series595.0ms

Counts

4 → 12

Calls

4 calls:

429.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
85.0ms	(* (sin phi2) (sin phi1))
60.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
21.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify3.4s

Counts

77 → 77

Iterations

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

prune849.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.9b

localize60.0ms

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))))))

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` `add-exp-log`
6×	`add-cbrt-cube`
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` `rem-log-exp`
1×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 77

Calls

4 calls:

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

series111.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 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)))))))
25.0ms	(log (exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))))
10.0ms	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))

simplify7.1s

Counts

89 → 89

Iterations

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

prune1.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 3.8b

localize100.0ms

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))))))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

138×	`add-sqr-sqrt`
123×	`*-un-lft-identity`
119×	`add-cube-cbrt`
117×	`prod-diff`
92×	`times-frac`
42×	`distribute-rgt-in` `distribute-lft-in`
21×	`associate-r`
13×	`fma-neg`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`div-inv`
9×	`associate-l`
6×	`add-log-exp`
5×	`unswap-sqr`
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/` `-commutative` `associate--r-`
2×	`flip3--` `flip--` `distribute-lft-out--`
1×	`diff-log` `cos-mult`

Counts

4 → 227

Calls

4 calls:

63.0ms	(* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)))
95.0ms	(* 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)))))
46.0ms	(- (/ PI 2) (asin (fma (sin phi2) (sin phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1))))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)))
122.0ms	(* 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)))))
75.0ms	(- (/ PI 2) (asin (fma (sin phi2) (sin phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1))))))

simplify2.7s

Counts

239 → 239

Iterations

Iter	Nodes
done	5001
2	1963
1	763
0	344

prune3.1s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 3.6b

regimes1.8s

Accuracy

0% (0.6b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample23.5s

Algorithm

intervals

Results

16.9s	4727×	body	1280	valid
4.9s	2132×	body	640	valid
981.0ms	705×	body	320	valid
219.0ms	291×	body	160	valid
65.0ms	11×	body	2560	valid
51.0ms	139×	body	80	valid