Details

sample1.1s

Algorithm

intervals

Results

702.0ms	153×	body	1280	valid
194.0ms	71×	body	640	valid
29.0ms	17×	body	320	valid
9.0ms	10×	body	160	valid
2.0ms	5×	body	80	valid

simplify49.0ms

Counts

1 → 1

Iterations

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

prune510.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize80.0ms

Local error

Found 4 expressions with local error:

0.3b	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
0.3b	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
1.3b	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
3.8b	(cos (- lambda1 lambda2))

rewrite51.0ms

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:

11.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
0.0ms	(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))))
21.0ms	(cos (- lambda1 lambda2))

series321.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
221.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
17.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
46.0ms	(cos (- lambda1 lambda2))

simplify1.8s

Counts

77 → 77

Iterations

Iter	Nodes
4	3367
3	1152
2	487
1	289
0	172

prune1.6s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 2.8b

localize110.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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:

12.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
11.0ms	(* 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))))

series535.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (sin lambda1) (sin lambda2))
408.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
36.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
15.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify2.4s

Counts

77 → 77

Iterations

Iter	Nodes
4	5035
3	1575
2	594
1	259
0	131

prune1.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 2.7b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(* R (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))))
0.4b	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
0.8b	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
1.3b	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

rewrite22.0ms

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:

17.0ms	(* R (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))))
2.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
3.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

series133.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* R (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))))
51.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
18.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
14.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

simplify1.8s

Counts

88 → 88

Iterations

Iter	Nodes
5	2222
4	945
3	435
2	237
1	157
0	105

prune2.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 2.6b

localize73.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))))
0.6b	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
0.8b	(log (exp (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))))
1.3b	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod` `exp-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
8×	`log-pow`
6×	`pow1` `exp-sum`
5×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`rem-log-exp`
1×	`acos-asin` `rem-exp-log`

Counts

4 → 64

Calls

4 calls:

10.0ms	(exp (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))))
2.0ms	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
8.0ms	(log (exp (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(exp (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))))
33.0ms	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
18.0ms	(log (exp (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))))
16.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

simplify5.6s

Counts

76 → 76

Iterations

Iter	Nodes
8	5871
7	1965
6	1000
5	638
4	406
3	239
2	153
1	118
0	89

prune2.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 2.6b

regimes1.6s

Accuracy

0% (0.5b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	26
1	26
0	22

end0.0ms

sample24.8s

Algorithm

intervals

Results

17.3s	4709×	body	1280	valid
5.2s	2157×	body	640	valid
1.5s	697×	body	320	valid
230.0ms	290×	body	160	valid
67.0ms	11×	body	2560	valid
54.0ms	138×	body	80	valid