Details

sample1.2s

Algorithm

intervals

Results

711.0ms	140×	body	1280	valid
208.0ms	68×	body	640	valid
77.0ms	31×	body	320	valid
13.0ms	9×	body	160	valid
7.0ms	1×	body	2560	valid
3.0ms	8×	body	80	valid

simplify48.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	46
4	46
3	44
2	38
1	27
0	17

prune52.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize172.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 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)))
0.6b	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
3.8b	(cos (- lambda1 lambda2))

rewrite69.0ms

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))))
53.0ms	(cos (- lambda1 lambda2))

series264.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
176.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
10.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
52.0ms	(cos (- lambda1 lambda2))

simplify1.7s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
3	2763
2	786
1	302
0	172

prune896.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.1b

localize84.0ms

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)))
0.6b	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite21.0ms

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:

11.0ms	(* (sin phi2) (sin phi1))
7.0ms	(* 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)))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

series527.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin phi2) (sin phi1))
46.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
403.0ms	(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))))

simplify1.6s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
2	830
1	258
0	130

prune890.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.0b

localize103.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))
0.4b	(exp (acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))
0.5b	(log (exp (acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))))
0.6b	(acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))

rewrite13.0ms

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 (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))
4.0ms	(exp (acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))
6.0ms	(log (exp (acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))))
2.0ms	(acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))

series475.0ms

Counts

4 → 12

Calls

4 calls:

389.0ms	(fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))
51.0ms	(exp (acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))
18.0ms	(log (exp (acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))))
17.0ms	(acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))

simplify3.5s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
3	1204
2	398
1	168
0	101

prune957.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 2.9b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* R (acos (fma (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (sin phi1) (sin phi2)))))
0.2b	(fma (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (sin phi1) (sin phi2)))
0.6b	(acos (fma (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (sin phi1) (sin phi2))))

rewrite40.0ms

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:

24.0ms	(* (sin phi1) (sin phi2))
12.0ms	(* R (acos (fma (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (sin phi1) (sin phi2)))))
1.0ms	(fma (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (sin phi1) (sin phi2)))
2.0ms	(acos (fma (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (sin phi1) (sin phi2))))

series558.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin phi1) (sin phi2))
31.0ms	(* R (acos (fma (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (sin phi1) (sin phi2)))))
467.0ms	(fma (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (sin phi1) (sin phi2)))
10.0ms	(acos (fma (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (sin phi1) (sin phi2))))

simplify3.0s

Counts

77 → 77

Iterations

Iter	Nodes
done	5002
3	3788
2	746
1	248
0	124

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 2.9b

regimes1.6s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	26
1	26
0	22

end0.0ms

sample24.6s

Algorithm

intervals

Results

16.2s	4773×	body	1280	valid
6.1s	2117×	body	640	valid
1.5s	666×	body	320	valid
209.0ms	278×	body	160	valid
127.0ms	18×	body	2560	valid
61.0ms	150×	body	80	valid