Details

sample622.0ms

Algorithm

intervals

Results

348.0ms	152×	body	1280	valid
64.0ms	63×	body	640	valid
19.0ms	24×	body	320	valid
4.0ms	9×	body	160	valid
2.0ms	8×	body	80	valid

simplify61.0ms

Counts

1 → 1

Iterations

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

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
0.2b	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
1.1b	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
3.4b	(cos (- lambda1 lambda2))

rewrite29.0ms

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` `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 → 61

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))))
19.0ms	(cos (- lambda1 lambda2))

series282.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(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))))
29.0ms	(cos (- lambda1 lambda2))

simplify1.8s

Counts

73 → 73

Iterations

Iter	Nodes
done	5002
3	2470
2	731
1	294
0	168

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.9b

localize82.0ms

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 lambda1) (sin lambda2))
0.2b	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
1.1b	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite22.0ms

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` `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 → 61

Calls

4 calls:

0.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
10.0ms	(* (sin lambda1) (sin lambda2))
10.0ms	(* 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))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

407.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
87.0ms	(* (sin lambda1) (sin lambda2))
60.0ms	(* 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))))

simplify3.0s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	4913
2	880
1	258
0	127

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.8b

localize121.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))
0.2b	(* R (log1p (expm1 (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))))
0.5b	(expm1 (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))
1.1b	(acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`acos-asin` `expm1-log1p` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `expm1-udef` `unswap-sqr`

Counts

4 → 51

Calls

4 calls:

0.0ms	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))
10.0ms	(* R (log1p (expm1 (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))))
1.0ms	(expm1 (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))
1.0ms	(acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))

series602.0ms

Counts

4 → 12

Calls

4 calls:

373.0ms	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))
118.0ms	(* R (log1p (expm1 (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))))
85.0ms	(expm1 (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))
25.0ms	(acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))

simplify2.0s

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
3	1974
2	559
1	196
0	105

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.7b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))
0.2b	(* R (log1p (expm1 (acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))))))
0.5b	(expm1 (acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))))
1.1b	(acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l`
5×	`log1p-expm1-u`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef` `add-log-exp`
2×	`*-commutative`
1×	`acos-asin` `expm1-log1p` `expm1-udef` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

24.0ms	(* (cos phi1) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))
10.0ms	(* R (log1p (expm1 (acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))))))
1.0ms	(expm1 (acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))))
1.0ms	(acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

345.0ms	(* (cos phi1) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))
141.0ms	(* R (log1p (expm1 (acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))))))
76.0ms	(expm1 (acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))))
13.0ms	(acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))))

simplify1.8s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
2	1244
1	311
0	139

prune947.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.7b

regimes1.4s

Accuracy

0% (0.3b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample18.2s

Algorithm

intervals

Results

13.6s	4761×	body	1280	valid
3.3s	2133×	body	640	valid
516.0ms	685×	body	320	valid
223.0ms	281×	body	160	valid
78.0ms	7×	body	2560	valid
35.0ms	134×	body	80	valid