Details

sample808.0ms

Algorithm

intervals

Results

519.0ms	140×	body	1280	valid
219.0ms	71×	body	640	valid
29.0ms	17×	body	320	valid
10.0ms	23×	body	80	valid
5.0ms	5×	body	160	valid

simplify54.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
4	80
3	77
2	47
1	28
0	17

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.4b	(cos (- lambda1 lambda2))
2.6b	(sin (- lambda1 lambda2))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
18×	`associate-l` `prod-diff`
11×	`pow1` `cos-sum` `add-cbrt-cube` `sin-sum` `add-exp-log`
9×	`associate-r`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`sub-neg`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult`

Counts

4 → 102

Calls

4 calls:

21.0ms	(* (cos phi1) (sin phi2))
83.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

series214.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos phi1) (sin phi2))
104.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))
37.0ms	(sin (- lambda1 lambda2))

simplify2.4s

Counts

114 → 114

Iterations

Iter	Nodes
done	5003
3	3677
2	1130
1	499
0	245

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.1b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.4b	(cos (- lambda1 lambda2))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
21×	`associate-l`
18×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`associate-r`
11×	`cos-sum`
9×	`prod-diff`
6×	`unswap-sqr`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-cos-mult`

Counts

4 → 101

Calls

4 calls:

14.0ms	(* (cos phi1) (sin phi2))
13.0ms	(* (cos lambda1) (sin lambda2))
58.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

series261.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (cos phi1) (sin phi2))
50.0ms	(* (cos lambda1) (sin lambda2))
135.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify2.2s

Counts

113 → 113

Iterations

Iter	Nodes
done	5003
3	4259
2	1280
1	517
0	245

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize80.0ms

Local error

Found 4 expressions with local error:

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

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate-l`
27×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
19×	`associate-r`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
14×	`add-cube-cbrt`
7×	`unswap-sqr`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-commutative`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `sin-cos-mult` `distribute-lft-out` `add-log-exp`
3×	`frac-times` `associate-*r/` `sin-mult`
2×	`distribute-rgt-in` `+-commutative` `distribute-lft-in` `flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`associate-*l/`

Counts

4 → 113

Calls

4 calls:

18.0ms	(* (cos phi1) (sin phi2))
21.0ms	(* (cos lambda1) (sin lambda2))
22.0ms	(* (sin lambda1) (sin lambda2))
225.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (cos phi1) (sin phi2))
62.0ms	(* (cos lambda1) (sin lambda2))
76.0ms	(* (sin lambda1) (sin lambda2))
214.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify2.0s

Counts

125 → 125

Iterations

Iter	Nodes
done	5022
2	2462
1	650
0	220

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize111.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (sin phi1)) (cos phi2)))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (sin phi1))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`expm1-log1p` `expm1-udef`

Counts

4 → 75

Calls

4 calls:

0.0ms	(expm1 (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (sin phi1)) (cos phi2)))
18.0ms	(* (cos phi1) (sin phi2))
20.0ms	(* (cos lambda1) (sin lambda2))
26.0ms	(* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (sin phi1))

series891.0ms

Counts

4 → 12

Calls

4 calls:

342.0ms	(expm1 (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (sin phi1)) (cos phi2)))
58.0ms	(* (cos phi1) (sin phi2))
59.0ms	(* (cos lambda1) (sin lambda2))
431.0ms	(* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (sin phi1))

simplify1.8s

Counts

87 → 87

Iterations

Iter	Nodes
done	5004
3	2722
2	850
1	329
0	152

prune771.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes868.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	35
1	35
0	26

end0.0ms

sample24.6s

Algorithm

intervals

Results

18.1s	4534×	body	1280	valid
4.3s	1950×	body	640	valid
970.0ms	618×	body	320	valid
671.0ms	682×	body	80	valid
246.0ms	216×	body	160	valid