Details

sample674.0ms

Algorithm

intervals

Results

449.0ms	140×	body	1280	valid
170.0ms	71×	body	640	valid
20.0ms	17×	body	320	valid
9.0ms	23×	body	80	valid
5.0ms	5×	body	160	valid

simplify83.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize89.0ms

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))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

19.0ms	(* (cos phi1) (sin phi2))
50.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))
19.0ms	(sin (- lambda1 lambda2))

series236.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (cos phi1) (sin phi2))
115.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(cos (- lambda1 lambda2))
37.0ms	(sin (- lambda1 lambda2))

simplify2.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
3	3559
2	1053
1	463
0	226

prune966.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.1b

localize106.0ms

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))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

21.0ms	(* (cos phi1) (sin phi2))
17.0ms	(* (cos lambda1) (sin lambda2))
37.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

series293.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (cos phi1) (sin phi2))
74.0ms	(* (cos lambda1) (sin lambda2))
120.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify2.8s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
3	4538
2	1240
1	483
0	226

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize89.0ms

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))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`associate-r`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `sin-cos-mult` `add-log-exp`
3×	`frac-times` `associate-*r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 94

Calls

4 calls:

11.0ms	(* (cos phi1) (sin phi2))
11.0ms	(* (cos lambda1) (sin lambda2))
22.0ms	(* (sin lambda1) (sin lambda2))
95.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (cos phi1) (sin phi2))
57.0ms	(* (cos lambda1) (sin lambda2))
82.0ms	(* (sin lambda1) (sin lambda2))
256.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify2.1s

Counts

106 → 106

Iterations

Iter	Nodes
done	5008
2	2090
1	567
0	201

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

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

rewrite929.0ms

Algorithm

rewrite-expression-head

Rules

87×	`pow1`
78×	`cos-mult` `sin-mult`
74×	`associate-*r/`
66×	`frac-times`
44×	`associate-*l/`
42×	`add-cbrt-cube` `add-exp-log`
37×	`pow-prod-down` `frac-sub`
34×	`sin-cos-mult`
33×	`associate-/l/`
22×	`prod-exp` `cbrt-unprod`
21×	`sub-div`
8×	`pow-sqr` `pow-prod-up`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow-plus` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `cbrt-undiv` `associate-/r` `distribute-lft-in` `times-frac` `div-exp` `associate-l` `-commutative`
2×	`pow2` `sub-neg` `swap-sqr` `prod-diff`
1×	`clear-num` `frac-2neg` `div-inv` `associate-/l*` `difference-of-squares`

Counts

4 → 204

Calls

4 calls:

329.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
469.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
67.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
56.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

749.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
284.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
60.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
74.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

simplify3.4s

Counts

216 → 216

Iterations

Iter	Nodes
done	5000
2	4570
1	1024
0	326

prune2.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes930.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	32
1	32
0	25

end0.0ms

sample24.9s

Algorithm

intervals

Results

18.6s	4534×	body	1280	valid
4.3s	1950×	body	640	valid
1.0s	618×	body	320	valid
297.0ms	682×	body	80	valid
205.0ms	216×	body	160	valid