Details

sample729.0ms

Algorithm

intervals

Results

554.0ms	149×	body	1280	valid
97.0ms	52×	body	640	valid
33.0ms	23×	body	320	valid
12.0ms	13×	body	160	valid
7.0ms	19×	body	80	valid

simplify57.0ms

Counts

1 → 1

Iterations

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

prune382.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.3b	(sin (- lambda1 lambda2))
2.4b	(cos (- lambda1 lambda2))

rewrite100.0ms

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` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

33.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
35.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(sin (- lambda1 lambda2))
15.0ms	(cos (- lambda1 lambda2))

series268.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
120.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
29.0ms	(sin (- lambda1 lambda2))
23.0ms	(cos (- lambda1 lambda2))

simplify723.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	2002
2	1063
1	436
0	214

prune1.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 4.9b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite168.0ms

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` `associate-l/` `-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `sin-cos-mult` `flip--`

Counts

4 → 90

Calls

4 calls:

15.0ms	(* (cos lambda1) (sin lambda2))
88.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
51.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms	(cos (- lambda1 lambda2))

series395.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (cos lambda1) (sin lambda2))
183.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
119.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(cos (- lambda1 lambda2))

simplify888.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	2000
2	1366
1	492
0	225

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize108.0ms

Local error

Found 4 expressions with local error:

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

rewrite251.0ms

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-l/` `associate-r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `flip--`

Counts

4 → 96

Calls

4 calls:

22.0ms	(* (cos lambda1) (sin lambda2))
115.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
23.0ms	(* (sin lambda1) (sin lambda2))
89.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (cos lambda1) (sin lambda2))
206.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
56.0ms	(* (sin lambda1) (sin lambda2))
256.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify509.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	2002
1	571
0	200

prune1.1s

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	(expm1 (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(log1p (expm1 (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

rewrite109.0ms

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-r`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `sin-cos-mult` `add-log-exp`
3×	`frac-times` `associate-*r/` `sin-mult`
2×	`flip3-+` `frac-add` `cos-mult` `*-commutative` `flip-+`
1×	`distribute-rgt-in` `log1p-udef` `expm1-log1p` `distribute-lft-in` `associate-*l/` `log1p-expm1` `expm1-udef` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

1.0ms	(expm1 (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2)))
22.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(log1p (expm1 (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))))
84.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series795.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(expm1 (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2)))
66.0ms	(* (sin lambda1) (sin lambda2))
232.0ms	(log1p (expm1 (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))))
245.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify1.0s

Counts

88 → 88

Iterations

Iter	Nodes
done	2000
2	1772
1	459
0	165

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes634.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	37
1	37
0	27

end0.0ms

sample25.9s

Algorithm

intervals

Results

18.9s	4567×	body	1280	valid
5.1s	1965×	body	640	valid
918.0ms	569×	body	320	valid
307.0ms	672×	body	80	valid
263.0ms	227×	body	160	valid