Details

sample311.0ms

Algorithm

intervals

Results

159.0ms	111×	body	1280	valid
99.0ms	80×	body	640	valid
12.0ms	22×	body	320	valid
7.0ms	31×	body	80	valid
4.0ms	12×	body	160	valid

simplify44.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
2	23
1	20
0	14

prune441.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
1.4b	(cos (- lambda1 lambda2))
1.5b	(sin (- lambda1 lambda2))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
17×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum` `sin-sum`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`cos-diff` `fma-def`
2×	`associate-+r+` `sub-neg`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `flip3-+` `sin-diff` `flip-+`

Counts

4 → 73

Calls

4 calls:

2.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
40.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms	(cos (- lambda1 lambda2))
39.0ms	(sin (- lambda1 lambda2))

series406.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
245.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
43.0ms	(cos (- lambda1 lambda2))
48.0ms	(sin (- lambda1 lambda2))

simplify4.8s

Counts

85 → 85

Iterations

Iter	Nodes
done	5004
3	1943
2	723
1	376
0	195

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 1.1b

localize147.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
1.4b	(cos (- lambda1 lambda2))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum` `prod-diff`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `insert-posit16` `log1p-expm1-u`
3×	`cos-diff` `sub-neg` `fma-def` `associate-r` `associate-l`
2×	`associate-+r+` `associate-*r/`
1×	`+-commutative` `sum-log` `flip3-+` `flip3--` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

85.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
25.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
30.0ms	(cos (- lambda1 lambda2))

series731.0ms

Counts

4 → 12

Calls

4 calls:

337.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
119.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
232.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
43.0ms	(cos (- lambda1 lambda2))

simplify6.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
3	3881
2	1193
1	458
0	212

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize156.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.6b	(fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))

rewrite141.0ms

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`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `prod-diff` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `fma-udef` `flip--` `sin-mult`

Counts

4 → 72

Calls

4 calls:

18.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
116.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
2.0ms	(fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))

series892.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (sin lambda1) (sin lambda2))
104.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
360.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
310.0ms	(fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))

simplify7.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	5002
3	3211
2	902
1	331
0	150

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize246.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (* (fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1)) (fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))) (fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))))
0.6b	(fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))
0.6b	(fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))
0.6b	(fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 46

Calls

4 calls:

20.0ms	(cbrt (* (* (fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1)) (fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))) (fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))))
2.0ms	(fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))
2.0ms	(fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))
2.0ms	(fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))

series1.6s

Counts

4 → 12

Calls

4 calls:

432.0ms	(cbrt (* (* (fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1)) (fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))) (fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))))
413.0ms	(fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))
387.0ms	(fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))
383.0ms	(fma (* (cos lambda2) (cos phi2)) (cos lambda1) (cos phi1))

simplify8.7s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
5	4595
4	1227
3	430
2	142
1	73
0	44

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes2.4s

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	35
1	35
0	26

end0.0ms

sample11.7s

Algorithm

intervals

Results

7.0s	3624×	body	1280	valid
2.7s	2363×	body	640	valid
899.0ms	937×	body	320	valid
435.0ms	669×	body	80	valid
238.0ms	407×	body	160	valid