Details

sample343.0ms

Algorithm

intervals

Results

169.0ms	104×	body	1280	valid
115.0ms	86×	body	640	valid
12.0ms	19×	body	320	valid
8.0ms	19×	body	160	valid
6.0ms	28×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
2	23
1	20
0	14

prune67.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.5b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.6b	(sin (- lambda1 lambda2))
3.8b	(cos (- lambda1 lambda2))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
16×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum` `sin-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg`
1×	`cos-diff` `sin-diff` `fma-udef`

Counts

4 → 61

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
17.0ms	(sin (- lambda1 lambda2))
11.0ms	(cos (- lambda1 lambda2))

series246.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
161.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
33.0ms	(sin (- lambda1 lambda2))
32.0ms	(cos (- lambda1 lambda2))

simplify1.4s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	1600
2	615
1	290
0	172

prune913.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.7b

localize61.0ms

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)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.5b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.8b	(cos (- lambda1 lambda2))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

70.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
11.0ms	(cos (- lambda1 lambda2))

series436.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
23.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
172.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
27.0ms	(cos (- lambda1 lambda2))

simplify1.5s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1353
1	374
0	189

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize100.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

rewrite91.0ms

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`
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 → 68

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
74.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
15.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series704.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
216.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
87.0ms	(* (sin lambda1) (sin lambda2))
383.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify1.5s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1560
1	344
0	148

prune949.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize93.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1)))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(* (sin lambda2) (sin lambda1))
0.5b	(+ (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1))

rewrite118.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
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×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip3--` `flip-+` `flip--` `sin-mult`

Counts

4 → 72

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1)))
94.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
13.0ms	(* (sin lambda2) (sin lambda1))
8.0ms	(+ (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1))

series574.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1)))
206.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
53.0ms	(* (sin lambda2) (sin lambda1))
298.0ms	(+ (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1))

simplify1.7s

Counts

84 → 84

Iterations

Iter	Nodes
done	5002
2	1738
1	398
0	160

prune900.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes959.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	33
1	33
0	26

end0.0ms

sample11.6s

Algorithm

intervals

Results

7.1s	3606×	body	1280	valid
2.8s	2359×	body	640	valid
678.0ms	900×	body	320	valid
202.0ms	429×	body	160	valid
172.0ms	706×	body	80	valid