Details

sample493.0ms

Algorithm

intervals

Results

323.0ms	112×	body	1280	valid
88.0ms	74×	body	640	valid
32.0ms	41×	body	320	valid
8.0ms	16×	body	160	valid
3.0ms	13×	body	80	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	14	20
1	20	20
2	23	19
done	23	19

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.0b	(sin (- lambda1 lambda2))
3.1b	(cos (- lambda1 lambda2))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
33×	`sin-sum`
32×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
11×	`distribute-rgt-in` `cos-sum` `distribute-lft-in`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`cos-diff` `pow-prod-down` `prod-exp` `sin-diff` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

73.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
1.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
30.0ms	(sin (- lambda1 lambda2))
52.0ms	(cos (- lambda1 lambda2))

series390.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
201.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
41.0ms	(sin (- lambda1 lambda2))
44.0ms	(cos (- lambda1 lambda2))

simplify1.9s

Counts

106 → 106

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	223	2679
1	493	2042
2	1906	1593
done	5000	1493

prune975.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.8b

localize103.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (- (* (cos lambda1) (sin lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.6b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.1b	(cos (- lambda1 lambda2))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

24.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (- (* (cos lambda1) (sin lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
1.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
27.0ms	(cos (- lambda1 lambda2))

series356.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (sin lambda1) (cos lambda2))
33.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (- (* (cos lambda1) (sin lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
209.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
31.0ms	(cos (- lambda1 lambda2))

simplify3.4s

Counts

73 → 73

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	180	1317
1	339	1140
2	951	948
3	4132	904
done	5001	902

prune958.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize110.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-cos-mult` `fma-udef` `sin-mult`

Counts

4 → 61

Calls

4 calls:

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

series641.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (sin lambda1) (cos lambda2))
36.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (- (* (cos lambda1) (sin lambda2))))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (cos phi1)))
99.0ms	(* (sin lambda2) (sin lambda1))
422.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (cos phi1))

simplify1.2s

Counts

73 → 73

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	136	1120
1	296	1067
2	1103	934
done	5001	929

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize117.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)))
0.6b	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))
0.7b	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-prod` `log-pow` `log1p-expm1-u`
3×	`associate-r` `associate-l` `fma-udef`
2×	`exp-sum`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `sin-mult` `unswap-sqr`

Counts

4 → 63

Calls

4 calls:

26.0ms	(* (sin lambda2) (sin lambda1))
5.0ms	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)))
1.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))
7.0ms	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))))

series1.5s

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (sin lambda2) (sin lambda1))
537.0ms	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)))
404.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))
430.0ms	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))))

simplify5.8s

Counts

75 → 75

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	116	1238
1	233	1177
2	716	1023
3	4624	1020
done	5000	1020

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes1.2s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	37
1	36	37
2	38	37
done	38	37

end0.0ms

sample15.8s

Algorithm

intervals

Results

9.1s	3558×	body	1280	valid
3.4s	2329×	body	640	valid
1.7s	980×	body	320	valid
411.0ms	441×	body	160	valid
280.0ms	692×	body	80	valid