Details

sample351.0ms

Algorithm

intervals

Results

166.0ms	114×	body	1280	valid
80.0ms	34×	body	320	valid
69.0ms	74×	body	640	valid
5.0ms	12×	body	160	valid
4.0ms	22×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.4b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.4b	(sin (- lambda1 lambda2))
5.6b	(cos (- lambda1 lambda2))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
29.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms	(sin (- lambda1 lambda2))
37.0ms	(cos (- lambda1 lambda2))

series225.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
141.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
39.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

simplify2.0s

Counts

81 → 81

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	191	1730
1	372	1402
2	907	1106
3	2872	1020
done	5002	911

prune547.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.8b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (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)))))
0.4b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.6b	(cos (- lambda1 lambda2))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

57.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
14.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
26.0ms	(cos (- lambda1 lambda2))

series400.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
17.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
160.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts

84 → 84

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	203	1783
1	483	1565
2	1816	1305
done	5002	1276

prune804.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `associate-+r+` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-rgt-in` `sub-neg` `fma-def` `distribute-lft-in` `associate-r` `associate-l` `prod-diff` `sin-mult`
2×	`cos-mult`
1×	`+-commutative` `flip3--` `flip3-+` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `sin-neg` `sum-log` `*-commutative` `distribute-rgt-neg-out` `frac-sub` `flip--` `cbrt-unprod` `flip-+` `sub-div` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

38.0ms	(- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))
1.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))
36.0ms	(* (sin lambda1) (sin (- lambda2)))
11.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))

series568.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))
37.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))
74.0ms	(* (sin lambda1) (sin (- lambda2)))
338.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))

simplify1.5s

Counts

83 → 83

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	168	1653
1	423	1571
2	1710	1299
done	5000	1261

prune842.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize95.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) 3))
0.4b	(pow (cos phi1) 3)
0.6b	(pow (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) 3)
1.4b	(- (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (cos phi1))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`unpow-prod-down` `cube-prod`
6×	`pow-unpow`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cube-mult` `pow-pow` `unpow3` `prod-diff` `pow-exp` `rem-cube-cbrt` `sqr-pow`
2×	`pow-to-exp` `associate--l+` `fma-udef`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `sum-cubes` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

32.0ms	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) 3))
7.0ms	(pow (cos phi1) 3)
16.0ms	(pow (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) 3)
24.0ms	(- (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (cos phi1))

series1.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) 3))
49.0ms	(pow (cos phi1) 3)
334.0ms	(pow (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) 3)
264.0ms	(- (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) (cos phi1))

simplify2.1s

Counts

108 → 108

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	195	1879
1	613	1657
2	3619	1502
done	5000	1498

prune922.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes867.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	94
1	45	94
done	45	94

end0.0ms

sample11.3s

Algorithm

intervals

Results

7.2s	3580×	body	1280	valid
2.5s	2341×	body	640	valid
703.0ms	946×	body	320	valid
189.0ms	714×	body	80	valid
144.0ms	419×	body	160	valid