Details

sample644.0ms

Algorithm

intervals

Results

398.0ms	148×	body	1280	valid
71.0ms	65×	body	640	valid
22.0ms	29×	body	320	valid
4.0ms	7×	body	160	valid
2.0ms	7×	body	80	valid

simplify38.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	36
3	36
2	33
1	26
0	17

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.2b	(cos (- lambda1 lambda2))

rewrite39.0ms

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×	`add-log-exp`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 55

Calls

4 calls:

18.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
10.0ms	(cos (- lambda1 lambda2))

series194.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (sin phi1) (sin phi2))
61.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
22.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
35.0ms	(cos (- lambda1 lambda2))

simplify647.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
2	721
1	208
0	111

prune775.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))) R)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 64

Calls

4 calls:

18.0ms	(* (sin lambda2) (sin lambda1))
17.0ms	(* (sin phi1) (sin phi2))
5.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))

series307.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin lambda2) (sin lambda1))
76.0ms	(* (sin phi1) (sin phi2))
121.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))) R)
43.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))

simplify710.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	1013
1	276
0	134

prune958.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.8b

localize110.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda2) (sin lambda1)) 3)))))) R)
0.3b	(pow (* (sin lambda2) (sin lambda1)) 3)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda2) (sin lambda1)) 3))))))
26.9b	(cbrt (pow (* (sin lambda2) (sin lambda1)) 3))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`cbrt-prod` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `sin-mult` `rem-cube-cbrt` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `cbrt-div` `pow1/3` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda2) (sin lambda1)) 3)))))) R)
14.0ms	(pow (* (sin lambda2) (sin lambda1)) 3)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda2) (sin lambda1)) 3))))))
7.0ms	(cbrt (pow (* (sin lambda2) (sin lambda1)) 3))

series350.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda2) (sin lambda1)) 3)))))) R)
100.0ms	(pow (* (sin lambda2) (sin lambda1)) 3)
40.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda2) (sin lambda1)) 3))))))
87.0ms	(cbrt (pow (* (sin lambda2) (sin lambda1)) 3))

simplify767.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1315
1	333
0	136

prune978.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.8b

localize90.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* (sin lambda2) (sin lambda1)) 3)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (cbrt (pow (pow (* (sin lambda2) (sin lambda1)) 3) 3)))))))
5.2b	(cbrt (pow (pow (* (sin lambda2) (sin lambda1)) 3) 3))
26.9b	(cbrt (cbrt (pow (pow (* (sin lambda2) (sin lambda1)) 3) 3)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cbrt-prod`
21×	`unpow-prod-down` `cube-prod`
12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`cube-mult` `pow1` `add-cbrt-cube` `unpow3` `add-exp-log` `sqr-pow`
5×	`cube-div`
4×	`add-log-exp`
3×	`pow-unpow` `cbrt-div` `sin-mult`
2×	`pow-pow` `pow1/3` `pow-exp` `rem-cube-cbrt`
1×	`acos-asin` `pow-to-exp` `pow-prod-down` `prod-exp` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 97

Calls

4 calls:

13.0ms	(pow (* (sin lambda2) (sin lambda1)) 3)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (cbrt (pow (pow (* (sin lambda2) (sin lambda1)) 3) 3)))))))
12.0ms	(cbrt (pow (pow (* (sin lambda2) (sin lambda1)) 3) 3))
13.0ms	(cbrt (cbrt (pow (pow (* (sin lambda2) (sin lambda1)) 3) 3)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(pow (* (sin lambda2) (sin lambda1)) 3)
38.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (cbrt (pow (pow (* (sin lambda2) (sin lambda1)) 3) 3)))))))
119.0ms	(cbrt (pow (pow (* (sin lambda2) (sin lambda1)) 3) 3))
67.0ms	(cbrt (cbrt (pow (pow (* (sin lambda2) (sin lambda1)) 3) 3)))

simplify1.5s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	1802
1	421
0	155

prune858.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 2.8b

regimes1.9s

Accuracy

0% (0.3b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	35
1	35
0	27

end0.0ms

sample17.4s

Algorithm

intervals

Results

11.9s	4762×	body	1280	valid
3.4s	2104×	body	640	valid
723.0ms	672×	body	320	valid
515.0ms	302×	body	160	valid
63.0ms	14×	body	2560	valid
34.0ms	147×	body	80	valid