Details

sample545.0ms

Algorithm

intervals

Results

365.0ms	141×	body	1280	valid
89.0ms	68×	body	640	valid
48.0ms	16×	body	320	valid
6.0ms	26×	body	80	valid
2.0ms	5×	body	160	valid

simplify53.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	79
4	79
3	71
2	46
1	27
0	17

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`cos-sum` `sub-neg` `sin-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

25.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
46.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(sin (- lambda1 lambda2))
8.0ms	(cos (- lambda1 lambda2))

series300.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
151.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms	(sin (- lambda1 lambda2))
26.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1349
1	272
0	116

prune699.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.7b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.8b	(cos (- lambda1 lambda2))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `flip--`

Counts

4 → 70

Calls

4 calls:

9.0ms	(* (sin phi1) (cos phi2))
76.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
23.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(cos (- lambda1 lambda2))

series400.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin phi1) (cos phi2))
187.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
125.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify1.5s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1886
1	344
0	133

prune930.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize88.0ms

Local error

Found 4 expressions with local error:

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

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`associate-r`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`sin-cos-mult`
4×	`*-commutative` `add-log-exp`
3×	`frac-times` `associate-l/` `associate-r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `flip--`

Counts

4 → 85

Calls

4 calls:

9.0ms	(* (sin phi1) (cos phi2))
74.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
18.0ms	(* (sin lambda1) (sin lambda2))
61.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin phi1) (cos phi2))
205.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
85.0ms	(* (sin lambda1) (sin lambda2))
240.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify2.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	3351
1	536
0	181

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize93.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (sin phi1) (cos phi2))) (cbrt (* (sin phi1) (cos phi2))))
0.6b	(cbrt (* (sin phi1) (cos phi2)))
0.6b	(cbrt (* (sin phi1) (cos phi2)))
0.6b	(cbrt (* (sin phi1) (cos phi2)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod` `cbrt-div` `sin-cos-mult`
6×	`add-exp-log`
4×	`add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

45.0ms	(* (cbrt (* (sin phi1) (cos phi2))) (cbrt (* (sin phi1) (cos phi2))))
8.0ms	(cbrt (* (sin phi1) (cos phi2)))
4.0ms	(cbrt (* (sin phi1) (cos phi2)))
12.0ms	(cbrt (* (sin phi1) (cos phi2)))

series626.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(* (cbrt (* (sin phi1) (cos phi2))) (cbrt (* (sin phi1) (cos phi2))))
139.0ms	(cbrt (* (sin phi1) (cos phi2)))
154.0ms	(cbrt (* (sin phi1) (cos phi2)))
148.0ms	(cbrt (* (sin phi1) (cos phi2)))

simplify1.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
2	950
1	211
0	84

prune870.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes888.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	38
1	38
0	28

end0.0ms

sample20.0s

Algorithm

intervals

Results

15.4s	4601×	body	1280	valid
3.0s	2007×	body	640	valid
589.0ms	542×	body	320	valid
248.0ms	650×	body	80	valid
108.0ms	200×	body	160	valid