Details

sample647.0ms

Algorithm

intervals

Results

457.0ms	151×	body	1280	valid
134.0ms	59×	body	640	valid
26.0ms	22×	body	320	valid
5.0ms	17×	body	80	valid
5.0ms	7×	body	160	valid

simplify347.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	73
4	73
3	69
2	45
1	27
0	17

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b	(cos (- lambda1 lambda2))
3.4b	(sin (- lambda1 lambda2))

rewrite94.0ms

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` `insert-posit16` `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 → 64

Calls

4 calls:

26.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
33.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

series238.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
113.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(cos (- lambda1 lambda2))
24.0ms	(sin (- lambda1 lambda2))

simplify885.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	2066
3	2066
2	805
1	276
0	120

prune569.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.9b

localize92.0ms

Local error

Found 4 expressions with local error:

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

rewrite136.0ms

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×	`insert-posit16` `add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `sin-cos-mult` `flip--`

Counts

4 → 73

Calls

4 calls:

11.0ms	(* (cos lambda1) (sin lambda2))
78.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
38.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))

series356.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (cos lambda1) (sin lambda2))
170.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
104.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify1.1s

Counts

85 → 85

Iterations

Iter	Nodes
done	2001
3	2001
2	1188
1	369
0	149

prune887.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
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))))

rewrite176.0ms

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`
4×	`*-commutative` `insert-posit16` `sin-cos-mult` `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 → 88

Calls

4 calls:

11.0ms	(* (cos lambda1) (sin lambda2))
79.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
14.0ms	(* (sin lambda1) (sin lambda2))
70.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (cos lambda1) (sin lambda2))
221.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
54.0ms	(* (sin lambda1) (sin lambda2))
233.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify929.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	2003
2	2003
1	557
0	192

prune782.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize111.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
0.4b	(cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.4b	(cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.4b	(cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-div`
25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1` `flip3-+` `frac-add` `cos-mult` `flip-+` `sin-mult`
9×	`frac-times` `pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`associate-l/` `associate-r/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 101

Calls

4 calls:

97.0ms	(* (cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
15.0ms	(cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
20.0ms	(cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
9.0ms	(cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series793.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(* (cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
191.0ms	(cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
179.0ms	(cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
231.0ms	(cbrt (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify1.2s

Counts

113 → 113

Iterations

Iter	Nodes
done	2004
3	2004
2	784
1	290
0	126

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes550.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	38
1	38
0	28

end0.0ms

sample25.1s

Algorithm

intervals

Results

18.1s	4596×	body	1280	valid
4.9s	1994×	body	640	valid
982.0ms	551×	body	320	valid
641.0ms	675×	body	80	valid
146.0ms	184×	body	160	valid