Details

sample586.0ms

Algorithm

intervals

Results

437.0ms	154×	body	1280	valid
96.0ms	62×	body	640	valid
15.0ms	15×	body	320	valid
6.0ms	19×	body	80	valid
3.0ms	6×	body	160	valid

simplify91.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
4	80
3	77
2	47
1	28
0	17

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.0b	(sin (- lambda1 lambda2))
2.0b	(cos (- lambda1 lambda2))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`prod-diff`
11×	`pow1` `cos-sum` `add-cbrt-cube` `sin-sum` `add-exp-log`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

48.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
32.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
15.0ms	(sin (- lambda1 lambda2))
9.0ms	(cos (- lambda1 lambda2))

series323.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
160.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
29.0ms	(sin (- lambda1 lambda2))
33.0ms	(cos (- lambda1 lambda2))

simplify2.8s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	3650
2	1063
1	436
0	214

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.7b

localize101.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.0b	(cos (- lambda1 lambda2))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1` `cos-sum` `add-cbrt-cube` `add-exp-log`
10×	`prod-diff`
6×	`associate-r` `add-log-exp`
5×	`cos-diff`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`associate-*l/`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `*-commutative` `flip--` `associate--r+`
1×	`fma-neg` `diff-log` `sin-cos-mult` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

13.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
74.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
50.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

series593.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
181.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
163.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify1.7s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1541
1	519
0	225

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize107.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-l/` `-commutative` `insert-posit16` `log1p-expm1-u` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 101

Calls

4 calls:

65.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
22.0ms	(* (sin lambda1) (sin lambda2))
80.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
92.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series545.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
65.0ms	(* (sin lambda1) (sin lambda2))
145.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
154.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.8s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	1724
1	449
0	175

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize129.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
8.2b	(cbrt (* (sin lambda1) (sin lambda2)))
8.2b	(cbrt (* (sin lambda1) (sin lambda2)))
8.2b	(cbrt (* (sin lambda1) (sin lambda2)))

rewrite49.0ms

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-mult`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `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 → 76

Calls

4 calls:

28.0ms	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
5.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
5.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
9.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
140.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
113.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
133.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

simplify1.7s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	1996
2	642
1	238
0	95

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes642.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample18.1s

Algorithm

intervals

Results

13.4s	4666×	body	1280	valid
3.4s	1945×	body	640	valid
621.0ms	564×	body	320	valid
202.0ms	641×	body	80	valid
141.0ms	184×	body	160	valid