Details

sample136.0ms

Algorithm

intervals

Results

42.0ms	44×	body	640	valid
30.0ms	244×	body	80	valid
17.0ms	23×	body	1280	valid
10.0ms	28×	body	320	valid
3.0ms	11×	body	160	valid

simplify5.3s

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	17	32
1	45	16
2	228	16
3	4012	16
done	5000	16

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.1b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.6b	(cos (/ (+ phi1 phi2) 2.0))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 63

Calls

4 calls:

1.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
11.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
46.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
21.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

629.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
725.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
117.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
35.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.1s

Counts

75 → 75

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	139	1279
1	664	1271
done	5001	1060

prune483.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
0.1b	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.1b	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
4.6b	(cos (* 0.5 (+ phi2 phi1)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
12×	`distribute-rgt-in` `distribute-lft-in`
8×	`pow1` `add-exp-log` `associate-r` `add-cbrt-cube`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `cos-sum` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

0.0ms	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
12.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
67.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
11.0ms	(cos (* 0.5 (+ phi2 phi1)))

series1.7s

Counts

4 → 12

Calls

4 calls:

823.0ms	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
725.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
165.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
31.0ms	(cos (* 0.5 (+ phi2 phi1)))

simplify2.6s

Counts

99 → 99

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	202	2041
1	1301	1784
done	5000	1586

prune441.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.1b	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
0.1b	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
0.2b	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

rewrite413.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`flip3--` `associate-l` `flip--` `sin-mult`
8×	`frac-times` `cos-mult`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-*l/` `frac-sub` `log1p-expm1-u` `sub-div`
3×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-*r/`
1×	`fma-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 117

Calls

4 calls:

12.0ms	(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
83.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
270.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
39.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

series2.6s

Counts

4 → 12

Calls

4 calls:

1.9s	(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
123.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
423.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
102.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

simplify3.1s

Counts

129 → 129

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	341	4795
1	2419	4345
done	5001	4039

prune940.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
0.3b	(pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)
0.4b	(* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (cos (* phi2 0.5)) (cos (* phi1 0.5))))
0.6b	(pow (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) 3)

rewrite433.0ms

Algorithm

rewrite-expression-head

Rules

88×	`pow1`
36×	`pow-prod-down`
34×	`add-exp-log` `add-cbrt-cube`
18×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `pow-pow` `pow-plus` `pow-exp` `log1p-expm1-u` `add-log-exp` `rem-cube-cbrt`
2×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-l/` `*-commutative` `sqr-pow`

Counts

4 → 128

Calls

4 calls:

204.0ms	(* (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
40.0ms	(pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)
148.0ms	(* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (cos (* phi2 0.5)) (cos (* phi1 0.5))))
36.0ms	(pow (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) 3)

series490.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
112.0ms	(pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)
123.0ms	(* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (cos (* phi2 0.5)) (cos (* phi1 0.5))))
141.0ms	(pow (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) 3)

simplify2.1s

Counts

140 → 140

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	195	2474
1	1368	1486
done	5000	1459

prune870.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes507.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	57
1	42	57
done	42	57

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.7s	8470×	body	80	valid
984.0ms	1295×	body	640	valid
726.0ms	776×	body	1280	valid
399.0ms	693×	body	320	valid
91.0ms	336×	body	160	valid