Details

sample156.0ms

Algorithm

intervals

Results

46.0ms	284×	body	80	valid
30.0ms	41×	body	640	valid
21.0ms	21×	body	1280	valid
11.0ms	21×	body	320	valid
3.0ms	8×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	17	32
1	34	16
2	76	16
3	259	16
4	1055	16
done	5001	16

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize23.0ms

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)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.1b	(cos (/ (+ phi1 phi2) 2.0))

rewrite62.0ms

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:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
8.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
28.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
24.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

539.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
752.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
112.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
35.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify965.0ms

Counts

75 → 75

Iterations

Useful iterations: done (961.0ms)

Iter	Nodes	Cost
0	139	1279
1	335	1271
2	1431	1079
done	5002	1069

prune866.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

localize23.0ms

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)
0.2b	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
3.1b	(cos (* 0.5 (+ phi2 phi1)))

rewrite129.0ms

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:

1.0ms	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
16.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
86.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
19.0ms	(cos (* 0.5 (+ phi2 phi1)))

series1.7s

Counts

4 → 12

Calls

4 calls:

832.0ms	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
670.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
182.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
52.0ms	(cos (* 0.5 (+ phi2 phi1)))

simplify1.3s

Counts

99 → 99

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	202	2041
1	444	1863
2	2046	1637
done	5000	1598

prune421.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

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))))
0.2b	(* (- (* (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)))

rewrite412.0ms

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:

15.0ms	(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
90.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
269.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
30.0ms	(* (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)
151.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
458.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
91.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

simplify511.0ms

Counts

129 → 129

Iterations

Useful iterations: done (503.0ms)

Iter	Nodes	Cost
0	341	4795
1	931	4417
done	5000	4039

prune847.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(* lambda2 (sin (* 0.5 phi2)))
0.1b	(* (sin (* 0.5 phi2)) lambda1)
0.2b	(* (sin (* 0.5 phi1)) (* (sin (* 0.5 phi2)) lambda1))
0.2b	(* (sin (* 0.5 phi1)) (* lambda2 (sin (* 0.5 phi2))))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt`
12×	`associate-l`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
2×	`unswap-sqr`

Counts

4 → 80

Calls

4 calls:

26.0ms	(* lambda2 (sin (* 0.5 phi2)))
24.0ms	(* (sin (* 0.5 phi2)) lambda1)
53.0ms	(* (sin (* 0.5 phi1)) (* (sin (* 0.5 phi2)) lambda1))
60.0ms	(* (sin (* 0.5 phi1)) (* lambda2 (sin (* 0.5 phi2))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* lambda2 (sin (* 0.5 phi2)))
70.0ms	(* (sin (* 0.5 phi2)) lambda1)
153.0ms	(* (sin (* 0.5 phi1)) (* (sin (* 0.5 phi2)) lambda1))
101.0ms	(* (sin (* 0.5 phi1)) (* lambda2 (sin (* 0.5 phi2))))

simplify869.0ms

Counts

92 → 92

Iterations

Useful iterations: done (864.0ms)

Iter	Nodes	Cost
0	108	1045
1	247	1033
2	1053	859
done	5000	853

prune821.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes748.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	51
1	34	51
done	34	51

end0.0ms

sample5.6s

Algorithm

intervals

Results

1.5s	8415×	body	80	valid
1.4s	1288×	body	640	valid
930.0ms	755×	body	320	valid
791.0ms	778×	body	1280	valid
91.0ms	338×	body	160	valid