Details

sample107.0ms

Algorithm

intervals

Results

26.0ms	47×	body	1280	valid
18.0ms	147×	body	80	valid
16.0ms	34×	body	640	valid
5.0ms	17×	body	320	valid
3.0ms	11×	body	160	valid

simplify6.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	2639
6	722
5	279
4	166
3	112
2	69
1	34
0	17

prune45.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (/ K 2.0)) J)
0.3b	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
8.8b	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
8.9b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite723.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`pow1`
16×	`*-un-lft-identity`
15×	`add-cbrt-cube`
12×	`add-cube-cbrt`
10×	`associate-l` `prod-exp`
8×	`unpow-prod-down` `sqrt-prod`
7×	`pow-prod-down` `cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-div` `associate-r` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp` `hypot-def`
2×	`flip3-+` `associate-l/` `-commutative` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

10.0ms	(* (cos (/ K 2.0)) J)
57.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
494.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
155.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (cos (/ K 2.0)) J)
473.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
603.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
398.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify3.9s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	1567
1	538
0	215

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize81.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
0.1b	(* (cos (/ K 2.0)) J)
0.1b	(* (cos (/ K 2.0)) J)
8.8b	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-cbrt-cube` `add-exp-log`
17×	`pow1`
15×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
9×	`associate-l`
8×	`pow-prod-down`
7×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `-commutative` `associate-/l`
2×	`unswap-sqr`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 92

Calls

4 calls:

31.0ms	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
10.0ms	(* (cos (/ K 2.0)) J)
16.0ms	(* (cos (/ K 2.0)) J)
98.0ms	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))

series2.4s

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
118.0ms	(* (cos (/ K 2.0)) J)
109.0ms	(* (cos (/ K 2.0)) J)
2.0s	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))

simplify3.9s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	1602
1	453
0	186

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.3b

localize165.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0)))
0.2b	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0))
8.8b	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
8.8b	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

rewrite412.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1`
27×	`add-cbrt-cube` `add-exp-log`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt` `associate-l` `sqrt-prod`
10×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 89

Calls

4 calls:

268.0ms	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0)))
129.0ms	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0))
5.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
5.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

series7.1s

Counts

4 → 12

Calls

4 calls:

2.0s	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0)))
2.1s	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0))
1.6s	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
1.5s	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

simplify4.6s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
2	1428
1	413
0	165

prune1.6s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.3b

localize135.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))) (* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0)))
8.8b	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
8.8b	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
8.8b	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
18×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
9×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate-r` `*-commutative`

Counts

4 → 81

Calls

4 calls:

285.0ms	(* (sqrt (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))) (* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0)))
2.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
4.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
5.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

series7.9s

Counts

4 → 12

Calls

4 calls:

3.2s	(* (sqrt (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))) (* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0)))
1.5s	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
1.8s	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
1.4s	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

simplify4.9s

Counts

93 → 93

Iterations

Iter	Nodes
done	5003
2	1437
1	404
0	160

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.3b

regimes1.6s

Accuracy

0% (4.6b remaining)

Error of 8.5b against oracle of 4.0b and baseline of 8.5b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	25
1	25
0	20

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.3s	1519×	body	1280	valid
1.3s	1262×	body	640	valid
674.0ms	4242×	body	80	valid
218.0ms	647×	body	320	valid
85.0ms	332×	body	160	valid