Details

sample122.0ms

Algorithm

intervals

Results

32.0ms	57×	body	640	valid
31.0ms	41×	body	1280	valid
19.0ms	131×	body	80	valid
7.0ms	17×	body	320	valid
3.0ms	10×	body	160	valid

simplify5.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5010
7	2302
6	688
5	280
4	167
3	113
2	69
1	34
0	17

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (/ K 2.0)) J)
0.2b	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
6.6b	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (cos (/ K 2.0)) J))
9.6b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite666.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
20×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`pow1`
12×	`add-cube-cbrt`
11×	`add-cbrt-cube`
10×	`associate-l`
8×	`unpow-prod-down` `sqrt-prod`
7×	`prod-exp`
4×	`expm1-log1p-u` `sqrt-div` `associate-r` `pow-prod-down` `pow-exp` `cbrt-unprod` `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 → 93

Calls

4 calls:

17.0ms	(* (cos (/ K 2.0)) J)
50.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
389.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (cos (/ K 2.0)) J))
204.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (cos (/ K 2.0)) J)
332.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
441.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (cos (/ K 2.0)) J))
306.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify5.0s

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
3	3974
2	1262
1	475
0	194

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize55.0ms

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)
6.6b	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (cos (/ K 2.0)) J))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

35.0ms	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
18.0ms	(* (cos (/ K 2.0)) J)
16.0ms	(* (cos (/ K 2.0)) J)
42.0ms	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (cos (/ K 2.0)) J))

series2.2s

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
96.0ms	(* (cos (/ K 2.0)) J)
88.0ms	(* (cos (/ K 2.0)) J)
1.9s	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (cos (/ K 2.0)) J))

simplify2.8s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	1346
1	395
0	165

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
0.1b	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (cos (/ K 2.0)))
0.1b	(* (cos (/ K 2.0)) J)
6.7b	(* (* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (cos (/ K 2.0))) J)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

37.0ms	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
17.0ms	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (cos (/ K 2.0)))
17.0ms	(* (cos (/ K 2.0)) J)
51.0ms	(* (* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (cos (/ K 2.0))) J)

series2.7s

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
1.0s	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (cos (/ K 2.0)))
88.0ms	(* (cos (/ K 2.0)) J)
1.4s	(* (* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (cos (/ K 2.0))) J)

simplify3.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	5003
2	1561
1	474
0	195

prune1.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.2b

localize89.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
6.7b	(* (* (* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) J)

rewrite503.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))
494.0ms	(* (* (* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) J)

series2.2s

Counts

4 → 12

Calls

4 calls:

335.0ms	(cbrt (cos (/ K 2.0)))
293.0ms	(cbrt (cos (/ K 2.0)))
295.0ms	(cbrt (cos (/ K 2.0)))
1.3s	(* (* (* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) J)

simplify7.8s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
3	4899
2	1110
1	329
0	137

prune878.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 3.2b

regimes1.2s

Accuracy

0% (3.8b remaining)

Error of 7.8b against oracle of 4.0b and baseline of 7.8b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample5.9s

Algorithm

intervals

Results

1.8s	1490×	body	1280	valid
1.7s	1267×	body	640	valid
931.0ms	4331×	body	80	valid
670.0ms	313×	body	160	valid
342.0ms	599×	body	320	valid