Details

sample73.0ms

Algorithm

intervals

Results

24.0ms	50×	body	1280	valid
13.0ms	38×	body	640	valid
12.0ms	138×	body	80	valid
5.0ms	18×	body	320	valid
2.0ms	12×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize56.0ms

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)
9.0b	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
9.1b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite454.0ms

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` `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 → 96

Calls

4 calls:

13.0ms	(* (cos (/ K 2.0)) J)
36.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
277.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
122.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series839.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (cos (/ K 2.0)) J)
221.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
328.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
207.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify1.9s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1553
1	531
0	211

prune809.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize49.0ms

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)
9.0b	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))

rewrite97.0ms

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` `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 → 88

Calls

4 calls:

25.0ms	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
7.0ms	(* (cos (/ K 2.0)) J)
6.0ms	(* (cos (/ K 2.0)) J)
55.0ms	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ U (* (* (cos (/ K 2.0)) J) 2.0))
83.0ms	(* (cos (/ K 2.0)) J)
70.0ms	(* (cos (/ K 2.0)) J)
1.1s	(* (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))

simplify2.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1603
1	450
0	183

prune871.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

localize88.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (/ K 2.0)) J)
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))
9.0b	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
9.0b	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
15×	`add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-l` `sqrt-prod`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative`
1×	`unswap-sqr`

Counts

4 → 76

Calls

4 calls:

13.0ms	(* (cos (/ K 2.0)) J)
75.0ms	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0))
2.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
2.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

series3.1s

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (cos (/ K 2.0)) J)
1.3s	(* (sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0))) (* (* (cos (/ K 2.0)) J) -2.0))
838.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))
863.0ms	(sqrt (hypot (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) (/ 2.0 2)) (sqrt 1.0)))

simplify4.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	4844
2	1213
1	365
0	153

prune848.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.1b

localize65.0ms

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)))
9.0b	(* (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)) -2.0))

rewrite377.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
372.0ms	(* (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)) -2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt (cos (/ K 2.0)))
202.0ms	(cbrt (cos (/ K 2.0)))
256.0ms	(cbrt (cos (/ K 2.0)))
1.0s	(* (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)) -2.0))

simplify2.7s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	1539
1	413
0	161

prune642.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 5.1b

regimes889.0ms

Accuracy

-17.1% (5.0b remaining)

Error of 8.7b against oracle of 3.7b and baseline of 8.0b

bsearch301.0ms

Steps

Iters	Range		Point
8	1.1230878641706415e-202	1.1274284215203474e-198	3.849360312491251e-202
10	-4.920101329217198e-211	-7.55818170176457e-223	-2.2730159516229644e-222

simplify7.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.2s	1545×	body	1280	valid
1.1s	1229×	body	640	valid
583.0ms	4249×	body	80	valid
289.0ms	663×	body	320	valid
73.0ms	317×	body	160	valid