Details

sample234.0ms

Algorithm

intervals

Results

77.0ms	240×	body	80	valid
63.0ms	80×	body	1280	valid
36.0ms	68×	body	640	valid
15.0ms	42×	body	320	valid
7.0ms	27×	body	160	valid

simplify244.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
7	134
6	122
5	110
4	98
3	80
2	55
1	26
0	12

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.1b	(* (fma a1 a1 (* a2 a2)) (cos th))
0.4b	(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (sqrt 2.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

1.0ms	(fma a1 a1 (* a2 a2))
17.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
27.0ms	(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (sqrt 2.0))

series598.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(fma a1 a1 (* a2 a2))
190.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
334.0ms	(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (sqrt 2.0))

simplify5.6s

Counts

68 → 68

Iterations

Iter	Nodes
done	5105
3	3927
2	691
1	194
0	100

prune585.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(/ (sqrt 2.0) (cos th))
0.4b	(/ (fma a1 a1 (* a2 a2)) (/ (sqrt 2.0) (cos th)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
93×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
48×	`sqrt-prod`
25×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`associate-/r/` `fma-udef`

Counts

3 → 159

Calls

3 calls:

1.0ms	(fma a1 a1 (* a2 a2))
14.0ms	(/ (sqrt 2.0) (cos th))
25.0ms	(/ (fma a1 a1 (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series504.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(fma a1 a1 (* a2 a2))
82.0ms	(/ (sqrt 2.0) (cos th))
362.0ms	(/ (fma a1 a1 (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify2.8s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
2	1559
1	577
0	240

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot a2 a1)
0.2b	(* (cos th) (/ (hypot a2 a1) (sqrt 2.0)))
0.3b	(* (hypot a2 a1) (* (cos th) (/ (hypot a2 a1) (sqrt 2.0))))
0.4b	(/ (hypot a2 a1) (sqrt 2.0))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
38×	`times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
23×	`associate-r`
22×	`sqrt-prod`
20×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `associate-/r*`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-r/` `div-exp` `associate-/l` `unswap-sqr`
2×	`hypot-udef` `*-commutative` `div-inv`
1×	`sqrt-undiv` `frac-2neg` `clear-num`

Counts

4 → 119

Calls

4 calls:

1.0ms	(hypot a2 a1)
42.0ms	(* (cos th) (/ (hypot a2 a1) (sqrt 2.0)))
72.0ms	(* (hypot a2 a1) (* (cos th) (/ (hypot a2 a1) (sqrt 2.0))))
13.0ms	(/ (hypot a2 a1) (sqrt 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

90.0ms	(hypot a2 a1)
401.0ms	(* (cos th) (/ (hypot a2 a1) (sqrt 2.0)))
450.0ms	(* (hypot a2 a1) (* (cos th) (/ (hypot a2 a1) (sqrt 2.0))))
198.0ms	(/ (hypot a2 a1) (sqrt 2.0))

simplify3.6s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
2	1210
1	362
0	160

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot a2 a1)
0.2b	(* (hypot a2 a1) (cos th))
0.3b	(* (* (hypot a2 a1) (cos th)) (/ (hypot a2 a1) (sqrt 2.0)))
0.4b	(/ (hypot a2 a1) (sqrt 2.0))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
25×	`associate-r`
21×	`sqrt-prod`
20×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`hypot-udef` `*-commutative` `div-inv`
1×	`sqrt-undiv` `frac-2neg` `associate-*r/` `clear-num` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

1.0ms	(hypot a2 a1)
29.0ms	(* (hypot a2 a1) (cos th))
65.0ms	(* (* (hypot a2 a1) (cos th)) (/ (hypot a2 a1) (sqrt 2.0)))
13.0ms	(/ (hypot a2 a1) (sqrt 2.0))

series846.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(hypot a2 a1)
187.0ms	(* (hypot a2 a1) (cos th))
360.0ms	(* (* (hypot a2 a1) (cos th)) (/ (hypot a2 a1) (sqrt 2.0)))
208.0ms	(/ (hypot a2 a1) (sqrt 2.0))

simplify3.3s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	1299
1	390
0	159

prune1.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes661.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample7.7s

Algorithm

intervals

Results

2.4s	2452×	body	1280	valid
1.9s	8203×	body	80	valid
1.4s	2141×	body	640	valid
1.0s	1047×	body	320	valid
242.0ms	487×	body	160	valid