Details

sample199.0ms

Algorithm

intervals

Results

62.0ms	68×	body	640	valid
59.0ms	80×	body	1280	valid
25.0ms	240×	body	80	valid
14.0ms	42×	body	320	valid
7.0ms	27×	body	160	valid

simplify213.0ms

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize38.0ms

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))

rewrite45.0ms

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))
16.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
26.0ms	(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (sqrt 2.0))

series563.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(fma a1 a1 (* a2 a2))
172.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
316.0ms	(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (sqrt 2.0))

simplify5.4s

Counts

68 → 68

Iterations

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

prune697.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

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)))

rewrite64.0ms

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))
35.0ms	(/ (fma a1 a1 (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series490.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(fma a1 a1 (* a2 a2))
83.0ms	(/ (sqrt 2.0) (cos th))
320.0ms	(/ (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))

rewrite143.0ms

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)))
77.0ms	(* (hypot a2 a1) (* (cos th) (/ (hypot a2 a1) (sqrt 2.0))))
13.0ms	(/ (hypot a2 a1) (sqrt 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

90.0ms	(hypot a2 a1)
375.0ms	(* (cos th) (/ (hypot a2 a1) (sqrt 2.0)))
356.0ms	(* (hypot a2 a1) (* (cos th) (/ (hypot a2 a1) (sqrt 2.0))))
207.0ms	(/ (hypot a2 a1) (sqrt 2.0))

simplify3.6s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
2	1210
1	362
0	160

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize41.0ms

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))

rewrite116.0ms

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)
27.0ms	(* (hypot a2 a1) (cos th))
67.0ms	(* (* (hypot a2 a1) (cos th)) (/ (hypot a2 a1) (sqrt 2.0)))
13.0ms	(/ (hypot a2 a1) (sqrt 2.0))

series826.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(hypot a2 a1)
175.0ms	(* (hypot a2 a1) (cos th))
360.0ms	(* (* (hypot a2 a1) (cos th)) (/ (hypot a2 a1) (sqrt 2.0)))
199.0ms	(/ (hypot a2 a1) (sqrt 2.0))

simplify3.2s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	1299
1	390
0	159

prune1.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes694.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample7.8s

Algorithm

intervals

Results

3.4s	2452×	body	1280	valid
1.7s	8203×	body	80	valid
1.3s	2141×	body	640	valid
453.0ms	1047×	body	320	valid
168.0ms	487×	body	160	valid