Details

sample65.0ms

Algorithm

intervals

Results

38.0ms	104×	body	1280	valid
8.0ms	124×	body	80	valid
6.0ms	20×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify75.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	114
6	114
5	111
4	89
3	69
2	43
1	21
0	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1 x)
0.0b	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b	(/ 1/2 (hypot 1 x))
0.9b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
21×	`prod-diff`
20×	`sqrt-prod`
10×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow1` `distribute-lft-out`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`associate-/r` `fma-neg` `associate-/l` `distribute-lft-out--`
2×	`sqrt-div` `hypot-def`
1×	`cbrt-undiv` `rem-sqrt-square` `hypot-udef` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `div-exp` `flip-+` `div-inv` `flip--`

Counts

4 → 108

Calls

4 calls:

0.0ms	(hypot 1 x)
9.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
5.0ms	(/ 1/2 (hypot 1 x))
49.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series319.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(hypot 1 x)
79.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
63.0ms	(/ 1/2 (hypot 1 x))
111.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify2.7s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
3	4229
2	1328
1	495
0	212

prune662.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
0.4b	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
12×	`prod-diff`
11×	`add-log-exp`
10×	`times-frac`
9×	`distribute-lft-out`
6×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `fma-def` `fma-neg` `associate-/l`
2×	`sum-log` `flip3-+` `sqrt-div` `diff-log` `flip-+` `hypot-def` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-exp` `div-inv` `flip--` `associate--r+`

Counts

4 → 107

Calls

4 calls:

7.0ms	(/ 1/2 (hypot 1 x))
38.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
17.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
43.0ms	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

series419.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 1/2 (hypot 1 x))
124.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
112.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
114.0ms	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

simplify3.6s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
3	4990
2	1581
1	530
0	211

prune589.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize98.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1/2 (hypot 1 x)) (- 1/2 (/ 1/2 (hypot 1 x))))
0.1b	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
0.4b	(- 1/2 (/ 1/2 (hypot 1 x)))
0.4b	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

181×	`add-sqr-sqrt`
167×	`*-un-lft-identity`
151×	`add-cube-cbrt`
133×	`times-frac`
129×	`prod-diff`
41×	`distribute-rgt-in` `distribute-lft-in`
26×	`associate-l`
21×	`add-cbrt-cube` `add-exp-log`
19×	`associate-r`
14×	`div-inv`
13×	`pow1` `swap-sqr`
11×	`add-log-exp`
6×	`fma-neg` `prod-exp` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out` `distribute-lft-out--`
3×	`frac-times` `diff-log` `associate-*r/`
2×	`pow-prod-down` `associate-l/` `-commutative`
1×	`pow2` `sum-log` `pow-plus` `pow-sqr` `pow-prod-up` `associate--r+`

Counts

4 → 290

Calls

4 calls:

37.0ms	(* (/ 1/2 (hypot 1 x)) (- 1/2 (/ 1/2 (hypot 1 x))))
28.0ms	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
14.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
66.0ms	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

series431.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (/ 1/2 (hypot 1 x)) (- 1/2 (/ 1/2 (hypot 1 x))))
91.0ms	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
95.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
108.0ms	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

simplify3.7s

Counts

302 → 302

Iterations

Iter	Nodes
done	5004
2	4172
1	1503
0	471

prune2.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2)))
0.0b	(hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2))
0.1b	(sqrt (/ 1/2 (hypot 1 x)))
0.4b	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
13×	`sqrt-prod`
12×	`prod-diff`
11×	`add-log-exp`
10×	`times-frac`
5×	`pow1` `distribute-lft-out`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `fma-neg`
2×	`rem-sqrt-square` `sum-log` `diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `hypot-udef` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `sqrt-div` `flip-+` `div-inv` `flip--` `associate--r+`

Counts

4 → 93

Calls

4 calls:

8.0ms	(+ 1 (hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2)))
0.0ms	(hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2))
5.0ms	(sqrt (/ 1/2 (hypot 1 x)))
64.0ms	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

series1.4s

Counts

4 → 12

Calls

4 calls:

560.0ms	(+ 1 (hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2)))
530.0ms	(hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2))
172.0ms	(sqrt (/ 1/2 (hypot 1 x)))
118.0ms	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

simplify3.1s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
3	4419
2	1466
1	501
0	217

prune584.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes147.0ms

Accuracy

98.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 14.7b

bsearch1.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	39
1	39
0	32

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	2797×	body	1280	valid
537.0ms	328×	body	320	valid
324.0ms	4095×	body	80	valid
221.0ms	613×	body	640	valid
22.0ms	167×	body	160	valid