Details

sample56.0ms

Algorithm

intervals

Results

29.0ms	83×	body	1280	valid
8.0ms	130×	body	80	valid
8.0ms	28×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	5×	body	160	valid

simplify70.0ms

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: 15.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)
1.4b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

6.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
4.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)
26.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
68.0ms	(/ 1/2 (hypot 1 x))
52.0ms	(hypot 1 x)
109.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify2.9s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
3	4459
2	1411
1	511
0	212

prune468.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)
0.0b	(hypot 1 x)
0.8b	(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
39×	`prod-diff`
37×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`associate-/r` `fma-neg` `associate-/l`
2×	`hypot-udef` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `flip--` `distribute-lft-out--`

Counts

4 → 112

Calls

4 calls:

7.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)
0.0ms	(hypot 1 x)
14.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ 1/2 (hypot 1 x))
53.0ms	(hypot 1 x)
66.0ms	(hypot 1 x)
77.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify3.7s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
3	4840
2	1586
1	548
0	217

prune567.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1 x)
0.0b	(hypot 1 x)
0.0b	(expm1 (log1p (- 1/2 (/ 1/2 (hypot 1 x)))))
0.8b	(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
39×	`prod-diff` `add-cube-cbrt`
28×	`times-frac`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `div-inv`
2×	`hypot-udef` `difference-of-squares`
1×	`expm1-log1p` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `expm1-udef`

Counts

4 → 94

Calls

4 calls:

0.0ms	(hypot 1 x)
0.0ms	(hypot 1 x)
0.0ms	(expm1 (log1p (- 1/2 (/ 1/2 (hypot 1 x)))))
7.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(hypot 1 x)
61.0ms	(hypot 1 x)
195.0ms	(expm1 (log1p (- 1/2 (/ 1/2 (hypot 1 x)))))
109.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify3.7s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
3	4530
2	1473
1	491
0	204

prune610.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* -11/128 (* (* x x) (* x x)))
0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) (* x x))
19.0b	(fma 69/1024 (* (* (* x x) (* x x)) (* x x)) (* -11/128 (* (* x x) (* x x))))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

244×	`pow1`
72×	`pow-prod-up`
59×	`pow-prod-down`
46×	`add-cbrt-cube` `add-exp-log`
44×	`pow-sqr`
36×	`pow-plus`
29×	`prod-exp` `cbrt-unprod`
26×	`pow2`
6×	`add-sqr-sqrt`
5×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `*-commutative` `unswap-sqr`
2×	`swap-sqr`
1×	`fma-udef`

Counts

4 → 174

Calls

4 calls:

120.0ms	(* -11/128 (* (* x x) (* x x)))
24.0ms	(* (* x x) (* x x))
43.0ms	(* (* x x) (* x x))
0.0ms	(fma 69/1024 (* (* (* x x) (* x x)) (* x x)) (* -11/128 (* (* x x) (* x x))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* -11/128 (* (* x x) (* x x)))
61.0ms	(* (* x x) (* x x))
61.0ms	(* (* x x) (* x x))
221.0ms	(fma 69/1024 (* (* (* x x) (* x x)) (* x x)) (* -11/128 (* (* x x) (* x x))))

simplify2.3s

Counts

186 → 186

Iterations

Iter	Nodes
done	5002
3	2271
2	573
1	225
0	97

prune332.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes102.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.5b

bsearch1.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.4s	2865×	body	1280	valid
371.0ms	3961×	body	80	valid
280.0ms	654×	body	640	valid
100.0ms	344×	body	320	valid
35.0ms	176×	body	160	valid