Details

sample104.0ms

Algorithm

intervals

Results

54.0ms	83×	body	1280	valid
16.0ms	130×	body	80	valid
15.0ms	28×	body	640	valid
4.0ms	10×	body	320	valid
1.0ms	5×	body	160	valid

simplify126.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize30.0ms

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)))))

rewrite110.0ms

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:

10.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
5.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)
93.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series392.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
81.0ms	(/ 1/2 (hypot 1 x))
58.0ms	(hypot 1 x)
169.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify3.2s

Counts

117 → 117

Iterations

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

prune521.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize23.0ms

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)))

rewrite35.0ms

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:

9.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)
1.0ms	(hypot 1 x)
18.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ 1/2 (hypot 1 x))
66.0ms	(hypot 1 x)
66.0ms	(hypot 1 x)
85.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify3.6s

Counts

124 → 124

Iterations

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

prune559.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize27.0ms

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)))

rewrite27.0ms

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`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`fma-neg` `div-inv`
2×	`expm1-log1p` `hypot-udef` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `expm1-udef`

Counts

4 → 95

Calls

4 calls:

0.0ms	(hypot 1 x)
1.0ms	(hypot 1 x)
5.0ms	(expm1 (log1p (- 1/2 (/ 1/2 (hypot 1 x)))))
15.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(hypot 1 x)
62.0ms	(hypot 1 x)
248.0ms	(expm1 (log1p (- 1/2 (/ 1/2 (hypot 1 x)))))
70.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify3.3s

Counts

107 → 107

Iterations

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

prune463.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize25.0ms

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))))

rewrite492.0ms

Algorithm

rewrite-expression-head

Rules

370×	`add-sqr-sqrt`
244×	`pow1`
199×	`unswap-sqr`
162×	`associate-r`
158×	`swap-sqr`
90×	`associate-l`
78×	`*-un-lft-identity`
72×	`pow-prod-up`
67×	`*-commutative`
66×	`add-cube-cbrt`
59×	`pow-prod-down`
46×	`add-cbrt-cube` `add-exp-log`
44×	`pow-sqr`
36×	`pow-plus`
29×	`prod-exp` `cbrt-unprod`
26×	`pow2`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`fma-udef`

Counts

4 → 434

Calls

4 calls:

311.0ms	(* -11/128 (* (* x x) (* x x)))
53.0ms	(* (* x x) (* x x))
92.0ms	(* (* x x) (* x x))
1.0ms	(fma 69/1024 (* (* (* x x) (* x x)) (* x x)) (* -11/128 (* (* x x) (* x x))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* -11/128 (* (* x x) (* x x)))
51.0ms	(* (* x x) (* x x))
45.0ms	(* (* x x) (* x x))
213.0ms	(fma 69/1024 (* (* (* x x) (* x x)) (* x x)) (* -11/128 (* (* x x) (* x x))))

simplify2.3s

Counts

446 → 446

Iterations

Iter	Nodes
done	5000
2	1982
1	644
0	195

prune1.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes438.0ms

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

sample3.1s

Algorithm

intervals

Results

2.0s	2865×	body	1280	valid
435.0ms	3961×	body	80	valid
369.0ms	654×	body	640	valid
101.0ms	344×	body	320	valid
32.0ms	176×	body	160	valid