Details

sample76.0ms

Algorithm

intervals

Results

44.0ms	102×	body	1280	valid
9.0ms	116×	body	80	valid
8.0ms	21×	body	640	valid
3.0ms	13×	body	320	valid
1.0ms	4×	body	160	valid

simplify100.0ms

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: 15.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(/ 1/2 (hypot 1 x))
2.4b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

3 calls:

6.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
4.0ms	(/ 1/2 (hypot 1 x))
43.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series345.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
91.0ms	(/ 1/2 (hypot 1 x))
185.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	2007
3	2007
2	1288
1	475
0	198

prune367.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)
2.0b	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

5.0ms	(/ 1/2 (hypot 1 x))
4.0ms	(/ 1/2 (hypot 1 x))
60.0ms	(+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)
40.0ms	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

series296.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ 1/2 (hypot 1 x))
59.0ms	(/ 1/2 (hypot 1 x))
94.0ms	(+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)
66.0ms	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

simplify1.3s

Counts

132 → 132

Iterations

Iter	Nodes
done	2000
3	2000
2	1463
1	461
0	186

prune618.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.1b	(* (* x x) (* x x))
16.6b	(fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128))
17.6b	(fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

129×	`pow1`
41×	`pow-prod-up`
26×	`pow-prod-down`
23×	`pow-sqr`
21×	`add-cbrt-cube` `add-exp-log`
19×	`pow-plus`
14×	`pow2`
11×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-r` `*-commutative` `fma-udef` `unswap-sqr`
1×	`cube-unmult` `swap-sqr`

Counts

4 → 115

Calls

4 calls:

14.0ms	(* x (* x x))
28.0ms	(* (* x x) (* x x))
0.0ms	(fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128))
0.0ms	(fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* x (* x x))
49.0ms	(* (* x x) (* x x))
125.0ms	(fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128))
100.0ms	(fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128)))

simplify1.0s

Counts

127 → 127

Iterations

Iter	Nodes
done	2182
3	2182
2	839
1	261
0	108

prune313.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

17.6b	(fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128)))
25.1b	(cbrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128))))
25.1b	(cbrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128))))
25.1b	(cbrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 53

Calls

4 calls:

0.0ms	(fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128)))
1.0ms	(cbrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128))))
1.0ms	(cbrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128))))
1.0ms	(cbrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128))))

series775.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128)))
236.0ms	(cbrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128))))
212.0ms	(cbrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128))))
243.0ms	(cbrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (fma (* x x) 1/8 (* (* (* x x) (* x x)) -11/128))))

simplify1.3s

Counts

65 → 65

Iterations

Iter	Nodes
done	2000
3	2000
2	546
1	190
0	90

prune385.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.9b

bsearch1.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.3s	2909×	body	1280	valid
390.0ms	4006×	body	80	valid
349.0ms	624×	body	640	valid
95.0ms	307×	body	320	valid
31.0ms	154×	body	160	valid