Details

sample100.0ms

Algorithm

intervals

Results

47.0ms	73×	body	1280	valid
22.0ms	144×	body	80	valid
11.0ms	21×	body	640	valid
4.0ms	10×	body	320	valid
2.0ms	8×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	27
3	27
2	25
1	21
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1 x)
0.0b	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b	(/ 1/2 (hypot 1 x))
2.6b	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite95.0ms

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)
20.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
7.0ms	(/ 1/2 (hypot 1 x))
65.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot 1 x)
72.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
82.0ms	(/ 1/2 (hypot 1 x))
157.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify1.5s

Counts

120 → 120

Iterations

Iter	Nodes
3	2880
2	1088
1	478
0	212

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

4.0ms	(/ 1/2 (hypot 1 x))
9.0ms	(/ 1/2 (hypot 1 x))
36.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
14.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ 1/2 (hypot 1 x))
75.0ms	(/ 1/2 (hypot 1 x))
109.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
93.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify3.6s

Counts

152 → 152

Iterations

Iter	Nodes
3	4111
2	1577
1	622
0	248

prune1.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))) (fma (+ 1/2 (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)) 1/4))
0.0b	(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))
0.2b	(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
1.9b	(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
31×	`add-cube-cbrt`
27×	`times-frac`
23×	`pow1`
21×	`prod-diff`
20×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/l*`
6×	`pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod` `add-log-exp`
5×	`div-inv` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `cbrt-undiv` `associate-/r*` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`hypot-udef` `fma-neg` `associate-r` `pow-prod-down`
2×	`pow2` `clear-num` `frac-2neg` `flip3--` `sqrt-unprod` `pow-sqr` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub` `associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

4 → 140

Calls

4 calls:

99.0ms	(/ (- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))) (fma (+ 1/2 (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)) 1/4))
33.0ms	(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))
32.0ms	(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
39.0ms	(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(/ (- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))) (fma (+ 1/2 (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)) 1/4))
75.0ms	(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))
113.0ms	(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
129.0ms	(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))

simplify3.6s

Counts

152 → 152

Iterations

Iter	Nodes
3	6580
2	1847
1	674
0	266

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))) (fma (+ 1/2 (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)) 1/4))
0.1b	(/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))
0.5b	(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
1.9b	(- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
142×	`add-sqr-sqrt`
112×	`*-un-lft-identity`
102×	`add-cube-cbrt`
75×	`prod-diff`
20×	`add-cbrt-cube` `add-exp-log`
19×	`div-inv`
17×	`associate-/l*`
15×	`difference-of-squares`
8×	`cbrt-undiv` `div-exp`
7×	`associate-/r*`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg` `fma-neg` `associate-/l/`
2×	`flip3--` `prod-exp` `cbrt-unprod` `flip--`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 221

Calls

4 calls:

83.0ms	(/ (- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))) (fma (+ 1/2 (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)) 1/4))
26.0ms	(/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))
14.0ms	(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
40.0ms	(- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(/ (- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))) (fma (+ 1/2 (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)) 1/4))
96.0ms	(/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))
81.0ms	(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
134.0ms	(- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)))

simplify1.9s

Counts

233 → 233

Iterations

Iter	Nodes
2	3269
1	1154
0	448

prune3.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes174.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.6b

bsearch181.0ms

Steps

Iters	Range		Point
8	0.00023203888932163942	0.10106394179147121	0.012795833219468917
7	-0.11981472621416538	-0.0008162261515098681	-0.010775316190533964

simplify8.0ms

Iterations

Iter	Nodes
2	51
1	51
0	44

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	2852×	body	1280	valid
705.0ms	4052×	body	80	valid
329.0ms	624×	body	640	valid
110.0ms	317×	body	320	valid
26.0ms	155×	body	160	valid