FastMath repmul

?

Percentage Accurate: 99.9% → 100.0%
Time: 1.7s
Precision: binary64
Cost: 6528

?

\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1 \]
↓
\[{d1}^{4} \]
(FPCore (d1) :precision binary64 (* (* (* d1 d1) d1) d1))
↓
(FPCore (d1) :precision binary64 (pow d1 4.0))
double code(double d1) {
	return ((d1 * d1) * d1) * d1;
}
↓
double code(double d1) {
	return pow(d1, 4.0);
}

real(8) function code(d1)
    real(8), intent (in) :: d1
    code = ((d1 * d1) * d1) * d1
end function
↓
real(8) function code(d1)
    real(8), intent (in) :: d1
    code = d1 ** 4.0d0
end function

public static double code(double d1) {
	return ((d1 * d1) * d1) * d1;
}
↓
public static double code(double d1) {
	return Math.pow(d1, 4.0);
}

def code(d1):
	return ((d1 * d1) * d1) * d1
↓
def code(d1):
	return math.pow(d1, 4.0)

function code(d1)
	return Float64(Float64(Float64(d1 * d1) * d1) * d1)
end
↓
function code(d1)
	return d1 ^ 4.0
end

function tmp = code(d1)
	tmp = ((d1 * d1) * d1) * d1;
end
↓
function tmp = code(d1)
	tmp = d1 ^ 4.0;
end

code[d1_] := N[(N[(N[(d1 * d1), $MachinePrecision] * d1), $MachinePrecision] * d1), $MachinePrecision]
↓
code[d1_] := N[Power[d1, 4.0], $MachinePrecision]

\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1
↓
{d1}^{4}

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Herbie found 3 alternatives:

AlternativeAccuracySpeedup

Accuracy vs Speed

The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Bogosity?

Bogosity

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original99.9%
Target100.0%
Herbie100.0%
\[{d1}^{4} \]

Derivation?

  1. Initial program 99.9%

    \[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1 \]

  2. Simplified100.0%

    \[\leadsto \color{blue}{{d1}^{4}} \]
    Step-by-step derivation

    [Start]99.9%

    \[ \left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1 \]

    unpow3 [<=]99.9%

    \[ \color{blue}{{d1}^{3}} \cdot d1 \]

    pow-plus [=>]100.0%

    \[ \color{blue}{{d1}^{\left(3 + 1\right)}} \]

    metadata-eval [=>]100.0%

    \[ {d1}^{\color{blue}{4}} \]

  3. Final simplification100.0%

    \[\leadsto {d1}^{4} \]

Alternatives

Alternative 1
Accuracy100.0%
Cost6528
\[{d1}^{4} \]
Alternative 2
Accuracy99.8%
Cost448
\[\left(d1 \cdot d1\right) \cdot \left(d1 \cdot d1\right) \]
Alternative 3
Accuracy99.9%
Cost448
\[d1 \cdot \left(d1 \cdot \left(d1 \cdot d1\right)\right) \]

Reproduce?

herbie shell --seed 2023178 
(FPCore (d1)
  :name "FastMath repmul"
  :precision binary64

  :herbie-target
  (pow d1 4.0)

  (* (* (* d1 d1) d1) d1))