Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3

Percentage Accurate: 98.0% → 100.0%

Time: 3.1s

Alternatives: 7

Speedup: 1.3×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot y + \left(1 - x\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* (- 1.0 x) z)))

C

double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * y) + ((1.0d0 - x) * z)
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}

Python

def code(x, y, z):
	return (x * y) + ((1.0 - x) * z)

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(Float64(1.0 - x) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + ((1.0 - x) * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot y + \left(1 - x\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* (- 1.0 x) z)))

C

double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * y) + ((1.0d0 - x) * z)
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}

Python

def code(x, y, z):
	return (x * y) + ((1.0 - x) * z)

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(Float64(1.0 - x) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + ((1.0 - x) * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y - z, z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma x (- y z) z))

C

double code(double x, double y, double z) {
	return fma(x, (y - z), z);
}

Julia

function code(x, y, z)
	return fma(x, Float64(y - z), z)
end

Wolfram

code[x_, y_, z_] := N[(x * N[(y - z), $MachinePrecision] + z), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[x \cdot y + \left(1 - x\right) \cdot z \]
2. Step-by-step derivation

   1. sub-neg 98.0%

      \[\leadsto x \cdot y + \color{blue}{\left(1 + \left(-x\right)\right)} \cdot z \]

   2. +-commutative 98.0%

      \[\leadsto x \cdot y + \color{blue}{\left(\left(-x\right) + 1\right)} \cdot z \]

   3. distribute-lft1-in 98.0%

      \[\leadsto x \cdot y + \color{blue}{\left(\left(-x\right) \cdot z + z\right)} \]

   4. associate-+r+ 98.0%

      \[\leadsto \color{blue}{\left(x \cdot y + \left(-x\right) \cdot z\right) + z} \]

   5. +-commutative 98.0%

      \[\leadsto \color{blue}{\left(\left(-x\right) \cdot z + x \cdot y\right)} + z \]

   6. *-commutative 98.0%

      \[\leadsto \left(\color{blue}{z \cdot \left(-x\right)} + x \cdot y\right) + z \]

   7. neg-mul-1 98.0%

      \[\leadsto \left(z \cdot \color{blue}{\left(-1 \cdot x\right)} + x \cdot y\right) + z \]

   8. associate-*r* 98.0%

      \[\leadsto \left(\color{blue}{\left(z \cdot -1\right) \cdot x} + x \cdot y\right) + z \]

   9. *-commutative 98.0%

      \[\leadsto \left(\left(z \cdot -1\right) \cdot x + \color{blue}{y \cdot x}\right) + z \]

   10. distribute-rgt-out 100.0%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot -1 + y\right)} + z \]

   11. fma-def 100.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, z \cdot -1 + y, z\right)} \]

   12. +-commutative 100.0%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{y + z \cdot -1}, z\right) \]

   13. *-commutative 100.0%

       \[\leadsto \mathsf{fma}\left(x, y + \color{blue}{-1 \cdot z}, z\right) \]

   14. neg-mul-1 100.0%

       \[\leadsto \mathsf{fma}\left(x, y + \color{blue}{\left(-z\right)}, z\right) \]

   15. unsub-neg 100.0%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{y - z}, z\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y - z, z\right)} \]

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, y - z, z\right) \]

Alternative 2: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-47}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+85} \lor \neg \left(x \leq 2.9 \cdot 10^{+147}\right) \land x \leq 3 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7e-47)
   (* x y)
   (if (<= x 1.0)
     z
     (if (or (<= x 1.4e+85) (and (not (<= x 2.9e+147)) (<= x 3e+175)))
       (* x (- z))
       (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7e-47) {
		tmp = x * y;
	} else if (x <= 1.0) {
		tmp = z;
	} else if ((x <= 1.4e+85) || (!(x <= 2.9e+147) && (x <= 3e+175))) {
		tmp = x * -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-7d-47)) then
        tmp = x * y
    else if (x <= 1.0d0) then
        tmp = z
    else if ((x <= 1.4d+85) .or. (.not. (x <= 2.9d+147)) .and. (x <= 3d+175)) then
        tmp = x * -z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7e-47) {
		tmp = x * y;
	} else if (x <= 1.0) {
		tmp = z;
	} else if ((x <= 1.4e+85) || (!(x <= 2.9e+147) && (x <= 3e+175))) {
		tmp = x * -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7e-47:
		tmp = x * y
	elif x <= 1.0:
		tmp = z
	elif (x <= 1.4e+85) or (not (x <= 2.9e+147) and (x <= 3e+175)):
		tmp = x * -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7e-47)
		tmp = Float64(x * y);
	elseif (x <= 1.0)
		tmp = z;
	elseif ((x <= 1.4e+85) || (!(x <= 2.9e+147) && (x <= 3e+175)))
		tmp = Float64(x * Float64(-z));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7e-47)
		tmp = x * y;
	elseif (x <= 1.0)
		tmp = z;
	elseif ((x <= 1.4e+85) || (~((x <= 2.9e+147)) && (x <= 3e+175)))
		tmp = x * -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7e-47], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.0], z, If[Or[LessEqual[x, 1.4e+85], And[N[Not[LessEqual[x, 2.9e+147]], $MachinePrecision], LessEqual[x, 3e+175]]], N[(x * (-z)), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.9999999999999996e-47 or 1.4e85 < x < 2.8999999999999998e147 or 3.0000000000000002e175 < x

   1. Initial program 95.7%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around inf 59.8%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -6.9999999999999996e-47 < x < 1

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around 0 73.7%

      \[\leadsto \color{blue}{z} \]

   if 1 < x < 1.4e85 or 2.8999999999999998e147 < x < 3.0000000000000002e175

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around 0 76.4%

      \[\leadsto \color{blue}{z \cdot \left(1 - x\right)} \]

   3. Taylor expanded in x around inf 66.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot x\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 66.4%

         \[\leadsto \color{blue}{\left(-1 \cdot z\right) \cdot x} \]

      2. mul-1-neg 66.4%

         \[\leadsto \color{blue}{\left(-z\right)} \cdot x \]

   5. Simplified 66.4%

      \[\leadsto \color{blue}{\left(-z\right) \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-47}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+85} \lor \neg \left(x \leq 2.9 \cdot 10^{+147}\right) \land x \leq 3 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-90} \lor \neg \left(z \leq 3.2 \cdot 10^{-64} \lor \neg \left(z \leq 6.6 \cdot 10^{+46}\right) \land z \leq 4.2 \cdot 10^{+80}\right):\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8e-90)
         (not (or (<= z 3.2e-64) (and (not (<= z 6.6e+46)) (<= z 4.2e+80)))))
   (* z (- 1.0 x))
   (* x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8e-90) || !((z <= 3.2e-64) || (!(z <= 6.6e+46) && (z <= 4.2e+80)))) {
		tmp = z * (1.0 - x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-8d-90)) .or. (.not. (z <= 3.2d-64) .or. (.not. (z <= 6.6d+46)) .and. (z <= 4.2d+80))) then
        tmp = z * (1.0d0 - x)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8e-90) || !((z <= 3.2e-64) || (!(z <= 6.6e+46) && (z <= 4.2e+80)))) {
		tmp = z * (1.0 - x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8e-90) or not ((z <= 3.2e-64) or (not (z <= 6.6e+46) and (z <= 4.2e+80))):
		tmp = z * (1.0 - x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8e-90) || !((z <= 3.2e-64) || (!(z <= 6.6e+46) && (z <= 4.2e+80))))
		tmp = Float64(z * Float64(1.0 - x));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8e-90) || ~(((z <= 3.2e-64) || (~((z <= 6.6e+46)) && (z <= 4.2e+80)))))
		tmp = z * (1.0 - x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8e-90], N[Not[Or[LessEqual[z, 3.2e-64], And[N[Not[LessEqual[z, 6.6e+46]], $MachinePrecision], LessEqual[z, 4.2e+80]]]], $MachinePrecision]], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999996e-90 or 3.19999999999999975e-64 < z < 6.5999999999999996e46 or 4.20000000000000003e80 < z

   1. Initial program 98.5%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around 0 88.4%

      \[\leadsto \color{blue}{z \cdot \left(1 - x\right)} \]

   if -7.99999999999999996e-90 < z < 3.19999999999999975e-64 or 6.5999999999999996e46 < z < 4.20000000000000003e80

   1. Initial program 97.4%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around inf 71.0%

      \[\leadsto \color{blue}{y \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-90} \lor \neg \left(z \leq 3.2 \cdot 10^{-64} \lor \neg \left(z \leq 6.6 \cdot 10^{+46}\right) \land z \leq 4.2 \cdot 10^{+80}\right):\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-48} \lor \neg \left(x \leq 48000000\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9e-48) (not (<= x 48000000.0))) (* x (- y z)) (* z (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9e-48) || !(x <= 48000000.0)) {
		tmp = x * (y - z);
	} else {
		tmp = z * (1.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-9d-48)) .or. (.not. (x <= 48000000.0d0))) then
        tmp = x * (y - z)
    else
        tmp = z * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9e-48) || !(x <= 48000000.0)) {
		tmp = x * (y - z);
	} else {
		tmp = z * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9e-48) or not (x <= 48000000.0):
		tmp = x * (y - z)
	else:
		tmp = z * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9e-48) || !(x <= 48000000.0))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = Float64(z * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9e-48) || ~((x <= 48000000.0)))
		tmp = x * (y - z);
	else
		tmp = z * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9e-48], N[Not[LessEqual[x, 48000000.0]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.99999999999999977e-48 or 4.8e7 < x

   1. Initial program 96.3%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around inf 97.2%

      \[\leadsto \color{blue}{\left(-1 \cdot z + y\right) \cdot x} \]
   3. Step-by-step derivation

      1. neg-mul-1 97.2%

         \[\leadsto \left(\color{blue}{\left(-z\right)} + y\right) \cdot x \]

      2. +-commutative 97.2%

         \[\leadsto \color{blue}{\left(y + \left(-z\right)\right)} \cdot x \]

      3. unsub-neg 97.2%

         \[\leadsto \color{blue}{\left(y - z\right)} \cdot x \]

   4. Simplified 97.2%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot x} \]

   if -8.99999999999999977e-48 < x < 4.8e7

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around 0 75.6%

      \[\leadsto \color{blue}{z \cdot \left(1 - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-48} \lor \neg \left(x \leq 48000000\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 61.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-48}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-30}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.4e-48) (* x y) (if (<= x 1.3e-30) z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.4e-48) {
		tmp = x * y;
	} else if (x <= 1.3e-30) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-4.4d-48)) then
        tmp = x * y
    else if (x <= 1.3d-30) then
        tmp = z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.4e-48) {
		tmp = x * y;
	} else if (x <= 1.3e-30) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.4e-48:
		tmp = x * y
	elif x <= 1.3e-30:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.4e-48)
		tmp = Float64(x * y);
	elseif (x <= 1.3e-30)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.4e-48)
		tmp = x * y;
	elseif (x <= 1.3e-30)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.4e-48], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.3e-30], z, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.40000000000000025e-48 or 1.29999999999999993e-30 < x

   1. Initial program 96.6%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around inf 53.1%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -4.40000000000000025e-48 < x < 1.29999999999999993e-30

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around 0 76.4%

      \[\leadsto \color{blue}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-48}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-30}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ z + x \cdot \left(y - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ z (* x (- y z))))

C

double code(double x, double y, double z) {
	return z + (x * (y - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z + (x * (y - z))
end function

Java

public static double code(double x, double y, double z) {
	return z + (x * (y - z));
}

Python

def code(x, y, z):
	return z + (x * (y - z))

Julia

function code(x, y, z)
	return Float64(z + Float64(x * Float64(y - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = z + (x * (y - z));
end

Wolfram

code[x_, y_, z_] := N[(z + N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[x \cdot y + \left(1 - x\right) \cdot z \]

2. Taylor expanded in x around 0 100.0%

   \[\leadsto \color{blue}{\left(-1 \cdot z + y\right) \cdot x + z} \]

3. Taylor expanded in z around 0 98.0%

   \[\leadsto \color{blue}{\left(1 + -1 \cdot x\right) \cdot z + y \cdot x} \]
4. Step-by-step derivation

   1. *-commutative 98.0%

      \[\leadsto \color{blue}{z \cdot \left(1 + -1 \cdot x\right)} + y \cdot x \]

   2. neg-mul-1 98.0%

      \[\leadsto z \cdot \left(1 + \color{blue}{\left(-x\right)}\right) + y \cdot x \]

   3. distribute-lft-in 98.0%

      \[\leadsto \color{blue}{\left(z \cdot 1 + z \cdot \left(-x\right)\right)} + y \cdot x \]

   4. *-rgt-identity 98.0%

      \[\leadsto \left(\color{blue}{z} + z \cdot \left(-x\right)\right) + y \cdot x \]

   5. associate-+l+ 98.0%

      \[\leadsto \color{blue}{z + \left(z \cdot \left(-x\right) + y \cdot x\right)} \]

   6. +-commutative 98.0%

      \[\leadsto z + \color{blue}{\left(y \cdot x + z \cdot \left(-x\right)\right)} \]

   7. distribute-rgt-neg-out 98.0%

      \[\leadsto z + \left(y \cdot x + \color{blue}{\left(-z \cdot x\right)}\right) \]

   8. unsub-neg 98.0%

      \[\leadsto z + \color{blue}{\left(y \cdot x - z \cdot x\right)} \]

   9. distribute-rgt-out-- 100.0%

      \[\leadsto z + \color{blue}{x \cdot \left(y - z\right)} \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{z + x \cdot \left(y - z\right)} \]

6. Final simplification 100.0%

   \[\leadsto z + x \cdot \left(y - z\right) \]

Alternative 7: 36.3% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 z)

C

double code(double x, double y, double z) {
	return z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z
end function

Java

public static double code(double x, double y, double z) {
	return z;
}

Python

def code(x, y, z):
	return z

Julia

function code(x, y, z)
	return z
end

MATLAB

function tmp = code(x, y, z)
	tmp = z;
end

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 98.0%

   \[x \cdot y + \left(1 - x\right) \cdot z \]

2. Taylor expanded in x around 0 35.9%

   \[\leadsto \color{blue}{z} \]

3. Final simplification 35.9%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023228 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))