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

Percentage Accurate: 97.8% → 100.0%

Time: 4.9s

Alternatives: 8

Speedup: 1.3×

• 20.4% 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: 97.8% 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 98.8%

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

   1. *-commutative 98.8%

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

   2. distribute-lft-out-- 98.8%

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

   3. *-rgt-identity 98.8%

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

   4. cancel-sign-sub-inv 98.8%

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

   5. +-commutative 98.8%

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

   6. associate-+r+ 98.8%

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

   7. *-commutative 98.8%

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

   8. distribute-rgt-out 100.0%

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

   9. +-commutative 100.0%

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

   10. fma-def 100.0%

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

   11. +-commutative 100.0%

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

   12. 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+126}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+32}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1150:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-19}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+133}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= x -1.65e+126)
     t_0
     (if (<= x -1.5e+32)
       (* x y)
       (if (<= x -1150.0)
         t_0
         (if (<= x -4.5e-19)
           (* x y)
           (if (<= x 1.05e-8) z (if (<= x 5e+133) (* x y) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (x <= -1.65e+126) {
		tmp = t_0;
	} else if (x <= -1.5e+32) {
		tmp = x * y;
	} else if (x <= -1150.0) {
		tmp = t_0;
	} else if (x <= -4.5e-19) {
		tmp = x * y;
	} else if (x <= 1.05e-8) {
		tmp = z;
	} else if (x <= 5e+133) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = z * -x
    if (x <= (-1.65d+126)) then
        tmp = t_0
    else if (x <= (-1.5d+32)) then
        tmp = x * y
    else if (x <= (-1150.0d0)) then
        tmp = t_0
    else if (x <= (-4.5d-19)) then
        tmp = x * y
    else if (x <= 1.05d-8) then
        tmp = z
    else if (x <= 5d+133) then
        tmp = x * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (x <= -1.65e+126) {
		tmp = t_0;
	} else if (x <= -1.5e+32) {
		tmp = x * y;
	} else if (x <= -1150.0) {
		tmp = t_0;
	} else if (x <= -4.5e-19) {
		tmp = x * y;
	} else if (x <= 1.05e-8) {
		tmp = z;
	} else if (x <= 5e+133) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if x <= -1.65e+126:
		tmp = t_0
	elif x <= -1.5e+32:
		tmp = x * y
	elif x <= -1150.0:
		tmp = t_0
	elif x <= -4.5e-19:
		tmp = x * y
	elif x <= 1.05e-8:
		tmp = z
	elif x <= 5e+133:
		tmp = x * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (x <= -1.65e+126)
		tmp = t_0;
	elseif (x <= -1.5e+32)
		tmp = Float64(x * y);
	elseif (x <= -1150.0)
		tmp = t_0;
	elseif (x <= -4.5e-19)
		tmp = Float64(x * y);
	elseif (x <= 1.05e-8)
		tmp = z;
	elseif (x <= 5e+133)
		tmp = Float64(x * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (x <= -1.65e+126)
		tmp = t_0;
	elseif (x <= -1.5e+32)
		tmp = x * y;
	elseif (x <= -1150.0)
		tmp = t_0;
	elseif (x <= -4.5e-19)
		tmp = x * y;
	elseif (x <= 1.05e-8)
		tmp = z;
	elseif (x <= 5e+133)
		tmp = x * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[x, -1.65e+126], t$95$0, If[LessEqual[x, -1.5e+32], N[(x * y), $MachinePrecision], If[LessEqual[x, -1150.0], t$95$0, If[LessEqual[x, -4.5e-19], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.05e-8], z, If[LessEqual[x, 5e+133], N[(x * y), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65000000000000006e126 or -1.5e32 < x < -1150 or 4.99999999999999961e133 < x

   1. Initial program 95.8%

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

   2. Taylor expanded in x around inf 96.1%

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

      1. neg-mul-1 96.1%

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

      2. unsub-neg 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in y around 0 67.2%

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

      1. mul-1-neg 67.2%

         \[\leadsto \color{blue}{-x \cdot z} \]

      2. distribute-lft-neg-out 67.2%

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

      3. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   if -1.65000000000000006e126 < x < -1.5e32 or -1150 < x < -4.50000000000000013e-19 or 1.04999999999999997e-8 < x < 4.99999999999999961e133

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 73.3%

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

   if -4.50000000000000013e-19 < x < 1.04999999999999997e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 74.4%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+126}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+32}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1150:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-19}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+133}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-19} \lor \neg \left(x \leq 5.8 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.3e-19) (not (<= x 5.8e-10))) (* x (- y z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.3e-19) || !(x <= 5.8e-10)) {
		tmp = x * (y - z);
	} else {
		tmp = z;
	}
	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 <= (-4.3d-19)) .or. (.not. (x <= 5.8d-10))) then
        tmp = x * (y - z)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.3e-19) || !(x <= 5.8e-10)) {
		tmp = x * (y - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.3e-19) or not (x <= 5.8e-10):
		tmp = x * (y - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.3e-19) || !(x <= 5.8e-10))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.3e-19) || ~((x <= 5.8e-10)))
		tmp = x * (y - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.3e-19], N[Not[LessEqual[x, 5.8e-10]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -4.3e-19 or 5.79999999999999962e-10 < x

   1. Initial program 97.5%

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

   2. Taylor expanded in x around inf 95.5%

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

      1. neg-mul-1 95.5%

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

      2. unsub-neg 95.5%

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

   4. Simplified 95.5%

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

   if -4.3e-19 < x < 5.79999999999999962e-10

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 74.4%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-19} \lor \neg \left(x \leq 5.8 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-19} \lor \neg \left(x \leq 2050\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.5e-19) (not (<= x 2050.0))) (* x (- y z)) (* z (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.5e-19) || !(x <= 2050.0)) {
		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 <= (-4.5d-19)) .or. (.not. (x <= 2050.0d0))) 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 <= -4.5e-19) || !(x <= 2050.0)) {
		tmp = x * (y - z);
	} else {
		tmp = z * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.5e-19) or not (x <= 2050.0):
		tmp = x * (y - z)
	else:
		tmp = z * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.5e-19) || !(x <= 2050.0))
		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 <= -4.5e-19) || ~((x <= 2050.0)))
		tmp = x * (y - z);
	else
		tmp = z * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.5e-19], N[Not[LessEqual[x, 2050.0]], $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 < -4.50000000000000013e-19 or 2050 < x

   1. Initial program 97.4%

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

   2. Taylor expanded in x around inf 96.7%

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

      1. neg-mul-1 96.7%

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

      2. unsub-neg 96.7%

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

   4. Simplified 96.7%

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

   if -4.50000000000000013e-19 < x < 2050

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.5%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-19} \lor \neg \left(x \leq 2050\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.5) (not (<= x 1.0))) (* x (- y z)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5) || !(x <= 1.0)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (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 <= (-8.5d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = x * (y - z)
    else
        tmp = z + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5) || !(x <= 1.0)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.5) or not (x <= 1.0):
		tmp = x * (y - z)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.5) || !(x <= 1.0))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = Float64(z + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.5) || ~((x <= 1.0)))
		tmp = x * (y - z);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.5], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5 or 1 < x

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 96.8%

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

      1. neg-mul-1 96.8%

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

      2. unsub-neg 96.8%

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

   4. Simplified 96.8%

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

   if -8.5 < x < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. neg-mul-1 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. neg-mul-1 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. *-lft-identity 100.0%

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

      5. associate-+r+ 100.0%

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

      6. +-commutative 100.0%

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

      7. cancel-sign-sub-inv 100.0%

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

      8. distribute-lft-out-- 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 99.2%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]

Alternative 6: 61.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-19}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.25e-19) (* x y) (if (<= x 2.9e-8) z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e-19) {
		tmp = x * y;
	} else if (x <= 2.9e-8) {
		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 <= (-1.25d-19)) then
        tmp = x * y
    else if (x <= 2.9d-8) 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 <= -1.25e-19) {
		tmp = x * y;
	} else if (x <= 2.9e-8) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.25e-19:
		tmp = x * y
	elif x <= 2.9e-8:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.25e-19)
		tmp = Float64(x * y);
	elseif (x <= 2.9e-8)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.25e-19)
		tmp = x * y;
	elseif (x <= 2.9e-8)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.25e-19], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.9e-8], z, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2500000000000001e-19 or 2.9000000000000002e-8 < x

   1. Initial program 97.5%

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

   2. Taylor expanded in y around inf 51.4%

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

   if -1.2500000000000001e-19 < x < 2.9000000000000002e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 74.4%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-19}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7: 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 98.8%

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

2. Taylor expanded in x around 0 100.0%

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

   1. neg-mul-1 100.0%

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

4. Simplified 100.0%

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

5. Taylor expanded in z around 0 98.8%

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

   1. +-commutative 98.8%

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

   2. neg-mul-1 98.8%

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

   3. distribute-rgt-in 98.8%

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

   4. *-lft-identity 98.8%

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

   5. associate-+r+ 98.8%

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

   6. +-commutative 98.8%

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

   7. cancel-sign-sub-inv 98.8%

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

   8. distribute-lft-out-- 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

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

Alternative 8: 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 98.8%

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

2. Taylor expanded in x around 0 41.4%

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

3. Final simplification 41.4%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023287 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))