Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3

Percentage Accurate: 98.0% → 99.7%

Time: 5.2s

Alternatives: 7

Speedup: 0.8×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + ((x - 1.0) * 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) + ((x - 1.0d0) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + ((x - 1.0) * 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) + ((x - 1.0d0) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot y + \left(x + -1\right) \cdot z\\ \mathbf{if}\;t\_0 \leq 5 \cdot 10^{+300}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* x y) (* (+ x -1.0) z))))
   (if (<= t_0 5e+300) t_0 (* x (+ y z)))))

C

double code(double x, double y, double z) {
	double t_0 = (x * y) + ((x + -1.0) * z);
	double tmp;
	if (t_0 <= 5e+300) {
		tmp = t_0;
	} else {
		tmp = x * (y + 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) :: t_0
    real(8) :: tmp
    t_0 = (x * y) + ((x + (-1.0d0)) * z)
    if (t_0 <= 5d+300) then
        tmp = t_0
    else
        tmp = x * (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * y) + ((x + -1.0) * z);
	double tmp;
	if (t_0 <= 5e+300) {
		tmp = t_0;
	} else {
		tmp = x * (y + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * y) + ((x + -1.0) * z)
	tmp = 0
	if t_0 <= 5e+300:
		tmp = t_0
	else:
		tmp = x * (y + z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * y) + Float64(Float64(x + -1.0) * z))
	tmp = 0.0
	if (t_0 <= 5e+300)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * y) + ((x + -1.0) * z);
	tmp = 0.0;
	if (t_0 <= 5e+300)
		tmp = t_0;
	else
		tmp = x * (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * y), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+300], t$95$0, N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 (-.f64 x #s(literal 1 binary64)) z)) < 5.00000000000000026e300

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   if 5.00000000000000026e300 < (+.f64 (*.f64 x y) (*.f64 (-.f64 x #s(literal 1 binary64)) z))

   1. Initial program 70.4%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 100.0

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

   5. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y + \left(x + -1\right) \cdot z \leq 5 \cdot 10^{+300}:\\ \;\;\;\;x \cdot y + \left(x + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-55}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-19}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+77}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e-55)
   (* x y)
   (if (<= x 9.6e-19) (- z) (if (<= x 3.1e+77) (* x z) (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e-55) {
		tmp = x * y;
	} else if (x <= 9.6e-19) {
		tmp = -z;
	} else if (x <= 3.1e+77) {
		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 <= (-1.55d-55)) then
        tmp = x * y
    else if (x <= 9.6d-19) then
        tmp = -z
    else if (x <= 3.1d+77) 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 <= -1.55e-55) {
		tmp = x * y;
	} else if (x <= 9.6e-19) {
		tmp = -z;
	} else if (x <= 3.1e+77) {
		tmp = x * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.55e-55:
		tmp = x * y
	elif x <= 9.6e-19:
		tmp = -z
	elif x <= 3.1e+77:
		tmp = x * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e-55)
		tmp = Float64(x * y);
	elseif (x <= 9.6e-19)
		tmp = Float64(-z);
	elseif (x <= 3.1e+77)
		tmp = Float64(x * z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.55e-55)
		tmp = x * y;
	elseif (x <= 9.6e-19)
		tmp = -z;
	elseif (x <= 3.1e+77)
		tmp = x * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e-55], N[(x * y), $MachinePrecision], If[LessEqual[x, 9.6e-19], (-z), If[LessEqual[x, 3.1e+77], N[(x * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.54999999999999998e-55 or 3.09999999999999999e77 < x

   1. Initial program 93.1%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 61.7

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

   5. Simplified 61.7%

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

   if -1.54999999999999998e-55 < x < 9.60000000000000092e-19

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. neg-lowering-neg.f64 73.9

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

   5. Simplified 73.9%

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

   if 9.60000000000000092e-19 < x < 3.09999999999999999e77

   1. Initial program 99.8%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 93.8

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

   5. Simplified 93.8%

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

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x \cdot z} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 55.9

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

   8. Simplified 55.9%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-55}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-19}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+77}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-24}:\\ \;\;\;\;x \cdot y - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -1.0) t_0 (if (<= x 2.6e-24) (- (* x y) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 2.6e-24) {
		tmp = (x * y) - z;
	} 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 = x * (y + z)
    if (x <= (-1.0d0)) then
        tmp = t_0
    else if (x <= 2.6d-24) then
        tmp = (x * y) - z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 2.6e-24) {
		tmp = (x * y) - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -1.0:
		tmp = t_0
	elif x <= 2.6e-24:
		tmp = (x * y) - z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -1.0)
		tmp = t_0;
	elseif (x <= 2.6e-24)
		tmp = Float64(Float64(x * y) - z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y + z);
	tmp = 0.0;
	if (x <= -1.0)
		tmp = t_0;
	elseif (x <= 2.6e-24)
		tmp = (x * y) - z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.0], t$95$0, If[LessEqual[x, 2.6e-24], N[(N[(x * y), $MachinePrecision] - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 2.6e-24 < x

   1. Initial program 93.6%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 98.8

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

   5. Simplified 98.8%

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

   if -1 < x < 2.6e-24

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 100.0

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

   5. Simplified 100.0%

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

      1. unsub-neg N/A

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

      2. --lowering--.f64 N/A

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

      3. *-lowering-*.f64 100.0

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

   7. Applied egg-rr 100.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-24}:\\ \;\;\;\;x \cdot y - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{-47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-128}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -1e-47) t_0 (if (<= x 8.2e-128) (- z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -1e-47) {
		tmp = t_0;
	} else if (x <= 8.2e-128) {
		tmp = -z;
	} 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 = x * (y + z)
    if (x <= (-1d-47)) then
        tmp = t_0
    else if (x <= 8.2d-128) then
        tmp = -z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -1e-47) {
		tmp = t_0;
	} else if (x <= 8.2e-128) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -1e-47:
		tmp = t_0
	elif x <= 8.2e-128:
		tmp = -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -1e-47)
		tmp = t_0;
	elseif (x <= 8.2e-128)
		tmp = Float64(-z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y + z);
	tmp = 0.0;
	if (x <= -1e-47)
		tmp = t_0;
	elseif (x <= 8.2e-128)
		tmp = -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e-47], t$95$0, If[LessEqual[x, 8.2e-128], (-z), t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.9999999999999997e-48 or 8.1999999999999999e-128 < x

   1. Initial program 95.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 89.6

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

   5. Simplified 89.6%

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

   if -9.9999999999999997e-48 < x < 8.1999999999999999e-128

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. neg-lowering-neg.f64 78.9

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

   5. Simplified 78.9%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-128}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-57}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-128}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.3e-57) (* x y) (if (<= x 8e-128) (- z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.3e-57) {
		tmp = x * y;
	} else if (x <= 8e-128) {
		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 <= (-3.3d-57)) then
        tmp = x * y
    else if (x <= 8d-128) 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 <= -3.3e-57) {
		tmp = x * y;
	} else if (x <= 8e-128) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.3e-57:
		tmp = x * y
	elif x <= 8e-128:
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.3e-57)
		tmp = Float64(x * y);
	elseif (x <= 8e-128)
		tmp = Float64(-z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.3e-57)
		tmp = x * y;
	elseif (x <= 8e-128)
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.3e-57], N[(x * y), $MachinePrecision], If[LessEqual[x, 8e-128], (-z), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.2999999999999998e-57 or 8.00000000000000043e-128 < x

   1. Initial program 95.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 56.6

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

   5. Simplified 56.6%

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

   if -3.2999999999999998e-57 < x < 8.00000000000000043e-128

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. neg-lowering-neg.f64 78.9

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

   5. Simplified 78.9%

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

Alternative 6: 36.5% accurate, 5.7× 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 Float64(-z)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := (-z)

Derivation

1. Initial program 96.9%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-1 \cdot z} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

   2. neg-lowering-neg.f64 37.5

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

5. Simplified 37.5%

   \[\leadsto \color{blue}{-z} \]
6. Add Preprocessing

Alternative 7: 2.6% accurate, 17.0× 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 96.9%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-1 \cdot z} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

   2. neg-lowering-neg.f64 37.5

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

5. Simplified 37.5%

   \[\leadsto \color{blue}{-z} \]
6. Step-by-step derivation

   1. neg-sub0 N/A

      \[\leadsto \color{blue}{0 - z} \]

   2. flip3-- N/A

      \[\leadsto \color{blue}{\frac{{0}^{3} - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}} \]

   3. metadata-eval N/A

      \[\leadsto \frac{\color{blue}{0} - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   4. neg-sub0 N/A

      \[\leadsto \frac{\color{blue}{\mathsf{neg}\left({z}^{3}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   5. cube-neg N/A

      \[\leadsto \frac{\color{blue}{{\left(\mathsf{neg}\left(z\right)\right)}^{3}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   6. sqr-pow N/A

      \[\leadsto \frac{\color{blue}{{\left(\mathsf{neg}\left(z\right)\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\mathsf{neg}\left(z\right)\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   7. pow-prod-down N/A

      \[\leadsto \frac{\color{blue}{{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   8. sqr-neg N/A

      \[\leadsto \frac{{\color{blue}{\left(z \cdot z\right)}}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   9. pow-prod-down N/A

      \[\leadsto \frac{\color{blue}{{z}^{\left(\frac{3}{2}\right)} \cdot {z}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   10. sqr-pow N/A

       \[\leadsto \frac{\color{blue}{{z}^{3}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   11. metadata-eval N/A

       \[\leadsto \frac{{z}^{3}}{\color{blue}{0} + \left(z \cdot z + 0 \cdot z\right)} \]

   12. +-lft-identity N/A

       \[\leadsto \frac{{z}^{3}}{\color{blue}{z \cdot z + 0 \cdot z}} \]

   13. distribute-rgt-out N/A

       \[\leadsto \frac{{z}^{3}}{\color{blue}{z \cdot \left(z + 0\right)}} \]

   14. +-commutative N/A

       \[\leadsto \frac{{z}^{3}}{z \cdot \color{blue}{\left(0 + z\right)}} \]

   15. +-lft-identity N/A

       \[\leadsto \frac{{z}^{3}}{z \cdot \color{blue}{z}} \]

   16. pow2 N/A

       \[\leadsto \frac{{z}^{3}}{\color{blue}{{z}^{2}}} \]

   17. pow-div N/A

       \[\leadsto \color{blue}{{z}^{\left(3 - 2\right)}} \]

   18. metadata-eval N/A

       \[\leadsto {z}^{\color{blue}{1}} \]

   19. unpow1 2.8

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

7. Applied egg-rr 2.8%

   \[\leadsto \color{blue}{z} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024204 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))