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

Percentage Accurate: 97.9% → 100.0%

Time: 22.5s

Alternatives: 7

Speedup: 1.1×

• 20.3% 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: 97.9% 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: 100.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. +-commutative N/A

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

   5. lower-+.f64 N/A

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

   6. lower-*.f64 100.0

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

5. Applied rewrites 100.0%

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

Alternative 2: 61.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+216}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-40}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-1 \cdot z\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+131}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.6e+216)
   (* z x)
   (if (<= x -9.6e-40)
     (* y x)
     (if (<= x 1.0) (* -1.0 z) (if (<= x 1.05e+131) (* z x) (* y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.6e+216) {
		tmp = z * x;
	} else if (x <= -9.6e-40) {
		tmp = y * x;
	} else if (x <= 1.0) {
		tmp = -1.0 * z;
	} else if (x <= 1.05e+131) {
		tmp = z * x;
	} else {
		tmp = y * 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 <= (-9.6d+216)) then
        tmp = z * x
    else if (x <= (-9.6d-40)) then
        tmp = y * x
    else if (x <= 1.0d0) then
        tmp = (-1.0d0) * z
    else if (x <= 1.05d+131) then
        tmp = z * x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.6e+216) {
		tmp = z * x;
	} else if (x <= -9.6e-40) {
		tmp = y * x;
	} else if (x <= 1.0) {
		tmp = -1.0 * z;
	} else if (x <= 1.05e+131) {
		tmp = z * x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.6e+216:
		tmp = z * x
	elif x <= -9.6e-40:
		tmp = y * x
	elif x <= 1.0:
		tmp = -1.0 * z
	elif x <= 1.05e+131:
		tmp = z * x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.6e+216)
		tmp = Float64(z * x);
	elseif (x <= -9.6e-40)
		tmp = Float64(y * x);
	elseif (x <= 1.0)
		tmp = Float64(-1.0 * z);
	elseif (x <= 1.05e+131)
		tmp = Float64(z * x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.6e+216)
		tmp = z * x;
	elseif (x <= -9.6e-40)
		tmp = y * x;
	elseif (x <= 1.0)
		tmp = -1.0 * z;
	elseif (x <= 1.05e+131)
		tmp = z * x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.6e+216], N[(z * x), $MachinePrecision], If[LessEqual[x, -9.6e-40], N[(y * x), $MachinePrecision], If[LessEqual[x, 1.0], N[(-1.0 * z), $MachinePrecision], If[LessEqual[x, 1.05e+131], N[(z * x), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5999999999999997e216 or 1 < x < 1.04999999999999993e131

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.9

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

   5. Applied rewrites 72.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 71.0%

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

   if -9.5999999999999997e216 < x < -9.59999999999999965e-40 or 1.04999999999999993e131 < x

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 47.1

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

   5. Applied rewrites 47.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 40.7%

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

   9. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 57.9

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

   11. Applied rewrites 57.9%

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

   if -9.59999999999999965e-40 < x < 1

   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. lower-*.f64 75.8

         \[\leadsto \color{blue}{-1 \cdot z} \]

   5. Applied rewrites 75.8%

      \[\leadsto \color{blue}{-1 \cdot z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double t_0 = (z + y) * x;
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = fma(y, x, (-1.0 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 95.8%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 97.6

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

   5. Applied rewrites 97.6%

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

   if -1 < x < 1

   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

   5. Applied rewrites 98.3%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot y + -1 \cdot z} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot y} + -1 \cdot z \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot x} + -1 \cdot z \]

      4. lower-fma.f64 98.3

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

   7. Applied rewrites 98.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, -1 \cdot z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z + y\right) \cdot x\\ \mathbf{if}\;x \leq -110:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-12}:\\ \;\;\;\;\left(x - 1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ z y) x)))
   (if (<= x -110.0) t_0 (if (<= x 5.2e-12) (* (- x 1.0) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z + y) * x;
	double tmp;
	if (x <= -110.0) {
		tmp = t_0;
	} else if (x <= 5.2e-12) {
		tmp = (x - 1.0) * 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 = (z + y) * x
    if (x <= (-110.0d0)) then
        tmp = t_0
    else if (x <= 5.2d-12) then
        tmp = (x - 1.0d0) * 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 = (z + y) * x;
	double tmp;
	if (x <= -110.0) {
		tmp = t_0;
	} else if (x <= 5.2e-12) {
		tmp = (x - 1.0) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z + y) * x
	tmp = 0
	if x <= -110.0:
		tmp = t_0
	elif x <= 5.2e-12:
		tmp = (x - 1.0) * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z + y) * x)
	tmp = 0.0
	if (x <= -110.0)
		tmp = t_0;
	elseif (x <= 5.2e-12)
		tmp = Float64(Float64(x - 1.0) * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z + y) * x;
	tmp = 0.0;
	if (x <= -110.0)
		tmp = t_0;
	elseif (x <= 5.2e-12)
		tmp = (x - 1.0) * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -110.0], t$95$0, If[LessEqual[x, 5.2e-12], N[(N[(x - 1.0), $MachinePrecision] * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -110 or 5.19999999999999965e-12 < x

   1. Initial program 95.9%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 98.0

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

   5. Applied rewrites 98.0%

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

   if -110 < x < 5.19999999999999965e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.7

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

   5. Applied rewrites 75.7%

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

Alternative 5: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z + y\right) \cdot x\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{-70}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-13}:\\ \;\;\;\;-1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ z y) x)))
   (if (<= x -1.45e-70) t_0 (if (<= x 1.5e-13) (* -1.0 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z + y) * x;
	double tmp;
	if (x <= -1.45e-70) {
		tmp = t_0;
	} else if (x <= 1.5e-13) {
		tmp = -1.0 * 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 = (z + y) * x
    if (x <= (-1.45d-70)) then
        tmp = t_0
    else if (x <= 1.5d-13) then
        tmp = (-1.0d0) * 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 = (z + y) * x;
	double tmp;
	if (x <= -1.45e-70) {
		tmp = t_0;
	} else if (x <= 1.5e-13) {
		tmp = -1.0 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z + y) * x
	tmp = 0
	if x <= -1.45e-70:
		tmp = t_0
	elif x <= 1.5e-13:
		tmp = -1.0 * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z + y) * x)
	tmp = 0.0
	if (x <= -1.45e-70)
		tmp = t_0;
	elseif (x <= 1.5e-13)
		tmp = Float64(-1.0 * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z + y) * x;
	tmp = 0.0;
	if (x <= -1.45e-70)
		tmp = t_0;
	elseif (x <= 1.5e-13)
		tmp = -1.0 * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.45e-70], t$95$0, If[LessEqual[x, 1.5e-13], N[(-1.0 * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999986e-70 or 1.49999999999999992e-13 < x

   1. Initial program 96.4%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 92.0

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

   5. Applied rewrites 92.0%

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

   if -1.44999999999999986e-70 < x < 1.49999999999999992e-13

   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. lower-*.f64 79.1

         \[\leadsto \color{blue}{-1 \cdot z} \]

   5. Applied rewrites 79.1%

      \[\leadsto \color{blue}{-1 \cdot z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 61.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.0) (* z x) (if (<= x 1.0) (* -1.0 z) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = z * x;
	} else if (x <= 1.0) {
		tmp = -1.0 * z;
	} else {
		tmp = z * 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 <= (-1.0d0)) then
        tmp = z * x
    else if (x <= 1.0d0) then
        tmp = (-1.0d0) * z
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 55.5

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

   5. Applied rewrites 55.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 53.1%

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

   if -1 < x < 1

   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. lower-*.f64 72.8

         \[\leadsto \color{blue}{-1 \cdot z} \]

   5. Applied rewrites 72.8%

      \[\leadsto \color{blue}{-1 \cdot z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 27.7% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 65.6

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

5. Applied rewrites 65.6%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 27.0%

   \[\leadsto z \cdot \color{blue}{x} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024297 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))