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

Percentage Accurate: 97.9% → 100.0%

Time: 4.0s

Alternatives: 8

Speedup: 1.3×

• 20.7% 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, 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), Float64(-z))
end

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. *-commutative 98.4%

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

   2. distribute-rgt-out-- 98.4%

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

   3. cancel-sign-sub-inv 98.4%

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

   4. metadata-eval 98.4%

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

   5. neg-mul-1 98.4%

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

   6. associate-+r+ 98.4%

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

   7. distribute-lft-out 100.0%

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

   8. fma-def 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 83.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -2.65 \cdot 10^{-36}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-120}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 0.084:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -2.65e-36)
     t_0
     (if (<= x 4.2e-120)
       (- z)
       (if (<= x 3.1e-37) (* x y) (if (<= x 0.084) (- z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -2.65e-36) {
		tmp = t_0;
	} else if (x <= 4.2e-120) {
		tmp = -z;
	} else if (x <= 3.1e-37) {
		tmp = x * y;
	} else if (x <= 0.084) {
		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 <= (-2.65d-36)) then
        tmp = t_0
    else if (x <= 4.2d-120) then
        tmp = -z
    else if (x <= 3.1d-37) then
        tmp = x * y
    else if (x <= 0.084d0) 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 <= -2.65e-36) {
		tmp = t_0;
	} else if (x <= 4.2e-120) {
		tmp = -z;
	} else if (x <= 3.1e-37) {
		tmp = x * y;
	} else if (x <= 0.084) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -2.65e-36:
		tmp = t_0
	elif x <= 4.2e-120:
		tmp = -z
	elif x <= 3.1e-37:
		tmp = x * y
	elif x <= 0.084:
		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 <= -2.65e-36)
		tmp = t_0;
	elseif (x <= 4.2e-120)
		tmp = Float64(-z);
	elseif (x <= 3.1e-37)
		tmp = Float64(x * y);
	elseif (x <= 0.084)
		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 <= -2.65e-36)
		tmp = t_0;
	elseif (x <= 4.2e-120)
		tmp = -z;
	elseif (x <= 3.1e-37)
		tmp = x * y;
	elseif (x <= 0.084)
		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, -2.65e-36], t$95$0, If[LessEqual[x, 4.2e-120], (-z), If[LessEqual[x, 3.1e-37], N[(x * y), $MachinePrecision], If[LessEqual[x, 0.084], (-z), t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6499999999999999e-36 or 0.0840000000000000052 < x

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 96.9%

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

      1. +-commutative 96.9%

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

   5. Simplified 96.9%

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

   if -2.6499999999999999e-36 < x < 4.2000000000000001e-120 or 3.09999999999999993e-37 < x < 0.0840000000000000052

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.0%

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

      1. neg-mul-1 80.0%

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

   5. Simplified 80.0%

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

   if 4.2000000000000001e-120 < x < 3.09999999999999993e-37

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 81.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-120}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 0.084:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ t_1 := z \cdot \left(x + -1\right)\\ \mathbf{if}\;x \leq -1.52 \cdot 10^{-37}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 11500:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))) (t_1 (* z (+ x -1.0))))
   (if (<= x -1.52e-37)
     t_0
     (if (<= x 5.4e-120)
       t_1
       (if (<= x 2.75e-36) (* x y) (if (<= x 11500.0) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double t_1 = z * (x + -1.0);
	double tmp;
	if (x <= -1.52e-37) {
		tmp = t_0;
	} else if (x <= 5.4e-120) {
		tmp = t_1;
	} else if (x <= 2.75e-36) {
		tmp = x * y;
	} else if (x <= 11500.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = x * (y + z)
    t_1 = z * (x + (-1.0d0))
    if (x <= (-1.52d-37)) then
        tmp = t_0
    else if (x <= 5.4d-120) then
        tmp = t_1
    else if (x <= 2.75d-36) then
        tmp = x * y
    else if (x <= 11500.0d0) then
        tmp = t_1
    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 t_1 = z * (x + -1.0);
	double tmp;
	if (x <= -1.52e-37) {
		tmp = t_0;
	} else if (x <= 5.4e-120) {
		tmp = t_1;
	} else if (x <= 2.75e-36) {
		tmp = x * y;
	} else if (x <= 11500.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	t_1 = z * (x + -1.0)
	tmp = 0
	if x <= -1.52e-37:
		tmp = t_0
	elif x <= 5.4e-120:
		tmp = t_1
	elif x <= 2.75e-36:
		tmp = x * y
	elif x <= 11500.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	t_1 = Float64(z * Float64(x + -1.0))
	tmp = 0.0
	if (x <= -1.52e-37)
		tmp = t_0;
	elseif (x <= 5.4e-120)
		tmp = t_1;
	elseif (x <= 2.75e-36)
		tmp = Float64(x * y);
	elseif (x <= 11500.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y + z);
	t_1 = z * (x + -1.0);
	tmp = 0.0;
	if (x <= -1.52e-37)
		tmp = t_0;
	elseif (x <= 5.4e-120)
		tmp = t_1;
	elseif (x <= 2.75e-36)
		tmp = x * y;
	elseif (x <= 11500.0)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.52e-37], t$95$0, If[LessEqual[x, 5.4e-120], t$95$1, If[LessEqual[x, 2.75e-36], N[(x * y), $MachinePrecision], If[LessEqual[x, 11500.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.52e-37 or 11500 < x

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf 97.8%

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

      1. +-commutative 97.8%

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

   5. Simplified 97.8%

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

   if -1.52e-37 < x < 5.3999999999999997e-120 or 2.74999999999999992e-36 < x < 11500

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.3%

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

   if 5.3999999999999997e-120 < x < 2.74999999999999992e-36

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 81.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 11500:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{-36}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-38}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 470000:\\ \;\;\;\;x \cdot z - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -2.4e-36)
     t_0
     (if (<= x 5.4e-120)
       (* z (+ x -1.0))
       (if (<= x 4.3e-38) (* x y) (if (<= x 470000.0) (- (* x z) z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -2.4e-36) {
		tmp = t_0;
	} else if (x <= 5.4e-120) {
		tmp = z * (x + -1.0);
	} else if (x <= 4.3e-38) {
		tmp = x * y;
	} else if (x <= 470000.0) {
		tmp = (x * z) - 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 <= (-2.4d-36)) then
        tmp = t_0
    else if (x <= 5.4d-120) then
        tmp = z * (x + (-1.0d0))
    else if (x <= 4.3d-38) then
        tmp = x * y
    else if (x <= 470000.0d0) then
        tmp = (x * z) - 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 <= -2.4e-36) {
		tmp = t_0;
	} else if (x <= 5.4e-120) {
		tmp = z * (x + -1.0);
	} else if (x <= 4.3e-38) {
		tmp = x * y;
	} else if (x <= 470000.0) {
		tmp = (x * z) - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -2.4e-36:
		tmp = t_0
	elif x <= 5.4e-120:
		tmp = z * (x + -1.0)
	elif x <= 4.3e-38:
		tmp = x * y
	elif x <= 470000.0:
		tmp = (x * z) - 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 <= -2.4e-36)
		tmp = t_0;
	elseif (x <= 5.4e-120)
		tmp = Float64(z * Float64(x + -1.0));
	elseif (x <= 4.3e-38)
		tmp = Float64(x * y);
	elseif (x <= 470000.0)
		tmp = Float64(Float64(x * z) - 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 <= -2.4e-36)
		tmp = t_0;
	elseif (x <= 5.4e-120)
		tmp = z * (x + -1.0);
	elseif (x <= 4.3e-38)
		tmp = x * y;
	elseif (x <= 470000.0)
		tmp = (x * z) - 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, -2.4e-36], t$95$0, If[LessEqual[x, 5.4e-120], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e-38], N[(x * y), $MachinePrecision], If[LessEqual[x, 470000.0], N[(N[(x * z), $MachinePrecision] - z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.4e-36 or 4.7e5 < x

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf 97.8%

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

      1. +-commutative 97.8%

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

   5. Simplified 97.8%

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

   if -2.4e-36 < x < 5.3999999999999997e-120

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.6%

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

   if 5.3999999999999997e-120 < x < 4.3000000000000002e-38

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 81.6%

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

   if 4.3000000000000002e-38 < x < 4.7e5

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. distribute-rgt-out-- 99.8%

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

      3. cancel-sign-sub-inv 99.8%

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

      4. metadata-eval 99.8%

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

      5. neg-mul-1 99.8%

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

      6. associate-+r+ 99.8%

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

      7. unsub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 87.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-38}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 470000:\\ \;\;\;\;x \cdot z - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-35} \lor \neg \left(x \leq 5.4 \cdot 10^{-120} \lor \neg \left(x \leq 2 \cdot 10^{-39}\right) \land x \leq 0.084\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.65e-35)
         (not (or (<= x 5.4e-120) (and (not (<= x 2e-39)) (<= x 0.084)))))
   (* x y)
   (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.65e-35) || !((x <= 5.4e-120) || (!(x <= 2e-39) && (x <= 0.084)))) {
		tmp = x * y;
	} 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 <= (-1.65d-35)) .or. (.not. (x <= 5.4d-120) .or. (.not. (x <= 2d-39)) .and. (x <= 0.084d0))) then
        tmp = x * y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.65e-35) || !((x <= 5.4e-120) || (!(x <= 2e-39) && (x <= 0.084)))) {
		tmp = x * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.65e-35) or not ((x <= 5.4e-120) or (not (x <= 2e-39) and (x <= 0.084))):
		tmp = x * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.65e-35) || !((x <= 5.4e-120) || (!(x <= 2e-39) && (x <= 0.084))))
		tmp = Float64(x * y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.65e-35) || ~(((x <= 5.4e-120) || (~((x <= 2e-39)) && (x <= 0.084)))))
		tmp = x * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.65e-35], N[Not[Or[LessEqual[x, 5.4e-120], And[N[Not[LessEqual[x, 2e-39]], $MachinePrecision], LessEqual[x, 0.084]]]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -1.65e-35 or 5.3999999999999997e-120 < x < 1.99999999999999986e-39 or 0.0840000000000000052 < x

   1. Initial program 97.3%

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

   3. Taylor expanded in y around inf 54.8%

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

   if -1.65e-35 < x < 5.3999999999999997e-120 or 1.99999999999999986e-39 < x < 0.0840000000000000052

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.0%

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

      1. neg-mul-1 80.0%

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

   5. Simplified 80.0%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-35} \lor \neg \left(x \leq 5.4 \cdot 10^{-120} \lor \neg \left(x \leq 2 \cdot 10^{-39}\right) \land x \leq 0.084\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-120}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-39}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 0.35:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.4e-36)
   (* x y)
   (if (<= x 5.4e-120)
     (- z)
     (if (<= x 3.7e-39) (* x y) (if (<= x 0.35) (- z) (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.4e-36) {
		tmp = x * y;
	} else if (x <= 5.4e-120) {
		tmp = -z;
	} else if (x <= 3.7e-39) {
		tmp = x * y;
	} else if (x <= 0.35) {
		tmp = -z;
	} else {
		tmp = x * 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 <= (-9.4d-36)) then
        tmp = x * y
    else if (x <= 5.4d-120) then
        tmp = -z
    else if (x <= 3.7d-39) then
        tmp = x * y
    else if (x <= 0.35d0) then
        tmp = -z
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.4e-36) {
		tmp = x * y;
	} else if (x <= 5.4e-120) {
		tmp = -z;
	} else if (x <= 3.7e-39) {
		tmp = x * y;
	} else if (x <= 0.35) {
		tmp = -z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.4e-36:
		tmp = x * y
	elif x <= 5.4e-120:
		tmp = -z
	elif x <= 3.7e-39:
		tmp = x * y
	elif x <= 0.35:
		tmp = -z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.4e-36)
		tmp = Float64(x * y);
	elseif (x <= 5.4e-120)
		tmp = Float64(-z);
	elseif (x <= 3.7e-39)
		tmp = Float64(x * y);
	elseif (x <= 0.35)
		tmp = Float64(-z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.4e-36)
		tmp = x * y;
	elseif (x <= 5.4e-120)
		tmp = -z;
	elseif (x <= 3.7e-39)
		tmp = x * y;
	elseif (x <= 0.35)
		tmp = -z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.4e-36], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.4e-120], (-z), If[LessEqual[x, 3.7e-39], N[(x * y), $MachinePrecision], If[LessEqual[x, 0.35], (-z), N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.4000000000000006e-36 or 5.3999999999999997e-120 < x < 3.70000000000000015e-39

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf 63.4%

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

   if -9.4000000000000006e-36 < x < 5.3999999999999997e-120 or 3.70000000000000015e-39 < x < 0.34999999999999998

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.0%

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

      1. neg-mul-1 80.0%

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

   5. Simplified 80.0%

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

   if 0.34999999999999998 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 61.5%

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

   4. Taylor expanded in x around inf 58.7%

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

      1. *-commutative 58.7%

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

   6. Simplified 58.7%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-120}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-39}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 0.35:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. *-commutative 98.4%

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

   2. distribute-rgt-out-- 98.4%

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

   3. cancel-sign-sub-inv 98.4%

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

   4. metadata-eval 98.4%

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

   5. neg-mul-1 98.4%

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

   6. associate-+r+ 98.4%

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

   7. unsub-neg 98.4%

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

   8. +-commutative 98.4%

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

   9. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 8: 36.7% accurate, 4.5× 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 98.4%

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

3. Taylor expanded in x around 0 34.7%

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

   1. neg-mul-1 34.7%

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

5. Simplified 34.7%

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

6. Final simplification 34.7%

   \[\leadsto -z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))