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

Percentage Accurate: 97.8% → 100.0%

Time: 4.4s

Alternatives: 6

Speedup: 1.3×

• 20.6% 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: 97.8% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. *-commutative 98.8%

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

   2. sub-neg 98.8%

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

   3. distribute-rgt-in 98.8%

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

   4. metadata-eval 98.8%

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

   5. neg-mul-1 98.8%

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

   6. associate-+r+ 98.8%

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

   7. unsub-neg 98.8%

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

   8. +-commutative 98.8%

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

   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. Step-by-step derivation

   1. *-commutative 100.0%

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

   2. fma-neg 100.0%

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

   3. +-commutative 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 59.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-87}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-179}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-124}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+30} \lor \neg \left(x \leq 1.12 \cdot 10^{+220}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.6e-87)
   (* y x)
   (if (<= x 6e-179)
     (- z)
     (if (<= x 7e-124)
       (* y x)
       (if (<= x 8.2e-49)
         (- z)
         (if (or (<= x 3.5e+30) (not (<= x 1.12e+220))) (* y x) (* z x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.6e-87) {
		tmp = y * x;
	} else if (x <= 6e-179) {
		tmp = -z;
	} else if (x <= 7e-124) {
		tmp = y * x;
	} else if (x <= 8.2e-49) {
		tmp = -z;
	} else if ((x <= 3.5e+30) || !(x <= 1.12e+220)) {
		tmp = y * x;
	} 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 <= (-6.6d-87)) then
        tmp = y * x
    else if (x <= 6d-179) then
        tmp = -z
    else if (x <= 7d-124) then
        tmp = y * x
    else if (x <= 8.2d-49) then
        tmp = -z
    else if ((x <= 3.5d+30) .or. (.not. (x <= 1.12d+220))) then
        tmp = y * x
    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 <= -6.6e-87) {
		tmp = y * x;
	} else if (x <= 6e-179) {
		tmp = -z;
	} else if (x <= 7e-124) {
		tmp = y * x;
	} else if (x <= 8.2e-49) {
		tmp = -z;
	} else if ((x <= 3.5e+30) || !(x <= 1.12e+220)) {
		tmp = y * x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.6e-87:
		tmp = y * x
	elif x <= 6e-179:
		tmp = -z
	elif x <= 7e-124:
		tmp = y * x
	elif x <= 8.2e-49:
		tmp = -z
	elif (x <= 3.5e+30) or not (x <= 1.12e+220):
		tmp = y * x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.6e-87)
		tmp = Float64(y * x);
	elseif (x <= 6e-179)
		tmp = Float64(-z);
	elseif (x <= 7e-124)
		tmp = Float64(y * x);
	elseif (x <= 8.2e-49)
		tmp = Float64(-z);
	elseif ((x <= 3.5e+30) || !(x <= 1.12e+220))
		tmp = Float64(y * x);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.6e-87)
		tmp = y * x;
	elseif (x <= 6e-179)
		tmp = -z;
	elseif (x <= 7e-124)
		tmp = y * x;
	elseif (x <= 8.2e-49)
		tmp = -z;
	elseif ((x <= 3.5e+30) || ~((x <= 1.12e+220)))
		tmp = y * x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.6e-87], N[(y * x), $MachinePrecision], If[LessEqual[x, 6e-179], (-z), If[LessEqual[x, 7e-124], N[(y * x), $MachinePrecision], If[LessEqual[x, 8.2e-49], (-z), If[Or[LessEqual[x, 3.5e+30], N[Not[LessEqual[x, 1.12e+220]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.6000000000000001e-87 or 6.00000000000000012e-179 < x < 6.9999999999999997e-124 or 8.2000000000000003e-49 < x < 3.50000000000000021e30 or 1.12000000000000006e220 < x

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 62.2%

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

   if -6.6000000000000001e-87 < x < 6.00000000000000012e-179 or 6.9999999999999997e-124 < x < 8.2000000000000003e-49

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.0%

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

      1. neg-mul-1 79.0%

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

   5. Simplified 79.0%

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

   if 3.50000000000000021e30 < x < 1.12000000000000006e220

   1. Initial program 97.3%

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

      1. *-commutative 97.3%

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

      2. sub-neg 97.3%

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

      3. distribute-rgt-in 97.3%

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

      4. metadata-eval 97.3%

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

      5. neg-mul-1 97.3%

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

      6. associate-+r+ 97.3%

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

      7. unsub-neg 97.3%

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

      8. +-commutative 97.3%

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

      9. distribute-lft-out 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 62.0%

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

   6. Taylor expanded in x around inf 62.0%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-87}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-179}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-124}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+30} \lor \neg \left(x \leq 1.12 \cdot 10^{+220}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y + z\right) \cdot x\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{-89}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-179}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-124}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-50}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ y z) x)))
   (if (<= x -1.6e-89)
     t_0
     (if (<= x 6e-179)
       (- z)
       (if (<= x 7e-124) (* y x) (if (<= x 2.3e-50) (- z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (y + z) * x;
	double tmp;
	if (x <= -1.6e-89) {
		tmp = t_0;
	} else if (x <= 6e-179) {
		tmp = -z;
	} else if (x <= 7e-124) {
		tmp = y * x;
	} else if (x <= 2.3e-50) {
		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 = (y + z) * x
    if (x <= (-1.6d-89)) then
        tmp = t_0
    else if (x <= 6d-179) then
        tmp = -z
    else if (x <= 7d-124) then
        tmp = y * x
    else if (x <= 2.3d-50) 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 = (y + z) * x;
	double tmp;
	if (x <= -1.6e-89) {
		tmp = t_0;
	} else if (x <= 6e-179) {
		tmp = -z;
	} else if (x <= 7e-124) {
		tmp = y * x;
	} else if (x <= 2.3e-50) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y + z) * x
	tmp = 0
	if x <= -1.6e-89:
		tmp = t_0
	elif x <= 6e-179:
		tmp = -z
	elif x <= 7e-124:
		tmp = y * x
	elif x <= 2.3e-50:
		tmp = -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y + z) * x)
	tmp = 0.0
	if (x <= -1.6e-89)
		tmp = t_0;
	elseif (x <= 6e-179)
		tmp = Float64(-z);
	elseif (x <= 7e-124)
		tmp = Float64(y * x);
	elseif (x <= 2.3e-50)
		tmp = Float64(-z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y + z) * x;
	tmp = 0.0;
	if (x <= -1.6e-89)
		tmp = t_0;
	elseif (x <= 6e-179)
		tmp = -z;
	elseif (x <= 7e-124)
		tmp = y * x;
	elseif (x <= 2.3e-50)
		tmp = -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.6e-89], t$95$0, If[LessEqual[x, 6e-179], (-z), If[LessEqual[x, 7e-124], N[(y * x), $MachinePrecision], If[LessEqual[x, 2.3e-50], (-z), t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.59999999999999999e-89 or 2.3000000000000002e-50 < x

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 92.1%

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

      1. +-commutative 92.1%

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

   5. Simplified 92.1%

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

   if -1.59999999999999999e-89 < x < 6.00000000000000012e-179 or 6.9999999999999997e-124 < x < 2.3000000000000002e-50

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.6%

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

      1. neg-mul-1 79.6%

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

   5. Simplified 79.6%

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

   if 6.00000000000000012e-179 < x < 6.9999999999999997e-124

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-89}:\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-179}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-124}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-50}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-86} \lor \neg \left(x \leq 6 \cdot 10^{-179} \lor \neg \left(x \leq 7 \cdot 10^{-124}\right) \land x \leq 7.5 \cdot 10^{-48}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.7e-86)
         (not (or (<= x 6e-179) (and (not (<= x 7e-124)) (<= x 7.5e-48)))))
   (* y x)
   (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.7e-86) || !((x <= 6e-179) || (!(x <= 7e-124) && (x <= 7.5e-48)))) {
		tmp = y * x;
	} 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 <= (-5.7d-86)) .or. (.not. (x <= 6d-179) .or. (.not. (x <= 7d-124)) .and. (x <= 7.5d-48))) then
        tmp = y * x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.7e-86) || !((x <= 6e-179) || (!(x <= 7e-124) && (x <= 7.5e-48)))) {
		tmp = y * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.7e-86) or not ((x <= 6e-179) or (not (x <= 7e-124) and (x <= 7.5e-48))):
		tmp = y * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.7e-86) || !((x <= 6e-179) || (!(x <= 7e-124) && (x <= 7.5e-48))))
		tmp = Float64(y * x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.7e-86) || ~(((x <= 6e-179) || (~((x <= 7e-124)) && (x <= 7.5e-48)))))
		tmp = y * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.7e-86], N[Not[Or[LessEqual[x, 6e-179], And[N[Not[LessEqual[x, 7e-124]], $MachinePrecision], LessEqual[x, 7.5e-48]]]], $MachinePrecision]], N[(y * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -5.7000000000000004e-86 or 6.00000000000000012e-179 < x < 6.9999999999999997e-124 or 7.50000000000000042e-48 < x

   1. Initial program 98.2%

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

   3. Taylor expanded in y around inf 58.3%

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

   if -5.7000000000000004e-86 < x < 6.00000000000000012e-179 or 6.9999999999999997e-124 < x < 7.50000000000000042e-48

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.0%

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

      1. neg-mul-1 79.0%

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

   5. Simplified 79.0%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-86} \lor \neg \left(x \leq 6 \cdot 10^{-179} \lor \neg \left(x \leq 7 \cdot 10^{-124}\right) \land x \leq 7.5 \cdot 10^{-48}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. *-commutative 98.8%

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

   2. sub-neg 98.8%

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

   3. distribute-rgt-in 98.8%

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

   4. metadata-eval 98.8%

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

   5. neg-mul-1 98.8%

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

   6. associate-+r+ 98.8%

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

   7. unsub-neg 98.8%

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

   8. +-commutative 98.8%

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

   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. Final simplification 100.0%

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

Alternative 6: 37.1% 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 98.8%

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

3. Taylor expanded in x around 0 33.2%

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

   1. neg-mul-1 33.2%

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

5. Simplified 33.2%

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

6. Final simplification 33.2%

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

Reproduce

herbie shell --seed 2024039 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))