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

Percentage Accurate: 97.8% → 100.0%

Time: 5.0s

Alternatives: 6

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: 97.8% 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, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (z + y)) - z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. *-commutative 99.2%

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

   2. distribute-rgt-out-- 99.2%

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

   3. cancel-sign-sub-inv 99.2%

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

   4. metadata-eval 99.2%

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

   5. neg-mul-1 99.2%

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

   6. associate-+r+ 99.2%

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

   7. unsub-neg 99.2%

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

   8. +-commutative 99.2%

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

   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%

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

Alternative 2: 58.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+176}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+140}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-122}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+117} \lor \neg \left(x \leq 8.6 \cdot 10^{+143}\right) \land x \leq 5.8 \cdot 10^{+174}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.25e+176)
   (* x y)
   (if (<= x -3.5e+140)
     (* x z)
     (if (<= x -7e+14)
       (* x y)
       (if (<= x 3.6e-122)
         (- z)
         (if (or (<= x 9.6e+117) (and (not (<= x 8.6e+143)) (<= x 5.8e+174)))
           (* x y)
           (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e+176) {
		tmp = x * y;
	} else if (x <= -3.5e+140) {
		tmp = x * z;
	} else if (x <= -7e+14) {
		tmp = x * y;
	} else if (x <= 3.6e-122) {
		tmp = -z;
	} else if ((x <= 9.6e+117) || (!(x <= 8.6e+143) && (x <= 5.8e+174))) {
		tmp = x * y;
	} 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 <= (-1.25d+176)) then
        tmp = x * y
    else if (x <= (-3.5d+140)) then
        tmp = x * z
    else if (x <= (-7d+14)) then
        tmp = x * y
    else if (x <= 3.6d-122) then
        tmp = -z
    else if ((x <= 9.6d+117) .or. (.not. (x <= 8.6d+143)) .and. (x <= 5.8d+174)) then
        tmp = x * y
    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 <= -1.25e+176) {
		tmp = x * y;
	} else if (x <= -3.5e+140) {
		tmp = x * z;
	} else if (x <= -7e+14) {
		tmp = x * y;
	} else if (x <= 3.6e-122) {
		tmp = -z;
	} else if ((x <= 9.6e+117) || (!(x <= 8.6e+143) && (x <= 5.8e+174))) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.25e+176:
		tmp = x * y
	elif x <= -3.5e+140:
		tmp = x * z
	elif x <= -7e+14:
		tmp = x * y
	elif x <= 3.6e-122:
		tmp = -z
	elif (x <= 9.6e+117) or (not (x <= 8.6e+143) and (x <= 5.8e+174)):
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.25e+176)
		tmp = Float64(x * y);
	elseif (x <= -3.5e+140)
		tmp = Float64(x * z);
	elseif (x <= -7e+14)
		tmp = Float64(x * y);
	elseif (x <= 3.6e-122)
		tmp = Float64(-z);
	elseif ((x <= 9.6e+117) || (!(x <= 8.6e+143) && (x <= 5.8e+174)))
		tmp = Float64(x * y);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.25e+176)
		tmp = x * y;
	elseif (x <= -3.5e+140)
		tmp = x * z;
	elseif (x <= -7e+14)
		tmp = x * y;
	elseif (x <= 3.6e-122)
		tmp = -z;
	elseif ((x <= 9.6e+117) || (~((x <= 8.6e+143)) && (x <= 5.8e+174)))
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.25e+176], N[(x * y), $MachinePrecision], If[LessEqual[x, -3.5e+140], N[(x * z), $MachinePrecision], If[LessEqual[x, -7e+14], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.6e-122], (-z), If[Or[LessEqual[x, 9.6e+117], And[N[Not[LessEqual[x, 8.6e+143]], $MachinePrecision], LessEqual[x, 5.8e+174]]], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25e176 or -3.49999999999999989e140 < x < -7e14 or 3.59999999999999994e-122 < x < 9.5999999999999996e117 or 8.60000000000000003e143 < x < 5.7999999999999999e174

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 63.4%

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

   if -1.25e176 < x < -3.49999999999999989e140 or 9.5999999999999996e117 < x < 8.60000000000000003e143 or 5.7999999999999999e174 < 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 81.4%

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

   4. Taylor expanded in x around inf 81.4%

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

      1. *-commutative 81.4%

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

   6. Simplified 81.4%

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

   if -7e14 < x < 3.59999999999999994e-122

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.8%

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

      1. neg-mul-1 76.8%

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

   5. Simplified 76.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+176}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+140}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-122}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+117} \lor \neg \left(x \leq 8.6 \cdot 10^{+143}\right) \land x \leq 5.8 \cdot 10^{+174}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{-15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-121}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-86}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-26}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -6.2e-15)
     t_0
     (if (<= x 9.5e-121)
       (- z)
       (if (<= x 2.25e-86) (* x y) (if (<= x 8.2e-26) (- z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -6.2e-15) {
		tmp = t_0;
	} else if (x <= 9.5e-121) {
		tmp = -z;
	} else if (x <= 2.25e-86) {
		tmp = x * y;
	} else if (x <= 8.2e-26) {
		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 * (z + y)
    if (x <= (-6.2d-15)) then
        tmp = t_0
    else if (x <= 9.5d-121) then
        tmp = -z
    else if (x <= 2.25d-86) then
        tmp = x * y
    else if (x <= 8.2d-26) 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 * (z + y);
	double tmp;
	if (x <= -6.2e-15) {
		tmp = t_0;
	} else if (x <= 9.5e-121) {
		tmp = -z;
	} else if (x <= 2.25e-86) {
		tmp = x * y;
	} else if (x <= 8.2e-26) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	tmp = 0
	if x <= -6.2e-15:
		tmp = t_0
	elif x <= 9.5e-121:
		tmp = -z
	elif x <= 2.25e-86:
		tmp = x * y
	elif x <= 8.2e-26:
		tmp = -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	tmp = 0.0
	if (x <= -6.2e-15)
		tmp = t_0;
	elseif (x <= 9.5e-121)
		tmp = Float64(-z);
	elseif (x <= 2.25e-86)
		tmp = Float64(x * y);
	elseif (x <= 8.2e-26)
		tmp = Float64(-z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	tmp = 0.0;
	if (x <= -6.2e-15)
		tmp = t_0;
	elseif (x <= 9.5e-121)
		tmp = -z;
	elseif (x <= 2.25e-86)
		tmp = x * y;
	elseif (x <= 8.2e-26)
		tmp = -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e-15], t$95$0, If[LessEqual[x, 9.5e-121], (-z), If[LessEqual[x, 2.25e-86], N[(x * y), $MachinePrecision], If[LessEqual[x, 8.2e-26], (-z), t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.1999999999999998e-15 or 8.1999999999999997e-26 < x

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf 95.2%

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

      1. +-commutative 95.2%

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

   5. Simplified 95.2%

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

   if -6.1999999999999998e-15 < x < 9.4999999999999994e-121 or 2.2499999999999999e-86 < x < 8.1999999999999997e-26

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.2%

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

      1. neg-mul-1 79.2%

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

   5. Simplified 79.2%

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

   if 9.4999999999999994e-121 < x < 2.2499999999999999e-86

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-121}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-86}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-26}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-121}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-88}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-25}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -7e+14)
     t_0
     (if (<= x 6.5e-121)
       (* z (+ x -1.0))
       (if (<= x 1.8e-88) (* x y) (if (<= x 6.5e-25) (- z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -7e+14) {
		tmp = t_0;
	} else if (x <= 6.5e-121) {
		tmp = z * (x + -1.0);
	} else if (x <= 1.8e-88) {
		tmp = x * y;
	} else if (x <= 6.5e-25) {
		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 * (z + y)
    if (x <= (-7d+14)) then
        tmp = t_0
    else if (x <= 6.5d-121) then
        tmp = z * (x + (-1.0d0))
    else if (x <= 1.8d-88) then
        tmp = x * y
    else if (x <= 6.5d-25) 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 * (z + y);
	double tmp;
	if (x <= -7e+14) {
		tmp = t_0;
	} else if (x <= 6.5e-121) {
		tmp = z * (x + -1.0);
	} else if (x <= 1.8e-88) {
		tmp = x * y;
	} else if (x <= 6.5e-25) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	tmp = 0
	if x <= -7e+14:
		tmp = t_0
	elif x <= 6.5e-121:
		tmp = z * (x + -1.0)
	elif x <= 1.8e-88:
		tmp = x * y
	elif x <= 6.5e-25:
		tmp = -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	tmp = 0.0
	if (x <= -7e+14)
		tmp = t_0;
	elseif (x <= 6.5e-121)
		tmp = Float64(z * Float64(x + -1.0));
	elseif (x <= 1.8e-88)
		tmp = Float64(x * y);
	elseif (x <= 6.5e-25)
		tmp = Float64(-z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	tmp = 0.0;
	if (x <= -7e+14)
		tmp = t_0;
	elseif (x <= 6.5e-121)
		tmp = z * (x + -1.0);
	elseif (x <= 1.8e-88)
		tmp = x * y;
	elseif (x <= 6.5e-25)
		tmp = -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+14], t$95$0, If[LessEqual[x, 6.5e-121], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e-88], N[(x * y), $MachinePrecision], If[LessEqual[x, 6.5e-25], (-z), t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7e14 or 6.5e-25 < x

   1. Initial program 98.6%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 -7e14 < x < 6.5000000000000003e-121

   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 6.5000000000000003e-121 < x < 1.8e-88

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   if 1.8e-88 < x < 6.5e-25

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 71.1%

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

      1. neg-mul-1 71.1%

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

   5. Simplified 71.1%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-121}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-88}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-25}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14} \lor \neg \left(x \leq 9.5 \cdot 10^{-121}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e+14) (not (<= x 9.5e-121))) (* x y) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+14) || !(x <= 9.5e-121)) {
		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 <= (-7d+14)) .or. (.not. (x <= 9.5d-121))) 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 <= -7e+14) || !(x <= 9.5e-121)) {
		tmp = x * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e+14) or not (x <= 9.5e-121):
		tmp = x * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e+14) || !(x <= 9.5e-121))
		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 <= -7e+14) || ~((x <= 9.5e-121)))
		tmp = x * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e+14], N[Not[LessEqual[x, 9.5e-121]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -7e14 or 9.4999999999999994e-121 < x

   1. Initial program 98.7%

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

   3. Taylor expanded in y around inf 55.3%

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

   if -7e14 < x < 9.4999999999999994e-121

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.8%

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

      1. neg-mul-1 76.8%

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

   5. Simplified 76.8%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14} \lor \neg \left(x \leq 9.5 \cdot 10^{-121}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 35.8% 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 99.2%

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

3. Taylor expanded in x around 0 35.2%

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

   1. neg-mul-1 35.2%

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

5. Simplified 35.2%

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

6. Final simplification 35.2%

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

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))