Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.8% → 98.3%

Time: 6.7s

Alternatives: 10

Speedup: 1.1×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(y - x\right)}{t} + x\\ t_2 := \mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-175}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ (* z (- y x)) t) x)) (t_2 (fma (/ z t) (- y x) x)))
   (if (<= t_1 -1e-175) t_2 (if (<= t_1 2e+302) t_1 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z * (y - x)) / t) + x;
	double t_2 = fma((z / t), (y - x), x);
	double tmp;
	if (t_1 <= -1e-175) {
		tmp = t_2;
	} else if (t_1 <= 2e+302) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z * Float64(y - x)) / t) + x)
	t_2 = fma(Float64(z / t), Float64(y - x), x)
	tmp = 0.0
	if (t_1 <= -1e-175)
		tmp = t_2;
	elseif (t_1 <= 2e+302)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-175], t$95$2, If[LessEqual[t$95$1, 2e+302], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -1e-175 or 2.0000000000000002e302 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 87.1%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 99.2

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

   4. Applied rewrites 99.2%

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

   if -1e-175 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 2.0000000000000002e302

   1. Initial program 99.8%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(y - x\right)}{t} + x \leq -1 \cdot 10^{-175}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \mathbf{elif}\;\frac{z \cdot \left(y - x\right)}{t} + x \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-75}:\\ \;\;\;\;\frac{y}{t} \cdot z + x\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+26}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7.2e-75)
   (+ (* (/ y t) z) x)
   (if (<= t 1.16e+26) (/ (* z (- y x)) t) (+ (/ (* z y) t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.2e-75) {
		tmp = ((y / t) * z) + x;
	} else if (t <= 1.16e+26) {
		tmp = (z * (y - x)) / t;
	} else {
		tmp = ((z * y) / t) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-7.2d-75)) then
        tmp = ((y / t) * z) + x
    else if (t <= 1.16d+26) then
        tmp = (z * (y - x)) / t
    else
        tmp = ((z * y) / t) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.2e-75) {
		tmp = ((y / t) * z) + x;
	} else if (t <= 1.16e+26) {
		tmp = (z * (y - x)) / t;
	} else {
		tmp = ((z * y) / t) + x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7.2e-75:
		tmp = ((y / t) * z) + x
	elif t <= 1.16e+26:
		tmp = (z * (y - x)) / t
	else:
		tmp = ((z * y) / t) + x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7.2e-75)
		tmp = Float64(Float64(Float64(y / t) * z) + x);
	elseif (t <= 1.16e+26)
		tmp = Float64(Float64(z * Float64(y - x)) / t);
	else
		tmp = Float64(Float64(Float64(z * y) / t) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7.2e-75)
		tmp = ((y / t) * z) + x;
	elseif (t <= 1.16e+26)
		tmp = (z * (y - x)) / t;
	else
		tmp = ((z * y) / t) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7.2e-75], N[(N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.16e+26], N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.2000000000000001e-75

   1. Initial program 84.5%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

         \[\leadsto x + \color{blue}{\frac{y}{t} \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{y}{t} \cdot z} \]

      3. lower-/.f64 82.9

         \[\leadsto x + \color{blue}{\frac{y}{t}} \cdot z \]

   5. Applied rewrites 82.9%

      \[\leadsto x + \color{blue}{\frac{y}{t} \cdot z} \]

   if -7.2000000000000001e-75 < t < 1.15999999999999996e26

   1. Initial program 98.8%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 88.1

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

   5. Applied rewrites 88.1%

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

   if 1.15999999999999996e26 < t

   1. Initial program 89.7%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 89.8

         \[\leadsto x + \frac{\color{blue}{y \cdot z}}{t} \]

   5. Applied rewrites 89.8%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-75}:\\ \;\;\;\;\frac{y}{t} \cdot z + x\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+26}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t} \cdot z + x\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+26}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ y t) z) x)))
   (if (<= t -7.2e-75) t_1 (if (<= t 1.16e+26) (/ (* z (- y x)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) * z) + x;
	double tmp;
	if (t <= -7.2e-75) {
		tmp = t_1;
	} else if (t <= 1.16e+26) {
		tmp = (z * (y - x)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y / t) * z) + x
    if (t <= (-7.2d-75)) then
        tmp = t_1
    else if (t <= 1.16d+26) then
        tmp = (z * (y - x)) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) * z) + x;
	double tmp;
	if (t <= -7.2e-75) {
		tmp = t_1;
	} else if (t <= 1.16e+26) {
		tmp = (z * (y - x)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y / t) * z) + x
	tmp = 0
	if t <= -7.2e-75:
		tmp = t_1
	elif t <= 1.16e+26:
		tmp = (z * (y - x)) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) * z) + x)
	tmp = 0.0
	if (t <= -7.2e-75)
		tmp = t_1;
	elseif (t <= 1.16e+26)
		tmp = Float64(Float64(z * Float64(y - x)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((y / t) * z) + x;
	tmp = 0.0;
	if (t <= -7.2e-75)
		tmp = t_1;
	elseif (t <= 1.16e+26)
		tmp = (z * (y - x)) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -7.2e-75], t$95$1, If[LessEqual[t, 1.16e+26], N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.2000000000000001e-75 or 1.15999999999999996e26 < t

   1. Initial program 86.7%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

         \[\leadsto x + \color{blue}{\frac{y}{t} \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{y}{t} \cdot z} \]

      3. lower-/.f64 85.3

         \[\leadsto x + \color{blue}{\frac{y}{t}} \cdot z \]

   5. Applied rewrites 85.3%

      \[\leadsto x + \color{blue}{\frac{y}{t} \cdot z} \]

   if -7.2000000000000001e-75 < t < 1.15999999999999996e26

   1. Initial program 98.8%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 88.1

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

   5. Applied rewrites 88.1%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-75}:\\ \;\;\;\;\frac{y}{t} \cdot z + x\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+26}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{t} \cdot z\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* (/ x t) z))))
   (if (<= t -3.2e+80) t_1 (if (<= t 2.8e+25) (/ (* z (- y x)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((x / t) * z);
	double tmp;
	if (t <= -3.2e+80) {
		tmp = t_1;
	} else if (t <= 2.8e+25) {
		tmp = (z * (y - x)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((x / t) * z)
    if (t <= (-3.2d+80)) then
        tmp = t_1
    else if (t <= 2.8d+25) then
        tmp = (z * (y - x)) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - ((x / t) * z);
	double tmp;
	if (t <= -3.2e+80) {
		tmp = t_1;
	} else if (t <= 2.8e+25) {
		tmp = (z * (y - x)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((x / t) * z)
	tmp = 0
	if t <= -3.2e+80:
		tmp = t_1
	elif t <= 2.8e+25:
		tmp = (z * (y - x)) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(x / t) * z))
	tmp = 0.0
	if (t <= -3.2e+80)
		tmp = t_1;
	elseif (t <= 2.8e+25)
		tmp = Float64(Float64(z * Float64(y - x)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - ((x / t) * z);
	tmp = 0.0;
	if (t <= -3.2e+80)
		tmp = t_1;
	elseif (t <= 2.8e+25)
		tmp = (z * (y - x)) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[(x / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+80], t$95$1, If[LessEqual[t, 2.8e+25], N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1999999999999999e80 or 2.8000000000000002e25 < t

   1. Initial program 83.6%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 71.7

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

   5. Applied rewrites 71.7%

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

   if -3.1999999999999999e80 < t < 2.8000000000000002e25

   1. Initial program 98.4%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 81.5

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

   5. Applied rewrites 81.5%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+80}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot y\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+85}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) y)))
   (if (<= y -5.8e+153) t_1 (if (<= y 1.7e+85) (- x (* (/ x t) z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * y;
	double tmp;
	if (y <= -5.8e+153) {
		tmp = t_1;
	} else if (y <= 1.7e+85) {
		tmp = x - ((x / t) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / t) * y
    if (y <= (-5.8d+153)) then
        tmp = t_1
    else if (y <= 1.7d+85) then
        tmp = x - ((x / t) * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * y;
	double tmp;
	if (y <= -5.8e+153) {
		tmp = t_1;
	} else if (y <= 1.7e+85) {
		tmp = x - ((x / t) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * y
	tmp = 0
	if y <= -5.8e+153:
		tmp = t_1
	elif y <= 1.7e+85:
		tmp = x - ((x / t) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * y)
	tmp = 0.0
	if (y <= -5.8e+153)
		tmp = t_1;
	elseif (y <= 1.7e+85)
		tmp = Float64(x - Float64(Float64(x / t) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * y;
	tmp = 0.0;
	if (y <= -5.8e+153)
		tmp = t_1;
	elseif (y <= 1.7e+85)
		tmp = x - ((x / t) * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -5.8e+153], t$95$1, If[LessEqual[y, 1.7e+85], N[(x - N[(N[(x / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.80000000000000004e153 or 1.7000000000000002e85 < y

   1. Initial program 84.8%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot z} \]

      3. lower-/.f64 61.6

         \[\leadsto \color{blue}{\frac{y}{t}} \cdot z \]

   5. Applied rewrites 61.6%

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

   7. Applied rewrites 66.8%

      \[\leadsto y \cdot \color{blue}{\frac{z}{t}} \]

   if -5.80000000000000004e153 < y < 1.7000000000000002e85

   1. Initial program 95.3%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 75.1

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

   5. Applied rewrites 75.1%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+153}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+85}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot y\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+57}:\\ \;\;\;\;\frac{\left(-x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) y)))
   (if (<= y -2.45e-20) t_1 (if (<= y 1.1e+57) (/ (* (- x) z) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * y;
	double tmp;
	if (y <= -2.45e-20) {
		tmp = t_1;
	} else if (y <= 1.1e+57) {
		tmp = (-x * z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / t) * y
    if (y <= (-2.45d-20)) then
        tmp = t_1
    else if (y <= 1.1d+57) then
        tmp = (-x * z) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * y;
	double tmp;
	if (y <= -2.45e-20) {
		tmp = t_1;
	} else if (y <= 1.1e+57) {
		tmp = (-x * z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * y
	tmp = 0
	if y <= -2.45e-20:
		tmp = t_1
	elif y <= 1.1e+57:
		tmp = (-x * z) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * y)
	tmp = 0.0
	if (y <= -2.45e-20)
		tmp = t_1;
	elseif (y <= 1.1e+57)
		tmp = Float64(Float64(Float64(-x) * z) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * y;
	tmp = 0.0;
	if (y <= -2.45e-20)
		tmp = t_1;
	elseif (y <= 1.1e+57)
		tmp = (-x * z) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.45e-20], t$95$1, If[LessEqual[y, 1.1e+57], N[(N[((-x) * z), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4500000000000001e-20 or 1.1e57 < y

   1. Initial program 86.6%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot z} \]

      3. lower-/.f64 53.4

         \[\leadsto \color{blue}{\frac{y}{t}} \cdot z \]

   5. Applied rewrites 53.4%

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

   7. Applied rewrites 57.7%

      \[\leadsto y \cdot \color{blue}{\frac{z}{t}} \]

   if -2.4500000000000001e-20 < y < 1.1e57

   1. Initial program 96.7%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 55.4

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

   5. Applied rewrites 55.4%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\left(-1 \cdot x\right) \cdot z}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 40.4%

      \[\leadsto \frac{\left(-x\right) \cdot z}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-20}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+57}:\\ \;\;\;\;\frac{\left(-x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-z}{t} \cdot x\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+28}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- z) t) x)))
   (if (<= x -3.1e+94) t_1 (if (<= x 3.2e+28) (* (/ z t) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-z / t) * x;
	double tmp;
	if (x <= -3.1e+94) {
		tmp = t_1;
	} else if (x <= 3.2e+28) {
		tmp = (z / t) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-z / t) * x
    if (x <= (-3.1d+94)) then
        tmp = t_1
    else if (x <= 3.2d+28) then
        tmp = (z / t) * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (-z / t) * x;
	double tmp;
	if (x <= -3.1e+94) {
		tmp = t_1;
	} else if (x <= 3.2e+28) {
		tmp = (z / t) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-z / t) * x
	tmp = 0
	if x <= -3.1e+94:
		tmp = t_1
	elif x <= 3.2e+28:
		tmp = (z / t) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-z) / t) * x)
	tmp = 0.0
	if (x <= -3.1e+94)
		tmp = t_1;
	elseif (x <= 3.2e+28)
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (-z / t) * x;
	tmp = 0.0;
	if (x <= -3.1e+94)
		tmp = t_1;
	elseif (x <= 3.2e+28)
		tmp = (z / t) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-z) / t), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -3.1e+94], t$95$1, If[LessEqual[x, 3.2e+28], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.09999999999999991e94 or 3.2e28 < x

   1. Initial program 86.6%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 45.3

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

   5. Applied rewrites 45.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \color{blue}{\frac{x \cdot z}{t}} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.2%

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

   10. Applied rewrites 41.7%

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

   if -3.09999999999999991e94 < x < 3.2e28

   1. Initial program 95.8%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot z} \]

      3. lower-/.f64 51.4

         \[\leadsto \color{blue}{\frac{y}{t}} \cdot z \]

   5. Applied rewrites 51.4%

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

   7. Applied rewrites 54.6%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+94}:\\ \;\;\;\;\frac{-z}{t} \cdot x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+28}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{y - x}{\frac{t}{z}} + x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ (/ (- y x) (/ t z)) x))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.7%

   \[x + \frac{\left(y - x\right) \cdot z}{t} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   6. lower-/.f64 N/A

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   7. lower-/.f64 96.3

      \[\leadsto x + \frac{y - x}{\color{blue}{\frac{t}{z}}} \]

4. Applied rewrites 96.3%

   \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

5. Final simplification 96.3%

   \[\leadsto \frac{y - x}{\frac{t}{z}} + x \]
6. Add Preprocessing

Alternative 9: 97.5% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (fma (/ z t) (- y x) x))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 91.7%

   \[x + \frac{\left(y - x\right) \cdot z}{t} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 96.2

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

4. Applied rewrites 96.2%

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

Alternative 10: 40.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{z}{t} \cdot y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]

Derivation

1. Initial program 91.7%

   \[x + \frac{\left(y - x\right) \cdot z}{t} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

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

   1. associate-*l/ N/A

      \[\leadsto \color{blue}{\frac{y}{t} \cdot z} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{y}{t} \cdot z} \]

   3. lower-/.f64 34.5

      \[\leadsto \color{blue}{\frac{y}{t}} \cdot z \]

5. Applied rewrites 34.5%

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

7. Applied rewrites 37.7%

   \[\leadsto y \cdot \color{blue}{\frac{z}{t}} \]

8. Final simplification 37.7%

   \[\leadsto \frac{z}{t} \cdot y \]
9. Add Preprocessing

Developer Target 1: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (< x -9.025511195533005e-135)
   (- x (* (/ z t) (- x y)))
   (if (< x 4.275032163700715e-250)
     (+ x (* (/ (- y x) t) z))
     (+ x (/ (- y x) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x < (-9.025511195533005d-135)) then
        tmp = x - ((z / t) * (x - y))
    else if (x < 4.275032163700715d-250) then
        tmp = x + (((y - x) / t) * z)
    else
        tmp = x + ((y - x) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x < -9.025511195533005e-135:
		tmp = x - ((z / t) * (x - y))
	elif x < 4.275032163700715e-250:
		tmp = x + (((y - x) / t) * z)
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x < -9.025511195533005e-135)
		tmp = Float64(x - Float64(Float64(z / t) * Float64(x - y)));
	elseif (x < 4.275032163700715e-250)
		tmp = Float64(x + Float64(Float64(Float64(y - x) / t) * z));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x < -9.025511195533005e-135)
		tmp = x - ((z / t) * (x - y));
	elseif (x < 4.275032163700715e-250)
		tmp = x + (((y - x) / t) * z);
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Less[x, -9.025511195533005e-135], N[(x - N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[x, 4.275032163700715e-250], N[(x + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024268 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -1805102239106601/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (* (/ z t) (- x y))) (if (< x 855006432740143/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z))))))

  (+ x (/ (* (- y x) z) t)))