Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 93.0% → 97.8%

Time: 8.6s

Alternatives: 12

Speedup: 1.1×

• 25.5% 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: 93.0% 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: 97.8% 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 95.3%

   \[x + \frac{\left(y - x\right) \cdot z}{t} \]
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 97.4

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

4. Applied rewrites 97.4%

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

Alternative 2: 49.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot z}{t} + x\\ t_2 := y \cdot \frac{z}{t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ (* (- y x) z) t) x)) (t_2 (* y (/ z t))))
   (if (<= t_1 -5e+43) t_2 (if (<= t_1 2e+151) (/ (* x t) t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((y - x) * z) / t) + x;
	double t_2 = y * (z / t);
	double tmp;
	if (t_1 <= -5e+43) {
		tmp = t_2;
	} else if (t_1 <= 2e+151) {
		tmp = (x * t) / t;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (((y - x) * z) / t) + x
    t_2 = y * (z / t)
    if (t_1 <= (-5d+43)) then
        tmp = t_2
    else if (t_1 <= 2d+151) then
        tmp = (x * t) / t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (((y - x) * z) / t) + x;
	double t_2 = y * (z / t);
	double tmp;
	if (t_1 <= -5e+43) {
		tmp = t_2;
	} else if (t_1 <= 2e+151) {
		tmp = (x * t) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (((y - x) * z) / t) + x
	t_2 = y * (z / t)
	tmp = 0
	if t_1 <= -5e+43:
		tmp = t_2
	elif t_1 <= 2e+151:
		tmp = (x * t) / t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(y - x) * z) / t) + x)
	t_2 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (t_1 <= -5e+43)
		tmp = t_2;
	elseif (t_1 <= 2e+151)
		tmp = Float64(Float64(x * t) / t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (((y - x) * z) / t) + x;
	t_2 = y * (z / t);
	tmp = 0.0;
	if (t_1 <= -5e+43)
		tmp = t_2;
	elseif (t_1 <= 2e+151)
		tmp = (x * t) / t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+43], t$95$2, If[LessEqual[t$95$1, 2e+151], N[(N[(x * t), $MachinePrecision] / t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -5.0000000000000004e43 or 2.00000000000000003e151 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 93.0%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 97.3

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

   4. Applied rewrites 97.3%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 46.3

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

   7. Applied rewrites 46.3%

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

   if -5.0000000000000004e43 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 2.00000000000000003e151

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 94.7

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

   5. Applied rewrites 94.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 58.2%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot z}{t} + x \leq -5 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot z}{t} + x \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 45.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot z}{t} + x\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ (* (- y x) z) t) x)))
   (if (<= t_1 -5e+43)
     (/ (* y z) t)
     (if (<= t_1 2e+151) (/ (* x t) t) (* (/ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((y - x) * z) / t) + x;
	double tmp;
	if (t_1 <= -5e+43) {
		tmp = (y * z) / t;
	} else if (t_1 <= 2e+151) {
		tmp = (x * t) / t;
	} else {
		tmp = (y / 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) :: t_1
    real(8) :: tmp
    t_1 = (((y - x) * z) / t) + x
    if (t_1 <= (-5d+43)) then
        tmp = (y * z) / t
    else if (t_1 <= 2d+151) then
        tmp = (x * t) / t
    else
        tmp = (y / t) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (((y - x) * z) / t) + x;
	double tmp;
	if (t_1 <= -5e+43) {
		tmp = (y * z) / t;
	} else if (t_1 <= 2e+151) {
		tmp = (x * t) / t;
	} else {
		tmp = (y / t) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (((y - x) * z) / t) + x
	tmp = 0
	if t_1 <= -5e+43:
		tmp = (y * z) / t
	elif t_1 <= 2e+151:
		tmp = (x * t) / t
	else:
		tmp = (y / t) * z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(y - x) * z) / t) + x)
	tmp = 0.0
	if (t_1 <= -5e+43)
		tmp = Float64(Float64(y * z) / t);
	elseif (t_1 <= 2e+151)
		tmp = Float64(Float64(x * t) / t);
	else
		tmp = Float64(Float64(y / t) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (((y - x) * z) / t) + x;
	tmp = 0.0;
	if (t_1 <= -5e+43)
		tmp = (y * z) / t;
	elseif (t_1 <= 2e+151)
		tmp = (x * t) / t;
	else
		tmp = (y / t) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+43], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 2e+151], N[(N[(x * t), $MachinePrecision] / t), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -5.0000000000000004e43

   1. Initial program 96.3%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 40.2

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

   5. Applied rewrites 40.2%

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

   7. Applied rewrites 43.7%

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

   if -5.0000000000000004e43 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 2.00000000000000003e151

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 94.7

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

   5. Applied rewrites 94.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 58.2%

      \[\leadsto \frac{t \cdot x}{t} \]

   if 2.00000000000000003e151 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 89.3%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 39.5

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

   5. Applied rewrites 39.5%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot z}{t} + x \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot z}{t} + x \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 45.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot t}{t}\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+55}:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-94}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x t) t)))
   (if (<= x -1.8e+55)
     (* (/ (- x) t) z)
     (if (<= x -1.2e-165)
       t_1
       (if (<= x 4.1e-94)
         (/ (* y z) t)
         (if (<= x 9.5e+69) t_1 (* (- x) (/ z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * t) / t;
	double tmp;
	if (x <= -1.8e+55) {
		tmp = (-x / t) * z;
	} else if (x <= -1.2e-165) {
		tmp = t_1;
	} else if (x <= 4.1e-94) {
		tmp = (y * z) / t;
	} else if (x <= 9.5e+69) {
		tmp = t_1;
	} else {
		tmp = -x * (z / t);
	}
	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 * t) / t
    if (x <= (-1.8d+55)) then
        tmp = (-x / t) * z
    else if (x <= (-1.2d-165)) then
        tmp = t_1
    else if (x <= 4.1d-94) then
        tmp = (y * z) / t
    else if (x <= 9.5d+69) then
        tmp = t_1
    else
        tmp = -x * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * t) / t;
	double tmp;
	if (x <= -1.8e+55) {
		tmp = (-x / t) * z;
	} else if (x <= -1.2e-165) {
		tmp = t_1;
	} else if (x <= 4.1e-94) {
		tmp = (y * z) / t;
	} else if (x <= 9.5e+69) {
		tmp = t_1;
	} else {
		tmp = -x * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * t) / t
	tmp = 0
	if x <= -1.8e+55:
		tmp = (-x / t) * z
	elif x <= -1.2e-165:
		tmp = t_1
	elif x <= 4.1e-94:
		tmp = (y * z) / t
	elif x <= 9.5e+69:
		tmp = t_1
	else:
		tmp = -x * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * t) / t)
	tmp = 0.0
	if (x <= -1.8e+55)
		tmp = Float64(Float64(Float64(-x) / t) * z);
	elseif (x <= -1.2e-165)
		tmp = t_1;
	elseif (x <= 4.1e-94)
		tmp = Float64(Float64(y * z) / t);
	elseif (x <= 9.5e+69)
		tmp = t_1;
	else
		tmp = Float64(Float64(-x) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * t) / t;
	tmp = 0.0;
	if (x <= -1.8e+55)
		tmp = (-x / t) * z;
	elseif (x <= -1.2e-165)
		tmp = t_1;
	elseif (x <= 4.1e-94)
		tmp = (y * z) / t;
	elseif (x <= 9.5e+69)
		tmp = t_1;
	else
		tmp = -x * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * t), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[x, -1.8e+55], N[(N[((-x) / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, -1.2e-165], t$95$1, If[LessEqual[x, 4.1e-94], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[x, 9.5e+69], t$95$1, N[((-x) * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.79999999999999994e55

   1. Initial program 93.9%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 49.4

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

   5. Applied rewrites 49.4%

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

   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 51.2%

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

   if -1.79999999999999994e55 < x < -1.2000000000000001e-165 or 4.10000000000000001e-94 < x < 9.4999999999999995e69

   1. Initial program 96.0%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 95.9

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

   5. Applied rewrites 95.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 53.3%

      \[\leadsto \frac{t \cdot x}{t} \]

   if -1.2000000000000001e-165 < x < 4.10000000000000001e-94

   1. Initial program 97.0%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 65.3

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

   5. Applied rewrites 65.3%

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

   7. Applied rewrites 70.0%

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

   if 9.4999999999999995e69 < x

   1. Initial program 92.9%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 52.8

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

   5. Applied rewrites 52.8%

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

   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 48.6%

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

   10. Applied rewrites 52.0%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+55}:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-165}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-94}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 45.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot t}{t}\\ t_2 := \frac{-x}{t} \cdot z\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-94}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x t) t)) (t_2 (* (/ (- x) t) z)))
   (if (<= x -1.8e+55)
     t_2
     (if (<= x -1.2e-165)
       t_1
       (if (<= x 4.1e-94) (/ (* y z) t) (if (<= x 9.5e+69) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * t) / t;
	double t_2 = (-x / t) * z;
	double tmp;
	if (x <= -1.8e+55) {
		tmp = t_2;
	} else if (x <= -1.2e-165) {
		tmp = t_1;
	} else if (x <= 4.1e-94) {
		tmp = (y * z) / t;
	} else if (x <= 9.5e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x * t) / t
    t_2 = (-x / t) * z
    if (x <= (-1.8d+55)) then
        tmp = t_2
    else if (x <= (-1.2d-165)) then
        tmp = t_1
    else if (x <= 4.1d-94) then
        tmp = (y * z) / t
    else if (x <= 9.5d+69) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * t) / t;
	double t_2 = (-x / t) * z;
	double tmp;
	if (x <= -1.8e+55) {
		tmp = t_2;
	} else if (x <= -1.2e-165) {
		tmp = t_1;
	} else if (x <= 4.1e-94) {
		tmp = (y * z) / t;
	} else if (x <= 9.5e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * t) / t
	t_2 = (-x / t) * z
	tmp = 0
	if x <= -1.8e+55:
		tmp = t_2
	elif x <= -1.2e-165:
		tmp = t_1
	elif x <= 4.1e-94:
		tmp = (y * z) / t
	elif x <= 9.5e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * t) / t)
	t_2 = Float64(Float64(Float64(-x) / t) * z)
	tmp = 0.0
	if (x <= -1.8e+55)
		tmp = t_2;
	elseif (x <= -1.2e-165)
		tmp = t_1;
	elseif (x <= 4.1e-94)
		tmp = Float64(Float64(y * z) / t);
	elseif (x <= 9.5e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * t) / t;
	t_2 = (-x / t) * z;
	tmp = 0.0;
	if (x <= -1.8e+55)
		tmp = t_2;
	elseif (x <= -1.2e-165)
		tmp = t_1;
	elseif (x <= 4.1e-94)
		tmp = (y * z) / t;
	elseif (x <= 9.5e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * t), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-x) / t), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[x, -1.8e+55], t$95$2, If[LessEqual[x, -1.2e-165], t$95$1, If[LessEqual[x, 4.1e-94], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[x, 9.5e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.79999999999999994e55 or 9.4999999999999995e69 < x

   1. Initial program 93.4%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 51.2

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

   5. Applied rewrites 51.2%

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

   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 51.4%

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

   if -1.79999999999999994e55 < x < -1.2000000000000001e-165 or 4.10000000000000001e-94 < x < 9.4999999999999995e69

   1. Initial program 96.0%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 95.9

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

   5. Applied rewrites 95.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 53.3%

      \[\leadsto \frac{t \cdot x}{t} \]

   if -1.2000000000000001e-165 < x < 4.10000000000000001e-94

   1. Initial program 97.0%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 65.3

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

   5. Applied rewrites 65.3%

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

   7. Applied rewrites 70.0%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+55}:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-165}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-94}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{t}, -x, x\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 0.000175:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ z t) (- x) x)))
   (if (<= x -9e+17) t_1 (if (<= x 0.000175) (+ (/ (* y z) t) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((z / t), -x, x);
	double tmp;
	if (x <= -9e+17) {
		tmp = t_1;
	} else if (x <= 0.000175) {
		tmp = ((y * z) / t) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(z / t), Float64(-x), x)
	tmp = 0.0
	if (x <= -9e+17)
		tmp = t_1;
	elseif (x <= 0.000175)
		tmp = Float64(Float64(Float64(y * z) / t) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * (-x) + x), $MachinePrecision]}, If[LessEqual[x, -9e+17], t$95$1, If[LessEqual[x, 0.000175], N[(N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9e17 or 1.74999999999999998e-4 < x

   1. Initial program 94.6%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{z}{t}, \color{blue}{-1 \cdot x}, x\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 95.0

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

   7. Applied rewrites 95.0%

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

   if -9e17 < x < 1.74999999999999998e-4

   1. Initial program 95.9%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 84.3

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

   5. Applied rewrites 84.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, -x, x\right)\\ \mathbf{elif}\;x \leq 0.000175:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, -x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{t} \cdot z\\ \mathbf{if}\;x \leq -9 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 0.000175:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* (/ x t) z))))
   (if (<= x -9e+17) t_1 (if (<= x 0.000175) (+ (/ (* y z) t) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((x / t) * z);
	double tmp;
	if (x <= -9e+17) {
		tmp = t_1;
	} else if (x <= 0.000175) {
		tmp = ((y * z) / t) + x;
	} 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 (x <= (-9d+17)) then
        tmp = t_1
    else if (x <= 0.000175d0) then
        tmp = ((y * z) / t) + x
    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 (x <= -9e+17) {
		tmp = t_1;
	} else if (x <= 0.000175) {
		tmp = ((y * z) / t) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((x / t) * z)
	tmp = 0
	if x <= -9e+17:
		tmp = t_1
	elif x <= 0.000175:
		tmp = ((y * z) / t) + x
	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 (x <= -9e+17)
		tmp = t_1;
	elseif (x <= 0.000175)
		tmp = Float64(Float64(Float64(y * z) / t) + x);
	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 (x <= -9e+17)
		tmp = t_1;
	elseif (x <= 0.000175)
		tmp = ((y * z) / t) + x;
	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[x, -9e+17], t$95$1, If[LessEqual[x, 0.000175], N[(N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9e17 or 1.74999999999999998e-4 < x

   1. Initial program 94.6%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 93.4

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

   5. Applied rewrites 93.4%

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

   if -9e17 < x < 1.74999999999999998e-4

   1. Initial program 95.9%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 84.3

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

   5. Applied rewrites 84.3%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+17}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{elif}\;x \leq 0.000175:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{t} \cdot z\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-94}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* (/ x t) z))))
   (if (<= x -9.5e-166) t_1 (if (<= x 4.1e-94) (/ (* (- y x) z) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((x / t) * z);
	double tmp;
	if (x <= -9.5e-166) {
		tmp = t_1;
	} else if (x <= 4.1e-94) {
		tmp = ((y - 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 = x - ((x / t) * z)
    if (x <= (-9.5d-166)) then
        tmp = t_1
    else if (x <= 4.1d-94) then
        tmp = ((y - 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 = x - ((x / t) * z);
	double tmp;
	if (x <= -9.5e-166) {
		tmp = t_1;
	} else if (x <= 4.1e-94) {
		tmp = ((y - x) * z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((x / t) * z)
	tmp = 0
	if x <= -9.5e-166:
		tmp = t_1
	elif x <= 4.1e-94:
		tmp = ((y - x) * z) / 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 (x <= -9.5e-166)
		tmp = t_1;
	elseif (x <= 4.1e-94)
		tmp = Float64(Float64(Float64(y - x) * z) / 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 (x <= -9.5e-166)
		tmp = t_1;
	elseif (x <= 4.1e-94)
		tmp = ((y - x) * z) / 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[x, -9.5e-166], t$95$1, If[LessEqual[x, 4.1e-94], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000046e-166 or 4.10000000000000001e-94 < x

   1. Initial program 94.6%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 84.6

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

   5. Applied rewrites 84.6%

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

   if -9.50000000000000046e-166 < x < 4.10000000000000001e-94

   1. Initial program 97.0%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 76.7

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

   5. Applied rewrites 76.7%

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

Alternative 9: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{t} \cdot z\\ \mathbf{if}\;x \leq -9 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-96}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* (/ x t) z))))
   (if (<= x -9e-37) t_1 (if (<= x 6.8e-96) (* (- y x) (/ z t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((x / t) * z);
	double tmp;
	if (x <= -9e-37) {
		tmp = t_1;
	} else if (x <= 6.8e-96) {
		tmp = (y - 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 = x - ((x / t) * z)
    if (x <= (-9d-37)) then
        tmp = t_1
    else if (x <= 6.8d-96) then
        tmp = (y - 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 = x - ((x / t) * z);
	double tmp;
	if (x <= -9e-37) {
		tmp = t_1;
	} else if (x <= 6.8e-96) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((x / t) * z)
	tmp = 0
	if x <= -9e-37:
		tmp = t_1
	elif x <= 6.8e-96:
		tmp = (y - x) * (z / 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 (x <= -9e-37)
		tmp = t_1;
	elseif (x <= 6.8e-96)
		tmp = Float64(Float64(y - x) * Float64(z / 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 (x <= -9e-37)
		tmp = t_1;
	elseif (x <= 6.8e-96)
		tmp = (y - x) * (z / 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[x, -9e-37], t$95$1, If[LessEqual[x, 6.8e-96], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.00000000000000081e-37 or 6.8000000000000002e-96 < x

   1. Initial program 95.9%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 88.4

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

   5. Applied rewrites 88.4%

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

   if -9.00000000000000081e-37 < x < 6.8000000000000002e-96

   1. Initial program 94.4%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 70.6

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

   5. Applied rewrites 70.6%

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

   7. Applied rewrites 69.7%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-37}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-96}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-184}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))))
   (if (<= z -1.75e-211) t_1 (if (<= z 2.7e-184) (/ (* x t) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double tmp;
	if (z <= -1.75e-211) {
		tmp = t_1;
	} else if (z <= 2.7e-184) {
		tmp = (x * t) / 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 - x) * (z / t)
    if (z <= (-1.75d-211)) then
        tmp = t_1
    else if (z <= 2.7d-184) then
        tmp = (x * t) / 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 - x) * (z / t);
	double tmp;
	if (z <= -1.75e-211) {
		tmp = t_1;
	} else if (z <= 2.7e-184) {
		tmp = (x * t) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	tmp = 0
	if z <= -1.75e-211:
		tmp = t_1
	elif z <= 2.7e-184:
		tmp = (x * t) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	tmp = 0.0
	if (z <= -1.75e-211)
		tmp = t_1;
	elseif (z <= 2.7e-184)
		tmp = Float64(Float64(x * t) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	tmp = 0.0;
	if (z <= -1.75e-211)
		tmp = t_1;
	elseif (z <= 2.7e-184)
		tmp = (x * t) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e-211], t$95$1, If[LessEqual[z, 2.7e-184], N[(N[(x * t), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e-211 or 2.7000000000000001e-184 < z

   1. Initial program 94.3%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 66.1

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

   5. Applied rewrites 66.1%

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

   7. Applied rewrites 67.7%

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

   if -1.75e-211 < z < 2.7000000000000001e-184

   1. Initial program 99.4%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 87.9

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

   5. Applied rewrites 87.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 70.7%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-211}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-184}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t} \cdot z\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-44}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ y t) z)))
   (if (<= z -6.5e-129) t_1 (if (<= z 1.15e-44) (/ (* x t) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / t) * z;
	double tmp;
	if (z <= -6.5e-129) {
		tmp = t_1;
	} else if (z <= 1.15e-44) {
		tmp = (x * t) / 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
    if (z <= (-6.5d-129)) then
        tmp = t_1
    else if (z <= 1.15d-44) then
        tmp = (x * t) / 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;
	double tmp;
	if (z <= -6.5e-129) {
		tmp = t_1;
	} else if (z <= 1.15e-44) {
		tmp = (x * t) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / t) * z
	tmp = 0
	if z <= -6.5e-129:
		tmp = t_1
	elif z <= 1.15e-44:
		tmp = (x * t) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / t) * z)
	tmp = 0.0
	if (z <= -6.5e-129)
		tmp = t_1;
	elseif (z <= 1.15e-44)
		tmp = Float64(Float64(x * t) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / t) * z;
	tmp = 0.0;
	if (z <= -6.5e-129)
		tmp = t_1;
	elseif (z <= 1.15e-44)
		tmp = (x * t) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -6.5e-129], t$95$1, If[LessEqual[z, 1.15e-44], N[(N[(x * t), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.49999999999999952e-129 or 1.14999999999999999e-44 < z

   1. Initial program 93.1%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 45.3

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

   5. Applied rewrites 45.3%

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

   if -6.49999999999999952e-129 < z < 1.14999999999999999e-44

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 51.1%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-129}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-44}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

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 / t) * z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

   \[x + \frac{\left(y - x\right) \cdot z}{t} \]
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 33.8

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

5. Applied rewrites 33.8%

   \[\leadsto \color{blue}{\frac{y}{t} \cdot z} \]
6. Add Preprocessing

Developer Target 1: 97.9% 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 2024276 
(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)))