Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.3% → 97.8%

Time: 9.9s

Alternatives: 11

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: 92.3% 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 96.0%

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

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

4. Applied rewrites 97.4%

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

Alternative 2: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{t}, -x, x\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1100:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ z t) (- x) x)))
   (if (<= x -3.5e+14) t_1 (if (<= x 1100.0) (+ x (/ (* z y) t)) 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 <= -3.5e+14) {
		tmp = t_1;
	} else if (x <= 1100.0) {
		tmp = x + ((z * y) / t);
	} 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 <= -3.5e+14)
		tmp = t_1;
	elseif (x <= 1100.0)
		tmp = Float64(x + Float64(Float64(z * y) / t));
	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, -3.5e+14], t$95$1, If[LessEqual[x, 1100.0], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5e14 or 1100 < x

   1. Initial program 93.9%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 86.1

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

   7. Applied rewrites 86.1%

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

   if -3.5e14 < x < 1100

   1. Initial program 98.1%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 91.4

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

   5. Applied rewrites 91.4%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, -x, x\right)\\ \mathbf{elif}\;x \leq 1100:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, -x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) (- y x))))
   (if (<= z -1.35e+50) t_1 (if (<= z 4.2e-13) (+ x (/ (* z y) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * (y - x);
	double tmp;
	if (z <= -1.35e+50) {
		tmp = t_1;
	} else if (z <= 4.2e-13) {
		tmp = x + ((z * y) / 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 - x)
    if (z <= (-1.35d+50)) then
        tmp = t_1
    else if (z <= 4.2d-13) then
        tmp = x + ((z * y) / 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 - x);
	double tmp;
	if (z <= -1.35e+50) {
		tmp = t_1;
	} else if (z <= 4.2e-13) {
		tmp = x + ((z * y) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * (y - x)
	tmp = 0
	if z <= -1.35e+50:
		tmp = t_1
	elif z <= 4.2e-13:
		tmp = x + ((z * y) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * Float64(y - x))
	tmp = 0.0
	if (z <= -1.35e+50)
		tmp = t_1;
	elseif (z <= 4.2e-13)
		tmp = Float64(x + Float64(Float64(z * y) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * (y - x);
	tmp = 0.0;
	if (z <= -1.35e+50)
		tmp = t_1;
	elseif (z <= 4.2e-13)
		tmp = x + ((z * y) / 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] * N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+50], t$95$1, If[LessEqual[z, 4.2e-13], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e50 or 4.19999999999999977e-13 < z

   1. Initial program 91.3%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 84.3

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

   5. Applied rewrites 84.3%

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

   7. Applied rewrites 84.8%

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

   if -1.35e50 < z < 4.19999999999999977e-13

   1. Initial program 99.7%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 89.1

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

   5. Applied rewrites 89.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+50}:\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y t)))))
   (if (<= t -1.15e-62) t_1 (if (<= t 2.8e+68) (* (/ z t) (- y x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * (y / t));
	double tmp;
	if (t <= -1.15e-62) {
		tmp = t_1;
	} else if (t <= 2.8e+68) {
		tmp = (z / t) * (y - 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 + (z * (y / t))
    if (t <= (-1.15d-62)) then
        tmp = t_1
    else if (t <= 2.8d+68) then
        tmp = (z / t) * (y - 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 + (z * (y / t));
	double tmp;
	if (t <= -1.15e-62) {
		tmp = t_1;
	} else if (t <= 2.8e+68) {
		tmp = (z / t) * (y - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * (y / t))
	tmp = 0
	if t <= -1.15e-62:
		tmp = t_1
	elif t <= 2.8e+68:
		tmp = (z / t) * (y - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * Float64(y / t)))
	tmp = 0.0
	if (t <= -1.15e-62)
		tmp = t_1;
	elseif (t <= 2.8e+68)
		tmp = Float64(Float64(z / t) * Float64(y - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * (y / t));
	tmp = 0.0;
	if (t <= -1.15e-62)
		tmp = t_1;
	elseif (t <= 2.8e+68)
		tmp = (z / t) * (y - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e-62], t$95$1, If[LessEqual[t, 2.8e+68], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15e-62 or 2.8e68 < t

   1. Initial program 92.9%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 87.3

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

   5. Applied rewrites 87.3%

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

   if -1.15e-62 < t < 2.8e68

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 76.1

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

   5. Applied rewrites 76.1%

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

   7. Applied rewrites 83.4%

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

Alternative 5: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-46}:\\ \;\;\;\;x - \frac{z \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) (- y x))))
   (if (<= y -1.3e-62) t_1 (if (<= y 2.1e-46) (- x (/ (* z x) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * (y - x);
	double tmp;
	if (y <= -1.3e-62) {
		tmp = t_1;
	} else if (y <= 2.1e-46) {
		tmp = x - ((z * 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 = (z / t) * (y - x)
    if (y <= (-1.3d-62)) then
        tmp = t_1
    else if (y <= 2.1d-46) then
        tmp = x - ((z * 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 = (z / t) * (y - x);
	double tmp;
	if (y <= -1.3e-62) {
		tmp = t_1;
	} else if (y <= 2.1e-46) {
		tmp = x - ((z * x) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * (y - x)
	tmp = 0
	if y <= -1.3e-62:
		tmp = t_1
	elif y <= 2.1e-46:
		tmp = x - ((z * x) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * Float64(y - x))
	tmp = 0.0
	if (y <= -1.3e-62)
		tmp = t_1;
	elseif (y <= 2.1e-46)
		tmp = Float64(x - Float64(Float64(z * x) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * (y - x);
	tmp = 0.0;
	if (y <= -1.3e-62)
		tmp = t_1;
	elseif (y <= 2.1e-46)
		tmp = x - ((z * x) / 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] * N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e-62], t$95$1, If[LessEqual[y, 2.1e-46], N[(x - N[(N[(z * x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e-62 or 2.09999999999999987e-46 < y

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 67.7

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

   5. Applied rewrites 67.7%

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

   7. Applied rewrites 72.2%

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

   if -1.3e-62 < y < 2.09999999999999987e-46

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{x \cdot 1 - x \cdot \frac{z}{t}} \]

      4. *-rgt-identity N/A

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

      5. associate-/l* N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 85.6

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

   5. Applied rewrites 85.6%

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

Alternative 6: 48.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 920:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) (- x))))
   (if (<= x -3.5e+14) t_1 (if (<= x 920.0) (/ (* z y) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * -x;
	double tmp;
	if (x <= -3.5e+14) {
		tmp = t_1;
	} else if (x <= 920.0) {
		tmp = (z * y) / 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) * -x
    if (x <= (-3.5d+14)) then
        tmp = t_1
    else if (x <= 920.0d0) then
        tmp = (z * y) / 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) * -x;
	double tmp;
	if (x <= -3.5e+14) {
		tmp = t_1;
	} else if (x <= 920.0) {
		tmp = (z * y) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * -x
	tmp = 0
	if x <= -3.5e+14:
		tmp = t_1
	elif x <= 920.0:
		tmp = (z * y) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * Float64(-x))
	tmp = 0.0
	if (x <= -3.5e+14)
		tmp = t_1;
	elseif (x <= 920.0)
		tmp = Float64(Float64(z * y) / t);
	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 <= -3.5e+14)
		tmp = t_1;
	elseif (x <= 920.0)
		tmp = (z * y) / 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] * (-x)), $MachinePrecision]}, If[LessEqual[x, -3.5e+14], t$95$1, If[LessEqual[x, 920.0], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5e14 or 920 < x

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 48.7

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

   5. Applied rewrites 48.7%

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

   7. Applied rewrites 53.4%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 39.8%

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

   if -3.5e14 < x < 920

   1. Initial program 98.1%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 94.8

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

   4. Applied rewrites 94.8%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 63.5

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

   7. Applied rewrites 63.5%

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

Alternative 7: 47.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -\frac{z \cdot x}{t}\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 920:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ (* z x) t))))
   (if (<= x -3.5e+14) t_1 (if (<= x 920.0) (/ (* z y) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -((z * x) / t);
	double tmp;
	if (x <= -3.5e+14) {
		tmp = t_1;
	} else if (x <= 920.0) {
		tmp = (z * y) / 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 * x) / t)
    if (x <= (-3.5d+14)) then
        tmp = t_1
    else if (x <= 920.0d0) then
        tmp = (z * y) / 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 * x) / t);
	double tmp;
	if (x <= -3.5e+14) {
		tmp = t_1;
	} else if (x <= 920.0) {
		tmp = (z * y) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -((z * x) / t)
	tmp = 0
	if x <= -3.5e+14:
		tmp = t_1
	elif x <= 920.0:
		tmp = (z * y) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-Float64(Float64(z * x) / t))
	tmp = 0.0
	if (x <= -3.5e+14)
		tmp = t_1;
	elseif (x <= 920.0)
		tmp = Float64(Float64(z * y) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -((z * x) / t);
	tmp = 0.0;
	if (x <= -3.5e+14)
		tmp = t_1;
	elseif (x <= 920.0)
		tmp = (z * y) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = (-N[(N[(z * x), $MachinePrecision] / t), $MachinePrecision])}, If[LessEqual[x, -3.5e+14], t$95$1, If[LessEqual[x, 920.0], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5e14 or 920 < x

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{x \cdot 1 - x \cdot \frac{z}{t}} \]

      4. *-rgt-identity N/A

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

      5. associate-/l* N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 81.6

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

   5. Applied rewrites 81.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 38.9%

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

   if -3.5e14 < x < 920

   1. Initial program 98.1%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 94.8

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

   4. Applied rewrites 94.8%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 63.5

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

   7. Applied rewrites 63.5%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;-\frac{z \cdot x}{t}\\ \mathbf{elif}\;x \leq 920:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;-\frac{z \cdot x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.4 \cdot 10^{-109}:\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.4e-109) (* (/ z t) (- y x)) (* z (/ (- y x) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.4e-109) {
		tmp = (z / t) * (y - x);
	} else {
		tmp = z * ((y - x) / 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) :: tmp
    if (t <= 1.4d-109) then
        tmp = (z / t) * (y - x)
    else
        tmp = z * ((y - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.4e-109) {
		tmp = (z / t) * (y - x);
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.4e-109:
		tmp = (z / t) * (y - x)
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.4e-109)
		tmp = Float64(Float64(z / t) * Float64(y - x));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.4e-109)
		tmp = (z / t) * (y - x);
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.4e-109], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.39999999999999989e-109

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 57.3

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

   5. Applied rewrites 57.3%

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

   7. Applied rewrites 64.4%

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

   if 1.39999999999999989e-109 < t

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 56.8

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

   5. Applied rewrites 56.8%

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

Alternative 9: 40.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{-138}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1e-138) (* (/ z t) y) (* z (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1e-138) {
		tmp = (z / t) * y;
	} else {
		tmp = z * (y / 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) :: tmp
    if (t <= 1d-138) then
        tmp = (z / t) * y
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1e-138) {
		tmp = (z / t) * y;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1e-138:
		tmp = (z / t) * y
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1e-138)
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1e-138)
		tmp = (z / t) * y;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1e-138], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.00000000000000007e-138

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 37.5

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

   5. Applied rewrites 37.5%

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

   7. Applied rewrites 44.9%

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

   if 1.00000000000000007e-138 < t

   1. Initial program 95.5%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 39.2

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

   5. Applied rewrites 39.2%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 10^{-138}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

3. Taylor expanded in z around inf

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

   1. div-sub N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 N/A

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

   4. lower--.f64 57.1

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

5. Applied rewrites 57.1%

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

Alternative 11: 41.2% 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 96.0%

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

3. Taylor expanded in x around 0

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 38.1

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

5. Applied rewrites 38.1%

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

7. Applied rewrites 41.3%

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

8. Final simplification 41.3%

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

Developer Target 1: 97.7% 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 2024221 
(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)))