Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.9% → 98.1%

Time: 7.6s

Alternatives: 11

Speedup: 1.1×

• 25.7% 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: 92.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;x - \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}} + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 1.6e-25) (- x (/ (- x y) (/ t z))) (+ (/ z (/ t (- y x))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.6e-25) {
		tmp = x - ((x - y) / (t / z));
	} else {
		tmp = (z / (t / (y - x))) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 1.6d-25) then
        tmp = x - ((x - y) / (t / z))
    else
        tmp = (z / (t / (y - x))) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.6e-25) {
		tmp = x - ((x - y) / (t / z));
	} else {
		tmp = (z / (t / (y - x))) + x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 1.6e-25:
		tmp = x - ((x - y) / (t / z))
	else:
		tmp = (z / (t / (y - x))) + x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.6e-25)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(t / z)));
	else
		tmp = Float64(Float64(z / Float64(t / Float64(y - x))) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 1.6e-25)
		tmp = x - ((x - y) / (t / z));
	else
		tmp = (z / (t / (y - x))) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 1.6e-25], N[(x - N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.6000000000000001e-25

   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

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 97.4

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

   4. Applied rewrites 97.4%

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

   if 1.6000000000000001e-25 < z

   1. Initial program 90.2%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/r* N/A

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

      5. clear-num-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;x - \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-13}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-71}:\\ \;\;\;\;\frac{\left(-x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7e-13)
   (* 1.0 x)
   (if (<= t -1.7e-71)
     (/ (* (- x) z) t)
     (if (<= t 2.1e-58) (* (/ z t) y) (* 1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e-13) {
		tmp = 1.0 * x;
	} else if (t <= -1.7e-71) {
		tmp = (-x * z) / t;
	} else if (t <= 2.1e-58) {
		tmp = (z / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-7d-13)) then
        tmp = 1.0d0 * x
    else if (t <= (-1.7d-71)) then
        tmp = (-x * z) / t
    else if (t <= 2.1d-58) then
        tmp = (z / t) * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e-13) {
		tmp = 1.0 * x;
	} else if (t <= -1.7e-71) {
		tmp = (-x * z) / t;
	} else if (t <= 2.1e-58) {
		tmp = (z / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7e-13:
		tmp = 1.0 * x
	elif t <= -1.7e-71:
		tmp = (-x * z) / t
	elif t <= 2.1e-58:
		tmp = (z / t) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7e-13)
		tmp = Float64(1.0 * x);
	elseif (t <= -1.7e-71)
		tmp = Float64(Float64(Float64(-x) * z) / t);
	elseif (t <= 2.1e-58)
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7e-13)
		tmp = 1.0 * x;
	elseif (t <= -1.7e-71)
		tmp = (-x * z) / t;
	elseif (t <= 2.1e-58)
		tmp = (z / t) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7e-13], N[(1.0 * x), $MachinePrecision], If[LessEqual[t, -1.7e-71], N[(N[((-x) * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 2.1e-58], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.0000000000000005e-13 or 2.09999999999999988e-58 < t

   1. Initial program 87.6%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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. frac-2neg N/A

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

      5. div-inv N/A

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

      6. lift-*.f64 N/A

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

      7. distribute-lft-neg-in N/A

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

      8. associate-*l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. neg-mul-1 N/A

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

      13. associate-/r* N/A

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

      14. metadata-eval N/A

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

      15. lower-/.f64 99.1

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 80.0

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

   7. Applied rewrites 80.0%

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

   8. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 64.0%

       \[\leadsto 1 \cdot x \]

   if -7.0000000000000005e-13 < t < -1.70000000000000002e-71

   1. Initial program 100.0%

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

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 76.2

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

   5. Applied rewrites 76.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 60.1%

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

   if -1.70000000000000002e-71 < t < 2.09999999999999988e-58

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0

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

      1. 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 58.2

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

   5. Applied rewrites 58.2%

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

   7. Applied rewrites 60.9%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-13}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-71}:\\ \;\;\;\;\frac{\left(-x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-13}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-71}:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7e-13)
   (* 1.0 x)
   (if (<= t -1.7e-71)
     (* (/ (- x) t) z)
     (if (<= t 2.1e-58) (* (/ z t) y) (* 1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e-13) {
		tmp = 1.0 * x;
	} else if (t <= -1.7e-71) {
		tmp = (-x / t) * z;
	} else if (t <= 2.1e-58) {
		tmp = (z / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-7d-13)) then
        tmp = 1.0d0 * x
    else if (t <= (-1.7d-71)) then
        tmp = (-x / t) * z
    else if (t <= 2.1d-58) then
        tmp = (z / t) * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e-13) {
		tmp = 1.0 * x;
	} else if (t <= -1.7e-71) {
		tmp = (-x / t) * z;
	} else if (t <= 2.1e-58) {
		tmp = (z / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7e-13:
		tmp = 1.0 * x
	elif t <= -1.7e-71:
		tmp = (-x / t) * z
	elif t <= 2.1e-58:
		tmp = (z / t) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7e-13)
		tmp = Float64(1.0 * x);
	elseif (t <= -1.7e-71)
		tmp = Float64(Float64(Float64(-x) / t) * z);
	elseif (t <= 2.1e-58)
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7e-13)
		tmp = 1.0 * x;
	elseif (t <= -1.7e-71)
		tmp = (-x / t) * z;
	elseif (t <= 2.1e-58)
		tmp = (z / t) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7e-13], N[(1.0 * x), $MachinePrecision], If[LessEqual[t, -1.7e-71], N[(N[((-x) / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t, 2.1e-58], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.0000000000000005e-13 or 2.09999999999999988e-58 < t

   1. Initial program 87.6%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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. frac-2neg N/A

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

      5. div-inv N/A

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

      6. lift-*.f64 N/A

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

      7. distribute-lft-neg-in N/A

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

      8. associate-*l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. neg-mul-1 N/A

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

      13. associate-/r* N/A

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

      14. metadata-eval N/A

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

      15. lower-/.f64 99.1

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 80.0

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

   7. Applied rewrites 80.0%

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

   8. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 64.0%

       \[\leadsto 1 \cdot x \]

   if -7.0000000000000005e-13 < t < -1.70000000000000002e-71

   1. Initial program 100.0%

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

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 76.2

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

   5. Applied rewrites 76.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 60.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 59.6%

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

   if -1.70000000000000002e-71 < t < 2.09999999999999988e-58

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0

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

      1. 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 58.2

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

   5. Applied rewrites 58.2%

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

   7. Applied rewrites 60.9%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-13}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-71}:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}} + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 3.8e-26) (fma (/ z t) (- y x) x) (+ (/ z (/ t (- y x))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3.8e-26) {
		tmp = fma((z / t), (y - x), x);
	} else {
		tmp = (z / (t / (y - x))) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 3.8e-26)
		tmp = fma(Float64(z / t), Float64(y - x), x);
	else
		tmp = Float64(Float64(z / Float64(t / Float64(y - x))) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 3.8e-26], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.80000000000000015e-26

   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 97.1

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

   4. Applied rewrites 97.1%

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

   if 3.80000000000000015e-26 < z

   1. Initial program 90.2%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/r* N/A

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

      5. clear-num-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (/ z t)) x)))
   (if (<= x -7.2e+27) t_1 (if (<= x 9.5e+72) (+ (/ (* y z) t) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (1.0 - (z / t)) * x;
	double tmp;
	if (x <= -7.2e+27) {
		tmp = t_1;
	} else if (x <= 9.5e+72) {
		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 = (1.0d0 - (z / t)) * x
    if (x <= (-7.2d+27)) then
        tmp = t_1
    else if (x <= 9.5d+72) 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 = (1.0 - (z / t)) * x;
	double tmp;
	if (x <= -7.2e+27) {
		tmp = t_1;
	} else if (x <= 9.5e+72) {
		tmp = ((y * z) / t) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (1.0 - (z / t)) * x
	tmp = 0
	if x <= -7.2e+27:
		tmp = t_1
	elif x <= 9.5e+72:
		tmp = ((y * z) / t) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(1.0 - Float64(z / t)) * x)
	tmp = 0.0
	if (x <= -7.2e+27)
		tmp = t_1;
	elseif (x <= 9.5e+72)
		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 = (1.0 - (z / t)) * x;
	tmp = 0.0;
	if (x <= -7.2e+27)
		tmp = t_1;
	elseif (x <= 9.5e+72)
		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[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -7.2e+27], t$95$1, If[LessEqual[x, 9.5e+72], N[(N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.19999999999999966e27 or 9.50000000000000054e72 < x

   1. Initial program 89.0%

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

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 94.8

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

   5. Applied rewrites 94.8%

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

   if -7.19999999999999966e27 < x < 9.50000000000000054e72

   1. Initial program 95.4%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 83.2

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

   5. Applied rewrites 83.2%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+27}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3900000:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (/ z t)) x)))
   (if (<= t -6.5e-60) t_1 (if (<= t 3900000.0) (/ (* (- y x) z) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (1.0 - (z / t)) * x;
	double tmp;
	if (t <= -6.5e-60) {
		tmp = t_1;
	} else if (t <= 3900000.0) {
		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 = (1.0d0 - (z / t)) * x
    if (t <= (-6.5d-60)) then
        tmp = t_1
    else if (t <= 3900000.0d0) 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 = (1.0 - (z / t)) * x;
	double tmp;
	if (t <= -6.5e-60) {
		tmp = t_1;
	} else if (t <= 3900000.0) {
		tmp = ((y - x) * z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (1.0 - (z / t)) * x
	tmp = 0
	if t <= -6.5e-60:
		tmp = t_1
	elif t <= 3900000.0:
		tmp = ((y - x) * z) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(1.0 - Float64(z / t)) * x)
	tmp = 0.0
	if (t <= -6.5e-60)
		tmp = t_1;
	elseif (t <= 3900000.0)
		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 = (1.0 - (z / t)) * x;
	tmp = 0.0;
	if (t <= -6.5e-60)
		tmp = t_1;
	elseif (t <= 3900000.0)
		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[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -6.5e-60], t$95$1, If[LessEqual[t, 3900000.0], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.49999999999999995e-60 or 3.9e6 < t

   1. Initial program 87.5%

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

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 80.6

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

   5. Applied rewrites 80.6%

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

   if -6.49999999999999995e-60 < t < 3.9e6

   1. Initial program 98.4%

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

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 88.1

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

   5. Applied rewrites 88.1%

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

Alternative 7: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot y\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+130}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) y)))
   (if (<= y -4.6e+63) t_1 (if (<= y 3.9e+130) (* (- 1.0 (/ z t)) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * y;
	double tmp;
	if (y <= -4.6e+63) {
		tmp = t_1;
	} else if (y <= 3.9e+130) {
		tmp = (1.0 - (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 = (z / t) * y
    if (y <= (-4.6d+63)) then
        tmp = t_1
    else if (y <= 3.9d+130) then
        tmp = (1.0d0 - (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 = (z / t) * y;
	double tmp;
	if (y <= -4.6e+63) {
		tmp = t_1;
	} else if (y <= 3.9e+130) {
		tmp = (1.0 - (z / t)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * y
	tmp = 0
	if y <= -4.6e+63:
		tmp = t_1
	elif y <= 3.9e+130:
		tmp = (1.0 - (z / t)) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * y)
	tmp = 0.0
	if (y <= -4.6e+63)
		tmp = t_1;
	elseif (y <= 3.9e+130)
		tmp = Float64(Float64(1.0 - Float64(z / t)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * y;
	tmp = 0.0;
	if (y <= -4.6e+63)
		tmp = t_1;
	elseif (y <= 3.9e+130)
		tmp = (1.0 - (z / t)) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.6e+63], t$95$1, If[LessEqual[y, 3.9e+130], N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.59999999999999986e63 or 3.9000000000000002e130 < y

   1. Initial program 94.3%

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

   3. Taylor expanded in x around 0

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

      1. 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 67.8

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

   5. Applied rewrites 67.8%

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

   7. Applied rewrites 73.3%

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

   if -4.59999999999999986e63 < y < 3.9000000000000002e130

   1. Initial program 91.9%

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

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 80.6

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

   5. Applied rewrites 80.6%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+63}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+130}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-60}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.5e-60) (* 1.0 x) (if (<= t 2.1e-58) (* (/ z t) y) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.5e-60) {
		tmp = 1.0 * x;
	} else if (t <= 2.1e-58) {
		tmp = (z / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-6.5d-60)) then
        tmp = 1.0d0 * x
    else if (t <= 2.1d-58) then
        tmp = (z / t) * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.5e-60) {
		tmp = 1.0 * x;
	} else if (t <= 2.1e-58) {
		tmp = (z / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.5e-60:
		tmp = 1.0 * x
	elif t <= 2.1e-58:
		tmp = (z / t) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.5e-60)
		tmp = Float64(1.0 * x);
	elseif (t <= 2.1e-58)
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.5e-60)
		tmp = 1.0 * x;
	elseif (t <= 2.1e-58)
		tmp = (z / t) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.5e-60], N[(1.0 * x), $MachinePrecision], If[LessEqual[t, 2.1e-58], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.49999999999999995e-60 or 2.09999999999999988e-58 < t

   1. Initial program 88.6%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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. frac-2neg N/A

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

      5. div-inv N/A

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

      6. lift-*.f64 N/A

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

      7. distribute-lft-neg-in N/A

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

      8. associate-*l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. neg-mul-1 N/A

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

      13. associate-/r* N/A

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

      14. metadata-eval N/A

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

      15. lower-/.f64 98.0

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

   4. Applied rewrites 98.0%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 79.7

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

   7. Applied rewrites 79.7%

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

   8. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 60.8%

       \[\leadsto 1 \cdot x \]

   if -6.49999999999999995e-60 < t < 2.09999999999999988e-58

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0

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

      1. 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 58.2

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

   5. Applied rewrites 58.2%

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

   7. Applied rewrites 60.9%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-60}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 2e-39) (fma (/ z t) (- y x) x) (fma (/ (- y x) t) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 2e-39) {
		tmp = fma((z / t), (y - x), x);
	} else {
		tmp = fma(((y - x) / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 2e-39)
		tmp = fma(Float64(z / t), Float64(y - x), x);
	else
		tmp = fma(Float64(Float64(y - x) / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 2e-39], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.99999999999999986e-39

   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 97.1

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

   4. Applied rewrites 97.1%

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

   if 1.99999999999999986e-39 < z

   1. Initial program 90.4%

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

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

Alternative 10: 97.6% 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 92.7%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 96.2

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

4. Applied rewrites 96.2%

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

Alternative 11: 37.9% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ 1 \cdot x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 1.0 x))

C

double code(double x, double y, double z, double t) {
	return 1.0 * x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 * x
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 * x;
}

Python

def code(x, y, z, t):
	return 1.0 * x

Julia

function code(x, y, z, t)
	return Float64(1.0 * x)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 * x;
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 * x), $MachinePrecision]

Derivation

1. Initial program 92.7%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. frac-2neg N/A

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

   5. div-inv N/A

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

   6. lift-*.f64 N/A

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

   7. distribute-lft-neg-in N/A

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

   8. associate-*l* N/A

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

   9. lower-fma.f64 N/A

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

   10. lower-neg.f64 N/A

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

   11. lower-*.f64 N/A

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

   12. neg-mul-1 N/A

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

   13. associate-/r* N/A

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

   14. metadata-eval N/A

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

   15. lower-/.f64 96.2

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

4. Applied rewrites 96.2%

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

5. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. mul-1-neg N/A

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

   4. unsub-neg N/A

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

   5. lower--.f64 N/A

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

   6. lower-/.f64 66.4

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

7. Applied rewrites 66.4%

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

8. Taylor expanded in z around 0

   \[\leadsto 1 \cdot x \]
9. Step-by-step derivation

10. Applied rewrites 39.5%

    \[\leadsto 1 \cdot x \]
11. 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 2024298 
(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)))