Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 93.2% → 97.2%

Time: 7.7s

Alternatives: 9

Speedup: 1.0×

• 24.7% 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: 93.2% 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: 97.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.25 \cdot 10^{-171}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 1.25e-171) (+ x (* (- y x) (/ z t))) (+ x (/ z (/ t (- y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.25e-171) {
		tmp = x + ((y - x) * (z / t));
	} else {
		tmp = x + (z / (t / (y - 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 <= 1.25d-171) then
        tmp = x + ((y - x) * (z / t))
    else
        tmp = x + (z / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.25e-171) {
		tmp = x + ((y - x) * (z / t));
	} else {
		tmp = x + (z / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 1.25e-171:
		tmp = x + ((y - x) * (z / t))
	else:
		tmp = x + (z / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.25e-171)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / t)));
	else
		tmp = Float64(x + Float64(z / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 1.25e-171)
		tmp = x + ((y - x) * (z / t));
	else
		tmp = x + (z / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 1.25e-171], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.24999999999999998e-171

   1. Initial program 93.5%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   if 1.24999999999999998e-171 < z

   1. Initial program 92.7%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around 0 86.1%

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

      1. +-commutative 86.1%

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

      2. associate-*r/ 80.7%

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

      3. mul-1-neg 80.7%

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

      4. associate-/l* 84.7%

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

      5. distribute-lft-neg-out 84.7%

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

      6. distribute-rgt-out 93.8%

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

      7. sub-neg 93.8%

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

      8. associate-*l/ 92.7%

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

      9. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   9. Applied egg-rr 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.25 \cdot 10^{-171}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-164} \lor \neg \left(z \leq 1.25 \cdot 10^{-171}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.4e-164) (not (<= z 1.25e-171)))
   (+ x (* z (/ (- y x) t)))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.4e-164) || !(z <= 1.25e-171)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.4d-164)) .or. (.not. (z <= 1.25d-171))) then
        tmp = x + (z * ((y - x) / t))
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.4e-164) || !(z <= 1.25e-171)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.4e-164) or not (z <= 1.25e-171):
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.4e-164) || !(z <= 1.25e-171))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.4e-164) || ~((z <= 1.25e-171)))
		tmp = x + (z * ((y - x) / t));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.4e-164], N[Not[LessEqual[z, 1.25e-171]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.39999999999999983e-164 or 1.24999999999999998e-171 < z

   1. Initial program 91.2%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in y around 0 87.4%

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

      1. +-commutative 87.4%

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

      2. associate-*r/ 85.2%

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

      3. mul-1-neg 85.2%

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

      4. associate-/l* 90.8%

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

      5. distribute-lft-neg-out 90.8%

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

      6. distribute-rgt-out 96.4%

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

      7. sub-neg 96.4%

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

      8. associate-*l/ 91.2%

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

      9. associate-*r/ 98.8%

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

   7. Simplified 98.8%

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

   if -2.39999999999999983e-164 < z < 1.24999999999999998e-171

   1. Initial program 98.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 93.0%

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

      1. associate-*r/ 94.3%

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

   7. Simplified 94.3%

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

      1. clear-num 94.2%

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

      2. div-inv 94.4%

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

   9. Applied egg-rr 94.4%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-164} \lor \neg \left(z \leq 1.25 \cdot 10^{-171}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+26} \lor \neg \left(y \leq 3 \cdot 10^{-28}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7e+26) (not (<= y 3e-28)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7e+26) || !(y <= 3e-28)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-7d+26)) .or. (.not. (y <= 3d-28))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7e+26) || !(y <= 3e-28)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7e+26) or not (y <= 3e-28):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7e+26) || !(y <= 3e-28))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7e+26) || ~((y <= 3e-28)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7e+26], N[Not[LessEqual[y, 3e-28]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9999999999999998e26 or 3.00000000000000003e-28 < y

   1. Initial program 92.8%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around inf 88.5%

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

      1. associate-*r/ 93.9%

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

   7. Simplified 93.9%

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

   if -6.9999999999999998e26 < y < 3.00000000000000003e-28

   1. Initial program 93.6%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in x around inf 86.5%

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

      1. mul-1-neg 86.5%

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

      2. unsub-neg 86.5%

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

   7. Simplified 86.5%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+26} \lor \neg \left(y \leq 3 \cdot 10^{-28}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.6e+25)
   (+ x (* y (/ z t)))
   (if (<= y 9.5e-126) (* x (- 1.0 (/ z t))) (+ x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.6e+25) {
		tmp = x + (y * (z / t));
	} else if (y <= 9.5e-126) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-8.6d+25)) then
        tmp = x + (y * (z / t))
    else if (y <= 9.5d-126) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.6e+25) {
		tmp = x + (y * (z / t));
	} else if (y <= 9.5e-126) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.6e+25:
		tmp = x + (y * (z / t))
	elif y <= 9.5e-126:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.6e+25)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (y <= 9.5e-126)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.6e+25)
		tmp = x + (y * (z / t));
	elseif (y <= 9.5e-126)
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.6e+25], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-126], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.59999999999999996e25

   1. Initial program 92.1%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 90.4%

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

      1. associate-*r/ 96.4%

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

   7. Simplified 96.4%

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

   if -8.59999999999999996e25 < y < 9.5000000000000003e-126

   1. Initial program 92.8%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf 87.9%

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

      1. mul-1-neg 87.9%

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

      2. unsub-neg 87.9%

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

   7. Simplified 87.9%

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

   if 9.5000000000000003e-126 < y

   1. Initial program 94.5%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in y around inf 85.9%

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

      1. associate-*r/ 89.0%

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

   7. Simplified 89.0%

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

      1. clear-num 88.9%

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

      2. div-inv 89.8%

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

   9. Applied egg-rr 89.8%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-21} \lor \neg \left(z \leq 5.5 \cdot 10^{+21}\right):\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.5e-21) (not (<= z 5.5e+21))) (* z (/ x (- t))) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5e-21) || !(z <= 5.5e+21)) {
		tmp = z * (x / -t);
	} else {
		tmp = 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 <= (-1.5d-21)) .or. (.not. (z <= 5.5d+21))) then
        tmp = z * (x / -t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5e-21) || !(z <= 5.5e+21)) {
		tmp = z * (x / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.5e-21) or not (z <= 5.5e+21):
		tmp = z * (x / -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.5e-21) || !(z <= 5.5e+21))
		tmp = Float64(z * Float64(x / Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.5e-21) || ~((z <= 5.5e+21)))
		tmp = z * (x / -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.5e-21], N[Not[LessEqual[z, 5.5e+21]], $MachinePrecision]], N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999996e-21 or 5.5e21 < z

   1. Initial program 87.5%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

      1. clear-num 95.6%

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

      2. un-div-inv 97.5%

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

   6. Applied egg-rr 97.5%

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

   7. Taylor expanded in y around 0 53.5%

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

      1. mul-1-neg 53.5%

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

      2. associate-*l/ 58.7%

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

      3. distribute-lft-neg-in 58.7%

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

      4. distribute-neg-frac 58.7%

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

   9. Simplified 58.7%

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

       1. add-sqr-sqrt 32.4%

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

       2. sqrt-unprod 30.7%

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

       3. sqr-neg 30.7%

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

       4. sqrt-unprod 6.3%

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

       5. add-sqr-sqrt 17.2%

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

       6. cancel-sign-sub 17.2%

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

       7. distribute-frac-neg 17.2%

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

       8. *-commutative 17.2%

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

       9. div-inv 17.2%

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

       10. div-inv 17.2%

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

       11. add-sqr-sqrt 10.9%

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

       12. sqrt-unprod 31.8%

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

       13. sqr-neg 31.8%

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

       14. sqrt-unprod 26.1%

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

       15. add-sqr-sqrt 58.7%

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

   11. Applied egg-rr 58.7%

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

   12. Taylor expanded in z around inf 42.3%

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

       1. mul-1-neg 42.3%

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

       2. associate-*l/ 43.6%

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

       3. distribute-rgt-neg-out 43.6%

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

   14. Simplified 43.6%

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

   if -1.49999999999999996e-21 < z < 5.5e21

   1. Initial program 99.1%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around 0 66.9%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-21} \lor \neg \left(z \leq 5.5 \cdot 10^{+21}\right):\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.25 \cdot 10^{-171}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 1.25e-171) (+ x (* (- y x) (/ z t))) (+ x (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.25e-171) {
		tmp = x + ((y - x) * (z / t));
	} else {
		tmp = x + (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 (z <= 1.25d-171) then
        tmp = x + ((y - x) * (z / t))
    else
        tmp = x + (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 (z <= 1.25e-171) {
		tmp = x + ((y - x) * (z / t));
	} else {
		tmp = x + (z * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 1.25e-171:
		tmp = x + ((y - x) * (z / t))
	else:
		tmp = x + (z * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.25e-171)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 1.25e-171)
		tmp = x + ((y - x) * (z / t));
	else
		tmp = x + (z * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 1.25e-171], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.24999999999999998e-171

   1. Initial program 93.5%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   if 1.24999999999999998e-171 < z

   1. Initial program 92.7%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around 0 86.1%

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

      1. +-commutative 86.1%

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

      2. associate-*r/ 80.7%

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

      3. mul-1-neg 80.7%

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

      4. associate-/l* 84.7%

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

      5. distribute-lft-neg-out 84.7%

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

      6. distribute-rgt-out 93.8%

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

      7. sub-neg 93.8%

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

      8. associate-*l/ 92.7%

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

      9. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.25 \cdot 10^{-171}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.2%

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

   1. associate-/l* 97.3%

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

3. Simplified 97.3%

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

   1. clear-num 96.9%

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

   2. un-div-inv 97.9%

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

6. Applied egg-rr 97.9%

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

7. Final simplification 97.9%

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

Alternative 8: 66.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{z}{t}\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * (1.0 - (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 * (1.0d0 - (z / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.2%

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

   1. associate-/l* 97.3%

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

3. Simplified 97.3%

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

5. Taylor expanded in x around inf 66.3%

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

   1. mul-1-neg 66.3%

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

   2. unsub-neg 66.3%

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

7. Simplified 66.3%

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

8. Final simplification 66.3%

   \[\leadsto x \cdot \left(1 - \frac{z}{t}\right) \]
9. Add Preprocessing

Alternative 9: 39.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 93.2%

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

   1. associate-/l* 97.3%

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

3. Simplified 97.3%

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

5. Taylor expanded in z around 0 41.4%

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

6. Final simplification 41.4%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.8% accurate, 0.5× 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 2024079 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :alt
  (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)))))

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