Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.8% → 95.3%

Time: 8.5s

Alternatives: 14

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: 92.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+91}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.9e+91) (+ x (* z (/ (- y x) t))) (+ x (/ (* (- y x) z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.9e+91) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x + (((y - x) * z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.9d+91)) then
        tmp = x + (z * ((y - x) / t))
    else
        tmp = x + (((y - x) * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.9e+91) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x + (((y - x) * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.9e+91:
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = x + (((y - x) * z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.9e+91)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.9e+91)
		tmp = x + (z * ((y - x) / t));
	else
		tmp = x + (((y - x) * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.9e+91], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.90000000000000014e91

   1. Initial program 79.4%

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

      1. associate-*l/ 96.6%

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

   3. Applied egg-rr 96.6%

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

   if -2.90000000000000014e91 < t

   1. Initial program 98.2%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+91}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]

Alternative 2: 54.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ t_2 := x \cdot \frac{-z}{t}\\ \mathbf{if}\;z \leq -6.1 \cdot 10^{+147}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1400:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+277}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))) (t_2 (* x (/ (- z) t))))
   (if (<= z -6.1e+147)
     (* z (/ y t))
     (if (<= z -1.2e+88)
       t_2
       (if (<= z -1.26e+30)
         t_1
         (if (<= z 1400.0)
           x
           (if (<= z 3e+198) t_1 (if (<= z 3e+277) t_2 (/ y (/ t z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double t_2 = x * (-z / t);
	double tmp;
	if (z <= -6.1e+147) {
		tmp = z * (y / t);
	} else if (z <= -1.2e+88) {
		tmp = t_2;
	} else if (z <= -1.26e+30) {
		tmp = t_1;
	} else if (z <= 1400.0) {
		tmp = x;
	} else if (z <= 3e+198) {
		tmp = t_1;
	} else if (z <= 3e+277) {
		tmp = t_2;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (z / t)
    t_2 = x * (-z / t)
    if (z <= (-6.1d+147)) then
        tmp = z * (y / t)
    else if (z <= (-1.2d+88)) then
        tmp = t_2
    else if (z <= (-1.26d+30)) then
        tmp = t_1
    else if (z <= 1400.0d0) then
        tmp = x
    else if (z <= 3d+198) then
        tmp = t_1
    else if (z <= 3d+277) then
        tmp = t_2
    else
        tmp = y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double t_2 = x * (-z / t);
	double tmp;
	if (z <= -6.1e+147) {
		tmp = z * (y / t);
	} else if (z <= -1.2e+88) {
		tmp = t_2;
	} else if (z <= -1.26e+30) {
		tmp = t_1;
	} else if (z <= 1400.0) {
		tmp = x;
	} else if (z <= 3e+198) {
		tmp = t_1;
	} else if (z <= 3e+277) {
		tmp = t_2;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	t_2 = x * (-z / t)
	tmp = 0
	if z <= -6.1e+147:
		tmp = z * (y / t)
	elif z <= -1.2e+88:
		tmp = t_2
	elif z <= -1.26e+30:
		tmp = t_1
	elif z <= 1400.0:
		tmp = x
	elif z <= 3e+198:
		tmp = t_1
	elif z <= 3e+277:
		tmp = t_2
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	t_2 = Float64(x * Float64(Float64(-z) / t))
	tmp = 0.0
	if (z <= -6.1e+147)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= -1.2e+88)
		tmp = t_2;
	elseif (z <= -1.26e+30)
		tmp = t_1;
	elseif (z <= 1400.0)
		tmp = x;
	elseif (z <= 3e+198)
		tmp = t_1;
	elseif (z <= 3e+277)
		tmp = t_2;
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	t_2 = x * (-z / t);
	tmp = 0.0;
	if (z <= -6.1e+147)
		tmp = z * (y / t);
	elseif (z <= -1.2e+88)
		tmp = t_2;
	elseif (z <= -1.26e+30)
		tmp = t_1;
	elseif (z <= 1400.0)
		tmp = x;
	elseif (z <= 3e+198)
		tmp = t_1;
	elseif (z <= 3e+277)
		tmp = t_2;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.1e+147], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e+88], t$95$2, If[LessEqual[z, -1.26e+30], t$95$1, If[LessEqual[z, 1400.0], x, If[LessEqual[z, 3e+198], t$95$1, If[LessEqual[z, 3e+277], t$95$2, N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.10000000000000033e147

   1. Initial program 82.4%

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

   2. Taylor expanded in t around 0 76.6%

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

   3. Taylor expanded in y around inf 54.1%

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

      1. associate-*l/ 65.5%

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

      2. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   if -6.10000000000000033e147 < z < -1.2e88 or 3.00000000000000019e198 < z < 2.99999999999999981e277

   1. Initial program 94.0%

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

   2. Taylor expanded in t around 0 88.0%

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

   3. Taylor expanded in y around 0 66.8%

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

      1. associate-*r/ 66.8%

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

      2. mul-1-neg 66.8%

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

      3. distribute-rgt-neg-out 66.8%

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

      4. associate-*l/ 69.7%

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

   5. Simplified 69.7%

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

   if -1.2e88 < z < -1.26e30 or 1400 < z < 3.00000000000000019e198

   1. Initial program 90.6%

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

   2. Taylor expanded in t around 0 80.7%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. associate-*r/ 66.8%

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

   5. Simplified 66.8%

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

   if -1.26e30 < z < 1400

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 69.7%

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

   if 2.99999999999999981e277 < z

   1. Initial program 77.7%

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

   2. Taylor expanded in t around 0 77.7%

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

   3. Taylor expanded in y around inf 65.2%

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

      1. associate-*r/ 75.2%

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

   5. Simplified 75.2%

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

      1. clear-num 75.2%

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

      2. un-div-inv 75.6%

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

   7. Applied egg-rr 75.6%

      \[\leadsto \color{blue}{\frac{y}{\frac{t}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+147}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1400:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+277}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 3: 70.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-106} \lor \neg \left(z \leq 15.6\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2e-19)
   (* z (/ (- y x) t))
   (if (<= z -1.6e-67)
     x
     (if (or (<= z -1.85e-106) (not (<= z 15.6))) (* (- y x) (/ z t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e-19) {
		tmp = z * ((y - x) / t);
	} else if (z <= -1.6e-67) {
		tmp = x;
	} else if ((z <= -1.85e-106) || !(z <= 15.6)) {
		tmp = (y - x) * (z / 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 <= (-2d-19)) then
        tmp = z * ((y - x) / t)
    else if (z <= (-1.6d-67)) then
        tmp = x
    else if ((z <= (-1.85d-106)) .or. (.not. (z <= 15.6d0))) then
        tmp = (y - x) * (z / 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 <= -2e-19) {
		tmp = z * ((y - x) / t);
	} else if (z <= -1.6e-67) {
		tmp = x;
	} else if ((z <= -1.85e-106) || !(z <= 15.6)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2e-19:
		tmp = z * ((y - x) / t)
	elif z <= -1.6e-67:
		tmp = x
	elif (z <= -1.85e-106) or not (z <= 15.6):
		tmp = (y - x) * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2e-19)
		tmp = Float64(z * Float64(Float64(y - x) / t));
	elseif (z <= -1.6e-67)
		tmp = x;
	elseif ((z <= -1.85e-106) || !(z <= 15.6))
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2e-19)
		tmp = z * ((y - x) / t);
	elseif (z <= -1.6e-67)
		tmp = x;
	elseif ((z <= -1.85e-106) || ~((z <= 15.6)))
		tmp = (y - x) * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2e-19], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e-67], x, If[Or[LessEqual[z, -1.85e-106], N[Not[LessEqual[z, 15.6]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e-19

   1. Initial program 86.9%

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

   2. Taylor expanded in t around 0 77.1%

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

      1. associate-*l/ 99.7%

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

   4. Applied egg-rr 85.0%

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

   if -2e-19 < z < -1.60000000000000011e-67 or -1.8499999999999999e-106 < z < 15.5999999999999996

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 75.3%

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

   if -1.60000000000000011e-67 < z < -1.8499999999999999e-106 or 15.5999999999999996 < z

   1. Initial program 91.8%

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

   2. Taylor expanded in t around 0 82.0%

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

      1. *-commutative 82.0%

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

      2. associate-*l/ 85.3%

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

   4. Applied egg-rr 85.3%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-106} \lor \neg \left(z \leq 15.6\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 83.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-91}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+29)
   (* z (/ (- y x) t))
   (if (<= z -7e-91)
     (- x (* x (/ z t)))
     (if (<= z 1.6e+66) (+ x (/ (* y z) t)) (* (- y x) (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+29) {
		tmp = z * ((y - x) / t);
	} else if (z <= -7e-91) {
		tmp = x - (x * (z / t));
	} else if (z <= 1.6e+66) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.8d+29)) then
        tmp = z * ((y - x) / t)
    else if (z <= (-7d-91)) then
        tmp = x - (x * (z / t))
    else if (z <= 1.6d+66) then
        tmp = x + ((y * z) / t)
    else
        tmp = (y - x) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+29) {
		tmp = z * ((y - x) / t);
	} else if (z <= -7e-91) {
		tmp = x - (x * (z / t));
	} else if (z <= 1.6e+66) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+29:
		tmp = z * ((y - x) / t)
	elif z <= -7e-91:
		tmp = x - (x * (z / t))
	elif z <= 1.6e+66:
		tmp = x + ((y * z) / t)
	else:
		tmp = (y - x) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+29)
		tmp = Float64(z * Float64(Float64(y - x) / t));
	elseif (z <= -7e-91)
		tmp = Float64(x - Float64(x * Float64(z / t)));
	elseif (z <= 1.6e+66)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = Float64(Float64(y - x) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e+29)
		tmp = z * ((y - x) / t);
	elseif (z <= -7e-91)
		tmp = x - (x * (z / t));
	elseif (z <= 1.6e+66)
		tmp = x + ((y * z) / t);
	else
		tmp = (y - x) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+29], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e-91], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+66], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8e29

   1. Initial program 85.7%

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

   2. Taylor expanded in t around 0 78.6%

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

      1. associate-*l/ 99.7%

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

   4. Applied egg-rr 87.3%

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

   if -2.8e29 < z < -6.9999999999999997e-91

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. distribute-lft-in 87.2%

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

      3. *-rgt-identity 87.2%

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

      4. mul-1-neg 87.2%

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

      5. distribute-rgt-neg-in 87.2%

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

      6. unsub-neg 87.2%

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

   4. Simplified 87.2%

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

   if -6.9999999999999997e-91 < z < 1.6e66

   1. Initial program 98.0%

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

   2. Taylor expanded in y around inf 94.6%

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

      1. *-commutative 94.6%

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

   4. Simplified 94.6%

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

   if 1.6e66 < z

   1. Initial program 90.7%

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

   2. Taylor expanded in t around 0 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-*l/ 91.8%

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

   4. Applied egg-rr 91.8%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-91}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-91}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+68}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.65e+30)
   (* z (/ (- y x) t))
   (if (<= z -7.5e-91)
     (- x (* x (/ z t)))
     (if (<= z 2.8e+68) (+ x (/ (* y z) t)) (/ (- y x) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.65e+30) {
		tmp = z * ((y - x) / t);
	} else if (z <= -7.5e-91) {
		tmp = x - (x * (z / t));
	} else if (z <= 2.8e+68) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = (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 (z <= (-1.65d+30)) then
        tmp = z * ((y - x) / t)
    else if (z <= (-7.5d-91)) then
        tmp = x - (x * (z / t))
    else if (z <= 2.8d+68) then
        tmp = x + ((y * z) / t)
    else
        tmp = (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 (z <= -1.65e+30) {
		tmp = z * ((y - x) / t);
	} else if (z <= -7.5e-91) {
		tmp = x - (x * (z / t));
	} else if (z <= 2.8e+68) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = (y - x) / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.65e+30:
		tmp = z * ((y - x) / t)
	elif z <= -7.5e-91:
		tmp = x - (x * (z / t))
	elif z <= 2.8e+68:
		tmp = x + ((y * z) / t)
	else:
		tmp = (y - x) / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.65e+30)
		tmp = Float64(z * Float64(Float64(y - x) / t));
	elseif (z <= -7.5e-91)
		tmp = Float64(x - Float64(x * Float64(z / t)));
	elseif (z <= 2.8e+68)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = Float64(Float64(y - x) / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.65e+30)
		tmp = z * ((y - x) / t);
	elseif (z <= -7.5e-91)
		tmp = x - (x * (z / t));
	elseif (z <= 2.8e+68)
		tmp = x + ((y * z) / t);
	else
		tmp = (y - x) / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.65e+30], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-91], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+68], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.65000000000000013e30

   1. Initial program 85.7%

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

   2. Taylor expanded in t around 0 78.6%

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

      1. associate-*l/ 99.7%

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

   4. Applied egg-rr 87.3%

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

   if -1.65000000000000013e30 < z < -7.50000000000000051e-91

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. distribute-lft-in 87.2%

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

      3. *-rgt-identity 87.2%

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

      4. mul-1-neg 87.2%

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

      5. distribute-rgt-neg-in 87.2%

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

      6. unsub-neg 87.2%

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

   4. Simplified 87.2%

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

   if -7.50000000000000051e-91 < z < 2.8e68

   1. Initial program 98.0%

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

   2. Taylor expanded in y around inf 94.6%

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

      1. *-commutative 94.6%

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

   4. Simplified 94.6%

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

   if 2.8e68 < z

   1. Initial program 90.7%

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

   2. Taylor expanded in t around 0 87.4%

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

      1. associate-*l/ 96.6%

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

   4. Applied egg-rr 90.2%

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

   5. Taylor expanded in y around 0 71.8%

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

      1. associate-*r/ 68.4%

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

      2. +-commutative 68.4%

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

      3. mul-1-neg 68.4%

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

      4. associate-*r/ 71.5%

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

      5. unsub-neg 71.5%

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

      6. associate-*r/ 73.5%

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

      7. associate-/l* 71.6%

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

      8. *-commutative 71.6%

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

      9. associate-*l/ 68.5%

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

      10. associate-/l* 71.5%

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

      11. div-sub 91.9%

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

      12. associate-/l* 87.4%

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

      13. *-commutative 87.4%

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

      14. associate-/l* 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in z around 0 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-/l* 91.9%

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

   10. Simplified 91.9%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-91}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+68}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Alternative 6: 95.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-102} \lor \neg \left(z \leq 4.55 \cdot 10^{-159}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.25e-102) (not (<= z 4.55e-159)))
   (+ x (* z (/ (- y x) t)))
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.25e-102) || !(z <= 4.55e-159)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x + ((y * 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 ((z <= (-1.25d-102)) .or. (.not. (z <= 4.55d-159))) then
        tmp = x + (z * ((y - x) / t))
    else
        tmp = x + ((y * z) / 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-102) || !(z <= 4.55e-159)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.25e-102) or not (z <= 4.55e-159):
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.25e-102) || !(z <= 4.55e-159))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.25e-102) || ~((z <= 4.55e-159)))
		tmp = x + (z * ((y - x) / t));
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.25e-102], N[Not[LessEqual[z, 4.55e-159]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25000000000000006e-102 or 4.54999999999999998e-159 < z

   1. Initial program 91.4%

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

      1. associate-*l/ 97.2%

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

   3. Applied egg-rr 97.2%

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

   if -1.25000000000000006e-102 < z < 4.54999999999999998e-159

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 97.8%

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

      1. *-commutative 97.8%

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

   4. Simplified 97.8%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-102} \lor \neg \left(z \leq 4.55 \cdot 10^{-159}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]

Alternative 7: 71.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.24 \cdot 10^{+51}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.25e+57) x (if (<= t 1.24e+51) (* (- y x) (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.25e+57) {
		tmp = x;
	} else if (t <= 1.24e+51) {
		tmp = (y - x) * (z / 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 (t <= (-1.25d+57)) then
        tmp = x
    else if (t <= 1.24d+51) then
        tmp = (y - x) * (z / 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 (t <= -1.25e+57) {
		tmp = x;
	} else if (t <= 1.24e+51) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.25e+57:
		tmp = x
	elif t <= 1.24e+51:
		tmp = (y - x) * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.25e+57)
		tmp = x;
	elseif (t <= 1.24e+51)
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.25e+57)
		tmp = x;
	elseif (t <= 1.24e+51)
		tmp = (y - x) * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.25e+57], x, If[LessEqual[t, 1.24e+51], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.24999999999999993e57 or 1.24000000000000001e51 < t

   1. Initial program 87.9%

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

   2. Taylor expanded in z around 0 72.3%

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

   if -1.24999999999999993e57 < t < 1.24000000000000001e51

   1. Initial program 98.9%

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

   2. Taylor expanded in t around 0 82.8%

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

      1. *-commutative 82.8%

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

      2. associate-*l/ 81.1%

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

   4. Applied egg-rr 81.1%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.24 \cdot 10^{+51}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+69}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.35e+54)
   (* z (/ (- y x) t))
   (if (<= z 2.9e+69) (+ x (* y (/ z t))) (* (- y x) (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.35e+54) {
		tmp = z * ((y - x) / t);
	} else if (z <= 2.9e+69) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.35d+54)) then
        tmp = z * ((y - x) / t)
    else if (z <= 2.9d+69) then
        tmp = x + (y * (z / t))
    else
        tmp = (y - x) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.35e+54) {
		tmp = z * ((y - x) / t);
	} else if (z <= 2.9e+69) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.35e+54:
		tmp = z * ((y - x) / t)
	elif z <= 2.9e+69:
		tmp = x + (y * (z / t))
	else:
		tmp = (y - x) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.35e+54)
		tmp = Float64(z * Float64(Float64(y - x) / t));
	elseif (z <= 2.9e+69)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(y - x) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.35e+54)
		tmp = z * ((y - x) / t);
	elseif (z <= 2.9e+69)
		tmp = x + (y * (z / t));
	else
		tmp = (y - x) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.35e+54], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+69], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35000000000000005e54

   1. Initial program 84.5%

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

   2. Taylor expanded in t around 0 78.9%

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

      1. associate-*l/ 99.8%

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

   4. Applied egg-rr 88.3%

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

   if -1.35000000000000005e54 < z < 2.8999999999999998e69

   1. Initial program 98.3%

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

   2. Taylor expanded in y around inf 89.7%

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

      1. associate-*r/ 23.8%

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

   4. Simplified 88.1%

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

   if 2.8999999999999998e69 < z

   1. Initial program 90.7%

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

   2. Taylor expanded in t around 0 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-*l/ 91.8%

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

   4. Applied egg-rr 91.8%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+69}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]

Alternative 9: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.45e+53)
   (* z (/ (- y x) t))
   (if (<= z 1.8e+69) (+ x (/ (* y z) t)) (* (- y x) (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e+53) {
		tmp = z * ((y - x) / t);
	} else if (z <= 1.8e+69) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.45d+53)) then
        tmp = z * ((y - x) / t)
    else if (z <= 1.8d+69) then
        tmp = x + ((y * z) / t)
    else
        tmp = (y - x) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e+53) {
		tmp = z * ((y - x) / t);
	} else if (z <= 1.8e+69) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.45e+53:
		tmp = z * ((y - x) / t)
	elif z <= 1.8e+69:
		tmp = x + ((y * z) / t)
	else:
		tmp = (y - x) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.45e+53)
		tmp = Float64(z * Float64(Float64(y - x) / t));
	elseif (z <= 1.8e+69)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = Float64(Float64(y - x) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.45e+53)
		tmp = z * ((y - x) / t);
	elseif (z <= 1.8e+69)
		tmp = x + ((y * z) / t);
	else
		tmp = (y - x) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.45e+53], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+69], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4500000000000001e53

   1. Initial program 84.5%

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

   2. Taylor expanded in t around 0 78.9%

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

      1. associate-*l/ 99.8%

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

   4. Applied egg-rr 88.3%

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

   if -1.4500000000000001e53 < z < 1.8000000000000001e69

   1. Initial program 98.3%

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

   2. Taylor expanded in y around inf 89.7%

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

      1. *-commutative 89.7%

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

   4. Simplified 89.7%

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

   if 1.8000000000000001e69 < z

   1. Initial program 90.7%

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

   2. Taylor expanded in t around 0 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-*l/ 91.8%

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

   4. Applied egg-rr 91.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]

Alternative 10: 55.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+29} \lor \neg \left(z \leq 360\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.2e+29) (not (<= z 360.0))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e+29) || !(z <= 360.0)) {
		tmp = y * (z / 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 <= (-2.2d+29)) .or. (.not. (z <= 360.0d0))) then
        tmp = y * (z / 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 <= -2.2e+29) || !(z <= 360.0)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e+29) or not (z <= 360.0):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e+29) || !(z <= 360.0))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.2e+29) || ~((z <= 360.0)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.2e+29], N[Not[LessEqual[z, 360.0]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e29 or 360 < z

   1. Initial program 88.4%

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

   2. Taylor expanded in t around 0 81.3%

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

   3. Taylor expanded in y around inf 53.7%

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

      1. associate-*r/ 59.5%

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

   5. Simplified 59.5%

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

   if -2.2000000000000001e29 < z < 360

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 69.7%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+29} \lor \neg \left(z \leq 360\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 55.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 3600:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e+30) (* z (/ y t)) (if (<= z 3600.0) x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+30) {
		tmp = z * (y / t);
	} else if (z <= 3600.0) {
		tmp = x;
	} else {
		tmp = y * (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 (z <= (-1.6d+30)) then
        tmp = z * (y / t)
    else if (z <= 3600.0d0) then
        tmp = x
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+30) {
		tmp = z * (y / t);
	} else if (z <= 3600.0) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e+30:
		tmp = z * (y / t)
	elif z <= 3600.0:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e+30)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 3600.0)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e+30)
		tmp = z * (y / t);
	elseif (z <= 3600.0)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e+30], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3600.0], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.59999999999999986e30

   1. Initial program 85.7%

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

   2. Taylor expanded in t around 0 78.6%

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

   3. Taylor expanded in y around inf 46.8%

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

      1. associate-*l/ 55.5%

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

      2. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   if -1.59999999999999986e30 < z < 3600

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 69.7%

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

   if 3600 < z

   1. Initial program 90.6%

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

   2. Taylor expanded in t around 0 83.4%

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

   3. Taylor expanded in y around inf 59.1%

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

      1. associate-*r/ 63.0%

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

   5. Simplified 63.0%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 3600:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 12: 55.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.7e+30) (* z (/ y t)) (if (<= z 550.0) x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e+30) {
		tmp = z * (y / t);
	} else if (z <= 550.0) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.7d+30)) then
        tmp = z * (y / t)
    else if (z <= 550.0d0) then
        tmp = x
    else
        tmp = y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e+30) {
		tmp = z * (y / t);
	} else if (z <= 550.0) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.7e+30:
		tmp = z * (y / t)
	elif z <= 550.0:
		tmp = x
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.7e+30)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 550.0)
		tmp = x;
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.7e+30)
		tmp = z * (y / t);
	elseif (z <= 550.0)
		tmp = x;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.7e+30], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 550.0], x, N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7000000000000001e30

   1. Initial program 85.7%

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

   2. Taylor expanded in t around 0 78.6%

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

   3. Taylor expanded in y around inf 46.8%

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

      1. associate-*l/ 55.5%

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

      2. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   if -1.7000000000000001e30 < z < 550

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 69.7%

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

   if 550 < z

   1. Initial program 90.6%

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

   2. Taylor expanded in t around 0 83.4%

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

   3. Taylor expanded in y around inf 59.1%

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

      1. associate-*r/ 63.0%

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

   5. Simplified 63.0%

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

      1. clear-num 63.0%

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

      2. un-div-inv 63.1%

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

   7. Applied egg-rr 63.1%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 13: 97.6% 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 93.9%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

4. Final simplification 97.7%

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

Alternative 14: 38.8% 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 93.9%

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

2. Taylor expanded in z around 0 42.7%

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

3. Final simplification 42.7%

   \[\leadsto x \]

Developer target: 97.7% accurate, 0.7× 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 2023181 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (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)))