Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.6% → 97.6%

Time: 7.6s

Alternatives: 9

Speedup: 1.0×

• 24.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.6% 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: 97.6% 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 92.5%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

   1. clear-num 98.7%

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

   2. un-div-inv 98.8%

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

6. Applied egg-rr 98.8%

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

7. Final simplification 98.8%

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

Alternative 2: 71.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ t_2 := \frac{y \cdot z}{t}\\ t_3 := x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-6}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 3500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+53}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+118}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+216}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))) (t_2 (/ (* y z) t)) (t_3 (* x (- 1.0 (/ z t)))))
   (if (<= y -2.05e+125)
     t_2
     (if (<= y 4e-6)
       t_3
       (if (<= y 3500.0)
         t_1
         (if (<= y 4.4e+53)
           t_3
           (if (<= y 6.4e+118) t_2 (if (<= y 1.3e+216) t_3 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double t_2 = (y * z) / t;
	double t_3 = x * (1.0 - (z / t));
	double tmp;
	if (y <= -2.05e+125) {
		tmp = t_2;
	} else if (y <= 4e-6) {
		tmp = t_3;
	} else if (y <= 3500.0) {
		tmp = t_1;
	} else if (y <= 4.4e+53) {
		tmp = t_3;
	} else if (y <= 6.4e+118) {
		tmp = t_2;
	} else if (y <= 1.3e+216) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (z / t)
    t_2 = (y * z) / t
    t_3 = x * (1.0d0 - (z / t))
    if (y <= (-2.05d+125)) then
        tmp = t_2
    else if (y <= 4d-6) then
        tmp = t_3
    else if (y <= 3500.0d0) then
        tmp = t_1
    else if (y <= 4.4d+53) then
        tmp = t_3
    else if (y <= 6.4d+118) then
        tmp = t_2
    else if (y <= 1.3d+216) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double t_2 = (y * z) / t;
	double t_3 = x * (1.0 - (z / t));
	double tmp;
	if (y <= -2.05e+125) {
		tmp = t_2;
	} else if (y <= 4e-6) {
		tmp = t_3;
	} else if (y <= 3500.0) {
		tmp = t_1;
	} else if (y <= 4.4e+53) {
		tmp = t_3;
	} else if (y <= 6.4e+118) {
		tmp = t_2;
	} else if (y <= 1.3e+216) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	t_2 = (y * z) / t
	t_3 = x * (1.0 - (z / t))
	tmp = 0
	if y <= -2.05e+125:
		tmp = t_2
	elif y <= 4e-6:
		tmp = t_3
	elif y <= 3500.0:
		tmp = t_1
	elif y <= 4.4e+53:
		tmp = t_3
	elif y <= 6.4e+118:
		tmp = t_2
	elif y <= 1.3e+216:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	t_2 = Float64(Float64(y * z) / t)
	t_3 = Float64(x * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (y <= -2.05e+125)
		tmp = t_2;
	elseif (y <= 4e-6)
		tmp = t_3;
	elseif (y <= 3500.0)
		tmp = t_1;
	elseif (y <= 4.4e+53)
		tmp = t_3;
	elseif (y <= 6.4e+118)
		tmp = t_2;
	elseif (y <= 1.3e+216)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	t_2 = (y * z) / t;
	t_3 = x * (1.0 - (z / t));
	tmp = 0.0;
	if (y <= -2.05e+125)
		tmp = t_2;
	elseif (y <= 4e-6)
		tmp = t_3;
	elseif (y <= 3500.0)
		tmp = t_1;
	elseif (y <= 4.4e+53)
		tmp = t_3;
	elseif (y <= 6.4e+118)
		tmp = t_2;
	elseif (y <= 1.3e+216)
		tmp = t_3;
	else
		tmp = t_1;
	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[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.05e+125], t$95$2, If[LessEqual[y, 4e-6], t$95$3, If[LessEqual[y, 3500.0], t$95$1, If[LessEqual[y, 4.4e+53], t$95$3, If[LessEqual[y, 6.4e+118], t$95$2, If[LessEqual[y, 1.3e+216], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.04999999999999996e125 or 4.39999999999999997e53 < y < 6.40000000000000032e118

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 64.5%

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

   6. Taylor expanded in y around inf 62.6%

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

      1. associate-*r/ 73.9%

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

   8. Applied egg-rr 73.9%

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

   if -2.04999999999999996e125 < y < 3.99999999999999982e-6 or 3500 < y < 4.39999999999999997e53 or 6.40000000000000032e118 < y < 1.2999999999999999e216

   1. Initial program 92.7%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around inf 82.4%

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

      1. mul-1-neg 82.4%

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

      2. unsub-neg 82.4%

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

   7. Simplified 82.4%

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

   if 3.99999999999999982e-6 < y < 3500 or 1.2999999999999999e216 < y

   1. Initial program 77.4%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 79.9%

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

   6. Taylor expanded in y around inf 83.4%

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

      1. clear-num 83.4%

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

      2. un-div-inv 83.4%

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

   8. Applied egg-rr 83.4%

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

   9. Taylor expanded in z around 0 67.3%

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

       1. associate-*r/ 86.4%

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

       2. *-commutative 86.4%

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

   11. Simplified 86.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+125}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;y \leq 3500:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+118}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+216}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+233} \lor \neg \left(z \leq 1.85 \cdot 10^{+282}\right):\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= z -5.2e-78)
     t_1
     (if (<= z 8.5e+34)
       x
       (if (or (<= z 1.15e+233) (not (<= z 1.85e+282)))
         (* x (/ z (- t)))
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (z <= -5.2e-78) {
		tmp = t_1;
	} else if (z <= 8.5e+34) {
		tmp = x;
	} else if ((z <= 1.15e+233) || !(z <= 1.85e+282)) {
		tmp = x * (z / -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if (z <= (-5.2d-78)) then
        tmp = t_1
    else if (z <= 8.5d+34) then
        tmp = x
    else if ((z <= 1.15d+233) .or. (.not. (z <= 1.85d+282))) then
        tmp = x * (z / -t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (z <= -5.2e-78) {
		tmp = t_1;
	} else if (z <= 8.5e+34) {
		tmp = x;
	} else if ((z <= 1.15e+233) || !(z <= 1.85e+282)) {
		tmp = x * (z / -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if z <= -5.2e-78:
		tmp = t_1
	elif z <= 8.5e+34:
		tmp = x
	elif (z <= 1.15e+233) or not (z <= 1.85e+282):
		tmp = x * (z / -t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (z <= -5.2e-78)
		tmp = t_1;
	elseif (z <= 8.5e+34)
		tmp = x;
	elseif ((z <= 1.15e+233) || !(z <= 1.85e+282))
		tmp = Float64(x * Float64(z / Float64(-t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (z <= -5.2e-78)
		tmp = t_1;
	elseif (z <= 8.5e+34)
		tmp = x;
	elseif ((z <= 1.15e+233) || ~((z <= 1.85e+282)))
		tmp = x * (z / -t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e-78], t$95$1, If[LessEqual[z, 8.5e+34], x, If[Or[LessEqual[z, 1.15e+233], N[Not[LessEqual[z, 1.85e+282]], $MachinePrecision]], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2000000000000002e-78 or 1.15e233 < z < 1.8500000000000001e282

   1. Initial program 90.7%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in z around inf 74.9%

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

   6. Taylor expanded in y around inf 55.2%

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

      1. clear-num 55.2%

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

      2. un-div-inv 55.2%

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

   8. Applied egg-rr 55.2%

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

   9. Taylor expanded in z around 0 55.3%

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

       1. associate-*r/ 60.4%

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

       2. *-commutative 60.4%

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

   11. Simplified 60.4%

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

   if -5.2000000000000002e-78 < z < 8.5000000000000003e34

   1. Initial program 97.4%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 z around 0 58.1%

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

   if 8.5000000000000003e34 < z < 1.15e233 or 1.8500000000000001e282 < z

   1. Initial program 83.3%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 74.7%

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

      1. mul-1-neg 74.7%

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

      2. unsub-neg 74.7%

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

   7. Simplified 74.7%

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

   8. Taylor expanded in z around inf 54.7%

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

      1. associate-*r/ 54.7%

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

      2. neg-mul-1 54.7%

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

      3. distribute-rgt-neg-in 54.7%

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

      4. associate-/l* 58.9%

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

   10. Simplified 58.9%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+233} \lor \neg \left(z \leq 1.85 \cdot 10^{+282}\right):\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+234}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+284}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= z -7.8e-79)
     t_1
     (if (<= z 1.35e+37)
       x
       (if (<= z 4.5e+234)
         (* z (- (/ x t)))
         (if (<= z 1.15e+284) t_1 (* x (/ z (- t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (z <= -7.8e-79) {
		tmp = t_1;
	} else if (z <= 1.35e+37) {
		tmp = x;
	} else if (z <= 4.5e+234) {
		tmp = z * -(x / t);
	} else if (z <= 1.15e+284) {
		tmp = t_1;
	} else {
		tmp = x * (z / -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if (z <= (-7.8d-79)) then
        tmp = t_1
    else if (z <= 1.35d+37) then
        tmp = x
    else if (z <= 4.5d+234) then
        tmp = z * -(x / t)
    else if (z <= 1.15d+284) then
        tmp = t_1
    else
        tmp = x * (z / -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (z <= -7.8e-79) {
		tmp = t_1;
	} else if (z <= 1.35e+37) {
		tmp = x;
	} else if (z <= 4.5e+234) {
		tmp = z * -(x / t);
	} else if (z <= 1.15e+284) {
		tmp = t_1;
	} else {
		tmp = x * (z / -t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if z <= -7.8e-79:
		tmp = t_1
	elif z <= 1.35e+37:
		tmp = x
	elif z <= 4.5e+234:
		tmp = z * -(x / t)
	elif z <= 1.15e+284:
		tmp = t_1
	else:
		tmp = x * (z / -t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (z <= -7.8e-79)
		tmp = t_1;
	elseif (z <= 1.35e+37)
		tmp = x;
	elseif (z <= 4.5e+234)
		tmp = Float64(z * Float64(-Float64(x / t)));
	elseif (z <= 1.15e+284)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(z / Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (z <= -7.8e-79)
		tmp = t_1;
	elseif (z <= 1.35e+37)
		tmp = x;
	elseif (z <= 4.5e+234)
		tmp = z * -(x / t);
	elseif (z <= 1.15e+284)
		tmp = t_1;
	else
		tmp = x * (z / -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e-79], t$95$1, If[LessEqual[z, 1.35e+37], x, If[LessEqual[z, 4.5e+234], N[(z * (-N[(x / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 1.15e+284], t$95$1, N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.80000000000000011e-79 or 4.49999999999999982e234 < z < 1.14999999999999992e284

   1. Initial program 90.7%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in z around inf 74.9%

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

   6. Taylor expanded in y around inf 55.2%

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

      1. clear-num 55.2%

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

      2. un-div-inv 55.2%

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

   8. Applied egg-rr 55.2%

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

   9. Taylor expanded in z around 0 55.3%

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

       1. associate-*r/ 60.4%

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

       2. *-commutative 60.4%

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

   11. Simplified 60.4%

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

   if -7.80000000000000011e-79 < z < 1.34999999999999993e37

   1. Initial program 97.4%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 z around 0 58.1%

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

   if 1.34999999999999993e37 < z < 4.49999999999999982e234

   1. Initial program 81.2%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around inf 82.0%

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

   6. Taylor expanded in y around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. distribute-frac-neg2 58.5%

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

   8. Simplified 58.5%

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

   if 1.14999999999999992e284 < z

   1. Initial program 99.7%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

   7. Simplified 80.0%

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

   8. Taylor expanded in z around inf 79.7%

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

      1. associate-*r/ 79.7%

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

      2. neg-mul-1 79.7%

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

      3. distribute-rgt-neg-in 79.7%

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

      4. associate-/l* 80.0%

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

   10. Simplified 80.0%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+234}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+284}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-54} \lor \neg \left(y \leq 2 \cdot 10^{-42}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.25e-54) (not (<= y 2e-42)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.25e-54) || !(y <= 2e-42)) {
		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 <= (-2.25d-54)) .or. (.not. (y <= 2d-42))) 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 <= -2.25e-54) || !(y <= 2e-42)) {
		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 <= -2.25e-54) or not (y <= 2e-42):
		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 <= -2.25e-54) || !(y <= 2e-42))
		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 <= -2.25e-54) || ~((y <= 2e-42)))
		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, -2.25e-54], N[Not[LessEqual[y, 2e-42]], $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 < -2.2499999999999999e-54 or 2.00000000000000008e-42 < y

   1. Initial program 94.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 83.8%

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

      1. associate-*r/ 88.2%

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

   7. Simplified 88.2%

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

   if -2.2499999999999999e-54 < y < 2.00000000000000008e-42

   1. Initial program 90.1%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 89.4%

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

      1. mul-1-neg 89.4%

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

      2. unsub-neg 89.4%

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

   7. Simplified 89.4%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-54} \lor \neg \left(y \leq 2 \cdot 10^{-42}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.02e-31) x (if (<= x 4.2e+53) (* z (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.02e-31) {
		tmp = x;
	} else if (x <= 4.2e+53) {
		tmp = z * (y / 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 (x <= (-1.02d-31)) then
        tmp = x
    else if (x <= 4.2d+53) then
        tmp = z * (y / 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 (x <= -1.02e-31) {
		tmp = x;
	} else if (x <= 4.2e+53) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.02e-31:
		tmp = x
	elif x <= 4.2e+53:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.02e-31)
		tmp = x;
	elseif (x <= 4.2e+53)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.02e-31)
		tmp = x;
	elseif (x <= 4.2e+53)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.02e-31], x, If[LessEqual[x, 4.2e+53], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.01999999999999999e-31 or 4.2000000000000004e53 < x

   1. Initial program 90.1%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 z around 0 51.9%

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

   if -1.01999999999999999e-31 < x < 4.2000000000000004e53

   1. Initial program 94.7%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around inf 71.2%

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

   6. Taylor expanded in y around inf 55.0%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+132}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.6e-30) x (if (<= x 6.2e+132) (* y (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.6e-30) {
		tmp = x;
	} else if (x <= 6.2e+132) {
		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 (x <= (-8.6d-30)) then
        tmp = x
    else if (x <= 6.2d+132) 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 (x <= -8.6e-30) {
		tmp = x;
	} else if (x <= 6.2e+132) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.6e-30:
		tmp = x
	elif x <= 6.2e+132:
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.6e-30)
		tmp = x;
	elseif (x <= 6.2e+132)
		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 (x <= -8.6e-30)
		tmp = x;
	elseif (x <= 6.2e+132)
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.6e-30], x, If[LessEqual[x, 6.2e+132], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.59999999999999932e-30 or 6.1999999999999995e132 < x

   1. Initial program 91.3%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   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 z around 0 54.5%

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

   if -8.59999999999999932e-30 < x < 6.1999999999999995e132

   1. Initial program 93.3%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around inf 69.8%

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

   6. Taylor expanded in y around inf 52.0%

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

      1. clear-num 52.0%

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

      2. un-div-inv 52.0%

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

   8. Applied egg-rr 52.0%

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

   9. Taylor expanded in z around 0 54.0%

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

       1. associate-*r/ 59.8%

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

       2. *-commutative 59.8%

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

   11. Simplified 59.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+132}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.5% accurate, 1.0× speedup

Math

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

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(y - x) * Float64(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[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.5%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 9: 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 92.5%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

5. Taylor expanded in z around 0 37.0%

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

6. Final simplification 37.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.6% 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 2024054 
(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)))