System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2

Percentage Accurate: 60.8% → 98.3%

Time: 22.0s

Alternatives: 8

Speedup: 211.0×

• could not determine a ground truth

  1. x = 6.43635400331616e+251
  2. y = 7.084566377026072e+45
  3. z = 9.233280192186823e+98
  4. t = -1468880603.7417562

Specification

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t) {
	return x - (Math.log(((1.0 - y) + (y * Math.exp(z)))) / t);
}

Python

def code(x, y, z, t):
	return x - (math.log(((1.0 - y) + (y * math.exp(z)))) / t)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t) {
	return x - (Math.log(((1.0 - y) + (y * Math.exp(z)))) / t);
}

Python

def code(x, y, z, t):
	return x - (math.log(((1.0 - y) + (y * math.exp(z)))) / t)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- x (/ (log1p (* y (expm1 z))) t)))

C

double code(double x, double y, double z, double t) {
	return x - (log1p((y * expm1(z))) / t);
}

Java

public static double code(double x, double y, double z, double t) {
	return x - (Math.log1p((y * Math.expm1(z))) / t);
}

Python

def code(x, y, z, t):
	return x - (math.log1p((y * math.expm1(z))) / t)

Julia

function code(x, y, z, t)
	return Float64(x - Float64(log1p(Float64(y * expm1(z))) / t))
end

Wolfram

code[x_, y_, z_, t_] := N[(x - N[(N[Log[1 + N[(y * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 60.7%

   \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 93.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+18}:\\ \;\;\;\;x - \frac{1}{\frac{\left(0.5 \cdot t\right) \cdot y + \frac{t}{\mathsf{expm1}\left(z\right)}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(\left(1 + z \cdot 0.5\right) \cdot \left(y \cdot z\right)\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.95e+18)
   (- x (/ 1.0 (/ (+ (* (* 0.5 t) y) (/ t (expm1 z))) y)))
   (- x (/ (log1p (* (+ 1.0 (* z 0.5)) (* y z))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.95e+18) {
		tmp = x - (1.0 / ((((0.5 * t) * y) + (t / expm1(z))) / y));
	} else {
		tmp = x - (log1p(((1.0 + (z * 0.5)) * (y * z))) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.95e+18) {
		tmp = x - (1.0 / ((((0.5 * t) * y) + (t / Math.expm1(z))) / y));
	} else {
		tmp = x - (Math.log1p(((1.0 + (z * 0.5)) * (y * z))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.95e+18:
		tmp = x - (1.0 / ((((0.5 * t) * y) + (t / math.expm1(z))) / y))
	else:
		tmp = x - (math.log1p(((1.0 + (z * 0.5)) * (y * z))) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.95e+18)
		tmp = Float64(x - Float64(1.0 / Float64(Float64(Float64(Float64(0.5 * t) * y) + Float64(t / expm1(z))) / y)));
	else
		tmp = Float64(x - Float64(log1p(Float64(Float64(1.0 + Float64(z * 0.5)) * Float64(y * z))) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.95e+18], N[(x - N[(1.0 / N[(N[(N[(N[(0.5 * t), $MachinePrecision] * y), $MachinePrecision] + N[(t / N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[1 + N[(N[(1.0 + N[(z * 0.5), $MachinePrecision]), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e18

   1. Initial program 85.3%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   if -1.95e18 < z

   1. Initial program 49.9%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 90.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+55}:\\ \;\;\;\;x - \frac{y \cdot \mathsf{expm1}\left(z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(y \cdot z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7e+55) (- x (/ (* y (expm1 z)) t)) (- x (/ (log1p (* y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7e+55) {
		tmp = x - ((y * expm1(z)) / t);
	} else {
		tmp = x - (log1p((y * z)) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7e+55) {
		tmp = x - ((y * Math.expm1(z)) / t);
	} else {
		tmp = x - (Math.log1p((y * z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7e+55:
		tmp = x - ((y * math.expm1(z)) / t)
	else:
		tmp = x - (math.log1p((y * z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7e+55)
		tmp = Float64(x - Float64(Float64(y * expm1(z)) / t));
	else
		tmp = Float64(x - Float64(log1p(Float64(y * z)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7e+55], N[(x - N[(N[(y * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[1 + N[(y * z), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.00000000000000021e55

   1. Initial program 84.3%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -7.00000000000000021e55 < z

   1. Initial program 51.2%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 87.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+54}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{-0.5}{y} \cdot \frac{\left(z \cdot \left(y - y \cdot y\right)\right) \cdot t}{y} + \frac{t}{y}}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(y \cdot z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.6e+54)
   (-
    x
    (/ 1.0 (/ (+ (* (/ -0.5 y) (/ (* (* z (- y (* y y))) t) y)) (/ t y)) z)))
   (- x (/ (log1p (* y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.6e+54) {
		tmp = x - (1.0 / ((((-0.5 / y) * (((z * (y - (y * y))) * t) / y)) + (t / y)) / z));
	} else {
		tmp = x - (log1p((y * z)) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.6e+54) {
		tmp = x - (1.0 / ((((-0.5 / y) * (((z * (y - (y * y))) * t) / y)) + (t / y)) / z));
	} else {
		tmp = x - (Math.log1p((y * z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.6e+54:
		tmp = x - (1.0 / ((((-0.5 / y) * (((z * (y - (y * y))) * t) / y)) + (t / y)) / z))
	else:
		tmp = x - (math.log1p((y * z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.6e+54)
		tmp = Float64(x - Float64(1.0 / Float64(Float64(Float64(Float64(-0.5 / y) * Float64(Float64(Float64(z * Float64(y - Float64(y * y))) * t) / y)) + Float64(t / y)) / z)));
	else
		tmp = Float64(x - Float64(log1p(Float64(y * z)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.6e+54], N[(x - N[(1.0 / N[(N[(N[(N[(-0.5 / y), $MachinePrecision] * N[(N[(N[(z * N[(y - N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[1 + N[(y * z), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.59999999999999993e54

   1. Initial program 84.5%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   if -9.59999999999999993e54 < z

   1. Initial program 51.0%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 83.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-178}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{-0.5}{y} \cdot \frac{\left(z \cdot \left(y - y \cdot y\right)\right) \cdot t}{y} + \frac{t}{y}}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(z \cdot \left(\frac{z \cdot 0.5}{t} + \frac{1}{t}\right) + \left(-0.5 \cdot y\right) \cdot \frac{z \cdot z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9e-178)
   (-
    x
    (/ 1.0 (/ (+ (* (/ -0.5 y) (/ (* (* z (- y (* y y))) t) y)) (/ t y)) z)))
   (-
    x
    (*
     y
     (+ (* z (+ (/ (* z 0.5) t) (/ 1.0 t))) (* (* -0.5 y) (/ (* z z) t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9e-178) {
		tmp = x - (1.0 / ((((-0.5 / y) * (((z * (y - (y * y))) * t) / y)) + (t / y)) / z));
	} else {
		tmp = x - (y * ((z * (((z * 0.5) / t) + (1.0 / t))) + ((-0.5 * y) * ((z * 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 <= (-9d-178)) then
        tmp = x - (1.0d0 / (((((-0.5d0) / y) * (((z * (y - (y * y))) * t) / y)) + (t / y)) / z))
    else
        tmp = x - (y * ((z * (((z * 0.5d0) / t) + (1.0d0 / t))) + (((-0.5d0) * y) * ((z * 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 <= -9e-178) {
		tmp = x - (1.0 / ((((-0.5 / y) * (((z * (y - (y * y))) * t) / y)) + (t / y)) / z));
	} else {
		tmp = x - (y * ((z * (((z * 0.5) / t) + (1.0 / t))) + ((-0.5 * y) * ((z * z) / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9e-178:
		tmp = x - (1.0 / ((((-0.5 / y) * (((z * (y - (y * y))) * t) / y)) + (t / y)) / z))
	else:
		tmp = x - (y * ((z * (((z * 0.5) / t) + (1.0 / t))) + ((-0.5 * y) * ((z * z) / t))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9e-178)
		tmp = Float64(x - Float64(1.0 / Float64(Float64(Float64(Float64(-0.5 / y) * Float64(Float64(Float64(z * Float64(y - Float64(y * y))) * t) / y)) + Float64(t / y)) / z)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(z * Float64(Float64(Float64(z * 0.5) / t) + Float64(1.0 / t))) + Float64(Float64(-0.5 * y) * Float64(Float64(z * z) / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9e-178)
		tmp = x - (1.0 / ((((-0.5 / y) * (((z * (y - (y * y))) * t) / y)) + (t / y)) / z));
	else
		tmp = x - (y * ((z * (((z * 0.5) / t) + (1.0 / t))) + ((-0.5 * y) * ((z * z) / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9e-178], N[(x - N[(1.0 / N[(N[(N[(N[(-0.5 / y), $MachinePrecision] * N[(N[(N[(z * N[(y - N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(z * N[(N[(N[(z * 0.5), $MachinePrecision] / t), $MachinePrecision] + N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-0.5 * y), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999957e-178

   1. Initial program 76.3%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   if -8.99999999999999957e-178 < z

   1. Initial program 44.5%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 80.8% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(z \cdot \left(\frac{z \cdot 0.5}{t} + \frac{1}{t}\right) + \left(-0.5 \cdot y\right) \cdot \frac{z \cdot z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.26e-76)
   x
   (-
    x
    (*
     y
     (+ (* z (+ (/ (* z 0.5) t) (/ 1.0 t))) (* (* -0.5 y) (/ (* z z) t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.26e-76) {
		tmp = x;
	} else {
		tmp = x - (y * ((z * (((z * 0.5) / t) + (1.0 / t))) + ((-0.5 * y) * ((z * 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 <= (-1.26d-76)) then
        tmp = x
    else
        tmp = x - (y * ((z * (((z * 0.5d0) / t) + (1.0d0 / t))) + (((-0.5d0) * y) * ((z * 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 <= -1.26e-76) {
		tmp = x;
	} else {
		tmp = x - (y * ((z * (((z * 0.5) / t) + (1.0 / t))) + ((-0.5 * y) * ((z * z) / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.26e-76:
		tmp = x
	else:
		tmp = x - (y * ((z * (((z * 0.5) / t) + (1.0 / t))) + ((-0.5 * y) * ((z * z) / t))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.26e-76)
		tmp = x;
	else
		tmp = Float64(x - Float64(y * Float64(Float64(z * Float64(Float64(Float64(z * 0.5) / t) + Float64(1.0 / t))) + Float64(Float64(-0.5 * y) * Float64(Float64(z * z) / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.26e-76)
		tmp = x;
	else
		tmp = x - (y * ((z * (((z * 0.5) / t) + (1.0 / t))) + ((-0.5 * y) * ((z * z) / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.26e-76], x, N[(x - N[(y * N[(N[(z * N[(N[(N[(z * 0.5), $MachinePrecision] / t), $MachinePrecision] + N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-0.5 * y), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.26e-76

   1. Initial program 79.2%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.26e-76 < z

   1. Initial program 48.0%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 81.2% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.2e-77) x (- x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.2e-77) {
		tmp = x;
	} 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 <= (-9.2d-77)) then
        tmp = x
    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 <= -9.2e-77) {
		tmp = x;
	} else {
		tmp = x - (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.2e-77:
		tmp = x
	else:
		tmp = x - (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.2e-77)
		tmp = x;
	else
		tmp = Float64(x - Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.2e-77)
		tmp = x;
	else
		tmp = x - (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.2e-77], x, N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.19999999999999994e-77

   1. Initial program 79.2%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -9.19999999999999994e-77 < z

   1. Initial program 48.0%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 70.9% accurate, 211.0× 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 60.7%

   \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in x around inf 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Developer target: 73.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-0.5}{y \cdot t}\\ \mathbf{if}\;z < -2.8874623088207947 \cdot 10^{+119}:\\ \;\;\;\;\left(x - \frac{t\_1}{z \cdot z}\right) - t\_1 \cdot \frac{\frac{2}{z}}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log \left(1 + z \cdot y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- 0.5) (* y t))))
   (if (< z -2.8874623088207947e+119)
     (- (- x (/ t_1 (* z z))) (* t_1 (/ (/ 2.0 z) (* z z))))
     (- x (/ (log (+ 1.0 (* z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.5 / (y * t);
	double tmp;
	if (z < -2.8874623088207947e+119) {
		tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z)));
	} else {
		tmp = x - (log((1.0 + (z * y))) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -0.5d0 / (y * t)
    if (z < (-2.8874623088207947d+119)) then
        tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0d0 / z) / (z * z)))
    else
        tmp = x - (log((1.0d0 + (z * y))) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -0.5 / (y * t);
	double tmp;
	if (z < -2.8874623088207947e+119) {
		tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z)));
	} else {
		tmp = x - (Math.log((1.0 + (z * y))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.5 / (y * t)
	tmp = 0
	if z < -2.8874623088207947e+119:
		tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z)))
	else:
		tmp = x - (math.log((1.0 + (z * y))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-0.5) / Float64(y * t))
	tmp = 0.0
	if (z < -2.8874623088207947e+119)
		tmp = Float64(Float64(x - Float64(t_1 / Float64(z * z))) - Float64(t_1 * Float64(Float64(2.0 / z) / Float64(z * z))));
	else
		tmp = Float64(x - Float64(log(Float64(1.0 + Float64(z * y))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.5 / (y * t);
	tmp = 0.0;
	if (z < -2.8874623088207947e+119)
		tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z)));
	else
		tmp = x - (log((1.0 + (z * y))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-0.5) / N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -2.8874623088207947e+119], N[(N[(x - N[(t$95$1 / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(N[(2.0 / z), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z t)
  :name "System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2"
  :precision binary64

  :alt
  (if (< z -2.8874623088207947e+119) (- (- x (/ (/ (- 0.5) (* y t)) (* z z))) (* (/ (- 0.5) (* y t)) (/ (/ 2.0 z) (* z z)))) (- x (/ (log (+ 1.0 (* z y))) t)))

  (- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))