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

Percentage Accurate: 60.7% → 93.9%

Time: 8.3s

Alternatives: 8

Speedup: 31.2×

• could not determine a ground truth

  1. x = 2.8738365213501226e+279
  2. y = 4.2363101666432e+205
  3. z = 3.465177896353189e+171
  4. t = -4.551850950398727e+211

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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: 60.7% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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: 93.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}{t}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+65}:\\ \;\;\;\;x - \mathsf{fma}\left(-0.5, \frac{\left(\mathsf{expm1}\left(z\right) \cdot \mathsf{expm1}\left(z\right)\right) \cdot y}{t}, \frac{\mathsf{expm1}\left(z\right)}{t}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (log (fma (expm1 z) y 1.0)) t))))
   (if (<= y -1.65e+17)
     t_1
     (if (<= y 6e+65)
       (-
        x
        (* (fma -0.5 (/ (* (* (expm1 z) (expm1 z)) y) t) (/ (expm1 z) t)) y))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (log(fma(expm1(z), y, 1.0)) / t);
	double tmp;
	if (y <= -1.65e+17) {
		tmp = t_1;
	} else if (y <= 6e+65) {
		tmp = x - (fma(-0.5, (((expm1(z) * expm1(z)) * y) / t), (expm1(z) / t)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(log(fma(expm1(z), y, 1.0)) / t))
	tmp = 0.0
	if (y <= -1.65e+17)
		tmp = t_1;
	elseif (y <= 6e+65)
		tmp = Float64(x - Float64(fma(-0.5, Float64(Float64(Float64(expm1(z) * expm1(z)) * y) / t), Float64(expm1(z) / t)) * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[Log[N[(N[(Exp[z] - 1), $MachinePrecision] * y + 1.0), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+17], t$95$1, If[LessEqual[y, 6e+65], N[(x - N[(N[(-0.5 * N[(N[(N[(N[(Exp[z] - 1), $MachinePrecision] * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision] + N[(N[(Exp[z] - 1), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e17 or 6.0000000000000004e65 < y

   1. Initial program 30.1%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-expm1.f64 84.9

         \[\leadsto x - \frac{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}{t} \]

   4. Applied rewrites 84.9%

      \[\leadsto x - \frac{\log \color{blue}{\left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}}{t} \]

   if -1.65e17 < y < 6.0000000000000004e65

   1. Initial program 77.2%

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

   2. Taylor expanded in y around 0

      \[\leadsto x - \color{blue}{y \cdot \left(\left(\frac{-1}{2} \cdot \frac{y \cdot {\left(e^{z} - 1\right)}^{2}}{t} + \frac{e^{z}}{t}\right) - \frac{1}{t}\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x - \left(\left(\frac{-1}{2} \cdot \frac{y \cdot {\left(e^{z} - 1\right)}^{2}}{t} + \frac{e^{z}}{t}\right) - \frac{1}{t}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto x - \left(\left(\frac{-1}{2} \cdot \frac{y \cdot {\left(e^{z} - 1\right)}^{2}}{t} + \frac{e^{z}}{t}\right) - \frac{1}{t}\right) \cdot \color{blue}{y} \]

   4. Applied rewrites 98.7%

      \[\leadsto x - \color{blue}{\mathsf{fma}\left(-0.5, \frac{\left(\mathsf{expm1}\left(z\right) \cdot \mathsf{expm1}\left(z\right)\right) \cdot y}{t}, \frac{\mathsf{expm1}\left(z\right)}{t}\right) \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 92.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\log \left(\left(1 - y\right) + y \cdot e^{z}\right) \leq 0:\\ \;\;\;\;x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (log (+ (- 1.0 y) (* y (exp z)))) 0.0)
   (- x (/ (* (expm1 z) y) t))
   (- x (/ (log (fma (expm1 z) y 1.0)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (log(((1.0 - y) + (y * exp(z)))) <= 0.0) {
		tmp = x - ((expm1(z) * y) / t);
	} else {
		tmp = x - (log(fma(expm1(z), y, 1.0)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (log(Float64(Float64(1.0 - y) + Float64(y * exp(z)))) <= 0.0)
		tmp = Float64(x - Float64(Float64(expm1(z) * y) / t));
	else
		tmp = Float64(x - Float64(log(fma(expm1(z), y, 1.0)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[Log[N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.0], N[(x - N[(N[(N[(Exp[z] - 1), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[N[(N[(Exp[z] - 1), $MachinePrecision] * y + 1.0), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) < 0.0

   1. Initial program 56.1%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-expm1.f64 91.6

         \[\leadsto x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t} \]

   4. Applied rewrites 91.6%

      \[\leadsto x - \frac{\color{blue}{\mathsf{expm1}\left(z\right) \cdot y}}{t} \]

   if 0.0 < (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z))))

   1. Initial program 94.6%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-expm1.f64 95.8

         \[\leadsto x - \frac{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}{t} \]

   4. Applied rewrites 95.8%

      \[\leadsto x - \frac{\log \color{blue}{\left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 92.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{expm1}\left(z\right) \cdot y\\ \mathbf{if}\;\log \left(\left(1 - y\right) + y \cdot e^{z}\right) \leq 0.0004:\\ \;\;\;\;x - \frac{t\_1}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log t\_1}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (expm1 z) y)))
   (if (<= (log (+ (- 1.0 y) (* y (exp z)))) 0.0004)
     (- x (/ t_1 t))
     (- x (/ (log t_1) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = expm1(z) * y;
	double tmp;
	if (log(((1.0 - y) + (y * exp(z)))) <= 0.0004) {
		tmp = x - (t_1 / t);
	} else {
		tmp = x - (log(t_1) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.expm1(z) * y;
	double tmp;
	if (Math.log(((1.0 - y) + (y * Math.exp(z)))) <= 0.0004) {
		tmp = x - (t_1 / t);
	} else {
		tmp = x - (Math.log(t_1) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.expm1(z) * y
	tmp = 0
	if math.log(((1.0 - y) + (y * math.exp(z)))) <= 0.0004:
		tmp = x - (t_1 / t)
	else:
		tmp = x - (math.log(t_1) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(expm1(z) * y)
	tmp = 0.0
	if (log(Float64(Float64(1.0 - y) + Float64(y * exp(z)))) <= 0.0004)
		tmp = Float64(x - Float64(t_1 / t));
	else
		tmp = Float64(x - Float64(log(t_1) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(Exp[z] - 1), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[N[Log[N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.0004], N[(x - N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[t$95$1], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) < 4.00000000000000019e-4

   1. Initial program 56.2%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-expm1.f64 91.5

         \[\leadsto x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t} \]

   4. Applied rewrites 91.5%

      \[\leadsto x - \frac{\color{blue}{\mathsf{expm1}\left(z\right) \cdot y}}{t} \]

   if 4.00000000000000019e-4 < (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z))))

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-expm1.f64 95.3

         \[\leadsto x - \frac{\log \left(\mathsf{expm1}\left(z\right) \cdot y\right)}{t} \]

   4. Applied rewrites 95.3%

      \[\leadsto x - \frac{\log \color{blue}{\left(\mathsf{expm1}\left(z\right) \cdot y\right)}}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 90.0% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (log (+ (- 1.0 y) (* y (exp z)))) 1.0)
   (- x (/ (* (expm1 z) y) t))
   (- (* (- (/ (log (- 1.0 y)) (* t x)) 1.0) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (log(((1.0 - y) + (y * exp(z)))) <= 1.0) {
		tmp = x - ((expm1(z) * y) / t);
	} else {
		tmp = -(((log((1.0 - y)) / (t * x)) - 1.0) * x);
	}
	return tmp;
}

Java

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

Python

def code(x, y, z, t):
	tmp = 0
	if math.log(((1.0 - y) + (y * math.exp(z)))) <= 1.0:
		tmp = x - ((math.expm1(z) * y) / t)
	else:
		tmp = -(((math.log((1.0 - y)) / (t * x)) - 1.0) * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (log(Float64(Float64(1.0 - y) + Float64(y * exp(z)))) <= 1.0)
		tmp = Float64(x - Float64(Float64(expm1(z) * y) / t));
	else
		tmp = Float64(-Float64(Float64(Float64(log(Float64(1.0 - y)) / Float64(t * x)) - 1.0) * x));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) < 1

   1. Initial program 56.3%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-expm1.f64 91.5

         \[\leadsto x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t} \]

   4. Applied rewrites 91.5%

      \[\leadsto x - \frac{\color{blue}{\mathsf{expm1}\left(z\right) \cdot y}}{t} \]

   if 1 < (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z))))

   1. Initial program 95.8%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 83.6%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 78.5%

      \[\leadsto -\left(\frac{\log \left(1 - y\right)}{t \cdot x} - 1\right) \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 87.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log \left(\left(1 - y\right) + y \cdot e^{z}\right)\\ \mathbf{if}\;t\_1 \leq 21:\\ \;\;\;\;x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t}\\ \mathbf{elif}\;t\_1 \leq 400:\\ \;\;\;\;-\frac{\log \left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (log (+ (- 1.0 y) (* y (exp z))))))
   (if (<= t_1 21.0)
     (- x (/ (* (expm1 z) y) t))
     (if (<= t_1 400.0) (- (/ (log (* y (expm1 z))) t)) x))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(((1.0 - y) + (y * exp(z))));
	double tmp;
	if (t_1 <= 21.0) {
		tmp = x - ((expm1(z) * y) / t);
	} else if (t_1 <= 400.0) {
		tmp = -(log((y * expm1(z))) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(((1.0 - y) + (y * Math.exp(z))));
	double tmp;
	if (t_1 <= 21.0) {
		tmp = x - ((Math.expm1(z) * y) / t);
	} else if (t_1 <= 400.0) {
		tmp = -(Math.log((y * Math.expm1(z))) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(((1.0 - y) + (y * math.exp(z))))
	tmp = 0
	if t_1 <= 21.0:
		tmp = x - ((math.expm1(z) * y) / t)
	elif t_1 <= 400.0:
		tmp = -(math.log((y * math.expm1(z))) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = log(Float64(Float64(1.0 - y) + Float64(y * exp(z))))
	tmp = 0.0
	if (t_1 <= 21.0)
		tmp = Float64(x - Float64(Float64(expm1(z) * y) / t));
	elseif (t_1 <= 400.0)
		tmp = Float64(-Float64(log(Float64(y * expm1(z))) / t));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Log[N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$1, 21.0], N[(x - N[(N[(N[(Exp[z] - 1), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 400.0], (-N[(N[Log[N[(y * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), x]]]

Derivation

1. Split input into 3 regimes

2. if (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) < 21

   1. Initial program 56.4%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-expm1.f64 91.3

         \[\leadsto x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t} \]

   4. Applied rewrites 91.3%

      \[\leadsto x - \frac{\color{blue}{\mathsf{expm1}\left(z\right) \cdot y}}{t} \]

   if 21 < (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) < 400

   1. Initial program 98.7%

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

   2. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

         \[\leadsto -\frac{\log \left(\mathsf{fma}\left(e^{z}, y, 1\right) - y\right)}{t} \]

      9. lift-exp.f64 51.6

         \[\leadsto -\frac{\log \left(\mathsf{fma}\left(e^{z}, y, 1\right) - y\right)}{t} \]

   4. Applied rewrites 51.6%

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

   5. Taylor expanded in y around inf

      \[\leadsto -\frac{\log \left(y \cdot \left(e^{z} - 1\right)\right)}{t} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lift-expm1.f64 52.5

         \[\leadsto -\frac{\log \left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t} \]

   7. Applied rewrites 52.5%

      \[\leadsto -\frac{\log \left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t} \]

   if 400 < (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z))))

   1. Initial program 92.5%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 49.9%

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

Alternative 6: 86.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\log \left(\left(1 - y\right) + y \cdot e^{z}\right) \leq 120:\\ \;\;\;\;x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (log (+ (- 1.0 y) (* y (exp z)))) 120.0)
   (- x (/ (* (expm1 z) y) t))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (log(((1.0 - y) + (y * exp(z)))) <= 120.0) {
		tmp = x - ((expm1(z) * y) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (Math.log(((1.0 - y) + (y * Math.exp(z)))) <= 120.0) {
		tmp = x - ((Math.expm1(z) * y) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if math.log(((1.0 - y) + (y * math.exp(z)))) <= 120.0:
		tmp = x - ((math.expm1(z) * y) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (log(Float64(Float64(1.0 - y) + Float64(y * exp(z)))) <= 120.0)
		tmp = Float64(x - Float64(Float64(expm1(z) * y) / t));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[Log[N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 120.0], N[(x - N[(N[(N[(Exp[z] - 1), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) < 120

   1. Initial program 57.1%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-expm1.f64 90.6

         \[\leadsto x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t} \]

   4. Applied rewrites 90.6%

      \[\leadsto x - \frac{\color{blue}{\mathsf{expm1}\left(z\right) \cdot y}}{t} \]

   if 120 < (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z))))

   1. Initial program 95.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 49.0%

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

Alternative 7: 81.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e+43) x (- x (* (/ z t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+43) {
		tmp = x;
	} else {
		tmp = x - ((z / t) * y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 <= (-1.05d+43)) then
        tmp = x
    else
        tmp = x - ((z / t) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+43) {
		tmp = x;
	} else {
		tmp = x - ((z / t) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e+43:
		tmp = x
	else:
		tmp = x - ((z / t) * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e+43)
		tmp = x;
	else
		tmp = Float64(x - Float64(Float64(z / t) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.05e+43)
		tmp = x;
	else
		tmp = x - ((z / t) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e+43], x, N[(x - N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000001e43

   1. Initial program 81.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 63.0%

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

   if -1.05000000000000001e43 < z

   1. Initial program 53.8%

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

   2. Taylor expanded in y around 0

      \[\leadsto x - \color{blue}{y \cdot \left(\left(\frac{-1}{2} \cdot \frac{y \cdot {\left(e^{z} - 1\right)}^{2}}{t} + \frac{e^{z}}{t}\right) - \frac{1}{t}\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x - \left(\left(\frac{-1}{2} \cdot \frac{y \cdot {\left(e^{z} - 1\right)}^{2}}{t} + \frac{e^{z}}{t}\right) - \frac{1}{t}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto x - \left(\left(\frac{-1}{2} \cdot \frac{y \cdot {\left(e^{z} - 1\right)}^{2}}{t} + \frac{e^{z}}{t}\right) - \frac{1}{t}\right) \cdot \color{blue}{y} \]

   4. Applied rewrites 87.2%

      \[\leadsto x - \color{blue}{\mathsf{fma}\left(-0.5, \frac{\left(\mathsf{expm1}\left(z\right) \cdot \mathsf{expm1}\left(z\right)\right) \cdot y}{t}, \frac{\mathsf{expm1}\left(z\right)}{t}\right) \cdot y} \]

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 87.8

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

   7. Applied rewrites 87.8%

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

Alternative 8: 71.1% accurate, 31.2× 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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%

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

2. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
3. Step-by-step derivation

4. Applied rewrites 71.1%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025115 
(FPCore (x y z t)
  :name "System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2"
  :precision binary64
  (- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))