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

Percentage Accurate: 61.9% → 99.0%

Time: 14.9s

Alternatives: 8

Speedup: 31.2×

• could not determine a ground truth

  1. x = 2.7890458139817935e-46
  2. y = 6.715188290302379e-107
  3. z = 1.7500910041411246e+217
  4. t = 8.878569804819702e+61

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: 61.9% 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: 99.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log \left(\left(1 - y\right) + y \cdot e^{z}\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(z \cdot y\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x - \frac{\mathsf{expm1}\left(z\right)}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log \left(\mathsf{expm1}\left(z\right) \cdot y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (log (+ (- 1.0 y) (* y (exp z))))))
   (if (<= t_1 (- INFINITY))
     (- x (/ (log1p (* z y)) t))
     (if (<= t_1 0.0)
       (- x (* (/ (expm1 z) t) y))
       (- x (/ (log (* (expm1 z) y)) t))))))

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 <= -((double) INFINITY)) {
		tmp = x - (log1p((z * y)) / t);
	} else if (t_1 <= 0.0) {
		tmp = x - ((expm1(z) / t) * y);
	} else {
		tmp = x - (log((expm1(z) * y)) / t);
	}
	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 <= -Double.POSITIVE_INFINITY) {
		tmp = x - (Math.log1p((z * y)) / t);
	} else if (t_1 <= 0.0) {
		tmp = x - ((Math.expm1(z) / t) * y);
	} else {
		tmp = x - (Math.log((Math.expm1(z) * y)) / t);
	}
	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 <= -math.inf:
		tmp = x - (math.log1p((z * y)) / t)
	elif t_1 <= 0.0:
		tmp = x - ((math.expm1(z) / t) * y)
	else:
		tmp = x - (math.log((math.expm1(z) * y)) / t)
	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 <= Float64(-Inf))
		tmp = Float64(x - Float64(log1p(Float64(z * y)) / t));
	elseif (t_1 <= 0.0)
		tmp = Float64(x - Float64(Float64(expm1(z) / t) * y));
	else
		tmp = Float64(x - Float64(log(Float64(expm1(z) * y)) / t));
	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, (-Infinity)], N[(x - N[(N[Log[1 + N[(z * y), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(x - N[(N[(N[(Exp[z] - 1), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[N[(N[(Exp[z] - 1), $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) < -inf.0

   1. Initial program 2.2%

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

   3. Applied rewrites 99.8%

      \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(z\right) \cdot y\right)}}{t} \]

   4. Taylor expanded in z around 0

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{z} \cdot y\right)}{t} \]
   5. Step-by-step derivation

   6. Applied rewrites 99.8%

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{z} \cdot y\right)}{t} \]

   if -inf.0 < (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) < 0.0

   1. Initial program 81.8%

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

   2. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. sub-div N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. sub-div N/A

         \[\leadsto x - \frac{e^{z} - 1}{t} \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto x - \frac{e^{z} - 1}{t} \cdot y \]

      7. lower-expm1.f64 99.7

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

   4. Applied rewrites 99.7%

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

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

   1. Initial program 95.9%

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

   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 93.8

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

   4. Applied rewrites 93.8%

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

Alternative 2: 98.6% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Initial program 61.9%

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

3. Applied rewrites 98.6%

   \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(z\right) \cdot y\right)}}{t} \]
4. Add Preprocessing

Alternative 3: 93.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log \left(\left(1 - y\right) + y \cdot e^{z}\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(z \cdot y\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 20:\\ \;\;\;\;x - \frac{\mathsf{expm1}\left(z\right)}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{\log \left(\mathsf{expm1}\left(z\right) \cdot y\right)}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (log (+ (- 1.0 y) (* y (exp z))))))
   (if (<= t_1 (- INFINITY))
     (- x (/ (log1p (* z y)) t))
     (if (<= t_1 20.0)
       (- x (* (/ (expm1 z) t) y))
       (/ (log (* (expm1 z) y)) (- t))))))

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 <= -((double) INFINITY)) {
		tmp = x - (log1p((z * y)) / t);
	} else if (t_1 <= 20.0) {
		tmp = x - ((expm1(z) / t) * y);
	} else {
		tmp = log((expm1(z) * y)) / -t;
	}
	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 <= -Double.POSITIVE_INFINITY) {
		tmp = x - (Math.log1p((z * y)) / t);
	} else if (t_1 <= 20.0) {
		tmp = x - ((Math.expm1(z) / t) * y);
	} else {
		tmp = Math.log((Math.expm1(z) * y)) / -t;
	}
	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 <= -math.inf:
		tmp = x - (math.log1p((z * y)) / t)
	elif t_1 <= 20.0:
		tmp = x - ((math.expm1(z) / t) * y)
	else:
		tmp = math.log((math.expm1(z) * y)) / -t
	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 <= Float64(-Inf))
		tmp = Float64(x - Float64(log1p(Float64(z * y)) / t));
	elseif (t_1 <= 20.0)
		tmp = Float64(x - Float64(Float64(expm1(z) / t) * y));
	else
		tmp = Float64(log(Float64(expm1(z) * y)) / Float64(-t));
	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, (-Infinity)], N[(x - N[(N[Log[1 + N[(z * y), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 20.0], N[(x - N[(N[(N[(Exp[z] - 1), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[Log[N[(N[(Exp[z] - 1), $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision] / (-t)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) < -inf.0

   1. Initial program 2.2%

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

   3. Applied rewrites 99.8%

      \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(z\right) \cdot y\right)}}{t} \]

   4. Taylor expanded in z around 0

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{z} \cdot y\right)}{t} \]
   5. Step-by-step derivation

   6. Applied rewrites 99.8%

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{z} \cdot y\right)}{t} \]

   if -inf.0 < (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) < 20

   1. Initial program 81.8%

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

   2. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. sub-div N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. sub-div N/A

         \[\leadsto x - \frac{e^{z} - 1}{t} \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto x - \frac{e^{z} - 1}{t} \cdot y \]

      7. lower-expm1.f64 99.2

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

   4. Applied rewrites 99.2%

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

   if 20 < (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z))))

   1. Initial program 97.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 48.1%

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

   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. *-commutative N/A

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

      2. lift-expm1.f64 N/A

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

      3. lift-*.f64 48.0

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

   7. Applied rewrites 48.0%

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

Alternative 4: 93.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log \left(\left(1 - y\right) + y \cdot e^{z}\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(z \cdot y\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 350:\\ \;\;\;\;x - \frac{\mathsf{expm1}\left(z\right)}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (log (+ (- 1.0 y) (* y (exp z))))))
   (if (<= t_1 (- INFINITY))
     (- x (/ (log1p (* z y)) t))
     (if (<= t_1 350.0) (- x (* (/ (expm1 z) t) y)) 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 <= -((double) INFINITY)) {
		tmp = x - (log1p((z * y)) / t);
	} else if (t_1 <= 350.0) {
		tmp = x - ((expm1(z) / t) * y);
	} 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 <= -Double.POSITIVE_INFINITY) {
		tmp = x - (Math.log1p((z * y)) / t);
	} else if (t_1 <= 350.0) {
		tmp = x - ((Math.expm1(z) / t) * y);
	} 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 <= -math.inf:
		tmp = x - (math.log1p((z * y)) / t)
	elif t_1 <= 350.0:
		tmp = x - ((math.expm1(z) / t) * y)
	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 <= Float64(-Inf))
		tmp = Float64(x - Float64(log1p(Float64(z * y)) / t));
	elseif (t_1 <= 350.0)
		tmp = Float64(x - Float64(Float64(expm1(z) / t) * y));
	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, (-Infinity)], N[(x - N[(N[Log[1 + N[(z * y), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 350.0], N[(x - N[(N[(N[(Exp[z] - 1), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $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)))) < -inf.0

   1. Initial program 2.2%

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

   3. Applied rewrites 99.8%

      \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(z\right) \cdot y\right)}}{t} \]

   4. Taylor expanded in z around 0

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{z} \cdot y\right)}{t} \]
   5. Step-by-step derivation

   6. Applied rewrites 99.8%

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{z} \cdot y\right)}{t} \]

   if -inf.0 < (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) < 350

   1. Initial program 83.1%

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

   2. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. sub-div N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. sub-div N/A

         \[\leadsto x - \frac{e^{z} - 1}{t} \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto x - \frac{e^{z} - 1}{t} \cdot y \]

      7. lower-expm1.f64 94.9

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

   4. Applied rewrites 94.9%

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

   if 350 < (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z))))

   1. Initial program 95.6%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 51.3%

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

Alternative 5: 87.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.2 \cdot 10^{+129}:\\ \;\;\;\;x - \frac{\mathsf{expm1}\left(z\right)}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log \left(\mathsf{fma}\left(z, y, 1\right)\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 7.2e+129)
   (- x (* (/ (expm1 z) t) y))
   (- x (/ (log (fma z y 1.0)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.2e+129) {
		tmp = x - ((expm1(z) / t) * y);
	} else {
		tmp = x - (log(fma(z, y, 1.0)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 7.2e+129)
		tmp = Float64(x - Float64(Float64(expm1(z) / t) * y));
	else
		tmp = Float64(x - Float64(log(fma(z, y, 1.0)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 7.2e+129], N[(x - N[(N[(N[(Exp[z] - 1), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[N[(z * y + 1.0), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.2000000000000002e129

   1. Initial program 66.6%

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

   2. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. sub-div N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. sub-div N/A

         \[\leadsto x - \frac{e^{z} - 1}{t} \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto x - \frac{e^{z} - 1}{t} \cdot y \]

      7. lower-expm1.f64 88.0

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

   4. Applied rewrites 88.0%

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

   if 7.2000000000000002e129 < y

   1. Initial program 6.7%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 81.0

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

   4. Applied rewrites 81.0%

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

Alternative 6: 86.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.2 \cdot 10^{+129}:\\ \;\;\;\;x - \frac{\mathsf{expm1}\left(z\right)}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log \left(y \cdot z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 7.2e+129) (- x (* (/ (expm1 z) t) y)) (- x (/ (log (* y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.2e+129) {
		tmp = x - ((expm1(z) / t) * y);
	} else {
		tmp = x - (log((y * z)) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.2e+129) {
		tmp = x - ((Math.expm1(z) / t) * y);
	} else {
		tmp = x - (Math.log((y * z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 7.2e+129:
		tmp = x - ((math.expm1(z) / t) * y)
	else:
		tmp = x - (math.log((y * z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 7.2e+129)
		tmp = Float64(x - Float64(Float64(expm1(z) / t) * y));
	else
		tmp = Float64(x - Float64(log(Float64(y * z)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 7.2e+129], N[(x - N[(N[(N[(Exp[z] - 1), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[N[(y * z), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.2000000000000002e129

   1. Initial program 66.6%

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

   2. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. sub-div N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. sub-div N/A

         \[\leadsto x - \frac{e^{z} - 1}{t} \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto x - \frac{e^{z} - 1}{t} \cdot y \]

      7. lower-expm1.f64 88.0

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

   4. Applied rewrites 88.0%

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

   if 7.2000000000000002e129 < y

   1. Initial program 6.7%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 81.0

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

   4. Applied rewrites 81.0%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 61.8

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

   7. Applied rewrites 61.8%

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

Alternative 7: 81.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.2e+89) x (- x (* (/ z t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.2e+89) {
		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 <= (-7.2d+89)) 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 <= -7.2e+89) {
		tmp = x;
	} else {
		tmp = x - ((z / t) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.2e+89:
		tmp = x
	else:
		tmp = x - ((z / t) * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.2e+89)
		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 <= -7.2e+89)
		tmp = x;
	else
		tmp = x - ((z / t) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.2e+89], x, N[(x - N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e89

   1. Initial program 82.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 65.9%

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

   if -7.2e89 < z

   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

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

      1. associate-/l* N/A

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

      2. sub-div N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. sub-div N/A

         \[\leadsto x - \frac{e^{z} - 1}{t} \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto x - \frac{e^{z} - 1}{t} \cdot y \]

      7. lower-expm1.f64 88.6

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

   4. Applied rewrites 88.6%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 85.9%

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

Alternative 8: 72.1% 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 61.9%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 72.1%

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

Reproduce

herbie shell --seed 2025130 
(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)))