Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

Percentage Accurate: 84.9% → 97.9%

Time: 7.7s

Alternatives: 11

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{y - z}{a - z}, t, x\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (fma (/ (- y z) (- a z)) t x))

C

double code(double x, double y, double z, double t, double a) {
	return fma(((y - z) / (a - z)), t, x);
}

Julia

function code(x, y, z, t, a)
	return fma(Float64(Float64(y - z) / Float64(a - z)), t, x)
end

Wolfram

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

Derivation

1. Initial program 84.9%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. +-commutative N/A

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

   8. associate-/l* N/A

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

   9. sub-div N/A

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

   10. *-commutative N/A

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

   11. lower-fma.f64 N/A

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

   12. sub-div N/A

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

   13. lower-/.f64 N/A

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

   14. lift--.f64 N/A

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

   15. lift--.f64 97.9

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

3. Applied rewrites 97.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t, x\right)} \]
4. Add Preprocessing

Alternative 2: 62.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-58}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 -5e-58) (+ x t) (if (<= t_1 2e-68) x (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -5e-58) {
		tmp = x + t;
	} else if (t_1 <= 2e-68) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y - z) * t) / (a - z)
    if (t_1 <= (-5d-58)) then
        tmp = x + t
    else if (t_1 <= 2d-68) then
        tmp = x
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -5e-58) {
		tmp = x + t;
	} else if (t_1 <= 2e-68) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_1 <= -5e-58:
		tmp = x + t
	elif t_1 <= 2e-68:
		tmp = x
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= -5e-58)
		tmp = Float64(x + t);
	elseif (t_1 <= 2e-68)
		tmp = x;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_1 <= -5e-58)
		tmp = x + t;
	elseif (t_1 <= 2e-68)
		tmp = x;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-58], N[(x + t), $MachinePrecision], If[LessEqual[t$95$1, 2e-68], x, N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -4.99999999999999977e-58 or 2.00000000000000013e-68 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 75.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 47.9%

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

   if -4.99999999999999977e-58 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 2.00000000000000013e-68

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 83.1%

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

Alternative 3: 54.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+198}:\\ \;\;\;\;t\\ \mathbf{elif}\;t\_1 \leq 10^{+164}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 -5e+198) t (if (<= t_1 1e+164) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -5e+198) {
		tmp = t;
	} else if (t_1 <= 1e+164) {
		tmp = x;
	} else {
		tmp = t;
	}
	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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y - z) * t) / (a - z)
    if (t_1 <= (-5d+198)) then
        tmp = t
    else if (t_1 <= 1d+164) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -5e+198) {
		tmp = t;
	} else if (t_1 <= 1e+164) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_1 <= -5e+198:
		tmp = t
	elif t_1 <= 1e+164:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= -5e+198)
		tmp = t;
	elseif (t_1 <= 1e+164)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_1 <= -5e+198)
		tmp = t;
	elseif (t_1 <= 1e+164)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+198], t, If[LessEqual[t$95$1, 1e+164], x, t]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -5.00000000000000049e198 or 1e164 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 51.3%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 83.9

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

   4. Applied rewrites 83.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 53.0%

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

   8. Taylor expanded in z around 0

      \[\leadsto y \cdot \frac{t}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 37.0%

       \[\leadsto y \cdot \frac{t}{a} \]

   11. Taylor expanded in z around inf

       \[\leadsto t \]
   12. Step-by-step derivation

   13. Applied rewrites 29.8%

       \[\leadsto t \]

   if -5.00000000000000049e198 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 1e164

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 65.8%

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

Alternative 4: 76.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+129}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{-z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.22e+129)
   (+ x t)
   (if (<= z 2.9e-31)
     (fma t (/ y a) x)
     (if (<= z 2e+109) (fma (/ y (- z)) t x) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.22e+129) {
		tmp = x + t;
	} else if (z <= 2.9e-31) {
		tmp = fma(t, (y / a), x);
	} else if (z <= 2e+109) {
		tmp = fma((y / -z), t, x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.22e+129)
		tmp = Float64(x + t);
	elseif (z <= 2.9e-31)
		tmp = fma(t, Float64(y / a), x);
	elseif (z <= 2e+109)
		tmp = fma(Float64(y / Float64(-z)), t, x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.22e+129], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.9e-31], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 2e+109], N[(N[(y / (-z)), $MachinePrecision] * t + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2200000000000001e129 or 1.99999999999999996e109 < z

   1. Initial program 65.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 84.7%

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

   if -1.2200000000000001e129 < z < 2.9000000000000001e-31

   1. Initial program 94.1%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto t \cdot \frac{y}{a} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\frac{y}{a}}, x\right) \]

      4. lower-/.f64 74.5

         \[\leadsto \mathsf{fma}\left(t, \frac{y}{\color{blue}{a}}, x\right) \]

   4. Applied rewrites 74.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \frac{y}{a}, x\right)} \]

   if 2.9000000000000001e-31 < z < 1.99999999999999996e109

   1. Initial program 90.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 99.7

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 75.1%

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

   7. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{\mathsf{neg}\left(z\right)}, t, x\right) \]

      2. lift-neg.f64 59.7

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

   9. Applied rewrites 59.7%

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

Alternative 5: 87.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - z}{-z}, t, x\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- y z) (- z)) t x)))
   (if (<= z -7e+115) t_1 (if (<= z 4.5e+98) (fma (/ y (- a z)) t x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((y - z) / -z), t, x);
	double tmp;
	if (z <= -7e+115) {
		tmp = t_1;
	} else if (z <= 4.5e+98) {
		tmp = fma((y / (a - z)), t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(y - z) / Float64(-z)), t, x)
	tmp = 0.0
	if (z <= -7e+115)
		tmp = t_1;
	elseif (z <= 4.5e+98)
		tmp = fma(Float64(y / Float64(a - z)), t, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] / (-z)), $MachinePrecision] * t + x), $MachinePrecision]}, If[LessEqual[z, -7e+115], t$95$1, If[LessEqual[z, 4.5e+98], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.00000000000000011e115 or 4.5000000000000002e98 < z

   1. Initial program 66.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 90.7

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

   6. Applied rewrites 90.7%

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

   if -7.00000000000000011e115 < z < 4.5000000000000002e98

   1. Initial program 93.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 97.0

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 85.1%

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

Alternative 6: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+129}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.55e+129)
   (+ x t)
   (if (<= z 2.1e+109) (fma (/ y (- a z)) t x) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e+129) {
		tmp = x + t;
	} else if (z <= 2.1e+109) {
		tmp = fma((y / (a - z)), t, x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.55e+129)
		tmp = Float64(x + t);
	elseif (z <= 2.1e+109)
		tmp = fma(Float64(y / Float64(a - z)), t, x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.55e+129], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.1e+109], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e129 or 2.1000000000000001e109 < z

   1. Initial program 65.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 84.7%

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

   if -1.55e129 < z < 2.1000000000000001e109

   1. Initial program 93.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 97.1

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

   3. Applied rewrites 97.1%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 84.7%

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

Alternative 7: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+129}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.22e+129)
   (+ x t)
   (if (<= z 5e+97) (fma t (/ (- y z) a) x) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.22e+129) {
		tmp = x + t;
	} else if (z <= 5e+97) {
		tmp = fma(t, ((y - z) / a), x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.22e+129)
		tmp = Float64(x + t);
	elseif (z <= 5e+97)
		tmp = fma(t, Float64(Float64(y - z) / a), x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.22e+129], N[(x + t), $MachinePrecision], If[LessEqual[z, 5e+97], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2200000000000001e129 or 4.99999999999999999e97 < z

   1. Initial program 66.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 84.0%

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

   if -1.2200000000000001e129 < z < 4.99999999999999999e97

   1. Initial program 93.7%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 74.4

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

   4. Applied rewrites 74.4%

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

Alternative 8: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+129}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.22e+129) (+ x t) (if (<= z 4.5e+98) (fma t (/ y a) x) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.22e+129) {
		tmp = x + t;
	} else if (z <= 4.5e+98) {
		tmp = fma(t, (y / a), x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.22e+129)
		tmp = Float64(x + t);
	elseif (z <= 4.5e+98)
		tmp = fma(t, Float64(y / a), x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.22e+129], N[(x + t), $MachinePrecision], If[LessEqual[z, 4.5e+98], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2200000000000001e129 or 4.5000000000000002e98 < z

   1. Initial program 65.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 84.0%

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

   if -1.2200000000000001e129 < z < 4.5000000000000002e98

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto t \cdot \frac{y}{a} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\frac{y}{a}}, x\right) \]

      4. lower-/.f64 71.7

         \[\leadsto \mathsf{fma}\left(t, \frac{y}{\color{blue}{a}}, x\right) \]

   4. Applied rewrites 71.7%

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

Alternative 9: 60.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-231}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-256}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e-231)
   (+ x t)
   (if (<= z 3.3e-256) (/ (* t y) a) (if (<= z 4.5e+98) x (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e-231) {
		tmp = x + t;
	} else if (z <= 3.3e-256) {
		tmp = (t * y) / a;
	} else if (z <= 4.5e+98) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.3d-231)) then
        tmp = x + t
    else if (z <= 3.3d-256) then
        tmp = (t * y) / a
    else if (z <= 4.5d+98) then
        tmp = x
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e-231) {
		tmp = x + t;
	} else if (z <= 3.3e-256) {
		tmp = (t * y) / a;
	} else if (z <= 4.5e+98) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e-231:
		tmp = x + t
	elif z <= 3.3e-256:
		tmp = (t * y) / a
	elif z <= 4.5e+98:
		tmp = x
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e-231)
		tmp = Float64(x + t);
	elseif (z <= 3.3e-256)
		tmp = Float64(Float64(t * y) / a);
	elseif (z <= 4.5e+98)
		tmp = x;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.3e-231)
		tmp = x + t;
	elseif (z <= 3.3e-256)
		tmp = (t * y) / a;
	elseif (z <= 4.5e+98)
		tmp = x;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e-231], N[(x + t), $MachinePrecision], If[LessEqual[z, 3.3e-256], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 4.5e+98], x, N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.29999999999999998e-231 or 4.5000000000000002e98 < z

   1. Initial program 79.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 68.9%

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

   if -4.29999999999999998e-231 < z < 3.3e-256

   1. Initial program 94.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 94.9

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

   3. Applied rewrites 94.9%

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

   4. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 46.0

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

   6. Applied rewrites 46.0%

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

   7. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{t \cdot y}{a} \]

      2. lower-*.f64 43.6

         \[\leadsto \frac{t \cdot y}{a} \]

   9. Applied rewrites 43.6%

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

   if 3.3e-256 < z < 4.5000000000000002e98

   1. Initial program 93.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 49.2%

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

Alternative 10: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-231}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-256}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e-231)
   (+ x t)
   (if (<= z 3.3e-256) (* (/ y a) t) (if (<= z 4.5e+98) x (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e-231) {
		tmp = x + t;
	} else if (z <= 3.3e-256) {
		tmp = (y / a) * t;
	} else if (z <= 4.5e+98) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.3d-231)) then
        tmp = x + t
    else if (z <= 3.3d-256) then
        tmp = (y / a) * t
    else if (z <= 4.5d+98) then
        tmp = x
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e-231) {
		tmp = x + t;
	} else if (z <= 3.3e-256) {
		tmp = (y / a) * t;
	} else if (z <= 4.5e+98) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e-231:
		tmp = x + t
	elif z <= 3.3e-256:
		tmp = (y / a) * t
	elif z <= 4.5e+98:
		tmp = x
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e-231)
		tmp = Float64(x + t);
	elseif (z <= 3.3e-256)
		tmp = Float64(Float64(y / a) * t);
	elseif (z <= 4.5e+98)
		tmp = x;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.3e-231)
		tmp = x + t;
	elseif (z <= 3.3e-256)
		tmp = (y / a) * t;
	elseif (z <= 4.5e+98)
		tmp = x;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e-231], N[(x + t), $MachinePrecision], If[LessEqual[z, 3.3e-256], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 4.5e+98], x, N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.29999999999999998e-231 or 4.5000000000000002e98 < z

   1. Initial program 79.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 68.9%

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

   if -4.29999999999999998e-231 < z < 3.3e-256

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto t \cdot \frac{y}{a} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\frac{y}{a}}, x\right) \]

      4. lower-/.f64 92.3

         \[\leadsto \mathsf{fma}\left(t, \frac{y}{\color{blue}{a}}, x\right) \]

   4. Applied rewrites 92.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \frac{y}{a}, x\right)} \]

   5. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

         \[\leadsto \frac{y}{a} \cdot t \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{y}{a} \cdot t \]

      4. lift-/.f64 44.7

         \[\leadsto \frac{y}{a} \cdot t \]

   7. Applied rewrites 44.7%

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

   if 3.3e-256 < z < 4.5000000000000002e98

   1. Initial program 93.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 49.2%

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

Alternative 11: 50.1% accurate, 26.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	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, a)
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), intent (in) :: a
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 84.9%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 50.1%

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

Developer Target 1: 99.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2025093 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -10682974490174067/10000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 312887599100691/80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t)))))

  (+ x (/ (* (- y z) t) (- a z))))