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

Percentage Accurate: 77.5% → 93.7%

Time: 7.2s

Alternatives: 10

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\left(\frac{t}{a - t} - -1\right) - \frac{z}{a - t}, y, x\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (fma (- (- (/ t (- a t)) -1.0) (/ z (- a t))) y x))

C

double code(double x, double y, double z, double t, double a) {
	return fma((((t / (a - t)) - -1.0) - (z / (a - t))), y, x);
}

Julia

function code(x, y, z, t, a)
	return fma(Float64(Float64(Float64(t / Float64(a - t)) - -1.0) - Float64(z / Float64(a - t))), y, x)
end

Wolfram

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

Derivation

1. Initial program 77.3%

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

3. Taylor expanded in y around 0

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

5. Applied rewrites 95.0%

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

6. Final simplification 95.0%

   \[\leadsto \mathsf{fma}\left(\left(\frac{t}{a - t} - -1\right) - \frac{z}{a - t}, y, x\right) \]
7. Add Preprocessing

Alternative 2: 67.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-255}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z t))) (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 -4e+306)
     t_1
     (if (<= t_2 -2e-255)
       (+ y x)
       (if (<= t_2 0.0) x (if (<= t_2 4e+307) (+ y x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / t);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -4e+306) {
		tmp = t_1;
	} else if (t_2 <= -2e-255) {
		tmp = y + x;
	} else if (t_2 <= 0.0) {
		tmp = x;
	} else if (t_2 <= 4e+307) {
		tmp = y + x;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y * (z / t)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 <= (-4d+306)) then
        tmp = t_1
    else if (t_2 <= (-2d-255)) then
        tmp = y + x
    else if (t_2 <= 0.0d0) then
        tmp = x
    else if (t_2 <= 4d+307) then
        tmp = y + x
    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 = y * (z / t);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -4e+306) {
		tmp = t_1;
	} else if (t_2 <= -2e-255) {
		tmp = y + x;
	} else if (t_2 <= 0.0) {
		tmp = x;
	} else if (t_2 <= 4e+307) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / t)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -4e+306:
		tmp = t_1
	elif t_2 <= -2e-255:
		tmp = y + x
	elif t_2 <= 0.0:
		tmp = x
	elif t_2 <= 4e+307:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / t))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -4e+306)
		tmp = t_1;
	elseif (t_2 <= -2e-255)
		tmp = Float64(y + x);
	elseif (t_2 <= 0.0)
		tmp = x;
	elseif (t_2 <= 4e+307)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / t);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -4e+306)
		tmp = t_1;
	elseif (t_2 <= -2e-255)
		tmp = y + x;
	elseif (t_2 <= 0.0)
		tmp = x;
	elseif (t_2 <= 4e+307)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+306], t$95$1, If[LessEqual[t$95$2, -2e-255], N[(y + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], x, If[LessEqual[t$95$2, 4e+307], N[(y + x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.00000000000000007e306 or 3.99999999999999994e307 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 42.6%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 57.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 47.1%

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

   if -4.00000000000000007e306 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2e-255 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 3.99999999999999994e307

   1. Initial program 95.9%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 79.6%

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

   if -2e-255 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 4.4%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 54.7%

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

Alternative 3: 93.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-255} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z - t}{a - t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (or (<= t_1 -2e-255) (not (<= t_1 0.0)))
     (fma (- 1.0 (/ (- z t) (- a t))) y x)
     (- x (/ (* y (- a z)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if ((t_1 <= -2e-255) || !(t_1 <= 0.0)) {
		tmp = fma((1.0 - ((z - t) / (a - t))), y, x);
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -2e-255) || !(t_1 <= 0.0))
		tmp = fma(Float64(1.0 - Float64(Float64(z - t) / Float64(a - t))), y, x);
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-255], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(1.0 - N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2e-255 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 83.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 92.0%

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

   if -2e-255 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 4.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 99.8%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq -2 \cdot 10^{-255} \lor \neg \left(\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z - t}{a - t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-26} \lor \neg \left(a \leq 1.28 \cdot 10^{-5}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z - t}{a - t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{-t} - \frac{z}{a - t}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3e-26) (not (<= a 1.28e-5)))
   (fma (- 1.0 (/ (- z t) (- a t))) y x)
   (fma (- (/ a (- t)) (/ z (- a t))) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3e-26) || !(a <= 1.28e-5)) {
		tmp = fma((1.0 - ((z - t) / (a - t))), y, x);
	} else {
		tmp = fma(((a / -t) - (z / (a - t))), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3e-26) || !(a <= 1.28e-5))
		tmp = fma(Float64(1.0 - Float64(Float64(z - t) / Float64(a - t))), y, x);
	else
		tmp = fma(Float64(Float64(a / Float64(-t)) - Float64(z / Float64(a - t))), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3e-26], N[Not[LessEqual[a, 1.28e-5]], $MachinePrecision]], N[(N[(1.0 - N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(N[(a / (-t)), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.00000000000000012e-26 or 1.2799999999999999e-5 < a

   1. Initial program 83.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 93.5%

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

   if -3.00000000000000012e-26 < a < 1.2799999999999999e-5

   1. Initial program 71.1%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 95.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 94.3%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-26} \lor \neg \left(a \leq 1.28 \cdot 10^{-5}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z - t}{a - t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{-t} - \frac{z}{a - t}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-41} \lor \neg \left(t \leq 3.6 \cdot 10^{+83}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z}{a - t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.4e-41) (not (<= t 3.6e+83)))
   (fma (/ z t) y x)
   (- (+ x y) (* (/ z (- a t)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.4e-41) || !(t <= 3.6e+83)) {
		tmp = fma((z / t), y, x);
	} else {
		tmp = (x + y) - ((z / (a - t)) * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.4e-41) || !(t <= 3.6e+83))
		tmp = fma(Float64(z / t), y, x);
	else
		tmp = Float64(Float64(x + y) - Float64(Float64(z / Float64(a - t)) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.4e-41], N[Not[LessEqual[t, 3.6e+83]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4e-41 or 3.5999999999999997e83 < t

   1. Initial program 60.3%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 92.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 83.6%

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

   if -4.4e-41 < t < 3.5999999999999997e83

   1. Initial program 94.8%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 95.9%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-41} \lor \neg \left(t \leq 3.6 \cdot 10^{+83}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z}{a - t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-79} \lor \neg \left(t \leq 76000000000000\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.7e-79) (not (<= t 76000000000000.0)))
   (fma (/ z t) y x)
   (- (+ x y) (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.7e-79) || !(t <= 76000000000000.0)) {
		tmp = fma((z / t), y, x);
	} else {
		tmp = (x + y) - ((z * y) / a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.7e-79) || !(t <= 76000000000000.0))
		tmp = fma(Float64(z / t), y, x);
	else
		tmp = Float64(Float64(x + y) - Float64(Float64(z * y) / a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.7e-79], N[Not[LessEqual[t, 76000000000000.0]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.69999999999999988e-79 or 7.6e13 < t

   1. Initial program 64.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 92.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 82.5%

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

   if -1.69999999999999988e-79 < t < 7.6e13

   1. Initial program 95.7%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 91.0%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-79} \lor \neg \left(t \leq 76000000000000\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{-29} \lor \neg \left(a \leq 7.2 \cdot 10^{+50}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.1e-29) (not (<= a 7.2e+50))) (+ y x) (fma (/ z t) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.1e-29) || !(a <= 7.2e+50)) {
		tmp = y + x;
	} else {
		tmp = fma((z / t), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.1e-29) || !(a <= 7.2e+50))
		tmp = Float64(y + x);
	else
		tmp = fma(Float64(z / t), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.1e-29], N[Not[LessEqual[a, 7.2e+50]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.09999999999999986e-29 or 7.19999999999999972e50 < a

   1. Initial program 84.4%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 78.3%

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

   if -5.09999999999999986e-29 < a < 7.19999999999999972e50

   1. Initial program 71.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 95.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 87.4%

      \[\leadsto \mathsf{fma}\left(\frac{z}{t}, y, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{-29} \lor \neg \left(a \leq 7.2 \cdot 10^{+50}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-51} \lor \neg \left(a \leq 5 \cdot 10^{+51}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.3e-51) (not (<= a 5e+51))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.3e-51) || !(a <= 5e+51)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	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 ((a <= (-1.3d-51)) .or. (.not. (a <= 5d+51))) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.3e-51) || !(a <= 5e+51)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.3e-51) or not (a <= 5e+51):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.3e-51) || !(a <= 5e+51))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.3e-51) || ~((a <= 5e+51)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.3e-51], N[Not[LessEqual[a, 5e+51]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.3e-51 or 5e51 < a

   1. Initial program 84.4%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 76.4%

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

   if -1.3e-51 < a < 5e51

   1. Initial program 70.3%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 54.4%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-51} \lor \neg \left(a \leq 5 \cdot 10^{+51}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-133}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.15e-145) x (if (<= x 4.3e-133) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.15e-145) {
		tmp = x;
	} else if (x <= 4.3e-133) {
		tmp = y;
	} else {
		tmp = x;
	}
	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 (x <= (-1.15d-145)) then
        tmp = x
    else if (x <= 4.3d-133) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.15e-145) {
		tmp = x;
	} else if (x <= 4.3e-133) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.15e-145:
		tmp = x
	elif x <= 4.3e-133:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.15e-145)
		tmp = x;
	elseif (x <= 4.3e-133)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.15e-145)
		tmp = x;
	elseif (x <= 4.3e-133)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.15e-145], x, If[LessEqual[x, 4.3e-133], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15000000000000004e-145 or 4.30000000000000016e-133 < x

   1. Initial program 82.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 63.6%

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

   if -1.15000000000000004e-145 < x < 4.30000000000000016e-133

   1. Initial program 63.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 59.7%

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

   6. Taylor expanded in a around inf

      \[\leadsto y \]
   7. Step-by-step derivation

   8. Applied rewrites 36.7%

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

Alternative 10: 50.6% accurate, 29.0× 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 77.3%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 50.2%

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

Developer Target 1: 89.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2025021 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -13664970889390727/100000000000000000000000) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 14754293444577233/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)))))

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