Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 68.2% → 93.0%

Time: 25.2s

Alternatives: 22

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{z - a}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+252}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{a}{a - z}, \mathsf{fma}\left(x, t\_1, \frac{t - x}{a - z} \cdot \left(y - z\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-1, \frac{z - y}{z - a}, t\_1\right) - \frac{a}{z - a}, \frac{t \cdot \left(z - y\right)}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{1}{z - a} \cdot y, \mathsf{fma}\left(t\_1, t - x, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (- z a))) (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -1e+252)
     (fma x (/ a (- a z)) (fma x t_1 (* (/ (- t x) (- a z)) (- y z))))
     (if (<= t_2 2e+116)
       (fma
        x
        (- (fma -1.0 (/ (- z y) (- z a)) t_1) (/ a (- z a)))
        (/ (* t (- z y)) (- z a)))
       (fma (- x t) (* (/ 1.0 (- z a)) y) (fma t_1 (- t x) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (z - a);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -1e+252) {
		tmp = fma(x, (a / (a - z)), fma(x, t_1, (((t - x) / (a - z)) * (y - z))));
	} else if (t_2 <= 2e+116) {
		tmp = fma(x, (fma(-1.0, ((z - y) / (z - a)), t_1) - (a / (z - a))), ((t * (z - y)) / (z - a)));
	} else {
		tmp = fma((x - t), ((1.0 / (z - a)) * y), fma(t_1, (t - x), x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(z - a))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -1e+252)
		tmp = fma(x, Float64(a / Float64(a - z)), fma(x, t_1, Float64(Float64(Float64(t - x) / Float64(a - z)) * Float64(y - z))));
	elseif (t_2 <= 2e+116)
		tmp = fma(x, Float64(fma(-1.0, Float64(Float64(z - y) / Float64(z - a)), t_1) - Float64(a / Float64(z - a))), Float64(Float64(t * Float64(z - y)) / Float64(z - a)));
	else
		tmp = fma(Float64(x - t), Float64(Float64(1.0 / Float64(z - a)) * y), fma(t_1, Float64(t - x), x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+252], N[(x * N[(a / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$1 + N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+116], N[(x * N[(N[(-1.0 * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(a / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - t), $MachinePrecision] * N[(N[(1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + N[(t$95$1 * N[(t - x), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.0000000000000001e252

   1. Initial program 68.2%

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

   3. Applied rewrites 83.2%

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

   if -1.0000000000000001e252 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2.00000000000000003e116

   1. Initial program 68.2%

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

   3. Applied rewrites 63.4%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 78.9%

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

   if 2.00000000000000003e116 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

Alternative 2: 92.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{z - a}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-278}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{a}{a - z}, \mathsf{fma}\left(x, t\_1, \frac{t - x}{a - z} \cdot \left(y - z\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{1}{z - a} \cdot y, \mathsf{fma}\left(t\_1, t - x, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (- z a))) (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e-278)
     (fma x (/ a (- a z)) (fma x t_1 (* (/ (- t x) (- a z)) (- y z))))
     (if (<= t_2 0.0)
       (+ t (* -1.0 (/ (- (* y (- t x)) (* a (- t x))) z)))
       (fma (- x t) (* (/ 1.0 (- z a)) y) (fma t_1 (- t x) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (z - a);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-278) {
		tmp = fma(x, (a / (a - z)), fma(x, t_1, (((t - x) / (a - z)) * (y - z))));
	} else if (t_2 <= 0.0) {
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z));
	} else {
		tmp = fma((x - t), ((1.0 / (z - a)) * y), fma(t_1, (t - x), x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(z - a))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e-278)
		tmp = fma(x, Float64(a / Float64(a - z)), fma(x, t_1, Float64(Float64(Float64(t - x) / Float64(a - z)) * Float64(y - z))));
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(-1.0 * Float64(Float64(Float64(y * Float64(t - x)) - Float64(a * Float64(t - x))) / z)));
	else
		tmp = fma(Float64(x - t), Float64(Float64(1.0 / Float64(z - a)) * y), fma(t_1, Float64(t - x), x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-278], N[(x * N[(a / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$1 + N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(-1.0 * N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - t), $MachinePrecision] * N[(N[(1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + N[(t$95$1 * N[(t - x), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999985e-278

   1. Initial program 68.2%

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

   3. Applied rewrites 83.2%

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

   if -4.99999999999999985e-278 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 68.2%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 45.8%

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

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

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

Alternative 3: 91.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{z - a}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-278}:\\ \;\;\;\;\mathsf{fma}\left(x - t, t\_1 \cdot \left(y - z\right), x\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, \left(t - x\right) \cdot \left(z - y\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a - z}, y, \mathsf{fma}\left(\frac{z}{z - a}, t - x, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 1.0 (- z a))) (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e-278)
     (fma (- x t) (* t_1 (- y z)) x)
     (if (<= t_2 0.0)
       (+ t (* -1.0 (/ (- (* y (- t x)) (* a (- t x))) z)))
       (if (<= t_2 2e+307)
         (fma t_1 (* (- t x) (- z y)) x)
         (fma (/ (- t x) (- a z)) y (fma (/ z (- z a)) (- t x) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 1.0 / (z - a);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-278) {
		tmp = fma((x - t), (t_1 * (y - z)), x);
	} else if (t_2 <= 0.0) {
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z));
	} else if (t_2 <= 2e+307) {
		tmp = fma(t_1, ((t - x) * (z - y)), x);
	} else {
		tmp = fma(((t - x) / (a - z)), y, fma((z / (z - a)), (t - x), x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(1.0 / Float64(z - a))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e-278)
		tmp = fma(Float64(x - t), Float64(t_1 * Float64(y - z)), x);
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(-1.0 * Float64(Float64(Float64(y * Float64(t - x)) - Float64(a * Float64(t - x))) / z)));
	elseif (t_2 <= 2e+307)
		tmp = fma(t_1, Float64(Float64(t - x) * Float64(z - y)), x);
	else
		tmp = fma(Float64(Float64(t - x) / Float64(a - z)), y, fma(Float64(z / Float64(z - a)), Float64(t - x), x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-278], N[(N[(x - t), $MachinePrecision] * N[(t$95$1 * N[(y - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(-1.0 * N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+307], N[(t$95$1 * N[(N[(t - x), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * y + N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999985e-278

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   5. Applied rewrites 84.1%

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

   if -4.99999999999999985e-278 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 68.2%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 45.8%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1.99999999999999997e307

   1. Initial program 68.2%

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

   3. Applied rewrites 68.2%

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

   if 1.99999999999999997e307 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 68.2%

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

   3. Applied rewrites 85.5%

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

Alternative 4: 91.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x - t, \frac{1}{z - a} \cdot y, \mathsf{fma}\left(\frac{z}{z - a}, t - x, x\right)\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- x t) (* (/ 1.0 (- z a)) y) (fma (/ z (- z a)) (- t x) x)))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e-278)
     t_1
     (if (<= t_2 0.0)
       (+ t (* -1.0 (/ (- (* y (- t x)) (* a (- t x))) z)))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - t), ((1.0 / (z - a)) * y), fma((z / (z - a)), (t - x), x));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-278) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - t), Float64(Float64(1.0 / Float64(z - a)) * y), fma(Float64(z / Float64(z - a)), Float64(t - x), x))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e-278)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(-1.0 * Float64(Float64(Float64(y * Float64(t - x)) - Float64(a * Float64(t - x))) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * N[(N[(1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-278], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(-1.0 * N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999985e-278 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   if -4.99999999999999985e-278 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 68.2%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 45.8%

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

Alternative 5: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-278}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{1}{z - a} \cdot \left(y - z\right), x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z - a}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -5e-278)
     (fma (- x t) (* (/ 1.0 (- z a)) (- y z)) x)
     (if (<= t_1 0.0)
       (+ t (* -1.0 (/ (- (* y (- t x)) (* a (- t x))) z)))
       (fma (/ (- z y) (- z a)) (- t x) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -5e-278) {
		tmp = fma((x - t), ((1.0 / (z - a)) * (y - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z));
	} else {
		tmp = fma(((z - y) / (z - a)), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -5e-278)
		tmp = fma(Float64(x - t), Float64(Float64(1.0 / Float64(z - a)) * Float64(y - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(-1.0 * Float64(Float64(Float64(y * Float64(t - x)) - Float64(a * Float64(t - x))) / z)));
	else
		tmp = fma(Float64(Float64(z - y) / Float64(z - a)), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-278], N[(N[(x - t), $MachinePrecision] * N[(N[(1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(-1.0 * N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999985e-278

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   5. Applied rewrites 84.1%

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

   if -4.99999999999999985e-278 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 68.2%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 45.8%

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

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

   1. Initial program 68.2%

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

   3. Applied rewrites 84.2%

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

Alternative 6: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-278}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{1}{z - a} \cdot \left(y - z\right), x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z - a}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -5e-278)
     (fma (- x t) (* (/ 1.0 (- z a)) (- y z)) x)
     (if (<= t_1 0.0)
       (+ t (/ (* y (- x t)) z))
       (fma (/ (- z y) (- z a)) (- t x) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -5e-278) {
		tmp = fma((x - t), ((1.0 / (z - a)) * (y - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = fma(((z - y) / (z - a)), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -5e-278)
		tmp = fma(Float64(x - t), Float64(Float64(1.0 / Float64(z - a)) * Float64(y - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	else
		tmp = fma(Float64(Float64(z - y) / Float64(z - a)), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-278], N[(N[(x - t), $MachinePrecision] * N[(N[(1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999985e-278

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   5. Applied rewrites 84.1%

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

   if -4.99999999999999985e-278 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 44.1%

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

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

   1. Initial program 68.2%

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

   3. Applied rewrites 84.2%

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

Alternative 7: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - y}{z - a}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-278}:\\ \;\;\;\;x + t\_1 \cdot \left(t - x\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z y) (- z a))) (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e-278)
     (+ x (* t_1 (- t x)))
     (if (<= t_2 0.0) (+ t (/ (* y (- x t)) z)) (fma t_1 (- t x) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - y) / (z - a);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-278) {
		tmp = x + (t_1 * (t - x));
	} else if (t_2 <= 0.0) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = fma(t_1, (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - y) / Float64(z - a))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e-278)
		tmp = Float64(x + Float64(t_1 * Float64(t - x)));
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	else
		tmp = fma(t_1, Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-278], N[(x + N[(t$95$1 * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999985e-278

   1. Initial program 68.2%

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

   3. Applied rewrites 84.2%

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

   if -4.99999999999999985e-278 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 44.1%

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

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

   1. Initial program 68.2%

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

   3. Applied rewrites 84.2%

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

Alternative 8: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{z - a}, t - x, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) (- z a)) (- t x) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e-278) t_1 (if (<= t_2 0.0) (+ t (/ (* y (- x t)) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - y) / (z - a)), (t - x), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-278) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / Float64(z - a)), Float64(t - x), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e-278)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-278], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999985e-278 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 68.2%

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

   3. Applied rewrites 84.2%

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

   if -4.99999999999999985e-278 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 44.1%

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

Alternative 9: 81.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+209}:\\ \;\;\;\;t \cdot \left(\frac{1}{z - a} \cdot \left(z - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z - a}, z - y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+209)
   (* t (* (/ 1.0 (- z a)) (- z y)))
   (fma (/ (- t x) (- z a)) (- z y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+209) {
		tmp = t * ((1.0 / (z - a)) * (z - y));
	} else {
		tmp = fma(((t - x) / (z - a)), (z - y), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+209)
		tmp = Float64(t * Float64(Float64(1.0 / Float64(z - a)) * Float64(z - y)));
	else
		tmp = fma(Float64(Float64(t - x) / Float64(z - a)), Float64(z - y), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+209], N[(t * N[(N[(1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000005e209

   1. Initial program 68.2%

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

   3. Applied rewrites 80.2%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 50.8%

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

   8. Applied rewrites 50.7%

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

   if -1.15000000000000005e209 < z

   1. Initial program 68.2%

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

   3. Applied rewrites 80.2%

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

Alternative 10: 72.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{z - a}, z - y, x\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+79}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-36}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t (- z a)) (- z y) x)))
   (if (<= a -1.7e+79)
     (+ x (* (/ y a) (- t x)))
     (if (<= a -1.8e-42)
       t_1
       (if (<= a 4e-36) (+ t (/ (* y (- x t)) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / (z - a)), (z - y), x);
	double tmp;
	if (a <= -1.7e+79) {
		tmp = x + ((y / a) * (t - x));
	} else if (a <= -1.8e-42) {
		tmp = t_1;
	} else if (a <= 4e-36) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / Float64(z - a)), Float64(z - y), x)
	tmp = 0.0
	if (a <= -1.7e+79)
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - x)));
	elseif (a <= -1.8e-42)
		tmp = t_1;
	elseif (a <= 4e-36)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.7e+79], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.8e-42], t$95$1, If[LessEqual[a, 4e-36], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.70000000000000016e79

   1. Initial program 68.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 44.3%

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

   6. Applied rewrites 49.2%

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

   if -1.70000000000000016e79 < a < -1.8000000000000001e-42 or 3.9999999999999998e-36 < a

   1. Initial program 68.2%

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

   3. Applied rewrites 80.2%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 63.6%

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

   if -1.8000000000000001e-42 < a < 3.9999999999999998e-36

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 44.1%

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

Alternative 11: 67.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-36}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ y a) (- t x)))))
   (if (<= a -1.4e+68) t_1 (if (<= a 4.5e-36) (+ t (/ (* y (- x t)) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y / a) * (t - x));
	double tmp;
	if (a <= -1.4e+68) {
		tmp = t_1;
	} else if (a <= 4.5e-36) {
		tmp = t + ((y * (x - t)) / 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 / a) * (t - x))
    if (a <= (-1.4d+68)) then
        tmp = t_1
    else if (a <= 4.5d-36) then
        tmp = t + ((y * (x - t)) / 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 / a) * (t - x));
	double tmp;
	if (a <= -1.4e+68) {
		tmp = t_1;
	} else if (a <= 4.5e-36) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y / a) * (t - x))
	tmp = 0
	if a <= -1.4e+68:
		tmp = t_1
	elif a <= 4.5e-36:
		tmp = t + ((y * (x - t)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y / a) * Float64(t - x)))
	tmp = 0.0
	if (a <= -1.4e+68)
		tmp = t_1;
	elseif (a <= 4.5e-36)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y / a) * (t - x));
	tmp = 0.0;
	if (a <= -1.4e+68)
		tmp = t_1;
	elseif (a <= 4.5e-36)
		tmp = t + ((y * (x - t)) / 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[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+68], t$95$1, If[LessEqual[a, 4.5e-36], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4e68 or 4.50000000000000024e-36 < a

   1. Initial program 68.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 44.3%

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

   6. Applied rewrites 49.2%

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

   if -1.4e68 < a < 4.50000000000000024e-36

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 44.1%

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

Alternative 12: 59.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \left(1 + \frac{z}{a - z}\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-9}:\\ \;\;\;\;\frac{\left(-x\right) \cdot a}{z - a}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+18}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.7e+189)
   (* x (+ 1.0 (/ z (- a z))))
   (if (<= a -3e+25)
     (* (/ y (- z a)) (- x t))
     (if (<= a -2.15e-9)
       (/ (* (- x) a) (- z a))
       (if (<= a 2.2e+18) (+ t (/ (* y (- x t)) z)) (+ x (/ (* t y) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e+189) {
		tmp = x * (1.0 + (z / (a - z)));
	} else if (a <= -3e+25) {
		tmp = (y / (z - a)) * (x - t);
	} else if (a <= -2.15e-9) {
		tmp = (-x * a) / (z - a);
	} else if (a <= 2.2e+18) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = x + ((t * y) / a);
	}
	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 <= (-1.7d+189)) then
        tmp = x * (1.0d0 + (z / (a - z)))
    else if (a <= (-3d+25)) then
        tmp = (y / (z - a)) * (x - t)
    else if (a <= (-2.15d-9)) then
        tmp = (-x * a) / (z - a)
    else if (a <= 2.2d+18) then
        tmp = t + ((y * (x - t)) / z)
    else
        tmp = x + ((t * y) / a)
    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 <= -1.7e+189) {
		tmp = x * (1.0 + (z / (a - z)));
	} else if (a <= -3e+25) {
		tmp = (y / (z - a)) * (x - t);
	} else if (a <= -2.15e-9) {
		tmp = (-x * a) / (z - a);
	} else if (a <= 2.2e+18) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.7e+189:
		tmp = x * (1.0 + (z / (a - z)))
	elif a <= -3e+25:
		tmp = (y / (z - a)) * (x - t)
	elif a <= -2.15e-9:
		tmp = (-x * a) / (z - a)
	elif a <= 2.2e+18:
		tmp = t + ((y * (x - t)) / z)
	else:
		tmp = x + ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.7e+189)
		tmp = Float64(x * Float64(1.0 + Float64(z / Float64(a - z))));
	elseif (a <= -3e+25)
		tmp = Float64(Float64(y / Float64(z - a)) * Float64(x - t));
	elseif (a <= -2.15e-9)
		tmp = Float64(Float64(Float64(-x) * a) / Float64(z - a));
	elseif (a <= 2.2e+18)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	else
		tmp = Float64(x + Float64(Float64(t * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.7e+189)
		tmp = x * (1.0 + (z / (a - z)));
	elseif (a <= -3e+25)
		tmp = (y / (z - a)) * (x - t);
	elseif (a <= -2.15e-9)
		tmp = (-x * a) / (z - a);
	elseif (a <= 2.2e+18)
		tmp = t + ((y * (x - t)) / z);
	else
		tmp = x + ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.7e+189], N[(x * N[(1.0 + N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3e+25], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.15e-9], N[(N[((-x) * a), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+18], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.69999999999999992e189

   1. Initial program 68.2%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 48.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 25.5%

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

   if -1.69999999999999992e189 < a < -3.00000000000000006e25

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 42.1%

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

   8. Applied rewrites 44.0%

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

   if -3.00000000000000006e25 < a < -2.14999999999999981e-9

   1. Initial program 68.2%

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

   3. Applied rewrites 63.4%

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

   4. Taylor expanded in a around inf

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(a \cdot x\right)}}{z - a} \]

   6. Applied rewrites 21.3%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(a \cdot x\right)}}{z - a} \]

   8. Applied rewrites 21.3%

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

   if -2.14999999999999981e-9 < a < 2.2e18

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 44.1%

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

   if 2.2e18 < a

   1. Initial program 68.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 44.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 38.1%

      \[\leadsto x + \frac{t \cdot y}{a} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 13: 56.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-164}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{t}{z - a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- z a)) (- x t))))
   (if (<= y -1.05e-60)
     t_1
     (if (<= y 8.5e-164)
       (* t (/ z (- z a)))
       (if (<= y 4.8e+24) (* (/ t (- z a)) (- z y)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * (x - t);
	double tmp;
	if (y <= -1.05e-60) {
		tmp = t_1;
	} else if (y <= 8.5e-164) {
		tmp = t * (z / (z - a));
	} else if (y <= 4.8e+24) {
		tmp = (t / (z - a)) * (z - y);
	} 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 = (y / (z - a)) * (x - t)
    if (y <= (-1.05d-60)) then
        tmp = t_1
    else if (y <= 8.5d-164) then
        tmp = t * (z / (z - a))
    else if (y <= 4.8d+24) then
        tmp = (t / (z - a)) * (z - y)
    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 - a)) * (x - t);
	double tmp;
	if (y <= -1.05e-60) {
		tmp = t_1;
	} else if (y <= 8.5e-164) {
		tmp = t * (z / (z - a));
	} else if (y <= 4.8e+24) {
		tmp = (t / (z - a)) * (z - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (z - a)) * (x - t)
	tmp = 0
	if y <= -1.05e-60:
		tmp = t_1
	elif y <= 8.5e-164:
		tmp = t * (z / (z - a))
	elif y <= 4.8e+24:
		tmp = (t / (z - a)) * (z - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(z - a)) * Float64(x - t))
	tmp = 0.0
	if (y <= -1.05e-60)
		tmp = t_1;
	elseif (y <= 8.5e-164)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (y <= 4.8e+24)
		tmp = Float64(Float64(t / Float64(z - a)) * Float64(z - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (z - a)) * (x - t);
	tmp = 0.0;
	if (y <= -1.05e-60)
		tmp = t_1;
	elseif (y <= 8.5e-164)
		tmp = t * (z / (z - a));
	elseif (y <= 4.8e+24)
		tmp = (t / (z - a)) * (z - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e-60], t$95$1, If[LessEqual[y, 8.5e-164], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+24], N[(N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04999999999999996e-60 or 4.8000000000000001e24 < y

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 42.1%

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

   8. Applied rewrites 44.0%

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

   if -1.04999999999999996e-60 < y < 8.50000000000000035e-164

   1. Initial program 68.2%

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

   3. Applied rewrites 80.2%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 50.8%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 29.0%

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

   if 8.50000000000000035e-164 < y < 4.8000000000000001e24

   1. Initial program 68.2%

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

   3. Applied rewrites 80.2%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 50.8%

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

   8. Applied rewrites 45.4%

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

Alternative 14: 55.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{+25}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- z a)) (- x t))))
   (if (<= y -1.05e-60)
     t_1
     (if (<= y 8.2e-54)
       (* t (/ z (- z a)))
       (if (<= y 3.15e+25) (/ (* t (- y z)) (- a z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * (x - t);
	double tmp;
	if (y <= -1.05e-60) {
		tmp = t_1;
	} else if (y <= 8.2e-54) {
		tmp = t * (z / (z - a));
	} else if (y <= 3.15e+25) {
		tmp = (t * (y - z)) / (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 = (y / (z - a)) * (x - t)
    if (y <= (-1.05d-60)) then
        tmp = t_1
    else if (y <= 8.2d-54) then
        tmp = t * (z / (z - a))
    else if (y <= 3.15d+25) then
        tmp = (t * (y - z)) / (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 = (y / (z - a)) * (x - t);
	double tmp;
	if (y <= -1.05e-60) {
		tmp = t_1;
	} else if (y <= 8.2e-54) {
		tmp = t * (z / (z - a));
	} else if (y <= 3.15e+25) {
		tmp = (t * (y - z)) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (z - a)) * (x - t)
	tmp = 0
	if y <= -1.05e-60:
		tmp = t_1
	elif y <= 8.2e-54:
		tmp = t * (z / (z - a))
	elif y <= 3.15e+25:
		tmp = (t * (y - z)) / (a - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(z - a)) * Float64(x - t))
	tmp = 0.0
	if (y <= -1.05e-60)
		tmp = t_1;
	elseif (y <= 8.2e-54)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (y <= 3.15e+25)
		tmp = Float64(Float64(t * Float64(y - z)) / Float64(a - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (z - a)) * (x - t);
	tmp = 0.0;
	if (y <= -1.05e-60)
		tmp = t_1;
	elseif (y <= 8.2e-54)
		tmp = t * (z / (z - a));
	elseif (y <= 3.15e+25)
		tmp = (t * (y - z)) / (a - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e-60], t$95$1, If[LessEqual[y, 8.2e-54], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.15e+25], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04999999999999996e-60 or 3.14999999999999987e25 < y

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 42.1%

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

   8. Applied rewrites 44.0%

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

   if -1.04999999999999996e-60 < y < 8.2000000000000001e-54

   1. Initial program 68.2%

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

   3. Applied rewrites 80.2%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 50.8%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 29.0%

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

   if 8.2000000000000001e-54 < y < 3.14999999999999987e25

   1. Initial program 68.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 39.0%

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

Alternative 15: 52.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t \cdot y}{a}\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* t y) a))))
   (if (<= a -3.9e+110) t_1 (if (<= a 1.8e+18) (* t (- 1.0 (/ y z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t * y) / a);
	double tmp;
	if (a <= -3.9e+110) {
		tmp = t_1;
	} else if (a <= 1.8e+18) {
		tmp = t * (1.0 - (y / 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 + ((t * y) / a)
    if (a <= (-3.9d+110)) then
        tmp = t_1
    else if (a <= 1.8d+18) then
        tmp = t * (1.0d0 - (y / 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 + ((t * y) / a);
	double tmp;
	if (a <= -3.9e+110) {
		tmp = t_1;
	} else if (a <= 1.8e+18) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t * y) / a)
	tmp = 0
	if a <= -3.9e+110:
		tmp = t_1
	elif a <= 1.8e+18:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t * y) / a))
	tmp = 0.0
	if (a <= -3.9e+110)
		tmp = t_1;
	elseif (a <= 1.8e+18)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t * y) / a);
	tmp = 0.0;
	if (a <= -3.9e+110)
		tmp = t_1;
	elseif (a <= 1.8e+18)
		tmp = t * (1.0 - (y / 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[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.9e+110], t$95$1, If[LessEqual[a, 1.8e+18], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.9000000000000003e110 or 1.8e18 < a

   1. Initial program 68.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 44.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 38.1%

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

   if -3.9000000000000003e110 < a < 1.8e18

   1. Initial program 68.2%

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

   3. Applied rewrites 80.2%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 50.8%

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

   7. Taylor expanded in a around 0

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

   9. Applied rewrites 35.8%

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

Alternative 16: 45.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+110}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.3e+110)
   (+ x t)
   (if (<= a 1.55e+40) (* t (- 1.0 (/ y z))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3e+110) {
		tmp = x + t;
	} else if (a <= 1.55e+40) {
		tmp = t * (1.0 - (y / z));
	} 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 (a <= (-1.3d+110)) then
        tmp = x + t
    else if (a <= 1.55d+40) then
        tmp = t * (1.0d0 - (y / z))
    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 (a <= -1.3e+110) {
		tmp = x + t;
	} else if (a <= 1.55e+40) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.3e+110:
		tmp = x + t
	elif a <= 1.55e+40:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.3e+110)
		tmp = Float64(x + t);
	elseif (a <= 1.55e+40)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.3e+110)
		tmp = x + t;
	elseif (a <= 1.55e+40)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.3e+110], N[(x + t), $MachinePrecision], If[LessEqual[a, 1.55e+40], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3e110 or 1.5499999999999999e40 < a

   1. Initial program 68.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   4. Applied rewrites 19.1%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]

   7. Applied rewrites 34.1%

      \[\leadsto x + t \]

   if -1.3e110 < a < 1.5499999999999999e40

   1. Initial program 68.2%

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

   3. Applied rewrites 80.2%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 50.8%

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

   7. Taylor expanded in a around 0

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

   9. Applied rewrites 35.8%

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

Alternative 17: 43.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+33}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- x t) z))))
   (if (<= y -8.6e+27) t_1 (if (<= y 7.8e+33) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / z);
	double tmp;
	if (y <= -8.6e+27) {
		tmp = t_1;
	} else if (y <= 7.8e+33) {
		tmp = x + 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) :: tmp
    t_1 = y * ((x - t) / z)
    if (y <= (-8.6d+27)) then
        tmp = t_1
    else if (y <= 7.8d+33) then
        tmp = x + 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 - t) / z);
	double tmp;
	if (y <= -8.6e+27) {
		tmp = t_1;
	} else if (y <= 7.8e+33) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((x - t) / z)
	tmp = 0
	if y <= -8.6e+27:
		tmp = t_1
	elif y <= 7.8e+33:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(x - t) / z))
	tmp = 0.0
	if (y <= -8.6e+27)
		tmp = t_1;
	elseif (y <= 7.8e+33)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((x - t) / z);
	tmp = 0.0;
	if (y <= -8.6e+27)
		tmp = t_1;
	elseif (y <= 7.8e+33)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.6e+27], t$95$1, If[LessEqual[y, 7.8e+33], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.60000000000000017e27 or 7.8000000000000004e33 < y

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 42.1%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 26.1%

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

   if -8.60000000000000017e27 < y < 7.8000000000000004e33

   1. Initial program 68.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   4. Applied rewrites 19.1%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]

   7. Applied rewrites 34.1%

      \[\leadsto x + t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 41.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+33}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- x t)) z)))
   (if (<= y -1.15e+28) t_1 (if (<= y 7.8e+33) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (x - t)) / z;
	double tmp;
	if (y <= -1.15e+28) {
		tmp = t_1;
	} else if (y <= 7.8e+33) {
		tmp = x + 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) :: tmp
    t_1 = (y * (x - t)) / z
    if (y <= (-1.15d+28)) then
        tmp = t_1
    else if (y <= 7.8d+33) then
        tmp = x + 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 - t)) / z;
	double tmp;
	if (y <= -1.15e+28) {
		tmp = t_1;
	} else if (y <= 7.8e+33) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (x - t)) / z
	tmp = 0
	if y <= -1.15e+28:
		tmp = t_1
	elif y <= 7.8e+33:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(x - t)) / z)
	tmp = 0.0
	if (y <= -1.15e+28)
		tmp = t_1;
	elseif (y <= 7.8e+33)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (x - t)) / z;
	tmp = 0.0;
	if (y <= -1.15e+28)
		tmp = t_1;
	elseif (y <= 7.8e+33)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -1.15e+28], t$95$1, If[LessEqual[y, 7.8e+33], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.14999999999999992e28 or 7.8000000000000004e33 < y

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 42.1%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 24.0%

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

   if -1.14999999999999992e28 < y < 7.8000000000000004e33

   1. Initial program 68.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   4. Applied rewrites 19.1%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]

   7. Applied rewrites 34.1%

      \[\leadsto x + t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 39.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y}{z - a}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+45}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) (- z a))))
   (if (<= y -4.6e+28) t_1 (if (<= y 2.7e+45) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / (z - a);
	double tmp;
	if (y <= -4.6e+28) {
		tmp = t_1;
	} else if (y <= 2.7e+45) {
		tmp = x + 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) :: tmp
    t_1 = (x * y) / (z - a)
    if (y <= (-4.6d+28)) then
        tmp = t_1
    else if (y <= 2.7d+45) then
        tmp = x + 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 = (x * y) / (z - a);
	double tmp;
	if (y <= -4.6e+28) {
		tmp = t_1;
	} else if (y <= 2.7e+45) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * y) / (z - a)
	tmp = 0
	if y <= -4.6e+28:
		tmp = t_1
	elif y <= 2.7e+45:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / Float64(z - a))
	tmp = 0.0
	if (y <= -4.6e+28)
		tmp = t_1;
	elseif (y <= 2.7e+45)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / (z - a);
	tmp = 0.0;
	if (y <= -4.6e+28)
		tmp = t_1;
	elseif (y <= 2.7e+45)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+28], t$95$1, If[LessEqual[y, 2.7e+45], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.59999999999999968e28 or 2.69999999999999984e45 < y

   1. Initial program 68.2%

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

   3. Applied rewrites 88.3%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 42.1%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 21.9%

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

   if -4.59999999999999968e28 < y < 2.69999999999999984e45

   1. Initial program 68.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   4. Applied rewrites 19.1%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]

   7. Applied rewrites 34.1%

      \[\leadsto x + t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 37.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{-42}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+38}:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.7e-42) (+ x t) (if (<= a 1.85e+38) (* t 1.0) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.7e-42) {
		tmp = x + t;
	} else if (a <= 1.85e+38) {
		tmp = t * 1.0;
	} 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 (a <= (-5.7d-42)) then
        tmp = x + t
    else if (a <= 1.85d+38) then
        tmp = t * 1.0d0
    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 (a <= -5.7e-42) {
		tmp = x + t;
	} else if (a <= 1.85e+38) {
		tmp = t * 1.0;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.7e-42:
		tmp = x + t
	elif a <= 1.85e+38:
		tmp = t * 1.0
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.7e-42)
		tmp = Float64(x + t);
	elseif (a <= 1.85e+38)
		tmp = Float64(t * 1.0);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.7e-42)
		tmp = x + t;
	elseif (a <= 1.85e+38)
		tmp = t * 1.0;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.7e-42], N[(x + t), $MachinePrecision], If[LessEqual[a, 1.85e+38], N[(t * 1.0), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.6999999999999999e-42 or 1.8500000000000001e38 < a

   1. Initial program 68.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   4. Applied rewrites 19.1%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]

   7. Applied rewrites 34.1%

      \[\leadsto x + t \]

   if -5.6999999999999999e-42 < a < 1.8500000000000001e38

   1. Initial program 68.2%

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

   3. Applied rewrites 80.2%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 50.8%

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

   7. Taylor expanded in z around inf

      \[\leadsto t \cdot 1 \]

   9. Applied rewrites 24.8%

      \[\leadsto t \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 37.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+124}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.2e+124) (* t (/ y a)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.2e+124) {
		tmp = t * (y / a);
	} 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 (y <= (-4.2d+124)) then
        tmp = t * (y / a)
    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 (y <= -4.2e+124) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.2e+124:
		tmp = t * (y / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.2e+124)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.2e+124)
		tmp = t * (y / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.2e+124], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.20000000000000023e124

   1. Initial program 68.2%

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

   3. Applied rewrites 80.2%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 50.8%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 19.0%

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

   if -4.20000000000000023e124 < y

   1. Initial program 68.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   4. Applied rewrites 19.1%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]

   7. Applied rewrites 34.1%

      \[\leadsto x + t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 34.1% accurate, 4.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + t), $MachinePrecision]

Derivation

1. Initial program 68.2%

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

2. Taylor expanded in z around inf

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]

4. Applied rewrites 19.1%

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]

5. Taylor expanded in x around 0

   \[\leadsto x + t \]

7. Applied rewrites 34.1%

   \[\leadsto x + t \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025153 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64
  (+ x (/ (* (- y z) (- t x)) (- a z))))