Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.2% → 91.9%

Time: 18.2s

Alternatives: 16

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \mathsf{fma}\left(b - y, z, y\right)\\ t_3 := \mathsf{fma}\left(\frac{z}{t\_2}, t - a, \frac{y}{t\_2} \cdot x\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-270}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-200}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{\mathsf{fma}\left(-1, \frac{x \cdot y}{b - y}, \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}{z}, \frac{t}{b - y}\right) - \frac{a}{b - y}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_2 (fma (- b y) z y))
        (t_3 (fma (/ z t_2) (- t a) (* (/ y t_2) x))))
   (if (<= t_1 -1e-270)
     t_3
     (if (<= t_1 5e-200)
       (-
        (fma
         -1.0
         (/
          (fma -1.0 (/ (* x y) (- b y)) (/ (* y (- t a)) (pow (- b y) 2.0)))
          z)
         (/ t (- b y)))
        (/ a (- b y)))
       (if (<= t_1 INFINITY) t_3 (/ (- t a) (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = fma((b - y), z, y);
	double t_3 = fma((z / t_2), (t - a), ((y / t_2) * x));
	double tmp;
	if (t_1 <= -1e-270) {
		tmp = t_3;
	} else if (t_1 <= 5e-200) {
		tmp = fma(-1.0, (fma(-1.0, ((x * y) / (b - y)), ((y * (t - a)) / pow((b - y), 2.0))) / z), (t / (b - y))) - (a / (b - y));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = fma(Float64(b - y), z, y)
	t_3 = fma(Float64(z / t_2), Float64(t - a), Float64(Float64(y / t_2) * x))
	tmp = 0.0
	if (t_1 <= -1e-270)
		tmp = t_3;
	elseif (t_1 <= 5e-200)
		tmp = Float64(fma(-1.0, Float64(fma(-1.0, Float64(Float64(x * y) / Float64(b - y)), Float64(Float64(y * Float64(t - a)) / (Float64(b - y) ^ 2.0))) / z), Float64(t / Float64(b - y))) - Float64(a / Float64(b - y)));
	elseif (t_1 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - y), $MachinePrecision] * z + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z / t$95$2), $MachinePrecision] * N[(t - a), $MachinePrecision] + N[(N[(y / t$95$2), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-270], t$95$3, If[LessEqual[t$95$1, 5e-200], N[(N[(-1.0 * N[(N[(-1.0 * N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$3, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1e-270 or 4.99999999999999991e-200 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 66.2%

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

   3. Applied rewrites 71.6%

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

   5. Applied rewrites 79.1%

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

   if -1e-270 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4.99999999999999991e-200

   1. Initial program 66.2%

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

   3. Applied rewrites 71.6%

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

   4. Taylor expanded in z around -inf

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

   6. Applied rewrites 46.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1, \frac{\mathsf{fma}\left(-1, \frac{x \cdot y}{b - y}, \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}{z}, \frac{t}{b - y}\right) - \frac{a}{b - y}} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 66.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 91.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - y, z, y\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t\_1}, x, \frac{z \cdot \left(t - a\right)}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- b y) z y)) (t_2 (/ (- t a) (- b y))))
   (if (<= z -3.9e+94)
     t_2
     (if (<= z 9.5e+67) (fma (/ y t_1) x (/ (* z (- t a)) t_1)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b - y), z, y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.9e+94) {
		tmp = t_2;
	} else if (z <= 9.5e+67) {
		tmp = fma((y / t_1), x, ((z * (t - a)) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(b - y), z, y)
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.9e+94)
		tmp = t_2;
	elseif (z <= 9.5e+67)
		tmp = fma(Float64(y / t_1), x, Float64(Float64(z * Float64(t - a)) / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - y), $MachinePrecision] * z + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e+94], t$95$2, If[LessEqual[z, 9.5e+67], N[(N[(y / t$95$1), $MachinePrecision] * x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.89999999999999986e94 or 9.5000000000000002e67 < z

   1. Initial program 66.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 51.6%

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

   if -3.89999999999999986e94 < z < 9.5000000000000002e67

   1. Initial program 66.2%

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

   3. Applied rewrites 73.3%

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

Alternative 3: 88.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := x \cdot y + z \cdot \left(t - a\right)\\ t_3 := \frac{t\_2}{y + z \cdot \left(b - y\right)}\\ t_4 := \mathsf{fma}\left(b - y, z, y\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t\_4}, t - a, 1 \cdot x\right)\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-272}:\\ \;\;\;\;\frac{t\_2}{t\_4}\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 10^{+278}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t - a, z, x \cdot y\right)}{t\_4}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (+ (* x y) (* z (- t a))))
        (t_3 (/ t_2 (+ y (* z (- b y)))))
        (t_4 (fma (- b y) z y)))
   (if (<= t_3 (- INFINITY))
     (fma (/ z t_4) (- t a) (* 1.0 x))
     (if (<= t_3 -2e-272)
       (/ t_2 t_4)
       (if (<= t_3 0.0)
         t_1
         (if (<= t_3 1e+278) (/ (fma (- t a) z (* x y)) t_4) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = (x * y) + (z * (t - a));
	double t_3 = t_2 / (y + (z * (b - y)));
	double t_4 = fma((b - y), z, y);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = fma((z / t_4), (t - a), (1.0 * x));
	} else if (t_3 <= -2e-272) {
		tmp = t_2 / t_4;
	} else if (t_3 <= 0.0) {
		tmp = t_1;
	} else if (t_3 <= 1e+278) {
		tmp = fma((t - a), z, (x * y)) / t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_3 = Float64(t_2 / Float64(y + Float64(z * Float64(b - y))))
	t_4 = fma(Float64(b - y), z, y)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = fma(Float64(z / t_4), Float64(t - a), Float64(1.0 * x));
	elseif (t_3 <= -2e-272)
		tmp = Float64(t_2 / t_4);
	elseif (t_3 <= 0.0)
		tmp = t_1;
	elseif (t_3 <= 1e+278)
		tmp = Float64(fma(Float64(t - a), z, Float64(x * y)) / t_4);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b - y), $MachinePrecision] * z + y), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(z / t$95$4), $MachinePrecision] * N[(t - a), $MachinePrecision] + N[(1.0 * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -2e-272], N[(t$95$2 / t$95$4), $MachinePrecision], If[LessEqual[t$95$3, 0.0], t$95$1, If[LessEqual[t$95$3, 1e+278], N[(N[(N[(t - a), $MachinePrecision] * z + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0

   1. Initial program 66.2%

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

   3. Applied rewrites 71.6%

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 59.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999986e-272

   1. Initial program 66.2%

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

   3. Applied rewrites 66.2%

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

   if -1.99999999999999986e-272 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 9.99999999999999964e277 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 66.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 51.6%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 9.99999999999999964e277

   1. Initial program 66.2%

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

   3. Applied rewrites 66.2%

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

Alternative 4: 88.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_3 := \mathsf{fma}\left(b - y, z, y\right)\\ t_4 := \frac{\mathsf{fma}\left(t - a, z, x \cdot y\right)}{t\_3}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t\_3}, t - a, 1 \cdot x\right)\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-272}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+278}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_3 (fma (- b y) z y))
        (t_4 (/ (fma (- t a) z (* x y)) t_3)))
   (if (<= t_2 (- INFINITY))
     (fma (/ z t_3) (- t a) (* 1.0 x))
     (if (<= t_2 -2e-272)
       t_4
       (if (<= t_2 0.0) t_1 (if (<= t_2 1e+278) t_4 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_3 = fma((b - y), z, y);
	double t_4 = fma((t - a), z, (x * y)) / t_3;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma((z / t_3), (t - a), (1.0 * x));
	} else if (t_2 <= -2e-272) {
		tmp = t_4;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+278) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = fma(Float64(b - y), z, y)
	t_4 = Float64(fma(Float64(t - a), z, Float64(x * y)) / t_3)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(Float64(z / t_3), Float64(t - a), Float64(1.0 * x));
	elseif (t_2 <= -2e-272)
		tmp = t_4;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 1e+278)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b - y), $MachinePrecision] * z + y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t - a), $MachinePrecision] * z + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(z / t$95$3), $MachinePrecision] * N[(t - a), $MachinePrecision] + N[(1.0 * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-272], t$95$4, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 1e+278], t$95$4, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0

   1. Initial program 66.2%

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

   3. Applied rewrites 71.6%

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 59.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999986e-272 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 9.99999999999999964e277

   1. Initial program 66.2%

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

   3. Applied rewrites 66.2%

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

   if -1.99999999999999986e-272 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 9.99999999999999964e277 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 66.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t - a, z, x \cdot y\right)}{\mathsf{fma}\left(b - y, z, y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -3.9e+94)
     t_1
     (if (<= z 9.5e+67) (/ (fma (- t a) z (* x y)) (fma (- b y) z y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.9e+94) {
		tmp = t_1;
	} else if (z <= 9.5e+67) {
		tmp = fma((t - a), z, (x * y)) / fma((b - y), z, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.9e+94)
		tmp = t_1;
	elseif (z <= 9.5e+67)
		tmp = Float64(fma(Float64(t - a), z, Float64(x * y)) / fma(Float64(b - y), z, y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e+94], t$95$1, If[LessEqual[z, 9.5e+67], N[(N[(N[(t - a), $MachinePrecision] * z + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(N[(b - y), $MachinePrecision] * z + y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.89999999999999986e94 or 9.5000000000000002e67 < z

   1. Initial program 66.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 51.6%

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

   if -3.89999999999999986e94 < z < 9.5000000000000002e67

   1. Initial program 66.2%

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

   3. Applied rewrites 66.2%

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

Alternative 6: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -5e+54)
     t_1
     (if (<= z 6.5e-6) (/ (fma y x (* z (- t a))) (+ y (* z b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -5e+54) {
		tmp = t_1;
	} else if (z <= 6.5e-6) {
		tmp = fma(y, x, (z * (t - a))) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5e+54)
		tmp = t_1;
	elseif (z <= 6.5e-6)
		tmp = Float64(fma(y, x, Float64(z * Float64(t - a))) / Float64(y + Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+54], t$95$1, If[LessEqual[z, 6.5e-6], N[(N[(y * x + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000005e54 or 6.4999999999999996e-6 < z

   1. Initial program 66.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 51.6%

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

   if -5.00000000000000005e54 < z < 6.4999999999999996e-6

   1. Initial program 66.2%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 57.1%

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

   6. Applied rewrites 57.1%

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

Alternative 7: 72.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-98}:\\ \;\;\;\;\frac{y \cdot x - a \cdot z}{\mathsf{fma}\left(b - y, z, y\right)}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, z, x \cdot y\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -5.6e-14)
     t_1
     (if (<= z 7.2e-98)
       (/ (- (* y x) (* a z)) (fma (- b y) z y))
       (if (<= z 6.5e-6) (/ (fma t z (* x y)) (+ y (* z (- b y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.6e-14) {
		tmp = t_1;
	} else if (z <= 7.2e-98) {
		tmp = ((y * x) - (a * z)) / fma((b - y), z, y);
	} else if (z <= 6.5e-6) {
		tmp = fma(t, z, (x * y)) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5.6e-14)
		tmp = t_1;
	elseif (z <= 7.2e-98)
		tmp = Float64(Float64(Float64(y * x) - Float64(a * z)) / fma(Float64(b - y), z, y));
	elseif (z <= 6.5e-6)
		tmp = Float64(fma(t, z, Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e-14], t$95$1, If[LessEqual[z, 7.2e-98], N[(N[(N[(y * x), $MachinePrecision] - N[(a * z), $MachinePrecision]), $MachinePrecision] / N[(N[(b - y), $MachinePrecision] * z + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-6], N[(N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6000000000000001e-14 or 6.4999999999999996e-6 < z

   1. Initial program 66.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 51.6%

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

   if -5.6000000000000001e-14 < z < 7.2000000000000005e-98

   1. Initial program 66.2%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 23.7%

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

   6. Applied rewrites 23.7%

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

   7. Taylor expanded in t around 0

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

   9. Applied rewrites 47.4%

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

   11. Applied rewrites 47.4%

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

   if 7.2000000000000005e-98 < z < 6.4999999999999996e-6

   1. Initial program 66.2%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 47.8%

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

Alternative 8: 71.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-66}:\\ \;\;\;\;\frac{y \cdot x - a \cdot z}{\mathsf{fma}\left(b - y, z, y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -5.6e-14)
     t_1
     (if (<= z 3.4e-66) (/ (- (* y x) (* a z)) (fma (- b y) z y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.6e-14) {
		tmp = t_1;
	} else if (z <= 3.4e-66) {
		tmp = ((y * x) - (a * z)) / fma((b - y), z, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5.6e-14)
		tmp = t_1;
	elseif (z <= 3.4e-66)
		tmp = Float64(Float64(Float64(y * x) - Float64(a * z)) / fma(Float64(b - y), z, y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e-14], t$95$1, If[LessEqual[z, 3.4e-66], N[(N[(N[(y * x), $MachinePrecision] - N[(a * z), $MachinePrecision]), $MachinePrecision] / N[(N[(b - y), $MachinePrecision] * z + y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.6000000000000001e-14 or 3.39999999999999997e-66 < z

   1. Initial program 66.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 51.6%

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

   if -5.6000000000000001e-14 < z < 3.39999999999999997e-66

   1. Initial program 66.2%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 23.7%

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

   6. Applied rewrites 23.7%

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

   7. Taylor expanded in t around 0

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

   9. Applied rewrites 47.4%

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

   11. Applied rewrites 47.4%

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

Alternative 9: 68.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-199}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{\mathsf{fma}\left(b - y, z, y\right)}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot \left(-1 \cdot \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -5e+54)
     t_1
     (if (<= z -2.2e-199)
       (/ (* z (- t a)) (fma (- b y) z y))
       (if (<= z 1.75e-67) (+ x (* z (* -1.0 (/ a y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -5e+54) {
		tmp = t_1;
	} else if (z <= -2.2e-199) {
		tmp = (z * (t - a)) / fma((b - y), z, y);
	} else if (z <= 1.75e-67) {
		tmp = x + (z * (-1.0 * (a / y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5e+54)
		tmp = t_1;
	elseif (z <= -2.2e-199)
		tmp = Float64(Float64(z * Float64(t - a)) / fma(Float64(b - y), z, y));
	elseif (z <= 1.75e-67)
		tmp = Float64(x + Float64(z * Float64(-1.0 * Float64(a / y))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+54], t$95$1, If[LessEqual[z, -2.2e-199], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(N[(b - y), $MachinePrecision] * z + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-67], N[(x + N[(z * N[(-1.0 * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000005e54 or 1.75e-67 < z

   1. Initial program 66.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 51.6%

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

   if -5.00000000000000005e54 < z < -2.1999999999999998e-199

   1. Initial program 66.2%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 23.7%

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

   6. Applied rewrites 23.7%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 41.7%

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

   if -2.1999999999999998e-199 < z < 1.75e-67

   1. Initial program 66.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 28.2%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 31.2%

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

Alternative 10: 67.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(t - a, z, x \cdot y\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -3.8e-28)
     t_1
     (if (<= z 1.75e-67) (* (fma (- t a) z (* x y)) (/ 1.0 y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.8e-28) {
		tmp = t_1;
	} else if (z <= 1.75e-67) {
		tmp = fma((t - a), z, (x * y)) * (1.0 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.8e-28)
		tmp = t_1;
	elseif (z <= 1.75e-67)
		tmp = Float64(fma(Float64(t - a), z, Float64(x * y)) * Float64(1.0 / y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e-28], t$95$1, If[LessEqual[z, 1.75e-67], N[(N[(N[(t - a), $MachinePrecision] * z + N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.80000000000000009e-28 or 1.75e-67 < z

   1. Initial program 66.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 51.6%

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

   if -3.80000000000000009e-28 < z < 1.75e-67

   1. Initial program 66.2%

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

   3. Applied rewrites 66.1%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 32.9%

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

Alternative 11: 67.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-199}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot \left(-1 \cdot \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -5000000.0)
     t_1
     (if (<= z -2.2e-199)
       (/ (* z (- t a)) (+ y (* z b)))
       (if (<= z 1.75e-67) (+ x (* z (* -1.0 (/ a y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -5000000.0) {
		tmp = t_1;
	} else if (z <= -2.2e-199) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else if (z <= 1.75e-67) {
		tmp = x + (z * (-1.0 * (a / 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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-5000000.0d0)) then
        tmp = t_1
    else if (z <= (-2.2d-199)) then
        tmp = (z * (t - a)) / (y + (z * b))
    else if (z <= 1.75d-67) then
        tmp = x + (z * ((-1.0d0) * (a / 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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -5000000.0) {
		tmp = t_1;
	} else if (z <= -2.2e-199) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else if (z <= 1.75e-67) {
		tmp = x + (z * (-1.0 * (a / y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -5000000.0:
		tmp = t_1
	elif z <= -2.2e-199:
		tmp = (z * (t - a)) / (y + (z * b))
	elif z <= 1.75e-67:
		tmp = x + (z * (-1.0 * (a / y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5000000.0)
		tmp = t_1;
	elseif (z <= -2.2e-199)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * b)));
	elseif (z <= 1.75e-67)
		tmp = Float64(x + Float64(z * Float64(-1.0 * Float64(a / y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -5000000.0)
		tmp = t_1;
	elseif (z <= -2.2e-199)
		tmp = (z * (t - a)) / (y + (z * b));
	elseif (z <= 1.75e-67)
		tmp = x + (z * (-1.0 * (a / y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5000000.0], t$95$1, If[LessEqual[z, -2.2e-199], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-67], N[(x + N[(z * N[(-1.0 * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5e6 or 1.75e-67 < z

   1. Initial program 66.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 51.6%

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

   if -5e6 < z < -2.1999999999999998e-199

   1. Initial program 66.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 41.7%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 35.1%

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

   if -2.1999999999999998e-199 < z < 1.75e-67

   1. Initial program 66.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 28.2%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 31.2%

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

Alternative 12: 67.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot \left(-1 \cdot \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -5.8e-32)
     t_1
     (if (<= z 1.75e-67) (+ x (* z (* -1.0 (/ a y)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.8e-32) {
		tmp = t_1;
	} else if (z <= 1.75e-67) {
		tmp = x + (z * (-1.0 * (a / 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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-5.8d-32)) then
        tmp = t_1
    else if (z <= 1.75d-67) then
        tmp = x + (z * ((-1.0d0) * (a / 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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.8e-32) {
		tmp = t_1;
	} else if (z <= 1.75e-67) {
		tmp = x + (z * (-1.0 * (a / y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -5.8e-32:
		tmp = t_1
	elif z <= 1.75e-67:
		tmp = x + (z * (-1.0 * (a / y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5.8e-32)
		tmp = t_1;
	elseif (z <= 1.75e-67)
		tmp = Float64(x + Float64(z * Float64(-1.0 * Float64(a / y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -5.8e-32)
		tmp = t_1;
	elseif (z <= 1.75e-67)
		tmp = x + (z * (-1.0 * (a / y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e-32], t$95$1, If[LessEqual[z, 1.75e-67], N[(x + N[(z * N[(-1.0 * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999991e-32 or 1.75e-67 < z

   1. Initial program 66.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 51.6%

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

   if -5.79999999999999991e-32 < z < 1.75e-67

   1. Initial program 66.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 28.2%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 31.2%

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

Alternative 13: 64.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-68}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.85e-83) t_1 (if (<= z 6.1e-68) (+ x (* x z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.85e-83) {
		tmp = t_1;
	} else if (z <= 6.1e-68) {
		tmp = x + (x * 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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.85d-83)) then
        tmp = t_1
    else if (z <= 6.1d-68) then
        tmp = x + (x * 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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.85e-83) {
		tmp = t_1;
	} else if (z <= 6.1e-68) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.85e-83:
		tmp = t_1
	elif z <= 6.1e-68:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.85e-83)
		tmp = t_1;
	elseif (z <= 6.1e-68)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.85e-83)
		tmp = t_1;
	elseif (z <= 6.1e-68)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e-83], t$95$1, If[LessEqual[z, 6.1e-68], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999997e-83 or 6.1e-68 < z

   1. Initial program 66.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 51.6%

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

   if -1.84999999999999997e-83 < z < 6.1e-68

   1. Initial program 66.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 28.2%

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

   5. Taylor expanded in y around inf

      \[\leadsto x + x \cdot \color{blue}{z} \]

   7. Applied rewrites 25.8%

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

Alternative 14: 48.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-68}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) b)))
   (if (<= z -2.35e-83) t_1 (if (<= z 6.1e-68) (+ x (* x z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double tmp;
	if (z <= -2.35e-83) {
		tmp = t_1;
	} else if (z <= 6.1e-68) {
		tmp = x + (x * 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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / b
    if (z <= (-2.35d-83)) then
        tmp = t_1
    else if (z <= 6.1d-68) then
        tmp = x + (x * 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 b) {
	double t_1 = (t - a) / b;
	double tmp;
	if (z <= -2.35e-83) {
		tmp = t_1;
	} else if (z <= 6.1e-68) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / b
	tmp = 0
	if z <= -2.35e-83:
		tmp = t_1
	elif z <= 6.1e-68:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / b)
	tmp = 0.0
	if (z <= -2.35e-83)
		tmp = t_1;
	elseif (z <= 6.1e-68)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / b;
	tmp = 0.0;
	if (z <= -2.35e-83)
		tmp = t_1;
	elseif (z <= 6.1e-68)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[z, -2.35e-83], t$95$1, If[LessEqual[z, 6.1e-68], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3500000000000002e-83 or 6.1e-68 < z

   1. Initial program 66.2%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 35.6%

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

   if -2.3500000000000002e-83 < z < 6.1e-68

   1. Initial program 66.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 28.2%

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

   5. Taylor expanded in y around inf

      \[\leadsto x + x \cdot \color{blue}{z} \]

   7. Applied rewrites 25.8%

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

Alternative 15: 36.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-39}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-67}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.5e-39) (/ t b) (if (<= z 1.75e-67) (+ x (* x z)) (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.5e-39) {
		tmp = t / b;
	} else if (z <= 1.75e-67) {
		tmp = x + (x * z);
	} else {
		tmp = t / b;
	}
	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, b)
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), intent (in) :: b
    real(8) :: tmp
    if (z <= (-6.5d-39)) then
        tmp = t / b
    else if (z <= 1.75d-67) then
        tmp = x + (x * z)
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.5e-39) {
		tmp = t / b;
	} else if (z <= 1.75e-67) {
		tmp = x + (x * z);
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.5e-39:
		tmp = t / b
	elif z <= 1.75e-67:
		tmp = x + (x * z)
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.5e-39)
		tmp = Float64(t / b);
	elseif (z <= 1.75e-67)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.5e-39)
		tmp = t / b;
	elseif (z <= 1.75e-67)
		tmp = x + (x * z);
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.5e-39], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.75e-67], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000027e-39 or 1.75e-67 < z

   1. Initial program 66.2%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 35.6%

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

   5. Taylor expanded in t around inf

      \[\leadsto \frac{t}{\color{blue}{b}} \]

   7. Applied rewrites 20.0%

      \[\leadsto \frac{t}{\color{blue}{b}} \]

   if -6.50000000000000027e-39 < z < 1.75e-67

   1. Initial program 66.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 28.2%

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

   5. Taylor expanded in y around inf

      \[\leadsto x + x \cdot \color{blue}{z} \]

   7. Applied rewrites 25.8%

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

Alternative 16: 20.0% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \frac{t}{b} \end{array} \]

FPCore

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

C

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

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, b)
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), intent (in) :: b
    code = t / b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(t / b), $MachinePrecision]

Derivation

1. Initial program 66.2%

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

2. Taylor expanded in y around 0

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

4. Applied rewrites 35.6%

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

5. Taylor expanded in t around inf

   \[\leadsto \frac{t}{\color{blue}{b}} \]

7. Applied rewrites 20.0%

   \[\leadsto \frac{t}{\color{blue}{b}} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025153 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64
  (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))