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

Percentage Accurate: 85.5% → 98.8%

Time: 3.6s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z - t, \frac{y}{z - a}, x\right)\\ t_2 := x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+268}:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(-t, y, z \cdot y\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- z t) (/ y (- z a)) x))
        (t_2 (+ x (/ (* y (- z t)) (- z a)))))
   (if (<= t_2 -5e+190)
     t_1
     (if (<= t_2 2e+268) (+ x (/ (fma (- t) y (* z y)) (- z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((z - t), (y / (z - a)), x);
	double t_2 = x + ((y * (z - t)) / (z - a));
	double tmp;
	if (t_2 <= -5e+190) {
		tmp = t_1;
	} else if (t_2 <= 2e+268) {
		tmp = x + (fma(-t, y, (z * y)) / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(z - t), Float64(y / Float64(z - a)), x)
	t_2 = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(z - a)))
	tmp = 0.0
	if (t_2 <= -5e+190)
		tmp = t_1;
	elseif (t_2 <= 2e+268)
		tmp = Float64(x + Float64(fma(Float64(-t), y, Float64(z * y)) / Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+190], t$95$1, If[LessEqual[t$95$2, 2e+268], N[(x + N[(N[((-t) * y + N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))) < -5.00000000000000036e190 or 1.9999999999999999e268 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

   1. Initial program 60.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 75.9

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

   4. Applied rewrites 75.9%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 97.5

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

   7. Applied rewrites 97.5%

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

   if -5.00000000000000036e190 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))) < 1.9999999999999999e268

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 99.6

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

   4. Applied rewrites 99.6%

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

Alternative 2: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z - t, \frac{y}{z - a}, x\right)\\ t_2 := x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+268}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- z t) (/ y (- z a)) x))
        (t_2 (+ x (/ (* y (- z t)) (- z a)))))
   (if (<= t_2 -5e+190) t_1 (if (<= t_2 2e+268) t_2 t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((z - t), (y / (z - a)), x);
	double t_2 = x + ((y * (z - t)) / (z - a));
	double tmp;
	if (t_2 <= -5e+190) {
		tmp = t_1;
	} else if (t_2 <= 2e+268) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(z - t), Float64(y / Float64(z - a)), x)
	t_2 = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(z - a)))
	tmp = 0.0
	if (t_2 <= -5e+190)
		tmp = t_1;
	elseif (t_2 <= 2e+268)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+190], t$95$1, If[LessEqual[t$95$2, 2e+268], t$95$2, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))) < -5.00000000000000036e190 or 1.9999999999999999e268 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

   1. Initial program 60.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 75.9

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

   4. Applied rewrites 75.9%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 97.5

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

   7. Applied rewrites 97.5%

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

   if -5.00000000000000036e190 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))) < 1.9999999999999999e268

   1. Initial program 99.6%

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

Alternative 3: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.5%

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

2. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. +-commutative N/A

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

   4. associate-/l* N/A

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

   5. lower-fma.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lift--.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lift--.f64 84.5

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

4. Applied rewrites 84.5%

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

5. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. associate-/l* N/A

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

   4. lower-fma.f64 N/A

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

   5. lift--.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lift--.f64 96.0

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

7. Applied rewrites 96.0%

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

Alternative 4: 80.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+24}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t\_1 \leq 6 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{z - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (<= t_1 -4e+24)
     (* (- z t) (/ y (- z a)))
     (if (<= t_1 6e-6) (fma y (/ z (- z a)) x) (fma (- z t) (/ y z) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_1 <= -4e+24) {
		tmp = (z - t) * (y / (z - a));
	} else if (t_1 <= 6e-6) {
		tmp = fma(y, (z / (z - a)), x);
	} else {
		tmp = fma((z - t), (y / z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -4e+24)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (t_1 <= 6e-6)
		tmp = fma(y, Float64(z / Float64(z - a)), x);
	else
		tmp = fma(Float64(z - t), Float64(y / z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+24], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 6e-6], N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -3.9999999999999999e24

   1. Initial program 69.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 56.5

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

   4. Applied rewrites 56.5%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 77.8

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

   6. Applied rewrites 77.8%

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

   if -3.9999999999999999e24 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 6.0000000000000002e-6

   1. Initial program 99.6%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 90.2

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

   4. Applied rewrites 90.2%

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

   if 6.0000000000000002e-6 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 71.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 96.7

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

   7. Applied rewrites 96.7%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 63.7%

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

Alternative 5: 80.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{z}{z - a}, x\right)\\ \mathbf{if}\;a \leq -9 \cdot 10^{-148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ z (- z a)) x)))
   (if (<= a -9e-148) t_1 (if (<= a 3.5e+37) (fma (- z t) (/ y z) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (z / (z - a)), x);
	double tmp;
	if (a <= -9e-148) {
		tmp = t_1;
	} else if (a <= 3.5e+37) {
		tmp = fma((z - t), (y / z), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(z / Float64(z - a)), x)
	tmp = 0.0
	if (a <= -9e-148)
		tmp = t_1;
	elseif (a <= 3.5e+37)
		tmp = fma(Float64(z - t), Float64(y / z), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -9e-148], t$95$1, If[LessEqual[a, 3.5e+37], N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -9.00000000000000029e-148 or 3.5e37 < a

   1. Initial program 84.1%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 76.7

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

   4. Applied rewrites 76.7%

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

   if -9.00000000000000029e-148 < a < 3.5e37

   1. Initial program 87.6%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 81.0

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

   4. Applied rewrites 81.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 95.0

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

   7. Applied rewrites 95.0%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 81.7%

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

Alternative 6: 78.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{z}{z - a}, x\right)\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ z (- z a)) x)))
   (if (<= a -1.35e-77) t_1 (if (<= a 3.5e+37) (fma y (/ (- z t) z) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (z / (z - a)), x);
	double tmp;
	if (a <= -1.35e-77) {
		tmp = t_1;
	} else if (a <= 3.5e+37) {
		tmp = fma(y, ((z - t) / z), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(z / Float64(z - a)), x)
	tmp = 0.0
	if (a <= -1.35e-77)
		tmp = t_1;
	elseif (a <= 3.5e+37)
		tmp = fma(y, Float64(Float64(z - t) / z), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.35e-77], t$95$1, If[LessEqual[a, 3.5e+37], N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.35e-77 or 3.5e37 < a

   1. Initial program 83.7%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 77.9

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

   4. Applied rewrites 77.9%

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

   if -1.35e-77 < a < 3.5e37

   1. Initial program 87.6%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 83.0

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

   4. Applied rewrites 83.0%

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

Alternative 7: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(-t\right) \cdot y}{z}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+180}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{z - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- t) y) z))))
   (if (<= t -1.9e+164) t_1 (if (<= t 5.8e+180) (fma y (/ z (- z a)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((-t * y) / z);
	double tmp;
	if (t <= -1.9e+164) {
		tmp = t_1;
	} else if (t <= 5.8e+180) {
		tmp = fma(y, (z / (z - a)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(-t) * y) / z))
	tmp = 0.0
	if (t <= -1.9e+164)
		tmp = t_1;
	elseif (t <= 5.8e+180)
		tmp = fma(y, Float64(z / Float64(z - a)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[((-t) * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+164], t$95$1, If[LessEqual[t, 5.8e+180], N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.90000000000000011e164 or 5.80000000000000015e180 < t

   1. Initial program 80.4%

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

   2. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

      5. distribute-lft-out-- N/A

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. distribute-rgt-out-- N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 53.5

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

   4. Applied rewrites 53.5%

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

   5. Taylor expanded in t around inf

      \[\leadsto x + -1 \cdot \color{blue}{\frac{t \cdot y}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. distribute-lft-neg-out N/A

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

      5. lift-neg.f64 N/A

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

      6. lower-*.f64 51.4

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

   7. Applied rewrites 51.4%

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

   if -1.90000000000000011e164 < t < 5.80000000000000015e180

   1. Initial program 87.0%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 81.0

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

   4. Applied rewrites 81.0%

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

Alternative 8: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.011:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-110}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.011) (+ x y) (if (<= z 1.9e-110) (fma t (/ y a) x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.011) {
		tmp = x + y;
	} else if (z <= 1.9e-110) {
		tmp = fma(t, (y / a), x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.011)
		tmp = Float64(x + y);
	elseif (z <= 1.9e-110)
		tmp = fma(t, Float64(y / a), x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.011], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.9e-110], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.010999999999999999 or 1.8999999999999999e-110 < z

   1. Initial program 78.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 72.1%

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

   if -0.010999999999999999 < z < 1.8999999999999999e-110

   1. Initial program 95.9%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 80.5

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

   4. Applied rewrites 80.5%

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

Alternative 9: 62.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.75 \cdot 10^{+239}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.75e+239) (+ x y) (* (- t) (/ y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.75e+239) {
		tmp = x + y;
	} else {
		tmp = -t * (y / z);
	}
	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 (t <= 1.75d+239) then
        tmp = x + y
    else
        tmp = -t * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.75e+239) {
		tmp = x + y;
	} else {
		tmp = -t * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.75e+239:
		tmp = x + y
	else:
		tmp = -t * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.75e+239)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(-t) * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1.75e+239)
		tmp = x + y;
	else
		tmp = -t * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.75e+239], N[(x + y), $MachinePrecision], N[((-t) * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.7500000000000001e239

   1. Initial program 85.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 62.3%

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

   if 1.7500000000000001e239 < t

   1. Initial program 79.3%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 59.4

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in z around 0

      \[\leadsto -1 \cdot \color{blue}{\frac{t \cdot y}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. distribute-lft-neg-out N/A

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

      5. lift-neg.f64 N/A

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

      6. lower-*.f64 33.8

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

   7. Applied rewrites 33.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 38.8

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

   9. Applied rewrites 38.8%

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

Alternative 10: 60.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -8.6e+94) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.6e+94) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, 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 <= (-8.6d+94)) then
        tmp = x
    else
        tmp = x + y
    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 <= -8.6e+94) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.6e+94:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.6e+94)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.6e+94)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.6e+94], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.6e94

   1. Initial program 81.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 65.2%

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

   if -8.6e94 < a

   1. Initial program 86.3%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 61.4%

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

Alternative 11: 52.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + ((y * (z - t)) / (z - a))) <= -((double) INFINITY)) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + ((y * (z - t)) / (z - a))) <= -Double.POSITIVE_INFINITY) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x + ((y * (z - t)) / (z - a))) <= -math.inf:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 40.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 40.7

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

   4. Applied rewrites 40.7%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 5.9%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r/ 31.1

         \[\leadsto y \]

   10. Applied rewrites 31.1%

       \[\leadsto y \]

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

   1. Initial program 91.5%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 55.8%

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

Alternative 12: 50.8% accurate, 15.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.5%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 50.8%

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

Reproduce

herbie shell --seed 2025112 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64
  (+ x (/ (* y (- z t)) (- z a))))