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

Percentage Accurate: 86.1% → 96.1%

Time: 6.8s

Alternatives: 11

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+298}\right):\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) t) (- a z)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+298)))
     (* (/ t (- a z)) (- y z))
     t_1)))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * t) / (a - z));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+298)) {
		tmp = (t / (a - z)) * (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * t) / (a - z));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+298)) {
		tmp = (t / (a - z)) * (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * t) / (a - z))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+298):
		tmp = (t / (a - z)) * (y - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+298))
		tmp = Float64(Float64(t / Float64(a - z)) * Float64(y - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * t) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+298)))
		tmp = (t / (a - z)) * (y - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+298]], $MachinePrecision]], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))) < -inf.0 or 5.0000000000000003e298 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

   1. Initial program 35.9%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

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

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. associate-*r/ N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 93.1

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

   5. Applied rewrites 93.1%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))) < 5.0000000000000003e298

   1. Initial program 99.4%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty \lor \neg \left(x + \frac{\left(y - z\right) \cdot t}{a - z} \leq 5 \cdot 10^{+298}\right):\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{a - z} \cdot \left(y - z\right)\\ t_2 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a - z}, -t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ t (- a z)) (- y z))) (t_2 (/ (* (- y z) t) (- a z))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -4e-88)
       t_2
       (if (<= t_2 2e+133) (fma (/ z (- a z)) (- t) x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / (a - z)) * (y - z);
	double t_2 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -4e-88) {
		tmp = t_2;
	} else if (t_2 <= 2e+133) {
		tmp = fma((z / (a - z)), -t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / Float64(a - z)) * Float64(y - z))
	t_2 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -4e-88)
		tmp = t_2;
	elseif (t_2 <= 2e+133)
		tmp = fma(Float64(z / Float64(a - z)), Float64(-t), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -4e-88], t$95$2, If[LessEqual[t$95$2, 2e+133], N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] * (-t) + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 2e133 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 49.5%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

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

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. associate-*r/ N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 91.1

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

   5. Applied rewrites 91.1%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -3.99999999999999974e-88

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 48.9

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

   5. Applied rewrites 48.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 26.4%

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

   9. Taylor expanded in x around 0

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

       1. lower-/.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 N/A

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

       4. lower--.f64 N/A

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

       5. lower--.f64 69.6

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

   11. Applied rewrites 69.6%

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

   if -3.99999999999999974e-88 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 2e133

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a - z} + x} \]

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 89.2

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

   5. Applied rewrites 89.2%

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

Alternative 3: 76.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{a - z} \cdot \left(y - z\right)\\ t_2 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-34}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ t (- a z)) (- y z))) (t_2 (/ (* (- y z) t) (- a z))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -4e-88) t_2 (if (<= t_2 2e-34) (* (- x) -1.0) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / (a - z)) * (y - z);
	double t_2 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -4e-88) {
		tmp = t_2;
	} else if (t_2 <= 2e-34) {
		tmp = -x * -1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / (a - z)) * (y - z);
	double t_2 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -4e-88) {
		tmp = t_2;
	} else if (t_2 <= 2e-34) {
		tmp = -x * -1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t / (a - z)) * (y - z)
	t_2 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -4e-88:
		tmp = t_2
	elif t_2 <= 2e-34:
		tmp = -x * -1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / Float64(a - z)) * Float64(y - z))
	t_2 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -4e-88)
		tmp = t_2;
	elseif (t_2 <= 2e-34)
		tmp = Float64(Float64(-x) * -1.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t / (a - z)) * (y - z);
	t_2 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -4e-88)
		tmp = t_2;
	elseif (t_2 <= 2e-34)
		tmp = -x * -1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -4e-88], t$95$2, If[LessEqual[t$95$2, 2e-34], N[((-x) * -1.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 1.99999999999999986e-34 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 58.0%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

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

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. associate-*r/ N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 85.5

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

   5. Applied rewrites 85.5%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -3.99999999999999974e-88

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 48.9

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

   5. Applied rewrites 48.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 26.4%

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

   9. Taylor expanded in x around 0

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

       1. lower-/.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 N/A

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

       4. lower--.f64 N/A

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

       5. lower--.f64 69.6

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

   11. Applied rewrites 69.6%

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

   if -3.99999999999999974e-88 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 1.99999999999999986e-34

   1. Initial program 99.0%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 77.3

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

   5. Applied rewrites 77.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 5.9%

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

   9. Taylor expanded in x around -inf

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

       1. mul-1-neg N/A

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

       2. distribute-lft-neg-in N/A

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

       3. lower-*.f64 N/A

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

       4. lower-neg.f64 N/A

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

       5. lower--.f64 N/A

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

       6. mul-1-neg N/A

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

       7. times-frac N/A

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

       8. distribute-lft-neg-in N/A

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

       9. lower-*.f64 N/A

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

       10. lower-neg.f64 N/A

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

       11. lower-/.f64 N/A

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

       12. lower-/.f64 N/A

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

       13. lower--.f64 N/A

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

       14. lower--.f64 98.0

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

   11. Applied rewrites 98.0%

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

   12. Taylor expanded in x around inf

       \[\leadsto \left(-x\right) \cdot -1 \]
   13. Step-by-step derivation

   14. Applied rewrites 86.7%

       \[\leadsto \left(-x\right) \cdot -1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 82.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+230} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+142}\right):\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (or (<= t_1 -2e+230) (not (<= t_1 5e+142)))
     (* (/ t (- a z)) (- y z))
     (+ x (/ (* t y) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -2e+230) || !(t_1 <= 5e+142)) {
		tmp = (t / (a - z)) * (y - z);
	} else {
		tmp = x + ((t * y) / (a - 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) :: t_1
    real(8) :: tmp
    t_1 = ((y - z) * t) / (a - z)
    if ((t_1 <= (-2d+230)) .or. (.not. (t_1 <= 5d+142))) then
        tmp = (t / (a - z)) * (y - z)
    else
        tmp = x + ((t * y) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -2e+230) || !(t_1 <= 5e+142)) {
		tmp = (t / (a - z)) * (y - z);
	} else {
		tmp = x + ((t * y) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if (t_1 <= -2e+230) or not (t_1 <= 5e+142):
		tmp = (t / (a - z)) * (y - z)
	else:
		tmp = x + ((t * y) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= -2e+230) || !(t_1 <= 5e+142))
		tmp = Float64(Float64(t / Float64(a - z)) * Float64(y - z));
	else
		tmp = Float64(x + Float64(Float64(t * y) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if ((t_1 <= -2e+230) || ~((t_1 <= 5e+142)))
		tmp = (t / (a - z)) * (y - z);
	else
		tmp = x + ((t * y) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+230], N[Not[LessEqual[t$95$1, 5e+142]], $MachinePrecision]], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -2.0000000000000002e230 or 5.0000000000000001e142 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 49.0%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

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

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. associate-*r/ N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 89.9

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

   5. Applied rewrites 89.9%

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

   if -2.0000000000000002e230 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 5.0000000000000001e142

   1. Initial program 99.3%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 84.7

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

   5. Applied rewrites 84.7%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -2 \cdot 10^{+230} \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 5 \cdot 10^{+142}\right):\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-196} \lor \neg \left(t\_1 \leq 10^{-98}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (or (<= t_1 -2e-196) (not (<= t_1 1e-98))) (+ t x) (* (- x) -1.0))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -2e-196) || !(t_1 <= 1e-98)) {
		tmp = t + x;
	} else {
		tmp = -x * -1.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y - z) * t) / (a - z)
    if ((t_1 <= (-2d-196)) .or. (.not. (t_1 <= 1d-98))) then
        tmp = t + x
    else
        tmp = -x * (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -2e-196) || !(t_1 <= 1e-98)) {
		tmp = t + x;
	} else {
		tmp = -x * -1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if (t_1 <= -2e-196) or not (t_1 <= 1e-98):
		tmp = t + x
	else:
		tmp = -x * -1.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= -2e-196) || !(t_1 <= 1e-98))
		tmp = Float64(t + x);
	else
		tmp = Float64(Float64(-x) * -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if ((t_1 <= -2e-196) || ~((t_1 <= 1e-98)))
		tmp = t + x;
	else
		tmp = -x * -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-196], N[Not[LessEqual[t$95$1, 1e-98]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[((-x) * -1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -2.0000000000000001e-196 or 9.99999999999999939e-99 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 76.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 49.6

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

   5. Applied rewrites 49.6%

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

   if -2.0000000000000001e-196 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 9.99999999999999939e-99

   1. Initial program 98.7%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 83.2

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

   5. Applied rewrites 83.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 5.6%

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

   9. Taylor expanded in x around -inf

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

       1. mul-1-neg N/A

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

       2. distribute-lft-neg-in N/A

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

       3. lower-*.f64 N/A

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

       4. lower-neg.f64 N/A

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

       5. lower--.f64 N/A

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

       6. mul-1-neg N/A

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

       7. times-frac N/A

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

       8. distribute-lft-neg-in N/A

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

       9. lower-*.f64 N/A

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

       10. lower-neg.f64 N/A

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

       11. lower-/.f64 N/A

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

       12. lower-/.f64 N/A

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

       13. lower--.f64 N/A

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

       14. lower--.f64 98.6

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

   11. Applied rewrites 98.6%

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

   12. Taylor expanded in x around inf

       \[\leadsto \left(-x\right) \cdot -1 \]
   13. Step-by-step derivation

   14. Applied rewrites 91.7%

       \[\leadsto \left(-x\right) \cdot -1 \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -2 \cdot 10^{-196} \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{-98}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+51} \lor \neg \left(z \leq 3.7 \cdot 10^{-34}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+51) (not (<= z 3.7e-34)))
   (+ t x)
   (fma t (/ (- y z) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+51) || !(z <= 3.7e-34)) {
		tmp = t + x;
	} else {
		tmp = fma(t, ((y - z) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+51) || !(z <= 3.7e-34))
		tmp = Float64(t + x);
	else
		tmp = fma(t, Float64(Float64(y - z) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+51], N[Not[LessEqual[z, 3.7e-34]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.34999999999999996e51 or 3.69999999999999988e-34 < z

   1. Initial program 75.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 80.8

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

   5. Applied rewrites 80.8%

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

   if -1.34999999999999996e51 < z < 3.69999999999999988e-34

   1. Initial program 89.6%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 77.7

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

   5. Applied rewrites 77.7%

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

   7. Applied rewrites 79.9%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+51} \lor \neg \left(z \leq 3.7 \cdot 10^{-34}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+50} \lor \neg \left(z \leq 3.4 \cdot 10^{-34}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.7e+50) (not (<= z 3.4e-34))) (+ t x) (fma (/ y a) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.7e+50) || !(z <= 3.4e-34)) {
		tmp = t + x;
	} else {
		tmp = fma((y / a), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.7e+50) || !(z <= 3.4e-34))
		tmp = Float64(t + x);
	else
		tmp = fma(Float64(y / a), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.7e+50], N[Not[LessEqual[z, 3.4e-34]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7000000000000001e50 or 3.4000000000000001e-34 < z

   1. Initial program 75.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 80.8

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

   5. Applied rewrites 80.8%

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

   if -3.7000000000000001e50 < z < 3.4000000000000001e-34

   1. Initial program 89.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 75.8

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

   5. Applied rewrites 75.8%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+50} \lor \neg \left(z \leq 3.4 \cdot 10^{-34}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+50} \lor \neg \left(z \leq 3.4 \cdot 10^{-34}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.7e+50) (not (<= z 3.4e-34))) (+ t x) (fma y (/ t a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.7e+50) || !(z <= 3.4e-34)) {
		tmp = t + x;
	} else {
		tmp = fma(y, (t / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.7e+50) || !(z <= 3.4e-34))
		tmp = Float64(t + x);
	else
		tmp = fma(y, Float64(t / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.7e+50], N[Not[LessEqual[z, 3.4e-34]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7000000000000001e50 or 3.4000000000000001e-34 < z

   1. Initial program 75.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 80.8

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

   5. Applied rewrites 80.8%

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

   if -3.7000000000000001e50 < z < 3.4000000000000001e-34

   1. Initial program 89.6%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-inverses N/A

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

      3. div-sub N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 77.1

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

   5. Applied rewrites 77.1%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 74.0

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

   8. Applied rewrites 74.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+50} \lor \neg \left(z \leq 3.4 \cdot 10^{-34}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+243} \lor \neg \left(y \leq 7.8 \cdot 10^{+216}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.5e+243) (not (<= y 7.8e+216))) (* y (/ t a)) (+ t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.5e+243) || !(y <= 7.8e+216)) {
		tmp = y * (t / a);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3.5d+243)) .or. (.not. (y <= 7.8d+216))) then
        tmp = y * (t / a)
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.5e+243) || !(y <= 7.8e+216)) {
		tmp = y * (t / a);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.5e+243) or not (y <= 7.8e+216):
		tmp = y * (t / a)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.5e+243) || !(y <= 7.8e+216))
		tmp = Float64(y * Float64(t / a));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.5e+243) || ~((y <= 7.8e+216)))
		tmp = y * (t / a);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.5e+243], N[Not[LessEqual[y, 7.8e+216]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.49999999999999988e243 or 7.79999999999999962e216 < y

   1. Initial program 78.2%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 71.5

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 50.8%

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

   10. Applied rewrites 64.3%

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

   if -3.49999999999999988e243 < y < 7.79999999999999962e216

   1. Initial program 83.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 63.6

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

   5. Applied rewrites 63.6%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+243} \lor \neg \left(y \leq 7.8 \cdot 10^{+216}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+243}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+214}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.5e+243)
   (* y (/ t a))
   (if (<= y 2.05e+214) (+ t x) (* (/ y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.5e+243) {
		tmp = y * (t / a);
	} else if (y <= 2.05e+214) {
		tmp = t + x;
	} else {
		tmp = (y / a) * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.5d+243)) then
        tmp = y * (t / a)
    else if (y <= 2.05d+214) then
        tmp = t + x
    else
        tmp = (y / a) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.5e+243) {
		tmp = y * (t / a);
	} else if (y <= 2.05e+214) {
		tmp = t + x;
	} else {
		tmp = (y / a) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.5e+243:
		tmp = y * (t / a)
	elif y <= 2.05e+214:
		tmp = t + x
	else:
		tmp = (y / a) * t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.5e+243)
		tmp = Float64(y * Float64(t / a));
	elseif (y <= 2.05e+214)
		tmp = Float64(t + x);
	else
		tmp = Float64(Float64(y / a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.5e+243)
		tmp = y * (t / a);
	elseif (y <= 2.05e+214)
		tmp = t + x;
	else
		tmp = (y / a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.5e+243], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e+214], N[(t + x), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.49999999999999988e243

   1. Initial program 74.4%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 72.6

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

   5. Applied rewrites 72.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 42.9%

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

   10. Applied rewrites 62.2%

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

   if -3.49999999999999988e243 < y < 2.05e214

   1. Initial program 83.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 63.6

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

   5. Applied rewrites 63.6%

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

   if 2.05e214 < y

   1. Initial program 81.2%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 70.6

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

   5. Applied rewrites 70.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 56.7%

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

   10. Applied rewrites 70.7%

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

Alternative 11: 60.0% accurate, 6.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.0%

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

3. Taylor expanded in z around inf

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

   1. lower-+.f64 56.6

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

5. Applied rewrites 56.6%

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

Developer Target 1: 99.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024363 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

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

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