Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Percentage Accurate: 97.8% → 98.5%

Time: 4.2s

Alternatives: 8

Speedup: 0.7×

• 25.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 10^{+243}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) 1e+243) (fma (/ z t) (- y x) x) (* (/ (- y x) t) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= 1e+243) {
		tmp = fma((z / t), (y - x), x);
	} else {
		tmp = ((y - x) / t) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= 1e+243)
		tmp = fma(Float64(z / t), Float64(y - x), x);
	else
		tmp = Float64(Float64(Float64(y - x) / t) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], 1e+243], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < 1.0000000000000001e243

   1. Initial program 98.4%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift--.f64 98.4

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

   3. Applied rewrites 98.4%

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

   if 1.0000000000000001e243 < (/.f64 z t)

   1. Initial program 92.3%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 99.9

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

   4. Applied rewrites 99.9%

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

Alternative 2: 96.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 7 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+243}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) (- y x))))
   (if (<= (/ z t) -4e+15)
     t_1
     (if (<= (/ z t) 7e-7)
       (fma (/ z t) y x)
       (if (<= (/ z t) 1e+243) t_1 (* (/ (- y x) t) z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * (y - x);
	double tmp;
	if ((z / t) <= -4e+15) {
		tmp = t_1;
	} else if ((z / t) <= 7e-7) {
		tmp = fma((z / t), y, x);
	} else if ((z / t) <= 1e+243) {
		tmp = t_1;
	} else {
		tmp = ((y - x) / t) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * Float64(y - x))
	tmp = 0.0
	if (Float64(z / t) <= -4e+15)
		tmp = t_1;
	elseif (Float64(z / t) <= 7e-7)
		tmp = fma(Float64(z / t), y, x);
	elseif (Float64(z / t) <= 1e+243)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(y - x) / t) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -4e+15], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 7e-7], N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e+243], t$95$1, N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -4e15 or 6.99999999999999968e-7 < (/.f64 z t) < 1.0000000000000001e243

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 90.5

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

   4. Applied rewrites 90.5%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift--.f64 96.3

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

   6. Applied rewrites 96.3%

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

   if -4e15 < (/.f64 z t) < 6.99999999999999968e-7

   1. Initial program 98.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 96.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-/.f64 96.9

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

   6. Applied rewrites 96.9%

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

   if 1.0000000000000001e243 < (/.f64 z t)

   1. Initial program 92.3%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 99.9

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

   4. Applied rewrites 99.9%

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

Alternative 3: 96.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 7 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) (- y x))))
   (if (<= (/ z t) -4e+15) t_1 (if (<= (/ z t) 7e-7) (fma (/ z t) y x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * (y - x);
	double tmp;
	if ((z / t) <= -4e+15) {
		tmp = t_1;
	} else if ((z / t) <= 7e-7) {
		tmp = fma((z / t), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * Float64(y - x))
	tmp = 0.0
	if (Float64(z / t) <= -4e+15)
		tmp = t_1;
	elseif (Float64(z / t) <= 7e-7)
		tmp = fma(Float64(z / t), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -4e+15], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 7e-7], N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4e15 or 6.99999999999999968e-7 < (/.f64 z t)

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 92.3

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

   4. Applied rewrites 92.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift--.f64 95.5

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

   6. Applied rewrites 95.5%

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

   if -4e15 < (/.f64 z t) < 6.99999999999999968e-7

   1. Initial program 98.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 96.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-/.f64 96.9

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

   6. Applied rewrites 96.9%

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

Alternative 4: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{if}\;y \leq -250000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-171}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ z t) y x)))
   (if (<= y -250000000000.0)
     t_1
     (if (<= y 8e-171) (* (- 1.0 (/ z t)) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((z / t), y, x);
	double tmp;
	if (y <= -250000000000.0) {
		tmp = t_1;
	} else if (y <= 8e-171) {
		tmp = (1.0 - (z / t)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(z / t), y, x)
	tmp = 0.0
	if (y <= -250000000000.0)
		tmp = t_1;
	elseif (y <= 8e-171)
		tmp = Float64(Float64(1.0 - Float64(z / t)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[y, -250000000000.0], t$95$1, If[LessEqual[y, 8e-171], N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5e11 or 7.9999999999999999e-171 < y

   1. Initial program 98.5%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 84.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-/.f64 84.8

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

   6. Applied rewrites 84.8%

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

   if -2.5e11 < y < 7.9999999999999999e-171

   1. Initial program 96.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. metadata-eval N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. *-lft-identity N/A

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

      6. lower--.f64 N/A

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

      7. lift-/.f64 85.8

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

   4. Applied rewrites 85.8%

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

Alternative 5: 76.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-227}:\\ \;\;\;\;\frac{-z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ z t) y x)))
   (if (<= t -1.8e-238) t_1 (if (<= t 8.2e-227) (* (/ (- z) t) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((z / t), y, x);
	double tmp;
	if (t <= -1.8e-238) {
		tmp = t_1;
	} else if (t <= 8.2e-227) {
		tmp = (-z / t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(z / t), y, x)
	tmp = 0.0
	if (t <= -1.8e-238)
		tmp = t_1;
	elseif (t <= 8.2e-227)
		tmp = Float64(Float64(Float64(-z) / t) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[t, -1.8e-238], t$95$1, If[LessEqual[t, 8.2e-227], N[(N[((-z) / t), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.80000000000000005e-238 or 8.20000000000000018e-227 < t

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 78.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-/.f64 78.7

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

   6. Applied rewrites 78.7%

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

   if -1.80000000000000005e-238 < t < 8.20000000000000018e-227

   1. Initial program 96.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. metadata-eval N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. *-lft-identity N/A

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

      6. lower--.f64 N/A

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

      7. lift-/.f64 61.6

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

   4. Applied rewrites 61.6%

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

   5. Taylor expanded in z around inf

      \[\leadsto \left(-1 \cdot \frac{z}{t}\right) \cdot x \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{-1 \cdot z}{t} \cdot x \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot z}{t} \cdot x \]

      3. mul-1-neg N/A

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

      4. lower-neg.f64 57.6

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

   7. Applied rewrites 57.6%

      \[\leadsto \frac{-z}{t} \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 65.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot y\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+139}:\\ \;\;\;\;\frac{-z}{t} \cdot x\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) y)))
   (if (<= (/ z t) -2e+139)
     (* (/ (- z) t) x)
     (if (<= (/ z t) -1e-6) t_1 (if (<= (/ z t) 5e-29) x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * y;
	double tmp;
	if ((z / t) <= -2e+139) {
		tmp = (-z / t) * x;
	} else if ((z / t) <= -1e-6) {
		tmp = t_1;
	} else if ((z / t) <= 5e-29) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (z / t) * y
    if ((z / t) <= (-2d+139)) then
        tmp = (-z / t) * x
    else if ((z / t) <= (-1d-6)) then
        tmp = t_1
    else if ((z / t) <= 5d-29) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * y;
	double tmp;
	if ((z / t) <= -2e+139) {
		tmp = (-z / t) * x;
	} else if ((z / t) <= -1e-6) {
		tmp = t_1;
	} else if ((z / t) <= 5e-29) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * y
	tmp = 0
	if (z / t) <= -2e+139:
		tmp = (-z / t) * x
	elif (z / t) <= -1e-6:
		tmp = t_1
	elif (z / t) <= 5e-29:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * y)
	tmp = 0.0
	if (Float64(z / t) <= -2e+139)
		tmp = Float64(Float64(Float64(-z) / t) * x);
	elseif (Float64(z / t) <= -1e-6)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e-29)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * y;
	tmp = 0.0;
	if ((z / t) <= -2e+139)
		tmp = (-z / t) * x;
	elseif ((z / t) <= -1e-6)
		tmp = t_1;
	elseif ((z / t) <= 5e-29)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e+139], N[(N[((-z) / t), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -1e-6], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e-29], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2.00000000000000007e139

   1. Initial program 94.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. metadata-eval N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. *-lft-identity N/A

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

      6. lower--.f64 N/A

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

      7. lift-/.f64 60.6

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

   4. Applied rewrites 60.6%

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

   5. Taylor expanded in z around inf

      \[\leadsto \left(-1 \cdot \frac{z}{t}\right) \cdot x \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{-1 \cdot z}{t} \cdot x \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot z}{t} \cdot x \]

      3. mul-1-neg N/A

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

      4. lower-neg.f64 60.6

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

   7. Applied rewrites 60.6%

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

   if -2.00000000000000007e139 < (/.f64 z t) < -9.99999999999999955e-7 or 4.99999999999999986e-29 < (/.f64 z t)

   1. Initial program 97.9%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lift-/.f64 53.7

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

   4. Applied rewrites 53.7%

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

   if -9.99999999999999955e-7 < (/.f64 z t) < 4.99999999999999986e-29

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 76.6%

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

Alternative 7: 64.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot y\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) y)))
   (if (<= (/ z t) -1e-6) t_1 (if (<= (/ z t) 5e-29) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * y;
	double tmp;
	if ((z / t) <= -1e-6) {
		tmp = t_1;
	} else if ((z / t) <= 5e-29) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (z / t) * y
    if ((z / t) <= (-1d-6)) then
        tmp = t_1
    else if ((z / t) <= 5d-29) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * y;
	double tmp;
	if ((z / t) <= -1e-6) {
		tmp = t_1;
	} else if ((z / t) <= 5e-29) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * y
	tmp = 0
	if (z / t) <= -1e-6:
		tmp = t_1
	elif (z / t) <= 5e-29:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * y)
	tmp = 0.0
	if (Float64(z / t) <= -1e-6)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e-29)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * y;
	tmp = 0.0;
	if ((z / t) <= -1e-6)
		tmp = t_1;
	elseif ((z / t) <= 5e-29)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e-6], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e-29], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -9.99999999999999955e-7 or 4.99999999999999986e-29 < (/.f64 z t)

   1. Initial program 97.0%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lift-/.f64 54.3

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

   4. Applied rewrites 54.3%

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

   if -9.99999999999999955e-7 < (/.f64 z t) < 4.99999999999999986e-29

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 76.6%

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

Alternative 8: 38.5% accurate, 12.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

2. Taylor expanded in z around 0

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

4. Applied rewrites 38.5%

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

Reproduce

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