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

Percentage Accurate: 97.8% → 97.7%

Time: 4.7s

Alternatives: 9

Speedup: N/A×

• 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: 97.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5e-11) (fma z (/ (- y x) t) x) (fma (/ z t) (- y x) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5e-11) {
		tmp = fma(z, ((y - x) / t), x);
	} else {
		tmp = fma((z / t), (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5e-11)
		tmp = fma(z, Float64(Float64(y - x) / t), x);
	else
		tmp = fma(Float64(z / t), Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5e-11], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000018e-11

   1. Initial program 89.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l/ N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   if -5.00000000000000018e-11 < t

   1. Initial program 98.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 98.9

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

   4. Applied rewrites 98.9%

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

Alternative 2: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000 \lor \neg \left(\frac{z}{t} \leq 1000\right):\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -10000000.0) (not (<= (/ z t) 1000.0)))
   (* (/ z t) (- y x))
   (fma (/ y t) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -10000000.0) || !((z / t) <= 1000.0)) {
		tmp = (z / t) * (y - x);
	} else {
		tmp = fma((y / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -10000000.0) || !(Float64(z / t) <= 1000.0))
		tmp = Float64(Float64(z / t) * Float64(y - x));
	else
		tmp = fma(Float64(y / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -10000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1000.0]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e7 or 1e3 < (/.f64 z t)

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 94.0

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

   5. Applied rewrites 94.0%

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

   7. Applied rewrites 98.6%

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

   if -1e7 < (/.f64 z t) < 1e3

   1. Initial program 94.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 94.4

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

   4. Applied rewrites 94.4%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 94.4

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. flip-- N/A

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

      10. lift-+.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. associate-*l/ N/A

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

      13. difference-of-squares N/A

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

      14. lift-+.f64 N/A

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

      15. lift--.f64 N/A

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

      16. associate-*r* N/A

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

      17. *-commutative N/A

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. lift-/.f64 79.8

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

   6. Applied rewrites 97.8%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 98.1

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

   9. Applied rewrites 98.1%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000 \lor \neg \left(\frac{z}{t} \leq 1000\right):\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+27} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1e+27) (not (<= (/ z t) 5e+288)))
   (* (- x) (/ z t))
   (fma (/ y t) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e+27) || !((z / t) <= 5e+288)) {
		tmp = -x * (z / t);
	} else {
		tmp = fma((y / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1e+27) || !(Float64(z / t) <= 5e+288))
		tmp = Float64(Float64(-x) * Float64(z / t));
	else
		tmp = fma(Float64(y / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1e+27], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e+288]], $MachinePrecision]], N[((-x) * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e27 or 5.0000000000000003e288 < (/.f64 z t)

   1. Initial program 98.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 98.6

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

   4. Applied rewrites 98.6%

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

   5. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 98.6

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

   7. Applied rewrites 98.6%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 67.1%

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

   12. Applied rewrites 69.6%

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

   if -1e27 < (/.f64 z t) < 5.0000000000000003e288

   1. Initial program 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 95.7

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

   4. Applied rewrites 95.7%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 95.7

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. flip-- N/A

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

      10. lift-+.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. associate-*l/ N/A

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

      13. difference-of-squares N/A

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

      14. lift-+.f64 N/A

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

      15. lift--.f64 N/A

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

      16. associate-*r* N/A

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

      17. *-commutative N/A

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. lift-/.f64 81.2

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

   6. Applied rewrites 96.2%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 88.5

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

   9. Applied rewrites 88.5%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+27} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+27} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;\frac{\left(-x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1e+27) (not (<= (/ z t) 5e+288)))
   (/ (* (- x) z) t)
   (fma (/ y t) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e+27) || !((z / t) <= 5e+288)) {
		tmp = (-x * z) / t;
	} else {
		tmp = fma((y / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1e+27) || !(Float64(z / t) <= 5e+288))
		tmp = Float64(Float64(Float64(-x) * z) / t);
	else
		tmp = fma(Float64(y / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1e+27], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e+288]], $MachinePrecision]], N[(N[((-x) * z), $MachinePrecision] / t), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e27 or 5.0000000000000003e288 < (/.f64 z t)

   1. Initial program 98.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 98.6

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

   4. Applied rewrites 98.6%

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

   5. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 98.6

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

   7. Applied rewrites 98.6%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 67.1%

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

   if -1e27 < (/.f64 z t) < 5.0000000000000003e288

   1. Initial program 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 95.7

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

   4. Applied rewrites 95.7%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 95.7

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. flip-- N/A

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

      10. lift-+.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. associate-*l/ N/A

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

      13. difference-of-squares N/A

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

      14. lift-+.f64 N/A

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

      15. lift--.f64 N/A

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

      16. associate-*r* N/A

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

      17. *-commutative N/A

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. lift-/.f64 81.2

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

   6. Applied rewrites 96.2%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 88.5

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

   9. Applied rewrites 88.5%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+27} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;\frac{\left(-x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+27} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1e+27) (not (<= (/ z t) 5e+288)))
   (* (/ (- x) t) z)
   (fma (/ y t) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e+27) || !((z / t) <= 5e+288)) {
		tmp = (-x / t) * z;
	} else {
		tmp = fma((y / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1e+27) || !(Float64(z / t) <= 5e+288))
		tmp = Float64(Float64(Float64(-x) / t) * z);
	else
		tmp = fma(Float64(y / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1e+27], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e+288]], $MachinePrecision]], N[(N[((-x) / t), $MachinePrecision] * z), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e27 or 5.0000000000000003e288 < (/.f64 z t)

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 96.2

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

   5. Applied rewrites 96.2%

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

   6. Taylor expanded in x around inf

      \[\leadsto \frac{-1 \cdot x}{t} \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 64.7%

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

   if -1e27 < (/.f64 z t) < 5.0000000000000003e288

   1. Initial program 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 95.7

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

   4. Applied rewrites 95.7%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 95.7

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. flip-- N/A

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

      10. lift-+.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. associate-*l/ N/A

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

      13. difference-of-squares N/A

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

      14. lift-+.f64 N/A

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

      15. lift--.f64 N/A

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

      16. associate-*r* N/A

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

      17. *-commutative N/A

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. lift-/.f64 81.2

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

   6. Applied rewrites 96.2%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 88.5

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

   9. Applied rewrites 88.5%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+27} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-11} \lor \neg \left(y \leq 8 \cdot 10^{-95}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.5e-11) (not (<= y 8e-95)))
   (fma (/ y t) z x)
   (* (- 1.0 (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e-11) || !(y <= 8e-95)) {
		tmp = fma((y / t), z, x);
	} else {
		tmp = (1.0 - (z / t)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.5e-11) || !(y <= 8e-95))
		tmp = fma(Float64(y / t), z, x);
	else
		tmp = Float64(Float64(1.0 - Float64(z / t)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.5e-11], N[Not[LessEqual[y, 8e-95]], $MachinePrecision]], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999953e-11 or 7.99999999999999992e-95 < y

   1. Initial program 94.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 94.9

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

   4. Applied rewrites 94.9%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 94.9

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. flip-- N/A

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

      10. lift-+.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. associate-*l/ N/A

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

      13. difference-of-squares N/A

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

      14. lift-+.f64 N/A

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

      15. lift--.f64 N/A

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

      16. associate-*r* N/A

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

      17. *-commutative N/A

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. lift-/.f64 78.4

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

   6. Applied rewrites 94.9%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 88.5

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

   9. Applied rewrites 88.5%

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

   if -6.49999999999999953e-11 < y < 7.99999999999999992e-95

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 91.7

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

   5. Applied rewrites 91.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-11} \lor \neg \left(y \leq 8 \cdot 10^{-95}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.4% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-/.f64 N/A

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

   6. associate-*l/ N/A

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

   7. associate-/l* N/A

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

   8. lower-fma.f64 N/A

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

   9. lower-/.f64 96.2

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

4. Applied rewrites 96.2%

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

Alternative 8: 72.8% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 96.6

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

4. Applied rewrites 96.6%

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

   1. lift-fma.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. +-commutative N/A

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

   4. lower-+.f64 96.6

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lift--.f64 N/A

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

   8. lift-/.f64 N/A

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

   9. flip-- N/A

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

   10. lift-+.f64 N/A

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

   11. lift-/.f64 N/A

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

   12. associate-*l/ N/A

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

   13. difference-of-squares N/A

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

   14. lift-+.f64 N/A

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

   15. lift--.f64 N/A

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

   16. associate-*r* N/A

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

   17. *-commutative N/A

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

   18. lift-*.f64 N/A

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

   19. lift-*.f64 N/A

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

   20. lift-/.f64 82.3

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

6. Applied rewrites 96.2%

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

7. Taylor expanded in x around 0

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

   1. lower-/.f64 75.5

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

9. Applied rewrites 75.5%

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

Alternative 9: 37.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{y}{t} \cdot z \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (y / t) * 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)
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 = (y / t) * z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

3. Taylor expanded in x around 0

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

   1. associate-*l/ N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 38.3

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

5. Applied rewrites 38.3%

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

6. Final simplification 38.3%

   \[\leadsto \frac{y}{t} \cdot z \]
7. Add Preprocessing

Developer Target 1: 97.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{if}\;t\_1 < -1013646692435.8867:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))) (t_2 (+ x (/ (- y x) (/ t z)))))
   (if (< t_1 -1013646692435.8867)
     t_2
     (if (< t_1 0.0) (+ x (/ (* (- y x) z) t)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    t_2 = x + ((y - x) / (t / z))
    if (t_1 < (-1013646692435.8867d0)) then
        tmp = t_2
    else if (t_1 < 0.0d0) then
        tmp = x + (((y - x) * z) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	t_2 = x + ((y - x) / (t / z))
	tmp = 0
	if t_1 < -1013646692435.8867:
		tmp = t_2
	elif t_1 < 0.0:
		tmp = x + (((y - x) * z) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(t / z)))
	tmp = 0.0
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	t_2 = x + ((y - x) / (t / z));
	tmp = 0.0;
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = x + (((y - x) * z) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$1, -1013646692435.8867], t$95$2, If[Less[t$95$1, 0.0], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2025015 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* (- y x) (/ z t)) -10136466924358867/10000) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z))))))

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