Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.1% → 99.7%

Time: 1.5min

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.7× speedup

Math

\[\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{z - t}\right), y, x, z, x\right) \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (134-z0z1z2z3z4 (/ -1 (- z t)) y x z x))

Derivation

1. Initial program 84.1%

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

   1. lift-/.f64 N/A

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

   2. mult-flip N/A

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

   3. *-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. lift--.f64 N/A

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

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

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

   7. lower-134-z0z1z2z3z4 N/A

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{t - z}\right), y, x, z, x\right)} \]

   8. frac-2neg N/A

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(t - z\right)\right)}\right)}, y, x, z, x\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(t - z\right)\right)}\right), y, x, z, x\right) \]

   10. lower-/.f64 N/A

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(\left(t - z\right)\right)}\right)}, y, x, z, x\right) \]

   11. lift--.f64 N/A

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(t - z\right)}\right)}\right), y, x, z, x\right) \]

   12. sub-negate-rev N/A

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{z - t}}\right), y, x, z, x\right) \]

   13. lower--.f64 99.7%

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\color{blue}{z - t}}\right), y, x, z, x\right) \]

3. Applied rewrites 99.7%

   \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{z - t}\right), y, x, z, x\right)} \]
4. Add Preprocessing

Alternative 2: 97.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.1%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lift--.f64 N/A

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

   7. sub-negate-rev N/A

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

   8. distribute-frac-neg N/A

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

   9. distribute-neg-frac2 N/A

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

   10. lower-/.f64 N/A

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

   11. lower--.f64 N/A

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

   12. lift--.f64 N/A

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

   13. sub-negate-rev N/A

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

   14. lower--.f64 97.0%

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

3. Applied rewrites 97.0%

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

   1. lift-/.f64 N/A

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

   2. mult-flip N/A

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

   3. metadata-eval N/A

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

   4. associate-*r/ N/A

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

   5. div-flip N/A

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

   6. metadata-eval N/A

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

   7. metadata-eval N/A

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

   8. *-rgt-identity N/A

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

   9. lower-unsound-/.f64 N/A

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

   10. metadata-eval N/A

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

   11. lower-unsound-/.f64 96.7%

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

5. Applied rewrites 96.7%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. mult-flip-rev N/A

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

   5. lower-/.f64 97.0%

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

   6. lift-/.f64 N/A

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

   7. frac-2neg N/A

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

   8. lower-/.f64 N/A

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

   9. lift--.f64 N/A

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

   10. sub-negate-rev N/A

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

   11. lower--.f64 N/A

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

   12. lift--.f64 N/A

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

   13. sub-negate-rev N/A

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

   14. lower--.f64 97.0%

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

7. Applied rewrites 97.0%

   \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]
8. Add Preprocessing

Alternative 3: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 = ((z - y) / (z - t)) * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.1%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lift--.f64 N/A

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

   7. sub-negate-rev N/A

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

   8. distribute-frac-neg N/A

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

   9. distribute-neg-frac2 N/A

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

   10. lower-/.f64 N/A

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

   11. lower--.f64 N/A

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

   12. lift--.f64 N/A

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

   13. sub-negate-rev N/A

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

   14. lower--.f64 97.0%

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

3. Applied rewrites 97.0%

   \[\leadsto \color{blue}{\frac{z - y}{z - t} \cdot x} \]
4. Add Preprocessing

Alternative 4: 88.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left|x\right|}{z - t} \cdot \left(z - y\right)\\ t_2 := \left|x\right| \cdot \left(y - z\right)\\ t_3 := \frac{t\_2}{t - z}\\ \mathsf{copysign}\left(1, x\right) \cdot \begin{array}{l} \mathbf{if}\;t\_3 \leq \frac{-4789048565205903}{11972621413014756705924586149611790497021399392059392}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq \frac{-10120113}{202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784}:\\ \;\;\;\;\frac{t\_2}{t}\\ \mathbf{elif}\;t\_3 \leq \frac{1723641332219371}{344728266443874206170545512964432112225507069317819522056079337263512430464013488758041250121488036739611555846958495676040441511948045769973944468809441663382665538511073745187088876036706973599091474545756168257536}:\\ \;\;\;\;\frac{z}{z - t} \cdot \left|x\right|\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* (/ (fabs x) (- z t)) (- z y)))
       (t_2 (* (fabs x) (- y z)))
       (t_3 (/ t_2 (- t z))))
  (*
   (copysign 1 x)
   (if (<=
        t_3
        -4789048565205903/11972621413014756705924586149611790497021399392059392)
     t_1
     (if (<=
          t_3
          -10120113/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784)
       (/ t_2 t)
       (if (<=
            t_3
            1723641332219371/344728266443874206170545512964432112225507069317819522056079337263512430464013488758041250121488036739611555846958495676040441511948045769973944468809441663382665538511073745187088876036706973599091474545756168257536)
         (* (/ z (- z t)) (fabs x))
         t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (fabs(x) / (z - t)) * (z - y);
	double t_2 = fabs(x) * (y - z);
	double t_3 = t_2 / (t - z);
	double tmp;
	if (t_3 <= -4e-37) {
		tmp = t_1;
	} else if (t_3 <= -5e-317) {
		tmp = t_2 / t;
	} else if (t_3 <= 5e-201) {
		tmp = (z / (z - t)) * fabs(x);
	} else {
		tmp = t_1;
	}
	return copysign(1.0, x) * tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (Math.abs(x) / (z - t)) * (z - y);
	double t_2 = Math.abs(x) * (y - z);
	double t_3 = t_2 / (t - z);
	double tmp;
	if (t_3 <= -4e-37) {
		tmp = t_1;
	} else if (t_3 <= -5e-317) {
		tmp = t_2 / t;
	} else if (t_3 <= 5e-201) {
		tmp = (z / (z - t)) * Math.abs(x);
	} else {
		tmp = t_1;
	}
	return Math.copySign(1.0, x) * tmp;
}

Python

def code(x, y, z, t):
	t_1 = (math.fabs(x) / (z - t)) * (z - y)
	t_2 = math.fabs(x) * (y - z)
	t_3 = t_2 / (t - z)
	tmp = 0
	if t_3 <= -4e-37:
		tmp = t_1
	elif t_3 <= -5e-317:
		tmp = t_2 / t
	elif t_3 <= 5e-201:
		tmp = (z / (z - t)) * math.fabs(x)
	else:
		tmp = t_1
	return math.copysign(1.0, x) * tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(abs(x) / Float64(z - t)) * Float64(z - y))
	t_2 = Float64(abs(x) * Float64(y - z))
	t_3 = Float64(t_2 / Float64(t - z))
	tmp = 0.0
	if (t_3 <= -4e-37)
		tmp = t_1;
	elseif (t_3 <= -5e-317)
		tmp = Float64(t_2 / t);
	elseif (t_3 <= 5e-201)
		tmp = Float64(Float64(z / Float64(z - t)) * abs(x));
	else
		tmp = t_1;
	end
	return Float64(copysign(1.0, x) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (abs(x) / (z - t)) * (z - y);
	t_2 = abs(x) * (y - z);
	t_3 = t_2 / (t - z);
	tmp = 0.0;
	if (t_3 <= -4e-37)
		tmp = t_1;
	elseif (t_3 <= -5e-317)
		tmp = t_2 / t;
	elseif (t_3 <= 5e-201)
		tmp = (z / (z - t)) * abs(x);
	else
		tmp = t_1;
	end
	tmp_2 = (sign(x) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[Abs[x], $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Abs[x], $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$3, -4789048565205903/11972621413014756705924586149611790497021399392059392], t$95$1, If[LessEqual[t$95$3, -10120113/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784], N[(t$95$2 / t), $MachinePrecision], If[LessEqual[t$95$3, 1723641332219371/344728266443874206170545512964432112225507069317819522056079337263512430464013488758041250121488036739611555846958495676040441511948045769973944468809441663382665538511073745187088876036706973599091474545756168257536], N[(N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision], t$95$1]]]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -4.0000000000000003e-37 or 4.9999999999999999e-201 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 N/A

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

      15. lower--.f64 85.1%

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

   3. Applied rewrites 85.1%

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

   if -4.0000000000000003e-37 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -5.0000001653313951e-317

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 48.1%

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

   if -5.0000001653313951e-317 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 4.9999999999999999e-201

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 54.3%

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

Alternative 5: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -170000000000000:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{elif}\;z \leq 7900:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<= z -170000000000000)
  (* (/ (- z y) z) x)
  (if (<= z 7900) (/ (* x y) (- t z)) (* (/ z (- z t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e+14) {
		tmp = ((z - y) / z) * x;
	} else if (z <= 7900.0) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = (z / (z - t)) * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: tmp
    if (z <= (-1.7d+14)) then
        tmp = ((z - y) / z) * x
    else if (z <= 7900.0d0) then
        tmp = (x * y) / (t - z)
    else
        tmp = (z / (z - t)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e+14) {
		tmp = ((z - y) / z) * x;
	} else if (z <= 7900.0) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = (z / (z - t)) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.7e+14:
		tmp = ((z - y) / z) * x
	elif z <= 7900.0:
		tmp = (x * y) / (t - z)
	else:
		tmp = (z / (z - t)) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.7e+14)
		tmp = Float64(Float64(Float64(z - y) / z) * x);
	elseif (z <= 7900.0)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	else
		tmp = Float64(Float64(z / Float64(z - t)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.7e+14)
		tmp = ((z - y) / z) * x;
	elseif (z <= 7900.0)
		tmp = (x * y) / (t - z);
	else
		tmp = (z / (z - t)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -170000000000000], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 7900], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e14

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 52.1%

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

   6. Applied rewrites 52.1%

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

   if -1.7e14 < z < 7900

   1. Initial program 84.1%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 50.2%

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

   4. Applied rewrites 50.2%

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

   if 7900 < z

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 54.3%

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

Alternative 6: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq \frac{-7307508186654515}{5846006549323611672814739330865132078623730171904}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{elif}\;z \leq 7900:\\ \;\;\;\;\frac{x}{t} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<=
     z
     -7307508186654515/5846006549323611672814739330865132078623730171904)
  (* (/ (- z y) z) x)
  (if (<= z 7900) (* (/ x t) (- y z)) (* (/ z (- z t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e-33) {
		tmp = ((z - y) / z) * x;
	} else if (z <= 7900.0) {
		tmp = (x / t) * (y - z);
	} else {
		tmp = (z / (z - t)) * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: tmp
    if (z <= (-1.25d-33)) then
        tmp = ((z - y) / z) * x
    else if (z <= 7900.0d0) then
        tmp = (x / t) * (y - z)
    else
        tmp = (z / (z - t)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e-33) {
		tmp = ((z - y) / z) * x;
	} else if (z <= 7900.0) {
		tmp = (x / t) * (y - z);
	} else {
		tmp = (z / (z - t)) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.25e-33:
		tmp = ((z - y) / z) * x
	elif z <= 7900.0:
		tmp = (x / t) * (y - z)
	else:
		tmp = (z / (z - t)) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.25e-33)
		tmp = Float64(Float64(Float64(z - y) / z) * x);
	elseif (z <= 7900.0)
		tmp = Float64(Float64(x / t) * Float64(y - z));
	else
		tmp = Float64(Float64(z / Float64(z - t)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.25e-33)
		tmp = ((z - y) / z) * x;
	elseif (z <= 7900.0)
		tmp = (x / t) * (y - z);
	else
		tmp = (z / (z - t)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7307508186654515/5846006549323611672814739330865132078623730171904], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 7900], N[(N[(x / t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2500000000000001e-33

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 52.1%

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

   6. Applied rewrites 52.1%

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

   if -1.2500000000000001e-33 < z < 7900

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 48.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. lower-/.f64 48.0%

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

   6. Applied rewrites 48.0%

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

   if 7900 < z

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 54.3%

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

Alternative 7: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - y}{z} \cdot x\\ \mathbf{if}\;z \leq \frac{-7307508186654515}{5846006549323611672814739330865132078623730171904}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{8410448953938583}{266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072}:\\ \;\;\;\;\frac{x}{t} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* (/ (- z y) z) x)))
  (if (<=
       z
       -7307508186654515/5846006549323611672814739330865132078623730171904)
    t_1
    (if (<=
         z
         8410448953938583/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072)
      (* (/ x t) (- y z))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z - y) / z) * x;
	double tmp;
	if (z <= -1.25e-33) {
		tmp = t_1;
	} else if (z <= 3.15e-80) {
		tmp = (x / t) * (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 - y) / z) * x
    if (z <= (-1.25d-33)) then
        tmp = t_1
    else if (z <= 3.15d-80) then
        tmp = (x / t) * (y - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((z - y) / z) * x;
	double tmp;
	if (z <= -1.25e-33) {
		tmp = t_1;
	} else if (z <= 3.15e-80) {
		tmp = (x / t) * (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((z - y) / z) * x
	tmp = 0
	if z <= -1.25e-33:
		tmp = t_1
	elif z <= 3.15e-80:
		tmp = (x / t) * (y - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z - y) / z) * x)
	tmp = 0.0
	if (z <= -1.25e-33)
		tmp = t_1;
	elseif (z <= 3.15e-80)
		tmp = Float64(Float64(x / t) * Float64(y - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((z - y) / z) * x;
	tmp = 0.0;
	if (z <= -1.25e-33)
		tmp = t_1;
	elseif (z <= 3.15e-80)
		tmp = (x / t) * (y - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -7307508186654515/5846006549323611672814739330865132078623730171904], t$95$1, If[LessEqual[z, 8410448953938583/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072], N[(N[(x / t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2500000000000001e-33 or 3.1499999999999998e-80 < z

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 52.1%

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

   6. Applied rewrites 52.1%

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

   if -1.2500000000000001e-33 < z < 3.1499999999999998e-80

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 48.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. lower-/.f64 48.0%

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

   6. Applied rewrites 48.0%

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

Alternative 8: 70.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - y}{z} \cdot x\\ \mathbf{if}\;z \leq \frac{-1908785286492599}{3291009114642412084309938365114701009965471731267159726697218048}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{6541460297507787}{133499189745056880149688856635597007162669032647290798121690100488888732861290034376435130433536}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* (/ (- z y) z) x)))
  (if (<=
       z
       -1908785286492599/3291009114642412084309938365114701009965471731267159726697218048)
    t_1
    (if (<=
         z
         6541460297507787/133499189745056880149688856635597007162669032647290798121690100488888732861290034376435130433536)
      (* (/ y t) x)
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z - y) / z) * x;
	double tmp;
	if (z <= -5.8e-49) {
		tmp = t_1;
	} else if (z <= 4.9e-80) {
		tmp = (y / t) * 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 - y) / z) * x
    if (z <= (-5.8d-49)) then
        tmp = t_1
    else if (z <= 4.9d-80) then
        tmp = (y / t) * 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 - y) / z) * x;
	double tmp;
	if (z <= -5.8e-49) {
		tmp = t_1;
	} else if (z <= 4.9e-80) {
		tmp = (y / t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((z - y) / z) * x
	tmp = 0
	if z <= -5.8e-49:
		tmp = t_1
	elif z <= 4.9e-80:
		tmp = (y / t) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z - y) / z) * x)
	tmp = 0.0
	if (z <= -5.8e-49)
		tmp = t_1;
	elseif (z <= 4.9e-80)
		tmp = Float64(Float64(y / t) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((z - y) / z) * x;
	tmp = 0.0;
	if (z <= -5.8e-49)
		tmp = t_1;
	elseif (z <= 4.9e-80)
		tmp = (y / t) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -1908785286492599/3291009114642412084309938365114701009965471731267159726697218048], t$95$1, If[LessEqual[z, 6541460297507787/133499189745056880149688856635597007162669032647290798121690100488888732861290034376435130433536], N[(N[(y / t), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e-49 or 4.8999999999999999e-80 < z

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 52.1%

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

   6. Applied rewrites 52.1%

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

   if -5.8e-49 < z < 4.8999999999999999e-80

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 39.8%

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

   6. Applied rewrites 39.8%

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

Alternative 9: 64.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{z} \cdot \left(z - y\right)\\ \mathbf{if}\;z \leq \frac{-1908785286492599}{3291009114642412084309938365114701009965471731267159726697218048}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{1303703024854071}{65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \mathbf{elif}\;z \leq 131999999999999995732829479729182984521565270605199181502927434978217495256815980946532544045455904183345115229288130516329082472407919079866539633304170532212076911079670051795518382896419281944207949824:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* (/ x z) (- z y))))
  (if (<=
       z
       -1908785286492599/3291009114642412084309938365114701009965471731267159726697218048)
    t_1
    (if (<=
         z
         1303703024854071/65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032)
      (* (/ y t) x)
      (if (<=
           z
           131999999999999995732829479729182984521565270605199181502927434978217495256815980946532544045455904183345115229288130516329082472407919079866539633304170532212076911079670051795518382896419281944207949824)
        t_1
        (* 1 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (z - y);
	double tmp;
	if (z <= -5.8e-49) {
		tmp = t_1;
	} else if (z <= 2e-77) {
		tmp = (y / t) * x;
	} else if (z <= 1.32e+203) {
		tmp = t_1;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 = (x / z) * (z - y)
    if (z <= (-5.8d-49)) then
        tmp = t_1
    else if (z <= 2d-77) then
        tmp = (y / t) * x
    else if (z <= 1.32d+203) then
        tmp = t_1
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (z - y);
	double tmp;
	if (z <= -5.8e-49) {
		tmp = t_1;
	} else if (z <= 2e-77) {
		tmp = (y / t) * x;
	} else if (z <= 1.32e+203) {
		tmp = t_1;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) * (z - y)
	tmp = 0
	if z <= -5.8e-49:
		tmp = t_1
	elif z <= 2e-77:
		tmp = (y / t) * x
	elif z <= 1.32e+203:
		tmp = t_1
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(z - y))
	tmp = 0.0
	if (z <= -5.8e-49)
		tmp = t_1;
	elseif (z <= 2e-77)
		tmp = Float64(Float64(y / t) * x);
	elseif (z <= 1.32e+203)
		tmp = t_1;
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (z - y);
	tmp = 0.0;
	if (z <= -5.8e-49)
		tmp = t_1;
	elseif (z <= 2e-77)
		tmp = (y / t) * x;
	elseif (z <= 1.32e+203)
		tmp = t_1;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1908785286492599/3291009114642412084309938365114701009965471731267159726697218048], t$95$1, If[LessEqual[z, 1303703024854071/65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032], N[(N[(y / t), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 131999999999999995732829479729182984521565270605199181502927434978217495256815980946532544045455904183345115229288130516329082472407919079866539633304170532212076911079670051795518382896419281944207949824], t$95$1, N[(1 * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8e-49 or 1.9999999999999999e-77 < z < 1.32e203

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 N/A

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

      15. lower--.f64 85.1%

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

   3. Applied rewrites 85.1%

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

   4. Taylor expanded in z around inf

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

      1. lower-/.f64 43.7%

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

   6. Applied rewrites 43.7%

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

   if -5.8e-49 < z < 1.9999999999999999e-77

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 39.8%

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

   6. Applied rewrites 39.8%

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

   if 1.32e203 < z

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto \color{blue}{1} \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 63.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \frac{x \cdot \left(z - y\right)}{z}\\ \mathbf{if}\;z \leq -33000000000000000128627334195332913561487311083386831082578898524556797239641395735025241395650988617910201006107670862092741819808675183300109028226172391299965865348819598937095355363042052000230728717746894673689659463271481709677622386218762240:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq \frac{-1908785286492599}{3291009114642412084309938365114701009965471731267159726697218048}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{1303703024854071}{65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \mathbf{elif}\;z \leq 299999999999999996630732362518988342952803379488649768992510454652087783547085600533328090838002069535557761603666926736444477839227214370924576161583627871744229584898717153533619263940649277593806176256:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (* x (- z y)) z)))
  (if (<=
       z
       -33000000000000000128627334195332913561487311083386831082578898524556797239641395735025241395650988617910201006107670862092741819808675183300109028226172391299965865348819598937095355363042052000230728717746894673689659463271481709677622386218762240)
    (* 1 x)
    (if (<=
         z
         -1908785286492599/3291009114642412084309938365114701009965471731267159726697218048)
      t_1
      (if (<=
           z
           1303703024854071/65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032)
        (* (/ y t) x)
        (if (<=
             z
             299999999999999996630732362518988342952803379488649768992510454652087783547085600533328090838002069535557761603666926736444477839227214370924576161583627871744229584898717153533619263940649277593806176256)
          t_1
          (* 1 x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * (z - y)) / z;
	double tmp;
	if (z <= -3.3e+247) {
		tmp = 1.0 * x;
	} else if (z <= -5.8e-49) {
		tmp = t_1;
	} else if (z <= 2e-77) {
		tmp = (y / t) * x;
	} else if (z <= 3e+203) {
		tmp = t_1;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 = (x * (z - y)) / z
    if (z <= (-3.3d+247)) then
        tmp = 1.0d0 * x
    else if (z <= (-5.8d-49)) then
        tmp = t_1
    else if (z <= 2d-77) then
        tmp = (y / t) * x
    else if (z <= 3d+203) then
        tmp = t_1
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * (z - y)) / z;
	double tmp;
	if (z <= -3.3e+247) {
		tmp = 1.0 * x;
	} else if (z <= -5.8e-49) {
		tmp = t_1;
	} else if (z <= 2e-77) {
		tmp = (y / t) * x;
	} else if (z <= 3e+203) {
		tmp = t_1;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * (z - y)) / z
	tmp = 0
	if z <= -3.3e+247:
		tmp = 1.0 * x
	elif z <= -5.8e-49:
		tmp = t_1
	elif z <= 2e-77:
		tmp = (y / t) * x
	elif z <= 3e+203:
		tmp = t_1
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(z - y)) / z)
	tmp = 0.0
	if (z <= -3.3e+247)
		tmp = Float64(1.0 * x);
	elseif (z <= -5.8e-49)
		tmp = t_1;
	elseif (z <= 2e-77)
		tmp = Float64(Float64(y / t) * x);
	elseif (z <= 3e+203)
		tmp = t_1;
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * (z - y)) / z;
	tmp = 0.0;
	if (z <= -3.3e+247)
		tmp = 1.0 * x;
	elseif (z <= -5.8e-49)
		tmp = t_1;
	elseif (z <= 2e-77)
		tmp = (y / t) * x;
	elseif (z <= 3e+203)
		tmp = t_1;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -33000000000000000128627334195332913561487311083386831082578898524556797239641395735025241395650988617910201006107670862092741819808675183300109028226172391299965865348819598937095355363042052000230728717746894673689659463271481709677622386218762240], N[(1 * x), $MachinePrecision], If[LessEqual[z, -1908785286492599/3291009114642412084309938365114701009965471731267159726697218048], t$95$1, If[LessEqual[z, 1303703024854071/65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032], N[(N[(y / t), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 299999999999999996630732362518988342952803379488649768992510454652087783547085600533328090838002069535557761603666926736444477839227214370924576161583627871744229584898717153533619263940649277593806176256], t$95$1, N[(1 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3e247 or 3e203 < z

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto \color{blue}{1} \cdot x \]

   if -3.3e247 < z < -5.8e-49 or 1.9999999999999999e-77 < z < 3e203

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 44.4%

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

   6. Applied rewrites 44.4%

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

   if -5.8e-49 < z < 1.9999999999999999e-77

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 39.8%

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

   6. Applied rewrites 39.8%

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

Alternative 11: 61.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -42000000000000000000:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 480000:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<= z -42000000000000000000)
  (* 1 x)
  (if (<= z 480000) (* (/ y t) x) (* 1 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e+19) {
		tmp = 1.0 * x;
	} else if (z <= 480000.0) {
		tmp = (y / t) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: tmp
    if (z <= (-4.2d+19)) then
        tmp = 1.0d0 * x
    else if (z <= 480000.0d0) then
        tmp = (y / t) * x
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e+19) {
		tmp = 1.0 * x;
	} else if (z <= 480000.0) {
		tmp = (y / t) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.2e+19:
		tmp = 1.0 * x
	elif z <= 480000.0:
		tmp = (y / t) * x
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.2e+19)
		tmp = Float64(1.0 * x);
	elseif (z <= 480000.0)
		tmp = Float64(Float64(y / t) * x);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.2e+19)
		tmp = 1.0 * x;
	elseif (z <= 480000.0)
		tmp = (y / t) * x;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -42000000000000000000], N[(1 * x), $MachinePrecision], If[LessEqual[z, 480000], N[(N[(y / t), $MachinePrecision] * x), $MachinePrecision], N[(1 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e19 or 4.8e5 < z

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto \color{blue}{1} \cdot x \]

   if -4.2e19 < z < 4.8e5

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 39.8%

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

   6. Applied rewrites 39.8%

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

Alternative 12: 60.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -2050000000000000000:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 480000:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<= z -2050000000000000000)
  (* 1 x)
  (if (<= z 480000) (/ (* x y) t) (* 1 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.05e+18) {
		tmp = 1.0 * x;
	} else if (z <= 480000.0) {
		tmp = (x * y) / t;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: tmp
    if (z <= (-2.05d+18)) then
        tmp = 1.0d0 * x
    else if (z <= 480000.0d0) then
        tmp = (x * y) / t
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.05e+18) {
		tmp = 1.0 * x;
	} else if (z <= 480000.0) {
		tmp = (x * y) / t;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.05e+18:
		tmp = 1.0 * x
	elif z <= 480000.0:
		tmp = (x * y) / t
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.05e+18)
		tmp = Float64(1.0 * x);
	elseif (z <= 480000.0)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.05e+18)
		tmp = 1.0 * x;
	elseif (z <= 480000.0)
		tmp = (x * y) / t;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2050000000000000000], N[(1 * x), $MachinePrecision], If[LessEqual[z, 480000], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], N[(1 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05e18 or 4.8e5 < z

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto \color{blue}{1} \cdot x \]

   if -2.05e18 < z < 4.8e5

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 38.1%

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

   4. Applied rewrites 38.1%

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

Alternative 13: 60.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -42000000000000000000:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 480000:\\ \;\;\;\;\frac{x}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<= z -42000000000000000000)
  (* 1 x)
  (if (<= z 480000) (* (/ x t) y) (* 1 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e+19) {
		tmp = 1.0 * x;
	} else if (z <= 480000.0) {
		tmp = (x / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: tmp
    if (z <= (-4.2d+19)) then
        tmp = 1.0d0 * x
    else if (z <= 480000.0d0) then
        tmp = (x / t) * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e+19) {
		tmp = 1.0 * x;
	} else if (z <= 480000.0) {
		tmp = (x / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.2e+19:
		tmp = 1.0 * x
	elif z <= 480000.0:
		tmp = (x / t) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.2e+19)
		tmp = Float64(1.0 * x);
	elseif (z <= 480000.0)
		tmp = Float64(Float64(x / t) * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.2e+19)
		tmp = 1.0 * x;
	elseif (z <= 480000.0)
		tmp = (x / t) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -42000000000000000000], N[(1 * x), $MachinePrecision], If[LessEqual[z, 480000], N[(N[(x / t), $MachinePrecision] * y), $MachinePrecision], N[(1 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e19 or 4.8e5 < z

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto \color{blue}{1} \cdot x \]

   if -4.2e19 < z < 4.8e5

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 38.1%

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

   4. Applied rewrites 38.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. lower-/.f64 38.1%

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

   6. Applied rewrites 38.1%

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

Alternative 14: 38.8% accurate, 0.1× speedup

Math

\[\mathsf{copysign}\left(1, x\right) \cdot \begin{array}{l} \mathbf{if}\;\frac{\left|x\right| \cdot \left(y - z\right)}{t - z} \leq 0:\\ \;\;\;\;\frac{\left|x\right| \cdot z}{z}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left|x\right|\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (*
 (copysign 1 x)
 (if (<= (/ (* (fabs x) (- y z)) (- t z)) 0)
   (/ (* (fabs x) z) z)
   (* 1 (fabs x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((fabs(x) * (y - z)) / (t - z)) <= 0.0) {
		tmp = (fabs(x) * z) / z;
	} else {
		tmp = 1.0 * fabs(x);
	}
	return copysign(1.0, x) * tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((Math.abs(x) * (y - z)) / (t - z)) <= 0.0) {
		tmp = (Math.abs(x) * z) / z;
	} else {
		tmp = 1.0 * Math.abs(x);
	}
	return Math.copySign(1.0, x) * tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((math.fabs(x) * (y - z)) / (t - z)) <= 0.0:
		tmp = (math.fabs(x) * z) / z
	else:
		tmp = 1.0 * math.fabs(x)
	return math.copysign(1.0, x) * tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(abs(x) * Float64(y - z)) / Float64(t - z)) <= 0.0)
		tmp = Float64(Float64(abs(x) * z) / z);
	else
		tmp = Float64(1.0 * abs(x));
	end
	return Float64(copysign(1.0, x) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((abs(x) * (y - z)) / (t - z)) <= 0.0)
		tmp = (abs(x) * z) / z;
	else
		tmp = 1.0 * abs(x);
	end
	tmp_2 = (sign(x) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(N[(N[Abs[x], $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], 0], N[(N[(N[Abs[x], $MachinePrecision] * z), $MachinePrecision] / z), $MachinePrecision], N[(1 * N[Abs[x], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -0.0

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 44.4%

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

   6. Applied rewrites 44.4%

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

   7. Taylor expanded in y around 0

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

      1. lower-*.f64 30.6%

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

   9. Applied rewrites 30.6%

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

   if -0.0 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 84.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{1} \cdot x \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto \color{blue}{1} \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 35.4% accurate, 3.8× speedup

Math

\[1 \cdot x \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 1.0 * 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 = 1.0d0 * x
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 * x;
}

Python

def code(x, y, z, t):
	return 1.0 * x

Julia

function code(x, y, z, t)
	return Float64(1.0 * x)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 * x;
end

Wolfram

code[x_, y_, z_, t_] := N[(1 * x), $MachinePrecision]

Derivation

1. Initial program 84.1%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lift--.f64 N/A

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

   7. sub-negate-rev N/A

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

   8. distribute-frac-neg N/A

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

   9. distribute-neg-frac2 N/A

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

   10. lower-/.f64 N/A

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

   11. lower--.f64 N/A

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

   12. lift--.f64 N/A

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

   13. sub-negate-rev N/A

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

   14. lower--.f64 97.0%

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

3. Applied rewrites 97.0%

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

4. Taylor expanded in z around inf

   \[\leadsto \color{blue}{1} \cdot x \]
5. Step-by-step derivation

6. Applied rewrites 35.4%

   \[\leadsto \color{blue}{1} \cdot x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64
  (/ (* x (- y z)) (- t z)))