Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

Alternatives: 11

Speedup: 1.2×

• 34.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. +-commutative N/A

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

   6. lower-fma.f64 N/A

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

   7. lift--.f64 N/A

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

   8. lift--.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 53.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+220}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+57}:\\ \;\;\;\;\left(-z\right) \cdot t\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+101}:\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.8e+220)
   (* z x)
   (if (<= z -2.15e+57)
     (* (- z) t)
     (if (<= z 2.8e-14)
       (fma t y x)
       (if (<= z 4.9e+101) (* (- x) y) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.8e+220) {
		tmp = z * x;
	} else if (z <= -2.15e+57) {
		tmp = -z * t;
	} else if (z <= 2.8e-14) {
		tmp = fma(t, y, x);
	} else if (z <= 4.9e+101) {
		tmp = -x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.8e+220)
		tmp = Float64(z * x);
	elseif (z <= -2.15e+57)
		tmp = Float64(Float64(-z) * t);
	elseif (z <= 2.8e-14)
		tmp = fma(t, y, x);
	elseif (z <= 4.9e+101)
		tmp = Float64(Float64(-x) * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.8e+220], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.15e+57], N[((-z) * t), $MachinePrecision], If[LessEqual[z, 2.8e-14], N[(t * y + x), $MachinePrecision], If[LessEqual[z, 4.9e+101], N[((-x) * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.8000000000000001e220 or 4.89999999999999983e101 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 63.4

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   5. Applied rewrites 63.4%

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

   6. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 58.4%

      \[\leadsto z \cdot x \]

   if -6.8000000000000001e220 < z < -2.15000000000000016e57

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. *-lft-identity N/A

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

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

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-rgt-out N/A

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

      11. associate-*r* N/A

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

      12. associate-+l+ N/A

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

      13. mul-1-neg N/A

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

      14. *-commutative N/A

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

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

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

      18. lift--.f64 N/A

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

      19. mul-1-neg N/A

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

      20. lower-neg.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-fma.f64 N/A

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 60.9

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

   7. Applied rewrites 60.9%

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

   8. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 47.4

         \[\leadsto \left(-z\right) \cdot t \]

   10. Applied rewrites 47.4%

       \[\leadsto \left(-z\right) \cdot t \]

   if -2.15000000000000016e57 < z < 2.8000000000000001e-14

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(t - x\right) \cdot y + x \]

      3. lower-fma.f64 N/A

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

      4. lift--.f64 86.6

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

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 64.3%

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

   if 2.8000000000000001e-14 < z < 4.89999999999999983e101

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 65.6

         \[\leadsto \left(t - x\right) \cdot y \]

   5. Applied rewrites 65.6%

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

   6. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) \cdot y \]

      2. lift-neg.f64 43.2

         \[\leadsto \left(-x\right) \cdot y \]

   8. Applied rewrites 43.2%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+220}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+57}:\\ \;\;\;\;\left(-z\right) \cdot t\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+101}:\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+73}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+101}:\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.9e+73)
   (* z x)
   (if (<= z 2.8e-14) (fma t y x) (if (<= z 4.9e+101) (* (- x) y) (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e+73) {
		tmp = z * x;
	} else if (z <= 2.8e-14) {
		tmp = fma(t, y, x);
	} else if (z <= 4.9e+101) {
		tmp = -x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.9e+73)
		tmp = Float64(z * x);
	elseif (z <= 2.8e-14)
		tmp = fma(t, y, x);
	elseif (z <= 4.9e+101)
		tmp = Float64(Float64(-x) * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.9e+73], N[(z * x), $MachinePrecision], If[LessEqual[z, 2.8e-14], N[(t * y + x), $MachinePrecision], If[LessEqual[z, 4.9e+101], N[((-x) * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9000000000000002e73 or 4.89999999999999983e101 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 56.8

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   5. Applied rewrites 56.8%

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

   6. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 50.3%

      \[\leadsto z \cdot x \]

   if -2.9000000000000002e73 < z < 2.8000000000000001e-14

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(t - x\right) \cdot y + x \]

      3. lower-fma.f64 N/A

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

      4. lift--.f64 85.6

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

   5. Applied rewrites 85.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 63.8%

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

   if 2.8000000000000001e-14 < z < 4.89999999999999983e101

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 65.6

         \[\leadsto \left(t - x\right) \cdot y \]

   5. Applied rewrites 65.6%

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

   6. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) \cdot y \]

      2. lift-neg.f64 43.2

         \[\leadsto \left(-x\right) \cdot y \]

   8. Applied rewrites 43.2%

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

Alternative 4: 38.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+73}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-297}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.9e+73)
   (* z x)
   (if (<= z -1.1e-297) (* t y) (if (<= z 1.6e-11) x (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e+73) {
		tmp = z * x;
	} else if (z <= -1.1e-297) {
		tmp = t * y;
	} else if (z <= 1.6e-11) {
		tmp = x;
	} else {
		tmp = z * 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 <= (-2.9d+73)) then
        tmp = z * x
    else if (z <= (-1.1d-297)) then
        tmp = t * y
    else if (z <= 1.6d-11) then
        tmp = x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e+73) {
		tmp = z * x;
	} else if (z <= -1.1e-297) {
		tmp = t * y;
	} else if (z <= 1.6e-11) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.9e+73:
		tmp = z * x
	elif z <= -1.1e-297:
		tmp = t * y
	elif z <= 1.6e-11:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.9e+73)
		tmp = Float64(z * x);
	elseif (z <= -1.1e-297)
		tmp = Float64(t * y);
	elseif (z <= 1.6e-11)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.9e+73)
		tmp = z * x;
	elseif (z <= -1.1e-297)
		tmp = t * y;
	elseif (z <= 1.6e-11)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.9e+73], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.1e-297], N[(t * y), $MachinePrecision], If[LessEqual[z, 1.6e-11], x, N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9000000000000002e73 or 1.59999999999999997e-11 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 59.3

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   5. Applied rewrites 59.3%

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

   6. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 44.3%

      \[\leadsto z \cdot x \]

   if -2.9000000000000002e73 < z < -1.0999999999999999e-297

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 60.2

         \[\leadsto \left(t - x\right) \cdot y \]

   5. Applied rewrites 60.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto t \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 41.5%

      \[\leadsto t \cdot y \]

   if -1.0999999999999999e-297 < z < 1.59999999999999997e-11

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(t - x\right) \cdot y + x \]

      3. lower-fma.f64 N/A

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

      4. lift--.f64 91.7

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

   5. Applied rewrites 91.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto x \]
   7. Step-by-step derivation

   8. Applied rewrites 44.8%

      \[\leadsto x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -480 \lor \neg \left(z \leq 4.9 \cdot 10^{+101}\right):\\ \;\;\;\;\left(-z\right) \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -480.0) (not (<= z 4.9e+101)))
   (* (- z) (- t x))
   (fma (- t x) y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -480.0) || !(z <= 4.9e+101)) {
		tmp = -z * (t - x);
	} else {
		tmp = fma((t - x), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -480.0) || !(z <= 4.9e+101))
		tmp = Float64(Float64(-z) * Float64(t - x));
	else
		tmp = fma(Float64(t - x), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -480.0], N[Not[LessEqual[z, 4.9e+101]], $MachinePrecision]], N[((-z) * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -480 or 4.89999999999999983e101 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 81.9

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

   5. Applied rewrites 81.9%

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

   if -480 < z < 4.89999999999999983e101

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(t - x\right) \cdot y + x \]

      3. lower-fma.f64 N/A

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

      4. lift--.f64 87.2

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

   5. Applied rewrites 87.2%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -480 \lor \neg \left(z \leq 4.9 \cdot 10^{+101}\right):\\ \;\;\;\;\left(-z\right) \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-6}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 1.86 \cdot 10^{+102}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.45e-6)
   (* (- y z) t)
   (if (<= z 1.86e+102) (fma (- t x) y x) (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e-6) {
		tmp = (y - z) * t;
	} else if (z <= 1.86e+102) {
		tmp = fma((t - x), y, x);
	} else {
		tmp = z * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.45e-6)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= 1.86e+102)
		tmp = fma(Float64(t - x), y, x);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.45e-6], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 1.86e+102], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4500000000000001e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 55.4

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

   5. Applied rewrites 55.4%

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

   if -1.4500000000000001e-6 < z < 1.8600000000000001e102

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(t - x\right) \cdot y + x \]

      3. lower-fma.f64 N/A

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

      4. lift--.f64 87.7

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

   5. Applied rewrites 87.7%

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

   if 1.8600000000000001e102 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 62.5

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   5. Applied rewrites 62.5%

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

   6. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 57.1%

      \[\leadsto z \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 66.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+53} \lor \neg \left(y \leq 8.6 \cdot 10^{-10}\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(1 + z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.85e+53) (not (<= y 8.6e-10))) (* (- t x) y) (* (+ 1.0 z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.85e+53) || !(y <= 8.6e-10)) {
		tmp = (t - x) * y;
	} else {
		tmp = (1.0 + z) * 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 ((y <= (-2.85d+53)) .or. (.not. (y <= 8.6d-10))) then
        tmp = (t - x) * y
    else
        tmp = (1.0d0 + z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.85e+53) || !(y <= 8.6e-10)) {
		tmp = (t - x) * y;
	} else {
		tmp = (1.0 + z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.85e+53) or not (y <= 8.6e-10):
		tmp = (t - x) * y
	else:
		tmp = (1.0 + z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.85e+53) || !(y <= 8.6e-10))
		tmp = Float64(Float64(t - x) * y);
	else
		tmp = Float64(Float64(1.0 + z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.85e+53) || ~((y <= 8.6e-10)))
		tmp = (t - x) * y;
	else
		tmp = (1.0 + z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.85e+53], N[Not[LessEqual[y, 8.6e-10]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision], N[(N[(1.0 + z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.85000000000000009e53 or 8.60000000000000029e-10 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 84.3

         \[\leadsto \left(t - x\right) \cdot y \]

   5. Applied rewrites 84.3%

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

   if -2.85000000000000009e53 < y < 8.60000000000000029e-10

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 61.4

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   5. Applied rewrites 61.4%

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

   6. Taylor expanded in y around 0

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

      1. lower-+.f64 59.2

         \[\leadsto \left(1 + z\right) \cdot x \]

   8. Applied rewrites 59.2%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+53} \lor \neg \left(y \leq 8.6 \cdot 10^{-10}\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(1 + z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-50} \lor \neg \left(t \leq 4.4 \cdot 10^{+35}\right):\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 + z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.8e-50) (not (<= t 4.4e+35))) (fma t y x) (* (+ 1.0 z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.8e-50) || !(t <= 4.4e+35)) {
		tmp = fma(t, y, x);
	} else {
		tmp = (1.0 + z) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.8e-50) || !(t <= 4.4e+35))
		tmp = fma(t, y, x);
	else
		tmp = Float64(Float64(1.0 + z) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.8e-50], N[Not[LessEqual[t, 4.4e+35]], $MachinePrecision]], N[(t * y + x), $MachinePrecision], N[(N[(1.0 + z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.80000000000000004e-50 or 4.3999999999999997e35 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(t - x\right) \cdot y + x \]

      3. lower-fma.f64 N/A

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

      4. lift--.f64 64.9

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 54.8%

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

   if -4.80000000000000004e-50 < t < 4.3999999999999997e35

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 84.1

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   5. Applied rewrites 84.1%

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

   6. Taylor expanded in y around 0

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

      1. lower-+.f64 57.3

         \[\leadsto \left(1 + z\right) \cdot x \]

   8. Applied rewrites 57.3%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-50} \lor \neg \left(t \leq 4.4 \cdot 10^{+35}\right):\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 + z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+73} \lor \neg \left(z \leq 1.55 \cdot 10^{+57}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.9e+73) (not (<= z 1.55e+57))) (* z x) (fma t y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+73) || !(z <= 1.55e+57)) {
		tmp = z * x;
	} else {
		tmp = fma(t, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.9e+73) || !(z <= 1.55e+57))
		tmp = Float64(z * x);
	else
		tmp = fma(t, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.9e+73], N[Not[LessEqual[z, 1.55e+57]], $MachinePrecision]], N[(z * x), $MachinePrecision], N[(t * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9000000000000002e73 or 1.55000000000000007e57 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 57.9

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   5. Applied rewrites 57.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 49.8%

      \[\leadsto z \cdot x \]

   if -2.9000000000000002e73 < z < 1.55000000000000007e57

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(t - x\right) \cdot y + x \]

      3. lower-fma.f64 N/A

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

      4. lift--.f64 82.9

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

   5. Applied rewrites 82.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 58.5%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+73} \lor \neg \left(z \leq 1.55 \cdot 10^{+57}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-6} \lor \neg \left(z \leq 1.6 \cdot 10^{-11}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.1e-6) (not (<= z 1.6e-11))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.1e-6) || !(z <= 1.6e-11)) {
		tmp = z * x;
	} else {
		tmp = 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 <= (-5.1d-6)) .or. (.not. (z <= 1.6d-11))) then
        tmp = z * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.1e-6) || !(z <= 1.6e-11)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.1e-6) or not (z <= 1.6e-11):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.1e-6) || !(z <= 1.6e-11))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.1e-6) || ~((z <= 1.6e-11)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.1e-6], N[Not[LessEqual[z, 1.6e-11]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.1000000000000003e-6 or 1.59999999999999997e-11 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 55.6

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 41.1%

      \[\leadsto z \cdot x \]

   if -5.1000000000000003e-6 < z < 1.59999999999999997e-11

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(t - x\right) \cdot y + x \]

      3. lower-fma.f64 N/A

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

      4. lift--.f64 92.5

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

   5. Applied rewrites 92.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto x \]
   7. Step-by-step derivation

   8. Applied rewrites 36.2%

      \[\leadsto x \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-6} \lor \neg \left(z \leq 1.6 \cdot 10^{-11}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 17.4% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

      \[\leadsto \left(t - x\right) \cdot y + x \]

   3. lower-fma.f64 N/A

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

   4. lift--.f64 63.0

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

5. Applied rewrites 63.0%

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

6. Taylor expanded in y around 0

   \[\leadsto x \]
7. Step-by-step derivation

8. Applied rewrites 18.4%

   \[\leadsto x \]
9. Add Preprocessing

Developer Target 1: 96.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025060 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

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