Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.5s

Alternatives: 12

Speedup: 1.1×

• 33.7% 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, 1.1× 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. 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

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

   4. lift--.f64 N/A

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

   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

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

3. Applied rewrites 100.0%

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

Alternative 2: 83.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+45}:\\ \;\;\;\;\left(x - t\right) \cdot z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, z, z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.1e+45)
   (* (- x t) z)
   (if (<= z 1.6e+26) (fma (- t x) y x) (fma (- t) z (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.1e+45) {
		tmp = (x - t) * z;
	} else if (z <= 1.6e+26) {
		tmp = fma((t - x), y, x);
	} else {
		tmp = fma(-t, z, (z * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.1e+45)
		tmp = Float64(Float64(x - t) * z);
	elseif (z <= 1.6e+26)
		tmp = fma(Float64(t - x), y, x);
	else
		tmp = fma(Float64(-t), z, Float64(z * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.1e+45], N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 1.6e+26], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], N[((-t) * z + N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.10000000000000012e45

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.6

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

   7. Applied rewrites 43.6%

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

   if -4.10000000000000012e45 < z < 1.60000000000000014e26

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y \cdot \left(t - x\right)} \]
   3. 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 61.1

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

   4. Applied rewrites 61.1%

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

   if 1.60000000000000014e26 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.6

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

   7. Applied rewrites 43.6%

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

   8. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 42.7

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

   10. Applied rewrites 42.7%

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

Alternative 3: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - t\right) \cdot z\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x t) z)))
   (if (<= z -4.1e+45) t_1 (if (<= z 1.6e+26) (fma (- t x) y x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - t) * z;
	double tmp;
	if (z <= -4.1e+45) {
		tmp = t_1;
	} else if (z <= 1.6e+26) {
		tmp = fma((t - x), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - t) * z)
	tmp = 0.0
	if (z <= -4.1e+45)
		tmp = t_1;
	elseif (z <= 1.6e+26)
		tmp = fma(Float64(t - x), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.1e+45], t$95$1, If[LessEqual[z, 1.6e+26], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.10000000000000012e45 or 1.60000000000000014e26 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.6

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

   7. Applied rewrites 43.6%

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

   if -4.10000000000000012e45 < z < 1.60000000000000014e26

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y \cdot \left(t - x\right)} \]
   3. 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 61.1

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

   4. Applied rewrites 61.1%

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

Alternative 4: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - t\right) \cdot z\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{-230}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+23}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x t) z)))
   (if (<= z -4.1e+45)
     t_1
     (if (<= z -7.3e-230) (fma t y x) (if (<= z 3.8e+23) (* (- t x) y) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - t) * z;
	double tmp;
	if (z <= -4.1e+45) {
		tmp = t_1;
	} else if (z <= -7.3e-230) {
		tmp = fma(t, y, x);
	} else if (z <= 3.8e+23) {
		tmp = (t - x) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - t) * z)
	tmp = 0.0
	if (z <= -4.1e+45)
		tmp = t_1;
	elseif (z <= -7.3e-230)
		tmp = fma(t, y, x);
	elseif (z <= 3.8e+23)
		tmp = Float64(Float64(t - x) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.1e+45], t$95$1, If[LessEqual[z, -7.3e-230], N[(t * y + x), $MachinePrecision], If[LessEqual[z, 3.8e+23], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.10000000000000012e45 or 3.79999999999999975e23 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.6

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

   7. Applied rewrites 43.6%

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

   if -4.10000000000000012e45 < z < -7.3000000000000001e-230

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y \cdot \left(t - x\right)} \]
   3. 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 61.1

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

   4. Applied rewrites 61.1%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 42.0%

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

   if -7.3000000000000001e-230 < z < 3.79999999999999975e23

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   3. 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 45.3

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

   4. Applied rewrites 45.3%

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

Alternative 5: 68.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - t\right) \cdot z\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 700000000000:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x t) z)))
   (if (<= z -4.1e+45) t_1 (if (<= z 700000000000.0) (fma t y x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - t) * z;
	double tmp;
	if (z <= -4.1e+45) {
		tmp = t_1;
	} else if (z <= 700000000000.0) {
		tmp = fma(t, y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - t) * z)
	tmp = 0.0
	if (z <= -4.1e+45)
		tmp = t_1;
	elseif (z <= 700000000000.0)
		tmp = fma(t, y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.1e+45], t$95$1, If[LessEqual[z, 700000000000.0], N[(t * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.10000000000000012e45 or 7e11 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.6

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

   7. Applied rewrites 43.6%

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

   if -4.10000000000000012e45 < z < 7e11

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y \cdot \left(t - x\right)} \]
   3. 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 61.1

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

   4. Applied rewrites 61.1%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 42.0%

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

Alternative 6: 53.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+45}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;-t \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.2e+45) (* z x) (if (<= z 2.25e+26) (fma t y x) (- (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+45) {
		tmp = z * x;
	} else if (z <= 2.25e+26) {
		tmp = fma(t, y, x);
	} else {
		tmp = -(t * z);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.2e+45)
		tmp = Float64(z * x);
	elseif (z <= 2.25e+26)
		tmp = fma(t, y, x);
	else
		tmp = Float64(-Float64(t * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.2e+45], N[(z * x), $MachinePrecision], If[LessEqual[z, 2.25e+26], N[(t * y + x), $MachinePrecision], (-N[(t * z), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if z < -5.20000000000000014e45

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.6

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

   7. Applied rewrites 43.6%

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

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 21.7

         \[\leadsto z \cdot x \]

   10. Applied rewrites 21.7%

       \[\leadsto z \cdot x \]

   if -5.20000000000000014e45 < z < 2.24999999999999989e26

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y \cdot \left(t - x\right)} \]
   3. 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 61.1

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

   4. Applied rewrites 61.1%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 42.0%

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

   if 2.24999999999999989e26 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

         \[\leadsto -t \cdot z \]

      3. lower-*.f64 26.0

         \[\leadsto -t \cdot z \]

   7. Applied rewrites 26.0%

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

Alternative 7: 45.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+81}:\\ \;\;\;\;-t \cdot z\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.8e+81) (- (* t z)) (if (<= t 7.2e+109) (fma z x x) (* t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.8e+81) {
		tmp = -(t * z);
	} else if (t <= 7.2e+109) {
		tmp = fma(z, x, x);
	} else {
		tmp = t * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.8e+81)
		tmp = Float64(-Float64(t * z));
	elseif (t <= 7.2e+109)
		tmp = fma(z, x, x);
	else
		tmp = Float64(t * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.8e+81], (-N[(t * z), $MachinePrecision]), If[LessEqual[t, 7.2e+109], N[(z * x + x), $MachinePrecision], N[(t * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.7999999999999999e81

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

         \[\leadsto -t \cdot z \]

      3. lower-*.f64 26.0

         \[\leadsto -t \cdot z \]

   7. Applied rewrites 26.0%

      \[\leadsto -t \cdot z \]

   if -5.7999999999999999e81 < t < 7.2e109

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in x around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 37.4

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

   7. Applied rewrites 37.4%

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

   8. Taylor expanded in z around 0

      \[\leadsto x + x \cdot \color{blue}{z} \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x \cdot z + x \]

      2. *-commutative N/A

         \[\leadsto z \cdot x + x \]

      3. lower-fma.f64 37.4

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

   10. Applied rewrites 37.4%

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

   if 7.2e109 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   3. 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 45.3

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

   4. Applied rewrites 45.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 26.4%

      \[\leadsto t \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 39.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-10}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;-t \cdot z\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+53}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+252}:\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e-10)
   (* t y)
   (if (<= y 5.5e-5)
     (- (* t z))
     (if (<= y 2.6e+53) (* t y) (if (<= y 1.66e+252) (* (- x) y) (* t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-10) {
		tmp = t * y;
	} else if (y <= 5.5e-5) {
		tmp = -(t * z);
	} else if (y <= 2.6e+53) {
		tmp = t * y;
	} else if (y <= 1.66e+252) {
		tmp = -x * y;
	} else {
		tmp = t * y;
	}
	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 <= (-5.5d-10)) then
        tmp = t * y
    else if (y <= 5.5d-5) then
        tmp = -(t * z)
    else if (y <= 2.6d+53) then
        tmp = t * y
    else if (y <= 1.66d+252) then
        tmp = -x * y
    else
        tmp = t * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-10) {
		tmp = t * y;
	} else if (y <= 5.5e-5) {
		tmp = -(t * z);
	} else if (y <= 2.6e+53) {
		tmp = t * y;
	} else if (y <= 1.66e+252) {
		tmp = -x * y;
	} else {
		tmp = t * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e-10:
		tmp = t * y
	elif y <= 5.5e-5:
		tmp = -(t * z)
	elif y <= 2.6e+53:
		tmp = t * y
	elif y <= 1.66e+252:
		tmp = -x * y
	else:
		tmp = t * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e-10)
		tmp = Float64(t * y);
	elseif (y <= 5.5e-5)
		tmp = Float64(-Float64(t * z));
	elseif (y <= 2.6e+53)
		tmp = Float64(t * y);
	elseif (y <= 1.66e+252)
		tmp = Float64(Float64(-x) * y);
	else
		tmp = Float64(t * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.5e-10)
		tmp = t * y;
	elseif (y <= 5.5e-5)
		tmp = -(t * z);
	elseif (y <= 2.6e+53)
		tmp = t * y;
	elseif (y <= 1.66e+252)
		tmp = -x * y;
	else
		tmp = t * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e-10], N[(t * y), $MachinePrecision], If[LessEqual[y, 5.5e-5], (-N[(t * z), $MachinePrecision]), If[LessEqual[y, 2.6e+53], N[(t * y), $MachinePrecision], If[LessEqual[y, 1.66e+252], N[((-x) * y), $MachinePrecision], N[(t * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4999999999999996e-10 or 5.5000000000000002e-5 < y < 2.59999999999999998e53 or 1.66e252 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   3. 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 45.3

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

   4. Applied rewrites 45.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 26.4%

      \[\leadsto t \cdot y \]

   if -5.4999999999999996e-10 < y < 5.5000000000000002e-5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

         \[\leadsto -t \cdot z \]

      3. lower-*.f64 26.0

         \[\leadsto -t \cdot z \]

   7. Applied rewrites 26.0%

      \[\leadsto -t \cdot z \]

   if 2.59999999999999998e53 < y < 1.66e252

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   3. 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 45.3

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

   4. Applied rewrites 45.3%

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

   5. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 23.3

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

   7. Applied rewrites 23.3%

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

Alternative 9: 38.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-10}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;-t \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e-10) (* t y) (if (<= y 5.5e-5) (- (* t z)) (* t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-10) {
		tmp = t * y;
	} else if (y <= 5.5e-5) {
		tmp = -(t * z);
	} else {
		tmp = t * y;
	}
	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 <= (-5.5d-10)) then
        tmp = t * y
    else if (y <= 5.5d-5) then
        tmp = -(t * z)
    else
        tmp = t * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-10) {
		tmp = t * y;
	} else if (y <= 5.5e-5) {
		tmp = -(t * z);
	} else {
		tmp = t * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e-10:
		tmp = t * y
	elif y <= 5.5e-5:
		tmp = -(t * z)
	else:
		tmp = t * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e-10)
		tmp = Float64(t * y);
	elseif (y <= 5.5e-5)
		tmp = Float64(-Float64(t * z));
	else
		tmp = Float64(t * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.5e-10)
		tmp = t * y;
	elseif (y <= 5.5e-5)
		tmp = -(t * z);
	else
		tmp = t * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e-10], N[(t * y), $MachinePrecision], If[LessEqual[y, 5.5e-5], (-N[(t * z), $MachinePrecision]), N[(t * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4999999999999996e-10 or 5.5000000000000002e-5 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   3. 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 45.3

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

   4. Applied rewrites 45.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 26.4%

      \[\leadsto t \cdot y \]

   if -5.4999999999999996e-10 < y < 5.5000000000000002e-5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

         \[\leadsto -t \cdot z \]

      3. lower-*.f64 26.0

         \[\leadsto -t \cdot z \]

   7. Applied rewrites 26.0%

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

Alternative 10: 38.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+45}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+69}:\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.2e+45) (* z x) (if (<= z 1.6e+69) (* t y) (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+45) {
		tmp = z * x;
	} else if (z <= 1.6e+69) {
		tmp = t * y;
	} 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 <= (-5.2d+45)) then
        tmp = z * x
    else if (z <= 1.6d+69) then
        tmp = t * y
    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 <= -5.2e+45) {
		tmp = z * x;
	} else if (z <= 1.6e+69) {
		tmp = t * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.2e+45:
		tmp = z * x
	elif z <= 1.6e+69:
		tmp = t * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.2e+45)
		tmp = Float64(z * x);
	elseif (z <= 1.6e+69)
		tmp = Float64(t * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.2e+45)
		tmp = z * x;
	elseif (z <= 1.6e+69)
		tmp = t * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.2e+45], N[(z * x), $MachinePrecision], If[LessEqual[z, 1.6e+69], N[(t * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000014e45 or 1.59999999999999992e69 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.6

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

   7. Applied rewrites 43.6%

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

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 21.7

         \[\leadsto z \cdot x \]

   10. Applied rewrites 21.7%

       \[\leadsto z \cdot x \]

   if -5.20000000000000014e45 < z < 1.59999999999999992e69

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   3. 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 45.3

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

   4. Applied rewrites 45.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 26.4%

      \[\leadsto t \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 36.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-32}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 0.00185:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.9e-32) (* z x) (if (<= z 0.00185) (* 1.0 x) (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.9e-32) {
		tmp = z * x;
	} else if (z <= 0.00185) {
		tmp = 1.0 * 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 <= (-3.9d-32)) then
        tmp = z * x
    else if (z <= 0.00185d0) then
        tmp = 1.0d0 * 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 <= -3.9e-32) {
		tmp = z * x;
	} else if (z <= 0.00185) {
		tmp = 1.0 * x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.9e-32:
		tmp = z * x
	elif z <= 0.00185:
		tmp = 1.0 * x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.9e-32)
		tmp = Float64(z * x);
	elseif (z <= 0.00185)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.9e-32)
		tmp = z * x;
	elseif (z <= 0.00185)
		tmp = 1.0 * x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.9e-32], N[(z * x), $MachinePrecision], If[LessEqual[z, 0.00185], N[(1.0 * x), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9000000000000001e-32 or 0.0018500000000000001 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.6

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

   7. Applied rewrites 43.6%

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

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 21.7

         \[\leadsto z \cdot x \]

   10. Applied rewrites 21.7%

       \[\leadsto z \cdot x \]

   if -3.9000000000000001e-32 < z < 0.0018500000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in x around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 37.4

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

   7. Applied rewrites 37.4%

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

   8. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 18.1%

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

Alternative 12: 21.7% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0

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

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

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

   2. lower--.f64 N/A

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

   3. metadata-eval N/A

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

   4. *-lft-identity N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 N/A

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

   7. lift--.f64 59.5

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

4. Applied rewrites 59.5%

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

5. Taylor expanded in z around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 43.6

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

7. Applied rewrites 43.6%

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

8. Taylor expanded in x around inf

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

   1. *-commutative N/A

      \[\leadsto z \cdot x \]

   2. lower-*.f64 21.7

      \[\leadsto z \cdot x \]

10. Applied rewrites 21.7%

    \[\leadsto z \cdot x \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025131 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64
  (+ x (* (- y z) (- t x))))