Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.3s

Alternatives: 14

Speedup: 1.0×

• 33.8% 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, 1.0× 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]

Derivation

1. Initial program 100.0%

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

Alternative 2: 83.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+102}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{elif}\;y \leq 0.0036:\\ \;\;\;\;\mathsf{fma}\left(x - t, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e+102)
   (* (- t x) y)
   (if (<= y 0.0036) (fma (- x t) z x) (fma (- t x) y x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e+102) {
		tmp = (t - x) * y;
	} else if (y <= 0.0036) {
		tmp = fma((x - t), z, x);
	} else {
		tmp = fma((t - x), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e+102)
		tmp = Float64(Float64(t - x) * y);
	elseif (y <= 0.0036)
		tmp = fma(Float64(x - t), z, x);
	else
		tmp = fma(Float64(t - x), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e+102], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 0.0036], N[(N[(x - t), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6e102

   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 86.6

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

   4. Applied rewrites 86.6%

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

   if -1.6e102 < y < 0.0035999999999999999

   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. associate-*r* N/A

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

      2. mul-1-neg N/A

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

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

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

      4. lower--.f64 N/A

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

      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 83.8

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

   4. Applied rewrites 83.8%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

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

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

      5. mul-1-neg N/A

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

      6. *-commutative N/A

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

      7. mul-1-neg N/A

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

      8. negate-sub2 N/A

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

      9. +-commutative N/A

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

      10. negate-sub2 N/A

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

      11. mul-1-neg N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. mul-1-neg N/A

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

      15. negate-sub2 N/A

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

      16. lower--.f64 83.8

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

   6. Applied rewrites 83.8%

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

   if 0.0035999999999999999 < y

   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 78.7

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

   4. Applied rewrites 78.7%

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

Alternative 3: 83.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - t\right) \cdot z\\ \mathbf{if}\;z \leq -3 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x t) z)))
   (if (<= z -3e-7) t_1 (if (<= z 1.2e+46) (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 <= -3e-7) {
		tmp = t_1;
	} else if (z <= 1.2e+46) {
		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 <= -3e-7)
		tmp = t_1;
	elseif (z <= 1.2e+46)
		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, -3e-7], t$95$1, If[LessEqual[z, 1.2e+46], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9999999999999999e-7 or 1.20000000000000004e46 < 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. associate-*r* N/A

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

      2. mul-1-neg N/A

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

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

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

      4. lower--.f64 N/A

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

      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 80.3

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

   4. Applied rewrites 80.3%

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

   5. Taylor expanded in z around inf

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

      1. negate-sub2 N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. negate-sub2 N/A

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

      7. lower--.f64 79.8

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

   7. Applied rewrites 79.8%

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

   if -2.9999999999999999e-7 < z < 1.20000000000000004e46

   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 86.6

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

   4. Applied rewrites 86.6%

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

Alternative 4: 70.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-247}:\\ \;\;\;\;\left(x - t\right) \cdot z\\ \mathbf{elif}\;y \leq 19000000000000:\\ \;\;\;\;x - t \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= y -1.6e+102)
     t_1
     (if (<= y 2.75e-247)
       (* (- x t) z)
       (if (<= y 19000000000000.0) (- x (* t z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -1.6e+102) {
		tmp = t_1;
	} else if (y <= 2.75e-247) {
		tmp = (x - t) * z;
	} else if (y <= 19000000000000.0) {
		tmp = x - (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * y
    if (y <= (-1.6d+102)) then
        tmp = t_1
    else if (y <= 2.75d-247) then
        tmp = (x - t) * z
    else if (y <= 19000000000000.0d0) then
        tmp = x - (t * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -1.6e+102) {
		tmp = t_1;
	} else if (y <= 2.75e-247) {
		tmp = (x - t) * z;
	} else if (y <= 19000000000000.0) {
		tmp = x - (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t - x) * y
	tmp = 0
	if y <= -1.6e+102:
		tmp = t_1
	elif y <= 2.75e-247:
		tmp = (x - t) * z
	elif y <= 19000000000000.0:
		tmp = x - (t * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * y)
	tmp = 0.0
	if (y <= -1.6e+102)
		tmp = t_1;
	elseif (y <= 2.75e-247)
		tmp = Float64(Float64(x - t) * z);
	elseif (y <= 19000000000000.0)
		tmp = Float64(x - Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t - x) * y;
	tmp = 0.0;
	if (y <= -1.6e+102)
		tmp = t_1;
	elseif (y <= 2.75e-247)
		tmp = (x - t) * z;
	elseif (y <= 19000000000000.0)
		tmp = x - (t * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.6e+102], t$95$1, If[LessEqual[y, 2.75e-247], N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[y, 19000000000000.0], N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6e102 or 1.9e13 < 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 82.8

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

   4. Applied rewrites 82.8%

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

   if -1.6e102 < y < 2.74999999999999997e-247

   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. associate-*r* N/A

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

      2. mul-1-neg N/A

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

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

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

      4. lower--.f64 N/A

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

      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 81.9

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

   4. Applied rewrites 81.9%

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

   5. Taylor expanded in z around inf

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

      1. negate-sub2 N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. negate-sub2 N/A

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

      7. lower--.f64 56.8

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

   7. Applied rewrites 56.8%

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

   if 2.74999999999999997e-247 < y < 1.9e13

   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. associate-*r* N/A

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

      2. mul-1-neg N/A

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

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

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

      4. lower--.f64 N/A

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

      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 85.3

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

   4. Applied rewrites 85.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 62.8

         \[\leadsto x - t \cdot z \]

   7. Applied rewrites 62.8%

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

Alternative 5: 68.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 48000000000000:\\ \;\;\;\;\left(x - t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= y -1.6e+102) t_1 (if (<= y 48000000000000.0) (* (- x t) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -1.6e+102) {
		tmp = t_1;
	} else if (y <= 48000000000000.0) {
		tmp = (x - t) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * y
    if (y <= (-1.6d+102)) then
        tmp = t_1
    else if (y <= 48000000000000.0d0) then
        tmp = (x - t) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -1.6e+102) {
		tmp = t_1;
	} else if (y <= 48000000000000.0) {
		tmp = (x - t) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t - x) * y
	tmp = 0
	if y <= -1.6e+102:
		tmp = t_1
	elif y <= 48000000000000.0:
		tmp = (x - t) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * y)
	tmp = 0.0
	if (y <= -1.6e+102)
		tmp = t_1;
	elseif (y <= 48000000000000.0)
		tmp = Float64(Float64(x - t) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t - x) * y;
	tmp = 0.0;
	if (y <= -1.6e+102)
		tmp = t_1;
	elseif (y <= 48000000000000.0)
		tmp = (x - t) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.6e+102], t$95$1, If[LessEqual[y, 48000000000000.0], N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e102 or 4.8e13 < 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 82.9

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

   4. Applied rewrites 82.9%

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

   if -1.6e102 < y < 4.8e13

   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. associate-*r* N/A

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

      2. mul-1-neg N/A

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

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

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

      4. lower--.f64 N/A

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

      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 83.1

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

   4. Applied rewrites 83.1%

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

   5. Taylor expanded in z around inf

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

      1. negate-sub2 N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. negate-sub2 N/A

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

      7. lower--.f64 56.6

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

   7. Applied rewrites 56.6%

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

Alternative 6: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - t\right) \cdot z\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-109}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x t) z)))
   (if (<= z -1.15e-37)
     t_1
     (if (<= z -3.7e-109)
       (* (- 1.0 y) x)
       (if (<= z 7.5e+32) (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 <= -1.15e-37) {
		tmp = t_1;
	} else if (z <= -3.7e-109) {
		tmp = (1.0 - y) * x;
	} else if (z <= 7.5e+32) {
		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 <= -1.15e-37)
		tmp = t_1;
	elseif (z <= -3.7e-109)
		tmp = Float64(Float64(1.0 - y) * x);
	elseif (z <= 7.5e+32)
		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, -1.15e-37], t$95$1, If[LessEqual[z, -3.7e-109], N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 7.5e+32], N[(t * y + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e-37 or 7.49999999999999959e32 < 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. associate-*r* N/A

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

      2. mul-1-neg N/A

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

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

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

      4. lower--.f64 N/A

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

      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 78.5

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

   4. Applied rewrites 78.5%

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

   5. Taylor expanded in z around inf

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

      1. negate-sub2 N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. negate-sub2 N/A

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

      7. lower--.f64 76.6

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

   7. Applied rewrites 76.6%

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

   if -1.15e-37 < z < -3.69999999999999981e-109

   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 83.0

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

   4. Applied rewrites 83.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 29.9%

      \[\leadsto x \]

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. negate-sub N/A

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

      5. lower--.f64 53.0

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

   10. Applied rewrites 53.0%

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

   if -3.69999999999999981e-109 < z < 7.49999999999999959e32

   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 88.9

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

   4. Applied rewrites 88.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 65.9%

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

Alternative 7: 53.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot t\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-109}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- z) t)))
   (if (<= z -5.1e+191)
     t_1
     (if (<= z -3.8e-10)
       (fma x z x)
       (if (<= z -3.7e-109)
         (* (- 1.0 y) x)
         (if (<= z 2e+38) (fma t y x) (if (<= z 1.5e+190) t_1 (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -z * t;
	double tmp;
	if (z <= -5.1e+191) {
		tmp = t_1;
	} else if (z <= -3.8e-10) {
		tmp = fma(x, z, x);
	} else if (z <= -3.7e-109) {
		tmp = (1.0 - y) * x;
	} else if (z <= 2e+38) {
		tmp = fma(t, y, x);
	} else if (z <= 1.5e+190) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-z) * t)
	tmp = 0.0
	if (z <= -5.1e+191)
		tmp = t_1;
	elseif (z <= -3.8e-10)
		tmp = fma(x, z, x);
	elseif (z <= -3.7e-109)
		tmp = Float64(Float64(1.0 - y) * x);
	elseif (z <= 2e+38)
		tmp = fma(t, y, x);
	elseif (z <= 1.5e+190)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-z) * t), $MachinePrecision]}, If[LessEqual[z, -5.1e+191], t$95$1, If[LessEqual[z, -3.8e-10], N[(x * z + x), $MachinePrecision], If[LessEqual[z, -3.7e-109], N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 2e+38], N[(t * y + x), $MachinePrecision], If[LessEqual[z, 1.5e+190], t$95$1, N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.09999999999999982e191 or 1.99999999999999995e38 < z < 1.49999999999999991e190

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 82.2

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

   4. Applied rewrites 82.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 44.1%

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

   if -5.09999999999999982e191 < z < -3.7999999999999998e-10

   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. associate-*r* N/A

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

      2. mul-1-neg N/A

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

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

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

      4. lower--.f64 N/A

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

      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 69.7

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

   4. Applied rewrites 69.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

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

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

      5. mul-1-neg N/A

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

      6. *-commutative N/A

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

      7. mul-1-neg N/A

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

      8. negate-sub2 N/A

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

      9. +-commutative N/A

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

      10. negate-sub2 N/A

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

      11. mul-1-neg N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. mul-1-neg N/A

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

      15. negate-sub2 N/A

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

      16. lower--.f64 69.8

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

   6. Applied rewrites 69.8%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 36.9%

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

   if -3.7999999999999998e-10 < z < -3.69999999999999981e-109

   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 80.9

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

   4. Applied rewrites 80.9%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 29.8%

      \[\leadsto x \]

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. negate-sub N/A

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

      5. lower--.f64 52.3

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

   10. Applied rewrites 52.3%

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

   if -3.69999999999999981e-109 < z < 1.99999999999999995e38

   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 88.5

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

   4. Applied rewrites 88.5%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 65.7%

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

   if 1.49999999999999991e190 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 91.6

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

   4. Applied rewrites 91.6%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 47.7

         \[\leadsto z \cdot x \]

   7. Applied rewrites 47.7%

      \[\leadsto z \cdot \color{blue}{x} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 8: 51.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot t\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-108}:\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- z) t)))
   (if (<= z -5.1e+191)
     t_1
     (if (<= z -2.7e-16)
       (fma x z x)
       (if (<= z -8.8e-108)
         (* (- x) y)
         (if (<= z 2e+38) (fma t y x) (if (<= z 1.5e+190) t_1 (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -z * t;
	double tmp;
	if (z <= -5.1e+191) {
		tmp = t_1;
	} else if (z <= -2.7e-16) {
		tmp = fma(x, z, x);
	} else if (z <= -8.8e-108) {
		tmp = -x * y;
	} else if (z <= 2e+38) {
		tmp = fma(t, y, x);
	} else if (z <= 1.5e+190) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-z) * t)
	tmp = 0.0
	if (z <= -5.1e+191)
		tmp = t_1;
	elseif (z <= -2.7e-16)
		tmp = fma(x, z, x);
	elseif (z <= -8.8e-108)
		tmp = Float64(Float64(-x) * y);
	elseif (z <= 2e+38)
		tmp = fma(t, y, x);
	elseif (z <= 1.5e+190)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-z) * t), $MachinePrecision]}, If[LessEqual[z, -5.1e+191], t$95$1, If[LessEqual[z, -2.7e-16], N[(x * z + x), $MachinePrecision], If[LessEqual[z, -8.8e-108], N[((-x) * y), $MachinePrecision], If[LessEqual[z, 2e+38], N[(t * y + x), $MachinePrecision], If[LessEqual[z, 1.5e+190], t$95$1, N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.09999999999999982e191 or 1.99999999999999995e38 < z < 1.49999999999999991e190

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 82.2

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

   4. Applied rewrites 82.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 44.1%

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

   if -5.09999999999999982e191 < z < -2.69999999999999999e-16

   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. associate-*r* N/A

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

      2. mul-1-neg N/A

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

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

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

      4. lower--.f64 N/A

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

      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 69.5

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

   4. Applied rewrites 69.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

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

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

      5. mul-1-neg N/A

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

      6. *-commutative N/A

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

      7. mul-1-neg N/A

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

      8. negate-sub2 N/A

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

      9. +-commutative N/A

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

      10. negate-sub2 N/A

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

      11. mul-1-neg N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. mul-1-neg N/A

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

      15. negate-sub2 N/A

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

      16. lower--.f64 69.5

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

   6. Applied rewrites 69.5%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 36.8%

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

   if -2.69999999999999999e-16 < z < -8.8000000000000005e-108

   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 53.8

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

   4. Applied rewrites 53.8%

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

   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 25.3

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

   7. Applied rewrites 25.3%

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

   if -8.8000000000000005e-108 < z < 1.99999999999999995e38

   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 88.5

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

   4. Applied rewrites 88.5%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 65.7%

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

   if 1.49999999999999991e190 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 91.6

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

   4. Applied rewrites 91.6%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 47.7

         \[\leadsto z \cdot x \]

   7. Applied rewrites 47.7%

      \[\leadsto z \cdot \color{blue}{x} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 9: 51.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot t\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+26}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-108}:\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- z) t)))
   (if (<= z -5.1e+191)
     t_1
     (if (<= z -2.6e+26)
       (* z x)
       (if (<= z -8.8e-108)
         (* (- x) y)
         (if (<= z 2e+38) (fma t y x) (if (<= z 1.5e+190) t_1 (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -z * t;
	double tmp;
	if (z <= -5.1e+191) {
		tmp = t_1;
	} else if (z <= -2.6e+26) {
		tmp = z * x;
	} else if (z <= -8.8e-108) {
		tmp = -x * y;
	} else if (z <= 2e+38) {
		tmp = fma(t, y, x);
	} else if (z <= 1.5e+190) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-z) * t)
	tmp = 0.0
	if (z <= -5.1e+191)
		tmp = t_1;
	elseif (z <= -2.6e+26)
		tmp = Float64(z * x);
	elseif (z <= -8.8e-108)
		tmp = Float64(Float64(-x) * y);
	elseif (z <= 2e+38)
		tmp = fma(t, y, x);
	elseif (z <= 1.5e+190)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-z) * t), $MachinePrecision]}, If[LessEqual[z, -5.1e+191], t$95$1, If[LessEqual[z, -2.6e+26], N[(z * x), $MachinePrecision], If[LessEqual[z, -8.8e-108], N[((-x) * y), $MachinePrecision], If[LessEqual[z, 2e+38], N[(t * y + x), $MachinePrecision], If[LessEqual[z, 1.5e+190], t$95$1, N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.09999999999999982e191 or 1.99999999999999995e38 < z < 1.49999999999999991e190

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 82.2

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

   4. Applied rewrites 82.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 44.1%

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

   if -5.09999999999999982e191 < z < -2.60000000000000002e26 or 1.49999999999999991e190 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 81.1

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

   4. Applied rewrites 81.1%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 43.1

         \[\leadsto z \cdot x \]

   7. Applied rewrites 43.1%

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

   if -2.60000000000000002e26 < z < -8.8000000000000005e-108

   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 51.9

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

   4. Applied rewrites 51.9%

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

   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 25.5

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

   7. Applied rewrites 25.5%

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

   if -8.8000000000000005e-108 < z < 1.99999999999999995e38

   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 88.5

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

   4. Applied rewrites 88.5%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 65.7%

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

Alternative 10: 38.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot t\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+26}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-109}:\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-214}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+38}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- z) t)))
   (if (<= z -5.1e+191)
     t_1
     (if (<= z -2.6e+26)
       (* z x)
       (if (<= z -3.9e-109)
         (* (- x) y)
         (if (<= z -1.76e-214)
           x
           (if (<= z 2e+38) (* y t) (if (<= z 1.5e+190) t_1 (* z x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -z * t;
	double tmp;
	if (z <= -5.1e+191) {
		tmp = t_1;
	} else if (z <= -2.6e+26) {
		tmp = z * x;
	} else if (z <= -3.9e-109) {
		tmp = -x * y;
	} else if (z <= -1.76e-214) {
		tmp = x;
	} else if (z <= 2e+38) {
		tmp = y * t;
	} else if (z <= 1.5e+190) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -z * t
    if (z <= (-5.1d+191)) then
        tmp = t_1
    else if (z <= (-2.6d+26)) then
        tmp = z * x
    else if (z <= (-3.9d-109)) then
        tmp = -x * y
    else if (z <= (-1.76d-214)) then
        tmp = x
    else if (z <= 2d+38) then
        tmp = y * t
    else if (z <= 1.5d+190) then
        tmp = t_1
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -z * t;
	double tmp;
	if (z <= -5.1e+191) {
		tmp = t_1;
	} else if (z <= -2.6e+26) {
		tmp = z * x;
	} else if (z <= -3.9e-109) {
		tmp = -x * y;
	} else if (z <= -1.76e-214) {
		tmp = x;
	} else if (z <= 2e+38) {
		tmp = y * t;
	} else if (z <= 1.5e+190) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -z * t
	tmp = 0
	if z <= -5.1e+191:
		tmp = t_1
	elif z <= -2.6e+26:
		tmp = z * x
	elif z <= -3.9e-109:
		tmp = -x * y
	elif z <= -1.76e-214:
		tmp = x
	elif z <= 2e+38:
		tmp = y * t
	elif z <= 1.5e+190:
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-z) * t)
	tmp = 0.0
	if (z <= -5.1e+191)
		tmp = t_1;
	elseif (z <= -2.6e+26)
		tmp = Float64(z * x);
	elseif (z <= -3.9e-109)
		tmp = Float64(Float64(-x) * y);
	elseif (z <= -1.76e-214)
		tmp = x;
	elseif (z <= 2e+38)
		tmp = Float64(y * t);
	elseif (z <= 1.5e+190)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -z * t;
	tmp = 0.0;
	if (z <= -5.1e+191)
		tmp = t_1;
	elseif (z <= -2.6e+26)
		tmp = z * x;
	elseif (z <= -3.9e-109)
		tmp = -x * y;
	elseif (z <= -1.76e-214)
		tmp = x;
	elseif (z <= 2e+38)
		tmp = y * t;
	elseif (z <= 1.5e+190)
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-z) * t), $MachinePrecision]}, If[LessEqual[z, -5.1e+191], t$95$1, If[LessEqual[z, -2.6e+26], N[(z * x), $MachinePrecision], If[LessEqual[z, -3.9e-109], N[((-x) * y), $MachinePrecision], If[LessEqual[z, -1.76e-214], x, If[LessEqual[z, 2e+38], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.5e+190], t$95$1, N[(z * x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.09999999999999982e191 or 1.99999999999999995e38 < z < 1.49999999999999991e190

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 82.2

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

   4. Applied rewrites 82.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 44.1%

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

   if -5.09999999999999982e191 < z < -2.60000000000000002e26 or 1.49999999999999991e190 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 81.1

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

   4. Applied rewrites 81.1%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 43.1

         \[\leadsto z \cdot x \]

   7. Applied rewrites 43.1%

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

   if -2.60000000000000002e26 < z < -3.90000000000000023e-109

   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 51.9

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

   4. Applied rewrites 51.9%

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

   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 25.4

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

   7. Applied rewrites 25.4%

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

   if -3.90000000000000023e-109 < z < -1.75999999999999997e-214

   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 93.3

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

   4. Applied rewrites 93.3%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 34.9%

      \[\leadsto x \]

   if -1.75999999999999997e-214 < z < 1.99999999999999995e38

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t \cdot \left(y - z\right)} \]
   3. 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 45.5

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

   4. Applied rewrites 45.5%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 35.8%

      \[\leadsto y \cdot t \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 11: 38.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+26}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-109}:\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-214}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+33}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.6e+26)
   (* z x)
   (if (<= z -3.9e-109)
     (* (- x) y)
     (if (<= z -1.76e-214) x (if (<= z 1.2e+33) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.6e+26) {
		tmp = z * x;
	} else if (z <= -3.9e-109) {
		tmp = -x * y;
	} else if (z <= -1.76e-214) {
		tmp = x;
	} else if (z <= 1.2e+33) {
		tmp = y * t;
	} 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 <= (-2.6d+26)) then
        tmp = z * x
    else if (z <= (-3.9d-109)) then
        tmp = -x * y
    else if (z <= (-1.76d-214)) then
        tmp = x
    else if (z <= 1.2d+33) then
        tmp = y * t
    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 <= -2.6e+26) {
		tmp = z * x;
	} else if (z <= -3.9e-109) {
		tmp = -x * y;
	} else if (z <= -1.76e-214) {
		tmp = x;
	} else if (z <= 1.2e+33) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.6e+26:
		tmp = z * x
	elif z <= -3.9e-109:
		tmp = -x * y
	elif z <= -1.76e-214:
		tmp = x
	elif z <= 1.2e+33:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.6e+26)
		tmp = Float64(z * x);
	elseif (z <= -3.9e-109)
		tmp = Float64(Float64(-x) * y);
	elseif (z <= -1.76e-214)
		tmp = x;
	elseif (z <= 1.2e+33)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.6e+26)
		tmp = z * x;
	elseif (z <= -3.9e-109)
		tmp = -x * y;
	elseif (z <= -1.76e-214)
		tmp = x;
	elseif (z <= 1.2e+33)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.6e+26], N[(z * x), $MachinePrecision], If[LessEqual[z, -3.9e-109], N[((-x) * y), $MachinePrecision], If[LessEqual[z, -1.76e-214], x, If[LessEqual[z, 1.2e+33], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.60000000000000002e26 or 1.2e33 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 81.3

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

   4. Applied rewrites 81.3%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 43.6

         \[\leadsto z \cdot x \]

   7. Applied rewrites 43.6%

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

   if -2.60000000000000002e26 < z < -3.90000000000000023e-109

   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 51.9

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

   4. Applied rewrites 51.9%

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

   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 25.4

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

   7. Applied rewrites 25.4%

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

   if -3.90000000000000023e-109 < z < -1.75999999999999997e-214

   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 93.3

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

   4. Applied rewrites 93.3%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 34.9%

      \[\leadsto x \]

   if -1.75999999999999997e-214 < z < 1.2e33

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t \cdot \left(y - z\right)} \]
   3. 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 45.2

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

   4. Applied rewrites 45.2%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 35.7%

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

Alternative 12: 38.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-214}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+33}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.0)
   (* z x)
   (if (<= z -1.76e-214) x (if (<= z 1.2e+33) (* y t) (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = z * x;
	} else if (z <= -1.76e-214) {
		tmp = x;
	} else if (z <= 1.2e+33) {
		tmp = y * t;
	} 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 <= (-1.0d0)) then
        tmp = z * x
    else if (z <= (-1.76d-214)) then
        tmp = x
    else if (z <= 1.2d+33) then
        tmp = y * t
    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 <= -1.0) {
		tmp = z * x;
	} else if (z <= -1.76e-214) {
		tmp = x;
	} else if (z <= 1.2e+33) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.0:
		tmp = z * x
	elif z <= -1.76e-214:
		tmp = x
	elif z <= 1.2e+33:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(z * x);
	elseif (z <= -1.76e-214)
		tmp = x;
	elseif (z <= 1.2e+33)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = z * x;
	elseif (z <= -1.76e-214)
		tmp = x;
	elseif (z <= 1.2e+33)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.0], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.76e-214], x, If[LessEqual[z, 1.2e+33], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 1.2e33 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 79.6

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

   4. Applied rewrites 79.6%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 42.4

         \[\leadsto z \cdot x \]

   7. Applied rewrites 42.4%

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

   if -1 < z < -1.75999999999999997e-214

   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 85.9

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

   4. Applied rewrites 85.9%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 31.5%

      \[\leadsto x \]

   if -1.75999999999999997e-214 < z < 1.2e33

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t \cdot \left(y - z\right)} \]
   3. 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 45.2

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

   4. Applied rewrites 45.2%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 35.7%

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

Alternative 13: 36.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y - z \leq -2 \cdot 10^{+37}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y - z \leq 0.0002:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (- y z) -2e+37) (* z x) (if (<= (- y z) 0.0002) x (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y - z) <= -2e+37) {
		tmp = z * x;
	} else if ((y - z) <= 0.0002) {
		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 ((y - z) <= (-2d+37)) then
        tmp = z * x
    else if ((y - z) <= 0.0002d0) 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 ((y - z) <= -2e+37) {
		tmp = z * x;
	} else if ((y - z) <= 0.0002) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y - z) <= -2e+37:
		tmp = z * x
	elif (y - z) <= 0.0002:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y - z) <= -2e+37)
		tmp = Float64(z * x);
	elseif (Float64(y - z) <= 0.0002)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y - z) <= -2e+37)
		tmp = z * x;
	elseif ((y - z) <= 0.0002)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(y - z), $MachinePrecision], -2e+37], N[(z * x), $MachinePrecision], If[LessEqual[N[(y - z), $MachinePrecision], 0.0002], x, N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -1.99999999999999991e37 or 2.0000000000000001e-4 < (-.f64 y z)

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 53.4

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

   4. Applied rewrites 53.4%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 28.8

         \[\leadsto z \cdot x \]

   7. Applied rewrites 28.8%

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

   if -1.99999999999999991e37 < (-.f64 y z) < 2.0000000000000001e-4

   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 76.3

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

   4. Applied rewrites 76.3%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 55.8%

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

Alternative 14: 18.1% accurate, 11.9× 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. 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 60.3

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

4. Applied rewrites 60.3%

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

5. Taylor expanded in y around 0

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

7. Applied rewrites 18.1%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025110 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64
  (+ x (* (- y z) (- t x))))