Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Percentage Accurate: 95.4% → 96.6%

Time: 9.3s

Alternatives: 24

Speedup: 1.1×

• 35.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(b - a, t, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (- b a) t (- (+ (fma (- y 2.0) b x) a) (* z (- y 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma((b - a), t, ((fma((y - 2.0), b, x) + a) - (z * (y - 1.0))));
}

Julia

function code(x, y, z, t, a, b)
	return fma(Float64(b - a), t, Float64(Float64(fma(Float64(y - 2.0), b, x) + a) - Float64(z * Float64(y - 1.0))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(b - a), $MachinePrecision] * t + N[(N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision] - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.1%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in t around 0

   \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
4. Step-by-step derivation

   1. associate--r+ N/A

      \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   2. lower--.f64 N/A

      \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

5. Applied rewrites 98.0%

   \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
6. Step-by-step derivation

7. Applied rewrites 98.0%

   \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]
8. Add Preprocessing

Alternative 2: 91.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+20}:\\ \;\;\;\;\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(-z\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-51}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(-z, y, z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.1e+20)
   (- (+ (fma (- b a) t (fma (- y 2.0) b x)) a) (- z))
   (if (<= t 7.2e-51)
     (+ (+ (fma -2.0 b (fma (- b z) y z)) x) a)
     (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b (fma (- z) y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.1e+20) {
		tmp = (fma((b - a), t, fma((y - 2.0), b, x)) + a) - -z;
	} else if (t <= 7.2e-51) {
		tmp = (fma(-2.0, b, fma((b - z), y, z)) + x) + a;
	} else {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, fma(-z, y, z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.1e+20)
		tmp = Float64(Float64(fma(Float64(b - a), t, fma(Float64(y - 2.0), b, x)) + a) - Float64(-z));
	elseif (t <= 7.2e-51)
		tmp = Float64(Float64(fma(-2.0, b, fma(Float64(b - z), y, z)) + x) + a);
	else
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, fma(Float64(-z), y, z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.1e+20], N[(N[(N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] - (-z)), $MachinePrecision], If[LessEqual[t, 7.2e-51], N[(N[(N[(-2.0 * b + N[(N[(b - z), $MachinePrecision] * y + z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + a), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[((-z) * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e20

   1. Initial program 92.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 98.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in y around 0

      \[\leadsto \left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - -1 \cdot \color{blue}{z} \]
   7. Step-by-step derivation

   8. Applied rewrites 92.9%

      \[\leadsto \left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(-z\right) \]

   if -1.1e20 < t < 7.2000000000000001e-51

   1. Initial program 99.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(x + \left(z + \left(-2 \cdot b + y \cdot \left(b - z\right)\right)\right)\right) - \color{blue}{-1 \cdot a} \]
   7. Step-by-step derivation

   8. Applied rewrites 99.3%

      \[\leadsto \left(\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + x\right) + \color{blue}{a} \]

   if 7.2000000000000001e-51 < t

   1. Initial program 92.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   5. Applied rewrites 94.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(-z, y, z\right)\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 89.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+167}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(b - z\right) \cdot y\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, x\right) + z\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+22}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(1 - y\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.75e+167)
   (fma (- b a) t (* (- b z) y))
   (if (<= t -3.1e+20)
     (fma (- t 2.0) b (+ (fma (- 1.0 t) a x) z))
     (if (<= t 7.2e+22)
       (+ (+ (fma -2.0 b (fma (- b z) y z)) x) a)
       (fma (- b a) t (* (- 1.0 y) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+167) {
		tmp = fma((b - a), t, ((b - z) * y));
	} else if (t <= -3.1e+20) {
		tmp = fma((t - 2.0), b, (fma((1.0 - t), a, x) + z));
	} else if (t <= 7.2e+22) {
		tmp = (fma(-2.0, b, fma((b - z), y, z)) + x) + a;
	} else {
		tmp = fma((b - a), t, ((1.0 - y) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.75e+167)
		tmp = fma(Float64(b - a), t, Float64(Float64(b - z) * y));
	elseif (t <= -3.1e+20)
		tmp = fma(Float64(t - 2.0), b, Float64(fma(Float64(1.0 - t), a, x) + z));
	elseif (t <= 7.2e+22)
		tmp = Float64(Float64(fma(-2.0, b, fma(Float64(b - z), y, z)) + x) + a);
	else
		tmp = fma(Float64(b - a), t, Float64(Float64(1.0 - y) * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.75e+167], N[(N[(b - a), $MachinePrecision] * t + N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.1e+20], N[(N[(t - 2.0), $MachinePrecision] * b + N[(N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+22], N[(N[(N[(-2.0 * b + N[(N[(b - z), $MachinePrecision] * y + z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + a), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t + N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.74999999999999994e167

   1. Initial program 84.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 96.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 96.1%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(b - a, t, y \cdot \left(b - z\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 96.5%

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

   if -1.74999999999999994e167 < t < -3.1e20

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(t - 2\right) \cdot b} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      5. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{t - 2}, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(t - 2, b, x - \color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)}\right) \]

      7. associate--r+ N/A

         \[\leadsto \mathsf{fma}\left(t - 2, b, \color{blue}{\left(x - a \cdot \left(t - 1\right)\right) - -1 \cdot z}\right) \]

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

         \[\leadsto \mathsf{fma}\left(t - 2, b, \color{blue}{\left(x - a \cdot \left(t - 1\right)\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot z}\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(t - 2, b, \left(x - a \cdot \left(t - 1\right)\right) + \color{blue}{1} \cdot z\right) \]

      10. *-lft-identity N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, \left(x - a \cdot \left(t - 1\right)\right) + \color{blue}{z}\right) \]

      11. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, \color{blue}{\left(x - a \cdot \left(t - 1\right)\right) + z}\right) \]

   5. Applied rewrites 87.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, x\right) + z\right)} \]

   if -3.1e20 < t < 7.2e22

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(x + \left(z + \left(-2 \cdot b + y \cdot \left(b - z\right)\right)\right)\right) - \color{blue}{-1 \cdot a} \]
   7. Step-by-step derivation

   8. Applied rewrites 97.8%

      \[\leadsto \left(\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + x\right) + \color{blue}{a} \]

   if 7.2e22 < t

   1. Initial program 91.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 94.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 94.6%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(b - a, t, z \cdot \left(1 - y\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 86.8%

       \[\leadsto \mathsf{fma}\left(b - a, t, \left(1 - y\right) \cdot z\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 57.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-113}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-42}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+133}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -1.1e+78)
     t_1
     (if (<= b 3.9e-113)
       (fma (- 1.0 y) z x)
       (if (<= b 1.5e-42)
         (* (- 1.0 t) a)
         (if (<= b 2.5e+133) (* (- b z) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.1e+78) {
		tmp = t_1;
	} else if (b <= 3.9e-113) {
		tmp = fma((1.0 - y), z, x);
	} else if (b <= 1.5e-42) {
		tmp = (1.0 - t) * a;
	} else if (b <= 2.5e+133) {
		tmp = (b - z) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.1e+78)
		tmp = t_1;
	elseif (b <= 3.9e-113)
		tmp = fma(Float64(1.0 - y), z, x);
	elseif (b <= 1.5e-42)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (b <= 2.5e+133)
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.1e+78], t$95$1, If[LessEqual[b, 3.9e-113], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[b, 1.5e-42], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[b, 2.5e+133], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.10000000000000007e78 or 2.4999999999999998e133 < b

   1. Initial program 88.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 95.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 95.0%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 83.2

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   10. Applied rewrites 83.2%

       \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   if -1.10000000000000007e78 < b < 3.8999999999999999e-113

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 90.7%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 61.4%

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

   if 3.8999999999999999e-113 < b < 1.50000000000000014e-42

   1. Initial program 99.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 65.0

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

   5. Applied rewrites 65.0%

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

   if 1.50000000000000014e-42 < b < 2.4999999999999998e133

   1. Initial program 96.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 60.4

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

   5. Applied rewrites 60.4%

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

Alternative 5: 90.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+20} \lor \neg \left(t \leq 7.2 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.1e+20) (not (<= t 7.2e+22)))
   (fma (- b a) t (* (- 1.0 y) z))
   (+ (+ (fma -2.0 b (fma (- b z) y z)) x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.1e+20) || !(t <= 7.2e+22)) {
		tmp = fma((b - a), t, ((1.0 - y) * z));
	} else {
		tmp = (fma(-2.0, b, fma((b - z), y, z)) + x) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.1e+20) || !(t <= 7.2e+22))
		tmp = fma(Float64(b - a), t, Float64(Float64(1.0 - y) * z));
	else
		tmp = Float64(Float64(fma(-2.0, b, fma(Float64(b - z), y, z)) + x) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.1e+20], N[Not[LessEqual[t, 7.2e+22]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t + N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-2.0 * b + N[(N[(b - z), $MachinePrecision] * y + z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1e20 or 7.2e22 < t

   1. Initial program 91.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 96.4%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 96.4%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(b - a, t, z \cdot \left(1 - y\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 85.0%

       \[\leadsto \mathsf{fma}\left(b - a, t, \left(1 - y\right) \cdot z\right) \]

   if -3.1e20 < t < 7.2e22

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(x + \left(z + \left(-2 \cdot b + y \cdot \left(b - z\right)\right)\right)\right) - \color{blue}{-1 \cdot a} \]
   7. Step-by-step derivation

   8. Applied rewrites 97.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+20} \lor \neg \left(t \leq 7.2 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+20}:\\ \;\;\;\;\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(-z\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+22}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(1 - y\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.1e+20)
   (- (+ (fma (- b a) t (fma (- y 2.0) b x)) a) (- z))
   (if (<= t 7.2e+22)
     (+ (+ (fma -2.0 b (fma (- b z) y z)) x) a)
     (fma (- b a) t (* (- 1.0 y) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.1e+20) {
		tmp = (fma((b - a), t, fma((y - 2.0), b, x)) + a) - -z;
	} else if (t <= 7.2e+22) {
		tmp = (fma(-2.0, b, fma((b - z), y, z)) + x) + a;
	} else {
		tmp = fma((b - a), t, ((1.0 - y) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.1e+20)
		tmp = Float64(Float64(fma(Float64(b - a), t, fma(Float64(y - 2.0), b, x)) + a) - Float64(-z));
	elseif (t <= 7.2e+22)
		tmp = Float64(Float64(fma(-2.0, b, fma(Float64(b - z), y, z)) + x) + a);
	else
		tmp = fma(Float64(b - a), t, Float64(Float64(1.0 - y) * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.1e+20], N[(N[(N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] - (-z)), $MachinePrecision], If[LessEqual[t, 7.2e+22], N[(N[(N[(-2.0 * b + N[(N[(b - z), $MachinePrecision] * y + z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + a), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t + N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e20

   1. Initial program 92.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 98.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in y around 0

      \[\leadsto \left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - -1 \cdot \color{blue}{z} \]
   7. Step-by-step derivation

   8. Applied rewrites 92.9%

      \[\leadsto \left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(-z\right) \]

   if -1.1e20 < t < 7.2e22

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(x + \left(z + \left(-2 \cdot b + y \cdot \left(b - z\right)\right)\right)\right) - \color{blue}{-1 \cdot a} \]
   7. Step-by-step derivation

   8. Applied rewrites 97.8%

      \[\leadsto \left(\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + x\right) + \color{blue}{a} \]

   if 7.2e22 < t

   1. Initial program 91.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 94.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 94.6%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(b - a, t, z \cdot \left(1 - y\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 86.8%

       \[\leadsto \mathsf{fma}\left(b - a, t, \left(1 - y\right) \cdot z\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 82.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+93} \lor \neg \left(b \leq 1.4 \cdot 10^{+21}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(-z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x - \left(t - 1\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.35e+93) (not (<= b 1.4e+21)))
   (fma (- (+ y t) 2.0) b (* (- z) y))
   (fma (- 1.0 y) z (- x (* (- t 1.0) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.35e+93) || !(b <= 1.4e+21)) {
		tmp = fma(((y + t) - 2.0), b, (-z * y));
	} else {
		tmp = fma((1.0 - y), z, (x - ((t - 1.0) * a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.35e+93) || !(b <= 1.4e+21))
		tmp = fma(Float64(Float64(y + t) - 2.0), b, Float64(Float64(-z) * y));
	else
		tmp = fma(Float64(1.0 - y), z, Float64(x - Float64(Float64(t - 1.0) * a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.35e+93], N[Not[LessEqual[b, 1.4e+21]], $MachinePrecision]], N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[((-z) * y), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z + N[(x - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.35e93 or 1.4e21 < b

   1. Initial program 90.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot z\right) \cdot y} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot z\right) \cdot y} + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot y + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lower-neg.f64 79.0

         \[\leadsto \color{blue}{\left(-z\right)} \cdot y + \left(\left(y + t\right) - 2\right) \cdot b \]

   5. Applied rewrites 79.0%

      \[\leadsto \color{blue}{\left(-z\right) \cdot y} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(-z\right) \cdot y + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(-z\right) \cdot y} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} + \left(-z\right) \cdot y \]

      4. lower-fma.f64 82.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(-z\right) \cdot y\right)} \]

   7. Applied rewrites 82.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(-z\right) \cdot y\right)} \]

   if -1.35e93 < b < 1.4e21

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 89.8%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+93} \lor \neg \left(b \leq 1.4 \cdot 10^{+21}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(-z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x - \left(t - 1\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 96.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (+ (fma (- b a) t (fma (- y 2.0) b x)) a) (* (- y 1.0) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (fma((b - a), t, fma((y - 2.0), b, x)) + a) - ((y - 1.0) * z);
}

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(fma(Float64(b - a), t, fma(Float64(y - 2.0), b, x)) + a) - Float64(Float64(y - 1.0) * z))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.1%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in t around 0

   \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
4. Step-by-step derivation

   1. associate--r+ N/A

      \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   2. lower--.f64 N/A

      \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

5. Applied rewrites 98.0%

   \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
6. Add Preprocessing

Alternative 9: 80.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+14} \lor \neg \left(t \leq 2.75 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -8.8e+14) (not (<= t 2.75e+22)))
   (fma (- b a) t (* (- 1.0 y) z))
   (+ (fma -2.0 b (fma (- b z) y z)) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8.8e+14) || !(t <= 2.75e+22)) {
		tmp = fma((b - a), t, ((1.0 - y) * z));
	} else {
		tmp = fma(-2.0, b, fma((b - z), y, z)) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -8.8e+14) || !(t <= 2.75e+22))
		tmp = fma(Float64(b - a), t, Float64(Float64(1.0 - y) * z));
	else
		tmp = Float64(fma(-2.0, b, fma(Float64(b - z), y, z)) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -8.8e+14], N[Not[LessEqual[t, 2.75e+22]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t + N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 * b + N[(N[(b - z), $MachinePrecision] * y + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.8e14 or 2.7500000000000001e22 < t

   1. Initial program 92.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 96.5%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 96.5%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(b - a, t, z \cdot \left(1 - y\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 84.5%

       \[\leadsto \mathsf{fma}\left(b - a, t, \left(1 - y\right) \cdot z\right) \]

   if -8.8e14 < t < 2.7500000000000001e22

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(x + \left(z + \left(-2 \cdot b + y \cdot \left(b - z\right)\right)\right)\right) - \color{blue}{-1 \cdot a} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.4%

      \[\leadsto \left(\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + x\right) + \color{blue}{a} \]

   9. Taylor expanded in x around 0

      \[\leadsto \left(z + \left(-2 \cdot b + y \cdot \left(b - z\right)\right)\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 82.7%

       \[\leadsto \mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + a \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+14} \lor \neg \left(t \leq 2.75 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -6 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-66}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -6e+23)
     t_1
     (if (<= t -5.2e-66)
       (fma (- 1.0 y) z x)
       (if (<= t 1.15e+23) (+ (fma b (+ y -2.0) x) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -6e+23) {
		tmp = t_1;
	} else if (t <= -5.2e-66) {
		tmp = fma((1.0 - y), z, x);
	} else if (t <= 1.15e+23) {
		tmp = fma(b, (y + -2.0), x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -6e+23)
		tmp = t_1;
	elseif (t <= -5.2e-66)
		tmp = fma(Float64(1.0 - y), z, x);
	elseif (t <= 1.15e+23)
		tmp = Float64(fma(b, Float64(y + -2.0), x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -6e+23], t$95$1, If[LessEqual[t, -5.2e-66], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[t, 1.15e+23], N[(N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.0000000000000002e23 or 1.15e23 < t

   1. Initial program 91.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      3. lower--.f64 67.0

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 67.0%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -6.0000000000000002e23 < t < -5.1999999999999998e-66

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 87.4%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 77.3%

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

   if -5.1999999999999998e-66 < t < 1.15e23

   1. Initial program 99.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 99.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(x + \left(z + \left(-2 \cdot b + y \cdot \left(b - z\right)\right)\right)\right) - \color{blue}{-1 \cdot a} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.0%

      \[\leadsto \left(\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + x\right) + \color{blue}{a} \]

   9. Taylor expanded in z around 0

      \[\leadsto \left(x + \left(-2 \cdot b + b \cdot y\right)\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 70.6%

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

Alternative 11: 74.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \lor \neg \left(y \leq 8.5 \cdot 10^{+21}\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(b - z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(x - \left(t - 1\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.4) (not (<= y 8.5e+21)))
   (fma (- b a) t (* (- b z) y))
   (+ z (- x (* (- t 1.0) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.4) || !(y <= 8.5e+21)) {
		tmp = fma((b - a), t, ((b - z) * y));
	} else {
		tmp = z + (x - ((t - 1.0) * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.4) || !(y <= 8.5e+21))
		tmp = fma(Float64(b - a), t, Float64(Float64(b - z) * y));
	else
		tmp = Float64(z + Float64(x - Float64(Float64(t - 1.0) * a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.4], N[Not[LessEqual[y, 8.5e+21]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t + N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(z + N[(x - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999991 or 8.5e21 < y

   1. Initial program 94.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 96.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 96.2%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(b - a, t, y \cdot \left(b - z\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 85.3%

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

   if -3.39999999999999991 < y < 8.5e21

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 71.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 71.3%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \lor \neg \left(y \leq 8.5 \cdot 10^{+21}\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(b - z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(x - \left(t - 1\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-66} \lor \neg \left(t \leq 1.05\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.2e-66) (not (<= t 1.05)))
   (fma (- b a) t (* (- 1.0 y) z))
   (+ (fma b (+ y -2.0) x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.2e-66) || !(t <= 1.05)) {
		tmp = fma((b - a), t, ((1.0 - y) * z));
	} else {
		tmp = fma(b, (y + -2.0), x) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.2e-66) || !(t <= 1.05))
		tmp = fma(Float64(b - a), t, Float64(Float64(1.0 - y) * z));
	else
		tmp = Float64(fma(b, Float64(y + -2.0), x) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.2e-66], N[Not[LessEqual[t, 1.05]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t + N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.1999999999999998e-66 or 1.05000000000000004 < t

   1. Initial program 93.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 97.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 97.2%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(b - a, t, z \cdot \left(1 - y\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 81.2%

       \[\leadsto \mathsf{fma}\left(b - a, t, \left(1 - y\right) \cdot z\right) \]

   if -5.1999999999999998e-66 < t < 1.05000000000000004

   1. Initial program 99.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(x + \left(z + \left(-2 \cdot b + y \cdot \left(b - z\right)\right)\right)\right) - \color{blue}{-1 \cdot a} \]
   7. Step-by-step derivation

   8. Applied rewrites 99.4%

      \[\leadsto \left(\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + x\right) + \color{blue}{a} \]

   9. Taylor expanded in z around 0

      \[\leadsto \left(x + \left(-2 \cdot b + b \cdot y\right)\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 72.3%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-66} \lor \neg \left(t \leq 1.05\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+22} \lor \neg \left(y \leq 2.2 \cdot 10^{+25}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x - \left(t - 1\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9.5e+22) (not (<= y 2.2e+25)))
   (* (- b z) y)
   (+ z (- x (* (- t 1.0) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.5e+22) || !(y <= 2.2e+25)) {
		tmp = (b - z) * y;
	} else {
		tmp = z + (x - ((t - 1.0) * a));
	}
	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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9.5d+22)) .or. (.not. (y <= 2.2d+25))) then
        tmp = (b - z) * y
    else
        tmp = z + (x - ((t - 1.0d0) * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.5e+22) || !(y <= 2.2e+25)) {
		tmp = (b - z) * y;
	} else {
		tmp = z + (x - ((t - 1.0) * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9.5e+22) or not (y <= 2.2e+25):
		tmp = (b - z) * y
	else:
		tmp = z + (x - ((t - 1.0) * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9.5e+22) || !(y <= 2.2e+25))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = Float64(z + Float64(x - Float64(Float64(t - 1.0) * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9.5e+22) || ~((y <= 2.2e+25)))
		tmp = (b - z) * y;
	else
		tmp = z + (x - ((t - 1.0) * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9.5e+22], N[Not[LessEqual[y, 2.2e+25]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(z + N[(x - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.49999999999999937e22 or 2.2000000000000001e25 < y

   1. Initial program 94.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.0

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

   5. Applied rewrites 72.0%

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

   if -9.49999999999999937e22 < y < 2.2000000000000001e25

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 71.5%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 70.8%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+22} \lor \neg \left(y \leq 2.2 \cdot 10^{+25}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x - \left(t - 1\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -6 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-283}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+24}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -6e+23)
     t_1
     (if (<= t 3.4e-283)
       (fma (- 1.0 y) z x)
       (if (<= t 1.4e+24) (* (- b z) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -6e+23) {
		tmp = t_1;
	} else if (t <= 3.4e-283) {
		tmp = fma((1.0 - y), z, x);
	} else if (t <= 1.4e+24) {
		tmp = (b - z) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -6e+23)
		tmp = t_1;
	elseif (t <= 3.4e-283)
		tmp = fma(Float64(1.0 - y), z, x);
	elseif (t <= 1.4e+24)
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -6e+23], t$95$1, If[LessEqual[t, 3.4e-283], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[t, 1.4e+24], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.0000000000000002e23 or 1.4000000000000001e24 < t

   1. Initial program 91.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      3. lower--.f64 67.0

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 67.0%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -6.0000000000000002e23 < t < 3.3999999999999998e-283

   1. Initial program 98.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z\right) - a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 76.0%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 59.9%

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

   if 3.3999999999999998e-283 < t < 1.4000000000000001e24

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 50.0

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

   5. Applied rewrites 50.0%

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

Alternative 15: 48.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -6 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-167}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+22}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -6e+23)
     t_1
     (if (<= t -5.8e-167)
       (* (- 1.0 y) z)
       (if (<= t 6.8e+22) (* (- y 2.0) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -6e+23) {
		tmp = t_1;
	} else if (t <= -5.8e-167) {
		tmp = (1.0 - y) * z;
	} else if (t <= 6.8e+22) {
		tmp = (y - 2.0) * b;
	} 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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-6d+23)) then
        tmp = t_1
    else if (t <= (-5.8d-167)) then
        tmp = (1.0d0 - y) * z
    else if (t <= 6.8d+22) then
        tmp = (y - 2.0d0) * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -6e+23) {
		tmp = t_1;
	} else if (t <= -5.8e-167) {
		tmp = (1.0 - y) * z;
	} else if (t <= 6.8e+22) {
		tmp = (y - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -6e+23:
		tmp = t_1
	elif t <= -5.8e-167:
		tmp = (1.0 - y) * z
	elif t <= 6.8e+22:
		tmp = (y - 2.0) * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -6e+23)
		tmp = t_1;
	elseif (t <= -5.8e-167)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (t <= 6.8e+22)
		tmp = Float64(Float64(y - 2.0) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -6e+23)
		tmp = t_1;
	elseif (t <= -5.8e-167)
		tmp = (1.0 - y) * z;
	elseif (t <= 6.8e+22)
		tmp = (y - 2.0) * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -6e+23], t$95$1, If[LessEqual[t, -5.8e-167], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t, 6.8e+22], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.0000000000000002e23 or 6.8e22 < t

   1. Initial program 91.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      3. lower--.f64 67.0

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 67.0%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -6.0000000000000002e23 < t < -5.80000000000000005e-167

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.3

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

   5. Applied rewrites 51.3%

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

   if -5.80000000000000005e-167 < t < 6.8e22

   1. Initial program 98.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 98.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 98.9%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 38.2

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   10. Applied rewrites 38.2%

       \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   11. Taylor expanded in t around 0

       \[\leadsto \left(y - 2\right) \cdot b \]
   12. Step-by-step derivation

   13. Applied rewrites 37.0%

       \[\leadsto \left(y - 2\right) \cdot b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 39.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+93}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -7.3 \cdot 10^{-224}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+21}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.7e+93)
   (* (- t 2.0) b)
   (if (<= b -7.3e-224)
     (* (- 1.0 y) z)
     (if (<= b 1.4e+21) (* (- 1.0 t) a) (* (- y 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e+93) {
		tmp = (t - 2.0) * b;
	} else if (b <= -7.3e-224) {
		tmp = (1.0 - y) * z;
	} else if (b <= 1.4e+21) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = (y - 2.0) * b;
	}
	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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.7d+93)) then
        tmp = (t - 2.0d0) * b
    else if (b <= (-7.3d-224)) then
        tmp = (1.0d0 - y) * z
    else if (b <= 1.4d+21) then
        tmp = (1.0d0 - t) * a
    else
        tmp = (y - 2.0d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e+93) {
		tmp = (t - 2.0) * b;
	} else if (b <= -7.3e-224) {
		tmp = (1.0 - y) * z;
	} else if (b <= 1.4e+21) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = (y - 2.0) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.7e+93:
		tmp = (t - 2.0) * b
	elif b <= -7.3e-224:
		tmp = (1.0 - y) * z
	elif b <= 1.4e+21:
		tmp = (1.0 - t) * a
	else:
		tmp = (y - 2.0) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.7e+93)
		tmp = Float64(Float64(t - 2.0) * b);
	elseif (b <= -7.3e-224)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (b <= 1.4e+21)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = Float64(Float64(y - 2.0) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.7e+93)
		tmp = (t - 2.0) * b;
	elseif (b <= -7.3e-224)
		tmp = (1.0 - y) * z;
	elseif (b <= 1.4e+21)
		tmp = (1.0 - t) * a;
	else
		tmp = (y - 2.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.7e+93], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, -7.3e-224], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[b, 1.4e+21], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.69999999999999987e93

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 97.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 97.7%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 84.5

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   10. Applied rewrites 84.5%

       \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   11. Taylor expanded in y around 0

       \[\leadsto \left(t - 2\right) \cdot b \]
   12. Step-by-step derivation

   13. Applied rewrites 62.6%

       \[\leadsto \left(t - 2\right) \cdot b \]

   if -3.69999999999999987e93 < b < -7.3e-224

   1. Initial program 98.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 45.2

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

   5. Applied rewrites 45.2%

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

   if -7.3e-224 < b < 1.4e21

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 47.1

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

   5. Applied rewrites 47.1%

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

   if 1.4e21 < b

   1. Initial program 90.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 95.1%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 63.9

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   10. Applied rewrites 63.9%

       \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   11. Taylor expanded in t around 0

       \[\leadsto \left(y - 2\right) \cdot b \]
   12. Step-by-step derivation

   13. Applied rewrites 49.1%

       \[\leadsto \left(y - 2\right) \cdot b \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 17: 37.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+93}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-221}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+21}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.7e+93)
   (* (- t 2.0) b)
   (if (<= b -4.4e-221)
     (* (- y) z)
     (if (<= b 1.4e+21) (* (- 1.0 t) a) (* (- y 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e+93) {
		tmp = (t - 2.0) * b;
	} else if (b <= -4.4e-221) {
		tmp = -y * z;
	} else if (b <= 1.4e+21) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = (y - 2.0) * b;
	}
	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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.7d+93)) then
        tmp = (t - 2.0d0) * b
    else if (b <= (-4.4d-221)) then
        tmp = -y * z
    else if (b <= 1.4d+21) then
        tmp = (1.0d0 - t) * a
    else
        tmp = (y - 2.0d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e+93) {
		tmp = (t - 2.0) * b;
	} else if (b <= -4.4e-221) {
		tmp = -y * z;
	} else if (b <= 1.4e+21) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = (y - 2.0) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.7e+93:
		tmp = (t - 2.0) * b
	elif b <= -4.4e-221:
		tmp = -y * z
	elif b <= 1.4e+21:
		tmp = (1.0 - t) * a
	else:
		tmp = (y - 2.0) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.7e+93)
		tmp = Float64(Float64(t - 2.0) * b);
	elseif (b <= -4.4e-221)
		tmp = Float64(Float64(-y) * z);
	elseif (b <= 1.4e+21)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = Float64(Float64(y - 2.0) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.7e+93)
		tmp = (t - 2.0) * b;
	elseif (b <= -4.4e-221)
		tmp = -y * z;
	elseif (b <= 1.4e+21)
		tmp = (1.0 - t) * a;
	else
		tmp = (y - 2.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.7e+93], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, -4.4e-221], N[((-y) * z), $MachinePrecision], If[LessEqual[b, 1.4e+21], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.69999999999999987e93

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 97.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 97.7%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 84.5

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   10. Applied rewrites 84.5%

       \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   11. Taylor expanded in y around 0

       \[\leadsto \left(t - 2\right) \cdot b \]
   12. Step-by-step derivation

   13. Applied rewrites 62.6%

       \[\leadsto \left(t - 2\right) \cdot b \]

   if -3.69999999999999987e93 < b < -4.40000000000000003e-221

   1. Initial program 98.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 45.2

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

   5. Applied rewrites 45.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 32.4%

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

   if -4.40000000000000003e-221 < b < 1.4e21

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 47.1

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

   5. Applied rewrites 47.1%

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

   if 1.4e21 < b

   1. Initial program 90.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 95.1%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 63.9

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   10. Applied rewrites 63.9%

       \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   11. Taylor expanded in t around 0

       \[\leadsto \left(y - 2\right) \cdot b \]
   12. Step-by-step derivation

   13. Applied rewrites 49.1%

       \[\leadsto \left(y - 2\right) \cdot b \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 18: 32.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+93}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-207}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+16}:\\ \;\;\;\;\left(-t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.7e+93)
   (* (- t 2.0) b)
   (if (<= b 2.5e-207)
     (* (- y) z)
     (if (<= b 3.1e+16) (* (- t) a) (* (- y 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e+93) {
		tmp = (t - 2.0) * b;
	} else if (b <= 2.5e-207) {
		tmp = -y * z;
	} else if (b <= 3.1e+16) {
		tmp = -t * a;
	} else {
		tmp = (y - 2.0) * b;
	}
	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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.7d+93)) then
        tmp = (t - 2.0d0) * b
    else if (b <= 2.5d-207) then
        tmp = -y * z
    else if (b <= 3.1d+16) then
        tmp = -t * a
    else
        tmp = (y - 2.0d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e+93) {
		tmp = (t - 2.0) * b;
	} else if (b <= 2.5e-207) {
		tmp = -y * z;
	} else if (b <= 3.1e+16) {
		tmp = -t * a;
	} else {
		tmp = (y - 2.0) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.7e+93:
		tmp = (t - 2.0) * b
	elif b <= 2.5e-207:
		tmp = -y * z
	elif b <= 3.1e+16:
		tmp = -t * a
	else:
		tmp = (y - 2.0) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.7e+93)
		tmp = Float64(Float64(t - 2.0) * b);
	elseif (b <= 2.5e-207)
		tmp = Float64(Float64(-y) * z);
	elseif (b <= 3.1e+16)
		tmp = Float64(Float64(-t) * a);
	else
		tmp = Float64(Float64(y - 2.0) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.7e+93)
		tmp = (t - 2.0) * b;
	elseif (b <= 2.5e-207)
		tmp = -y * z;
	elseif (b <= 3.1e+16)
		tmp = -t * a;
	else
		tmp = (y - 2.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.7e+93], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 2.5e-207], N[((-y) * z), $MachinePrecision], If[LessEqual[b, 3.1e+16], N[((-t) * a), $MachinePrecision], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.69999999999999987e93

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 97.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 97.7%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 84.5

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   10. Applied rewrites 84.5%

       \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   11. Taylor expanded in y around 0

       \[\leadsto \left(t - 2\right) \cdot b \]
   12. Step-by-step derivation

   13. Applied rewrites 62.6%

       \[\leadsto \left(t - 2\right) \cdot b \]

   if -3.69999999999999987e93 < b < 2.50000000000000007e-207

   1. Initial program 99.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.3

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

   5. Applied rewrites 43.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 33.5%

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

   if 2.50000000000000007e-207 < b < 3.1e16

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 50.4

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

   5. Applied rewrites 50.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 35.4%

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

   if 3.1e16 < b

   1. Initial program 90.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 95.1%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 63.9

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   10. Applied rewrites 63.9%

       \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   11. Taylor expanded in t around 0

       \[\leadsto \left(y - 2\right) \cdot b \]
   12. Step-by-step derivation

   13. Applied rewrites 49.1%

       \[\leadsto \left(y - 2\right) \cdot b \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 19: 27.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+93}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-207}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+18}:\\ \;\;\;\;\left(-t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.7e+93)
   (* t b)
   (if (<= b 2.5e-207) (* (- y) z) (if (<= b 5.8e+18) (* (- t) a) (* b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e+93) {
		tmp = t * b;
	} else if (b <= 2.5e-207) {
		tmp = -y * z;
	} else if (b <= 5.8e+18) {
		tmp = -t * a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.7d+93)) then
        tmp = t * b
    else if (b <= 2.5d-207) then
        tmp = -y * z
    else if (b <= 5.8d+18) then
        tmp = -t * a
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e+93) {
		tmp = t * b;
	} else if (b <= 2.5e-207) {
		tmp = -y * z;
	} else if (b <= 5.8e+18) {
		tmp = -t * a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.7e+93:
		tmp = t * b
	elif b <= 2.5e-207:
		tmp = -y * z
	elif b <= 5.8e+18:
		tmp = -t * a
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.7e+93)
		tmp = Float64(t * b);
	elseif (b <= 2.5e-207)
		tmp = Float64(Float64(-y) * z);
	elseif (b <= 5.8e+18)
		tmp = Float64(Float64(-t) * a);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.7e+93)
		tmp = t * b;
	elseif (b <= 2.5e-207)
		tmp = -y * z;
	elseif (b <= 5.8e+18)
		tmp = -t * a;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.7e+93], N[(t * b), $MachinePrecision], If[LessEqual[b, 2.5e-207], N[((-y) * z), $MachinePrecision], If[LessEqual[b, 5.8e+18], N[((-t) * a), $MachinePrecision], N[(b * y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.69999999999999987e93

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      3. lower--.f64 49.0

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 49.0%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in a around 0

      \[\leadsto b \cdot \color{blue}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 44.7%

      \[\leadsto t \cdot \color{blue}{b} \]

   if -3.69999999999999987e93 < b < 2.50000000000000007e-207

   1. Initial program 99.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.3

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

   5. Applied rewrites 43.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 33.5%

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

   if 2.50000000000000007e-207 < b < 5.8e18

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 50.4

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

   5. Applied rewrites 50.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 35.4%

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

   if 5.8e18 < b

   1. Initial program 90.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 95.1%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 63.9

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   10. Applied rewrites 63.9%

       \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   11. Taylor expanded in y around inf

       \[\leadsto b \cdot \color{blue}{y} \]
   12. Step-by-step derivation

   13. Applied rewrites 39.5%

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

Alternative 20: 48.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+20} \lor \neg \left(y \leq 104\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9.5e+20) (not (<= y 104.0))) (* (- b z) y) (* (- 1.0 t) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.5e+20) || !(y <= 104.0)) {
		tmp = (b - z) * y;
	} else {
		tmp = (1.0 - t) * a;
	}
	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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9.5d+20)) .or. (.not. (y <= 104.0d0))) then
        tmp = (b - z) * y
    else
        tmp = (1.0d0 - t) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.5e+20) || !(y <= 104.0)) {
		tmp = (b - z) * y;
	} else {
		tmp = (1.0 - t) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9.5e+20) or not (y <= 104.0):
		tmp = (b - z) * y
	else:
		tmp = (1.0 - t) * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9.5e+20) || !(y <= 104.0))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = Float64(Float64(1.0 - t) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9.5e+20) || ~((y <= 104.0)))
		tmp = (b - z) * y;
	else
		tmp = (1.0 - t) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9.5e+20], N[Not[LessEqual[y, 104.0]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5e20 or 104 < y

   1. Initial program 94.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 70.9

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

   5. Applied rewrites 70.9%

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

   if -9.5e20 < y < 104

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.5

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

   5. Applied rewrites 41.5%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+20} \lor \neg \left(y \leq 104\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 33.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+47} \lor \neg \left(y \leq 5.4 \cdot 10^{+15}\right):\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.2e+47) (not (<= y 5.4e+15))) (* (- y) z) (* (- t 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.2e+47) || !(y <= 5.4e+15)) {
		tmp = -y * z;
	} else {
		tmp = (t - 2.0) * b;
	}
	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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.2d+47)) .or. (.not. (y <= 5.4d+15))) then
        tmp = -y * z
    else
        tmp = (t - 2.0d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.2e+47) || !(y <= 5.4e+15)) {
		tmp = -y * z;
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.2e+47) or not (y <= 5.4e+15):
		tmp = -y * z
	else:
		tmp = (t - 2.0) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.2e+47) || !(y <= 5.4e+15))
		tmp = Float64(Float64(-y) * z);
	else
		tmp = Float64(Float64(t - 2.0) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.2e+47) || ~((y <= 5.4e+15)))
		tmp = -y * z;
	else
		tmp = (t - 2.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.2e+47], N[Not[LessEqual[y, 5.4e+15]], $MachinePrecision]], N[((-y) * z), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e47 or 5.4e15 < y

   1. Initial program 94.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 45.5

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

   5. Applied rewrites 45.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 45.5%

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

   if -4.2e47 < y < 5.4e15

   1. Initial program 97.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.2%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 34.9

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   10. Applied rewrites 34.9%

       \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   11. Taylor expanded in y around 0

       \[\leadsto \left(t - 2\right) \cdot b \]
   12. Step-by-step derivation

   13. Applied rewrites 32.8%

       \[\leadsto \left(t - 2\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+47} \lor \neg \left(y \leq 5.4 \cdot 10^{+15}\right):\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 27.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+93}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+18}:\\ \;\;\;\;\left(-t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+93) (* t b) (if (<= b 5.8e+18) (* (- t) a) (* b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+93) {
		tmp = t * b;
	} else if (b <= 5.8e+18) {
		tmp = -t * a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.25d+93)) then
        tmp = t * b
    else if (b <= 5.8d+18) then
        tmp = -t * a
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+93) {
		tmp = t * b;
	} else if (b <= 5.8e+18) {
		tmp = -t * a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e+93:
		tmp = t * b
	elif b <= 5.8e+18:
		tmp = -t * a
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+93)
		tmp = Float64(t * b);
	elseif (b <= 5.8e+18)
		tmp = Float64(Float64(-t) * a);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.25e+93)
		tmp = t * b;
	elseif (b <= 5.8e+18)
		tmp = -t * a;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+93], N[(t * b), $MachinePrecision], If[LessEqual[b, 5.8e+18], N[((-t) * a), $MachinePrecision], N[(b * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.25e93

   1. Initial program 91.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      3. lower--.f64 47.9

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 47.9%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in a around 0

      \[\leadsto b \cdot \color{blue}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 43.7%

      \[\leadsto t \cdot \color{blue}{b} \]

   if -1.25e93 < b < 5.8e18

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 36.8

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

   5. Applied rewrites 36.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 24.5%

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

   if 5.8e18 < b

   1. Initial program 90.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 95.1%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 63.9

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   10. Applied rewrites 63.9%

       \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   11. Taylor expanded in y around inf

       \[\leadsto b \cdot \color{blue}{y} \]
   12. Step-by-step derivation

   13. Applied rewrites 39.5%

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

Alternative 23: 26.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+23} \lor \neg \left(t \leq 1.18 \cdot 10^{+44}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.2e+23) (not (<= t 1.18e+44))) (* t b) (* b y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.2e+23) || !(t <= 1.18e+44)) {
		tmp = t * b;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-7.2d+23)) .or. (.not. (t <= 1.18d+44))) then
        tmp = t * b
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.2e+23) || !(t <= 1.18e+44)) {
		tmp = t * b;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.2e+23) or not (t <= 1.18e+44):
		tmp = t * b
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7.2e+23) || !(t <= 1.18e+44))
		tmp = Float64(t * b);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7.2e+23) || ~((t <= 1.18e+44)))
		tmp = t * b;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7.2e+23], N[Not[LessEqual[t, 1.18e+44]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(b * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.1999999999999997e23 or 1.17999999999999997e44 < t

   1. Initial program 91.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      3. lower--.f64 66.9

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 66.9%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in a around 0

      \[\leadsto b \cdot \color{blue}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.7%

      \[\leadsto t \cdot \color{blue}{b} \]

   if -7.1999999999999997e23 < t < 1.17999999999999997e44

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - -1 \cdot a\right) - z \cdot \left(y - 1\right)} \]

   5. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.3%

      \[\leadsto \mathsf{fma}\left(b - a, \color{blue}{t}, \left(\mathsf{fma}\left(y - 2, b, x\right) + a\right) - z \cdot \left(y - 1\right)\right) \]

   8. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 32.2

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   10. Applied rewrites 32.2%

       \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   11. Taylor expanded in y around inf

       \[\leadsto b \cdot \color{blue}{y} \]
   12. Step-by-step derivation

   13. Applied rewrites 21.6%

       \[\leadsto b \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+23} \lor \neg \left(t \leq 1.18 \cdot 10^{+44}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 17.3% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ t \cdot b \end{array} \]

FPCore

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

C

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

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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    code = t * b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(t * b), $MachinePrecision]

Derivation

1. Initial program 96.1%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in t around inf

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

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   3. lower--.f64 31.2

      \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

5. Applied rewrites 31.2%

   \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

6. Taylor expanded in a around 0

   \[\leadsto b \cdot \color{blue}{t} \]
7. Step-by-step derivation

8. Applied rewrites 16.7%

   \[\leadsto t \cdot \color{blue}{b} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2025008 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))