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

Percentage Accurate: 95.2% → 96.2%

Time: 8.4s

Alternatives: 20

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: 95.2% 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: 96.2% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

3. Taylor expanded in 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 97.2%

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

Alternative 2: 84.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot a\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+183}:\\ \;\;\;\;t \cdot b - t\_1\\ \mathbf{elif}\;t \leq -0.031:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) - t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+42}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + \mathsf{fma}\left(b - z, y, x\right)\right) + a\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) a)))
   (if (<= t -2.1e+183)
     (- (* t b) t_1)
     (if (<= t -0.031)
       (- (fma (- 1.0 y) z x) t_1)
       (if (<= t 1.6e+42)
         (+ (+ (fma -2.0 b z) (fma (- b z) y x)) a)
         (* (- b a) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * a;
	double tmp;
	if (t <= -2.1e+183) {
		tmp = (t * b) - t_1;
	} else if (t <= -0.031) {
		tmp = fma((1.0 - y), z, x) - t_1;
	} else if (t <= 1.6e+42) {
		tmp = (fma(-2.0, b, z) + fma((b - z), y, x)) + a;
	} else {
		tmp = (b - a) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * a)
	tmp = 0.0
	if (t <= -2.1e+183)
		tmp = Float64(Float64(t * b) - t_1);
	elseif (t <= -0.031)
		tmp = Float64(fma(Float64(1.0 - y), z, x) - t_1);
	elseif (t <= 1.6e+42)
		tmp = Float64(Float64(fma(-2.0, b, z) + fma(Float64(b - z), y, x)) + a);
	else
		tmp = Float64(Float64(b - a) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t, -2.1e+183], N[(N[(t * b), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, -0.031], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 1.6e+42], N[(N[(N[(-2.0 * b + z), $MachinePrecision] + N[(N[(b - z), $MachinePrecision] * y + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.1e183

   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 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 96.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 83.1%

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

   if -2.1e183 < t < -0.031

   1. Initial program 92.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 92.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 78.0%

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

   if -0.031 < t < 1.60000000000000001e42

   1. Initial program 97.9%

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

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

   if 1.60000000000000001e42 < t

   1. Initial program 93.0%

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

   3. Taylor expanded in t around 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 81.3

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

   5. Applied rewrites 81.3%

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

Alternative 3: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, x\right) + a\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -25500:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-214}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) + a\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (fma (- 1.0 y) z x) a)) (t_2 (* (- b a) t)))
   (if (<= t -25500.0)
     t_2
     (if (<= t -4.5e-106)
       t_1
       (if (<= t 1.85e-214)
         (+ (fma (- y 2.0) b x) a)
         (if (<= t 6.2e+41) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - y), z, x) + a;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -25500.0) {
		tmp = t_2;
	} else if (t <= -4.5e-106) {
		tmp = t_1;
	} else if (t <= 1.85e-214) {
		tmp = fma((y - 2.0), b, x) + a;
	} else if (t <= 6.2e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(1.0 - y), z, x) + a)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -25500.0)
		tmp = t_2;
	elseif (t <= -4.5e-106)
		tmp = t_1;
	elseif (t <= 1.85e-214)
		tmp = Float64(fma(Float64(y - 2.0), b, x) + a);
	elseif (t <= 6.2e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] + a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -25500.0], t$95$2, If[LessEqual[t, -4.5e-106], t$95$1, If[LessEqual[t, 1.85e-214], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 6.2e+41], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -25500 or 6.2e41 < t

   1. Initial program 93.0%

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

   3. Taylor expanded in t around 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 72.5

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

   5. Applied rewrites 72.5%

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

   if -25500 < t < -4.49999999999999955e-106 or 1.8500000000000001e-214 < t < 6.2e41

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 98.7%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 72.6%

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

   if -4.49999999999999955e-106 < t < 1.8500000000000001e-214

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 82.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 82.5%

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

Alternative 4: 88.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -22000 \lor \neg \left(t \leq 4.6 \cdot 10^{+41}\right):\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, x\right) + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + \mathsf{fma}\left(b - z, y, x\right)\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -22000.0) (not (<= t 4.6e+41)))
   (fma (- t 2.0) b (+ (fma (- 1.0 t) a x) z))
   (+ (+ (fma -2.0 b z) (fma (- b z) y x)) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -22000.0) || !(t <= 4.6e+41)) {
		tmp = fma((t - 2.0), b, (fma((1.0 - t), a, x) + z));
	} else {
		tmp = (fma(-2.0, b, z) + fma((b - z), y, x)) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -22000.0) || !(t <= 4.6e+41))
		tmp = fma(Float64(t - 2.0), b, Float64(fma(Float64(1.0 - t), a, x) + z));
	else
		tmp = Float64(Float64(fma(-2.0, b, z) + fma(Float64(b - z), y, x)) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -22000.0], N[Not[LessEqual[t, 4.6e+41]], $MachinePrecision]], N[(N[(t - 2.0), $MachinePrecision] * b + N[(N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-2.0 * b + z), $MachinePrecision] + N[(N[(b - z), $MachinePrecision] * y + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -22000 or 4.5999999999999997e41 < t

   1. Initial program 93.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   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 86.0%

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

   if -22000 < t < 4.5999999999999997e41

   1. Initial program 97.9%

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

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -22000 \lor \neg \left(t \leq 4.6 \cdot 10^{+41}\right):\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, x\right) + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + \mathsf{fma}\left(b - z, y, x\right)\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1400 \lor \neg \left(t \leq 4.6 \cdot 10^{+41}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + \mathsf{fma}\left(b - z, y, x\right)\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1400.0) (not (<= t 4.6e+41)))
   (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x))
   (+ (+ (fma -2.0 b z) (fma (- b z) y x)) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1400.0) || !(t <= 4.6e+41)) {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	} else {
		tmp = (fma(-2.0, b, z) + fma((b - z), y, x)) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1400.0) || !(t <= 4.6e+41))
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x));
	else
		tmp = Float64(Float64(fma(-2.0, b, z) + fma(Float64(b - z), y, x)) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1400.0], N[Not[LessEqual[t, 4.6e+41]], $MachinePrecision]], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-2.0 * b + z), $MachinePrecision] + N[(N[(b - z), $MachinePrecision] * y + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1400 or 4.5999999999999997e41 < t

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 80.9%

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

   if -1400 < t < 4.5999999999999997e41

   1. Initial program 97.9%

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

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1400 \lor \neg \left(t \leq 4.6 \cdot 10^{+41}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + \mathsf{fma}\left(b - z, y, x\right)\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-273}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-256}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, x\right) + a\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+41}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -2.8e+24)
     t_1
     (if (<= t -3.4e-273)
       (fma (- y 2.0) b a)
       (if (<= t 4.6e-256)
         (+ (fma -2.0 b x) a)
         (if (<= t 4.6e+41) (* (- 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 <= -2.8e+24) {
		tmp = t_1;
	} else if (t <= -3.4e-273) {
		tmp = fma((y - 2.0), b, a);
	} else if (t <= 4.6e-256) {
		tmp = fma(-2.0, b, x) + a;
	} else if (t <= 4.6e+41) {
		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 <= -2.8e+24)
		tmp = t_1;
	elseif (t <= -3.4e-273)
		tmp = fma(Float64(y - 2.0), b, a);
	elseif (t <= 4.6e-256)
		tmp = Float64(fma(-2.0, b, x) + a);
	elseif (t <= 4.6e+41)
		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, -2.8e+24], t$95$1, If[LessEqual[t, -3.4e-273], N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision], If[LessEqual[t, 4.6e-256], N[(N[(-2.0 * b + x), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 4.6e+41], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.8000000000000002e24 or 4.5999999999999997e41 < t

   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 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 73.7

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

   5. Applied rewrites 73.7%

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

   if -2.8000000000000002e24 < t < -3.39999999999999991e-273

   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 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 70.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 67.9%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 53.3%

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

   if -3.39999999999999991e-273 < t < 4.6e-256

   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 z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 90.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 90.0%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 83.2%

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

   if 4.6e-256 < t < 4.5999999999999997e41

   1. Initial program 94.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 52.5

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

   5. Applied rewrites 52.5%

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

Alternative 7: 51.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.48 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-236}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)) (t_2 (* (- b a) t)))
   (if (<= t -1.48e+26)
     t_2
     (if (<= t -3.4e-273)
       t_1
       (if (<= t 7e-236) (+ a x) (if (<= t 4.6e+41) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -1.48e+26) {
		tmp = t_2;
	} else if (t <= -3.4e-273) {
		tmp = t_1;
	} else if (t <= 7e-236) {
		tmp = a + x;
	} else if (t <= 4.6e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (b - z) * y
    t_2 = (b - a) * t
    if (t <= (-1.48d+26)) then
        tmp = t_2
    else if (t <= (-3.4d-273)) then
        tmp = t_1
    else if (t <= 7d-236) then
        tmp = a + x
    else if (t <= 4.6d+41) then
        tmp = t_1
    else
        tmp = t_2
    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 - z) * y;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -1.48e+26) {
		tmp = t_2;
	} else if (t <= -3.4e-273) {
		tmp = t_1;
	} else if (t <= 7e-236) {
		tmp = a + x;
	} else if (t <= 4.6e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	t_2 = (b - a) * t
	tmp = 0
	if t <= -1.48e+26:
		tmp = t_2
	elif t <= -3.4e-273:
		tmp = t_1
	elif t <= 7e-236:
		tmp = a + x
	elif t <= 4.6e+41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -1.48e+26)
		tmp = t_2;
	elseif (t <= -3.4e-273)
		tmp = t_1;
	elseif (t <= 7e-236)
		tmp = Float64(a + x);
	elseif (t <= 4.6e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	t_2 = (b - a) * t;
	tmp = 0.0;
	if (t <= -1.48e+26)
		tmp = t_2;
	elseif (t <= -3.4e-273)
		tmp = t_1;
	elseif (t <= 7e-236)
		tmp = a + x;
	elseif (t <= 4.6e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.48e+26], t$95$2, If[LessEqual[t, -3.4e-273], t$95$1, If[LessEqual[t, 7e-236], N[(a + x), $MachinePrecision], If[LessEqual[t, 4.6e+41], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.48e26 or 4.5999999999999997e41 < t

   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 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 73.7

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

   5. Applied rewrites 73.7%

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

   if -1.48e26 < t < -3.39999999999999991e-273 or 6.99999999999999988e-236 < t < 4.5999999999999997e41

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 53.4

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

   5. Applied rewrites 53.4%

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

   if -3.39999999999999991e-273 < t < 6.99999999999999988e-236

   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 z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 85.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 85.0%

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

   9. Taylor expanded in b around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 56.1%

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

Alternative 8: 49.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -25500:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-6}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)) (t_2 (* (- b a) t)))
   (if (<= t -25500.0)
     t_2
     (if (<= t -6.3e-111)
       t_1
       (if (<= t 8.8e-6) (+ a x) (if (<= t 2.6e+41) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -25500.0) {
		tmp = t_2;
	} else if (t <= -6.3e-111) {
		tmp = t_1;
	} else if (t <= 8.8e-6) {
		tmp = a + x;
	} else if (t <= 2.6e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (1.0d0 - y) * z
    t_2 = (b - a) * t
    if (t <= (-25500.0d0)) then
        tmp = t_2
    else if (t <= (-6.3d-111)) then
        tmp = t_1
    else if (t <= 8.8d-6) then
        tmp = a + x
    else if (t <= 2.6d+41) then
        tmp = t_1
    else
        tmp = t_2
    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 = (1.0 - y) * z;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -25500.0) {
		tmp = t_2;
	} else if (t <= -6.3e-111) {
		tmp = t_1;
	} else if (t <= 8.8e-6) {
		tmp = a + x;
	} else if (t <= 2.6e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - y) * z
	t_2 = (b - a) * t
	tmp = 0
	if t <= -25500.0:
		tmp = t_2
	elif t <= -6.3e-111:
		tmp = t_1
	elif t <= 8.8e-6:
		tmp = a + x
	elif t <= 2.6e+41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -25500.0)
		tmp = t_2;
	elseif (t <= -6.3e-111)
		tmp = t_1;
	elseif (t <= 8.8e-6)
		tmp = Float64(a + x);
	elseif (t <= 2.6e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - y) * z;
	t_2 = (b - a) * t;
	tmp = 0.0;
	if (t <= -25500.0)
		tmp = t_2;
	elseif (t <= -6.3e-111)
		tmp = t_1;
	elseif (t <= 8.8e-6)
		tmp = a + x;
	elseif (t <= 2.6e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -25500.0], t$95$2, If[LessEqual[t, -6.3e-111], t$95$1, If[LessEqual[t, 8.8e-6], N[(a + x), $MachinePrecision], If[LessEqual[t, 2.6e+41], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -25500 or 2.6000000000000001e41 < t

   1. Initial program 93.0%

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

   3. Taylor expanded in t around 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 72.5

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

   5. Applied rewrites 72.5%

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

   if -25500 < t < -6.3000000000000004e-111 or 8.8000000000000004e-6 < t < 2.6000000000000001e41

   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 52.9

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

   5. Applied rewrites 52.9%

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

   if -6.3000000000000004e-111 < t < 8.8000000000000004e-6

   1. Initial program 97.0%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.0%

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

   9. Taylor expanded in b around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 40.1%

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

Alternative 9: 85.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+51} \lor \neg \left(b \leq 6.8 \cdot 10^{+61}\right):\\ \;\;\;\;\mathsf{fma}\left(1, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.1e+51) (not (<= b 6.8e+61)))
   (fma 1.0 a (fma (- (+ t y) 2.0) b x))
   (- (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 <= -1.1e+51) || !(b <= 6.8e+61)) {
		tmp = fma(1.0, a, fma(((t + y) - 2.0), b, x));
	} 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 <= -1.1e+51) || !(b <= 6.8e+61))
		tmp = fma(1.0, a, fma(Float64(Float64(t + y) - 2.0), b, x));
	else
		tmp = Float64(fma(Float64(1.0 - y), z, x) - Float64(Float64(t - 1.0) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.1e+51], N[Not[LessEqual[b, 6.8e+61]], $MachinePrecision]], N[(1.0 * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.09999999999999996e51 or 6.80000000000000051e61 < b

   1. Initial program 89.6%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 90.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 89.3%

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

   if -1.09999999999999996e51 < b < 6.80000000000000051e61

   1. Initial program 99.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 99.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 86.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+51} \lor \neg \left(b \leq 6.8 \cdot 10^{+61}\right):\\ \;\;\;\;\mathsf{fma}\left(1, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+129} \lor \neg \left(t \leq 6.2 \cdot 10^{+41}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.3e+129) (not (<= t 6.2e+41)))
   (* (- b a) t)
   (+ (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 <= -4.3e+129) || !(t <= 6.2e+41)) {
		tmp = (b - a) * t;
	} 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 <= -4.3e+129) || !(t <= 6.2e+41))
		tmp = Float64(Float64(b - a) * t);
	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, -4.3e+129], N[Not[LessEqual[t, 6.2e+41]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $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 < -4.30000000000000021e129 or 6.2e41 < t

   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 80.3

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

   5. Applied rewrites 80.3%

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

   if -4.30000000000000021e129 < t < 6.2e41

   1. Initial program 97.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 98.8%

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

   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 92.7%

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

   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 75.5%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+129} \lor \neg \left(t \leq 6.2 \cdot 10^{+41}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+41}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -2.8e+24)
     t_1
     (if (<= t 2.9e-8)
       (fma (- y 2.0) b a)
       (if (<= t 4.6e+41) (* (- 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 <= -2.8e+24) {
		tmp = t_1;
	} else if (t <= 2.9e-8) {
		tmp = fma((y - 2.0), b, a);
	} else if (t <= 4.6e+41) {
		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 <= -2.8e+24)
		tmp = t_1;
	elseif (t <= 2.9e-8)
		tmp = fma(Float64(y - 2.0), b, a);
	elseif (t <= 4.6e+41)
		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, -2.8e+24], t$95$1, If[LessEqual[t, 2.9e-8], N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision], If[LessEqual[t, 4.6e+41], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8000000000000002e24 or 4.5999999999999997e41 < t

   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 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 73.7

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

   5. Applied rewrites 73.7%

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

   if -2.8000000000000002e24 < t < 2.9000000000000002e-8

   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 z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 73.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 71.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 52.8%

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

   if 2.9000000000000002e-8 < t < 4.5999999999999997e41

   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 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 75.1

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

   5. Applied rewrites 75.1%

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

Alternative 12: 36.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -14000:\\ \;\;\;\;\left(-t\right) \cdot a\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-5}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+41}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -14000.0)
   (* (- t) a)
   (if (<= t 2.55e-5) (+ a x) (if (<= t 2.9e+41) (* (- y) z) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -14000.0) {
		tmp = -t * a;
	} else if (t <= 2.55e-5) {
		tmp = a + x;
	} else if (t <= 2.9e+41) {
		tmp = -y * z;
	} else {
		tmp = b * t;
	}
	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 <= (-14000.0d0)) then
        tmp = -t * a
    else if (t <= 2.55d-5) then
        tmp = a + x
    else if (t <= 2.9d+41) then
        tmp = -y * z
    else
        tmp = b * t
    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 <= -14000.0) {
		tmp = -t * a;
	} else if (t <= 2.55e-5) {
		tmp = a + x;
	} else if (t <= 2.9e+41) {
		tmp = -y * z;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -14000.0:
		tmp = -t * a
	elif t <= 2.55e-5:
		tmp = a + x
	elif t <= 2.9e+41:
		tmp = -y * z
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -14000.0)
		tmp = Float64(Float64(-t) * a);
	elseif (t <= 2.55e-5)
		tmp = Float64(a + x);
	elseif (t <= 2.9e+41)
		tmp = Float64(Float64(-y) * z);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -14000.0)
		tmp = -t * a;
	elseif (t <= 2.55e-5)
		tmp = a + x;
	elseif (t <= 2.9e+41)
		tmp = -y * z;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -14000.0], N[((-t) * a), $MachinePrecision], If[LessEqual[t, 2.55e-5], N[(a + x), $MachinePrecision], If[LessEqual[t, 2.9e+41], N[((-y) * z), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -14000

   1. Initial program 93.0%

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

   3. Taylor expanded in 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 43.9

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

   5. Applied rewrites 43.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 43.5%

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

   if -14000 < t < 2.54999999999999998e-5

   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 z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 72.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 72.7%

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

   9. Taylor expanded in b around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 37.6%

       \[\leadsto a + x \]

   if 2.54999999999999998e-5 < t < 2.89999999999999988e41

   1. Initial program 99.8%

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

   3. Taylor expanded in 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 66.8

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

   5. Applied rewrites 66.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 57.7%

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

   if 2.89999999999999988e41 < t

   1. Initial program 93.0%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 67.8

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

   5. Applied rewrites 67.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 46.5%

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

Alternative 13: 65.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+25} \lor \neg \left(t \leq 65000000\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.3e+25) (not (<= t 65000000.0)))
   (* (- b a) t)
   (+ (fma (- y 2.0) b x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.3e+25) || !(t <= 65000000.0)) {
		tmp = (b - a) * t;
	} else {
		tmp = fma((y - 2.0), b, x) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.3e+25) || !(t <= 65000000.0))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = Float64(fma(Float64(y - 2.0), b, x) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.3e+25], N[Not[LessEqual[t, 65000000.0]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.29999999999999973e25 or 6.5e7 < t

   1. Initial program 93.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 71.1

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

   5. Applied rewrites 71.1%

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

   if -6.29999999999999973e25 < t < 6.5e7

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 72.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 71.3%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+25} \lor \neg \left(t \leq 65000000\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+98} \lor \neg \left(b \leq 5 \cdot 10^{+30}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.25e+98) (not (<= b 5e+30)))
   (* (- (+ t y) 2.0) b)
   (fma (- 1.0 t) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.25e+98) || !(b <= 5e+30)) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = fma((1.0 - t), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.25e+98) || !(b <= 5e+30))
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = fma(Float64(1.0 - t), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.25e+98], N[Not[LessEqual[b, 5e+30]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.2500000000000001e98 or 4.9999999999999998e30 < b

   1. Initial program 90.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 93.7%

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

   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 69.5%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   10. 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 76.4

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

   11. Applied rewrites 76.4%

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

   if -2.2500000000000001e98 < b < 4.9999999999999998e30

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 67.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 56.0%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+98} \lor \neg \left(b \leq 5 \cdot 10^{+30}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -14000:\\ \;\;\;\;\left(-t\right) \cdot a\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-90}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+55}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -14000.0)
   (* (- t) a)
   (if (<= t 3.6e-90) (+ a x) (if (<= t 3.3e+55) (* y b) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -14000.0) {
		tmp = -t * a;
	} else if (t <= 3.6e-90) {
		tmp = a + x;
	} else if (t <= 3.3e+55) {
		tmp = y * b;
	} else {
		tmp = b * t;
	}
	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 <= (-14000.0d0)) then
        tmp = -t * a
    else if (t <= 3.6d-90) then
        tmp = a + x
    else if (t <= 3.3d+55) then
        tmp = y * b
    else
        tmp = b * t
    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 <= -14000.0) {
		tmp = -t * a;
	} else if (t <= 3.6e-90) {
		tmp = a + x;
	} else if (t <= 3.3e+55) {
		tmp = y * b;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -14000.0:
		tmp = -t * a
	elif t <= 3.6e-90:
		tmp = a + x
	elif t <= 3.3e+55:
		tmp = y * b
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -14000.0)
		tmp = Float64(Float64(-t) * a);
	elseif (t <= 3.6e-90)
		tmp = Float64(a + x);
	elseif (t <= 3.3e+55)
		tmp = Float64(y * b);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -14000.0)
		tmp = -t * a;
	elseif (t <= 3.6e-90)
		tmp = a + x;
	elseif (t <= 3.3e+55)
		tmp = y * b;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -14000.0], N[((-t) * a), $MachinePrecision], If[LessEqual[t, 3.6e-90], N[(a + x), $MachinePrecision], If[LessEqual[t, 3.3e+55], N[(y * b), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -14000

   1. Initial program 93.0%

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

   3. Taylor expanded in 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 43.9

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

   5. Applied rewrites 43.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 43.5%

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

   if -14000 < t < 3.59999999999999981e-90

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 71.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 71.3%

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

   9. Taylor expanded in b around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 38.7%

       \[\leadsto a + x \]

   if 3.59999999999999981e-90 < t < 3.3e55

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 68.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 37.6%

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

   if 3.3e55 < t

   1. Initial program 92.6%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 68.5

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

   5. Applied rewrites 68.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 48.5%

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

Alternative 16: 34.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+40}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-90}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+55}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.75e+40)
   (* b t)
   (if (<= t 3.6e-90) (+ a x) (if (<= t 3.3e+55) (* y b) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+40) {
		tmp = b * t;
	} else if (t <= 3.6e-90) {
		tmp = a + x;
	} else if (t <= 3.3e+55) {
		tmp = y * b;
	} else {
		tmp = b * t;
	}
	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 <= (-1.75d+40)) then
        tmp = b * t
    else if (t <= 3.6d-90) then
        tmp = a + x
    else if (t <= 3.3d+55) then
        tmp = y * b
    else
        tmp = b * t
    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 <= -1.75e+40) {
		tmp = b * t;
	} else if (t <= 3.6e-90) {
		tmp = a + x;
	} else if (t <= 3.3e+55) {
		tmp = y * b;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.75e+40:
		tmp = b * t
	elif t <= 3.6e-90:
		tmp = a + x
	elif t <= 3.3e+55:
		tmp = y * b
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.75e+40)
		tmp = Float64(b * t);
	elseif (t <= 3.6e-90)
		tmp = Float64(a + x);
	elseif (t <= 3.3e+55)
		tmp = Float64(y * b);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.75e+40)
		tmp = b * t;
	elseif (t <= 3.6e-90)
		tmp = a + x;
	elseif (t <= 3.3e+55)
		tmp = y * b;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.75e+40], N[(b * t), $MachinePrecision], If[LessEqual[t, 3.6e-90], N[(a + x), $MachinePrecision], If[LessEqual[t, 3.3e+55], N[(y * b), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75e40 or 3.3e55 < t

   1. Initial program 92.6%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 64.5

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

   5. Applied rewrites 64.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 37.4%

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

   if -1.75e40 < t < 3.59999999999999981e-90

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 72.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 69.4%

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

   9. Taylor expanded in b around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 37.3%

       \[\leadsto a + x \]

   if 3.59999999999999981e-90 < t < 3.3e55

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 68.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 37.6%

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

Alternative 17: 41.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+45} \lor \neg \left(z \leq 1.35 \cdot 10^{+156}\right):\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.6e+45) (not (<= z 1.35e+156)))
   (* (- 1.0 y) z)
   (* (- 1.0 t) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.6e+45) || !(z <= 1.35e+156)) {
		tmp = (1.0 - y) * z;
	} 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 ((z <= (-1.6d+45)) .or. (.not. (z <= 1.35d+156))) then
        tmp = (1.0d0 - y) * z
    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 ((z <= -1.6e+45) || !(z <= 1.35e+156)) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = (1.0 - t) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.6e+45) or not (z <= 1.35e+156):
		tmp = (1.0 - y) * z
	else:
		tmp = (1.0 - t) * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.6e+45) || !(z <= 1.35e+156))
		tmp = Float64(Float64(1.0 - y) * z);
	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 ((z <= -1.6e+45) || ~((z <= 1.35e+156)))
		tmp = (1.0 - y) * z;
	else
		tmp = (1.0 - t) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.6e+45], N[Not[LessEqual[z, 1.35e+156]], $MachinePrecision]], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6000000000000001e45 or 1.35e156 < z

   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 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 65.9

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

   5. Applied rewrites 65.9%

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

   if -1.6000000000000001e45 < z < 1.35e156

   1. Initial program 98.2%

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

   3. Taylor expanded in 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 38.9

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

   5. Applied rewrites 38.9%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+45} \lor \neg \left(z \leq 1.35 \cdot 10^{+156}\right):\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+45} \lor \neg \left(z \leq 1.35 \cdot 10^{+156}\right):\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.95e+45) (not (<= z 1.35e+156))) (* (- y) z) (* (- 1.0 t) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.95e+45) || !(z <= 1.35e+156)) {
		tmp = -y * z;
	} 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 ((z <= (-1.95d+45)) .or. (.not. (z <= 1.35d+156))) then
        tmp = -y * z
    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 ((z <= -1.95e+45) || !(z <= 1.35e+156)) {
		tmp = -y * z;
	} else {
		tmp = (1.0 - t) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.95e+45) or not (z <= 1.35e+156):
		tmp = -y * z
	else:
		tmp = (1.0 - t) * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.95e+45) || !(z <= 1.35e+156))
		tmp = Float64(Float64(-y) * z);
	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 ((z <= -1.95e+45) || ~((z <= 1.35e+156)))
		tmp = -y * z;
	else
		tmp = (1.0 - t) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.95e+45], N[Not[LessEqual[z, 1.35e+156]], $MachinePrecision]], N[((-y) * z), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e45 or 1.35e156 < z

   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 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 65.9

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

   5. Applied rewrites 65.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 46.4%

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

   if -1.95e45 < z < 1.35e156

   1. Initial program 98.2%

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

   3. Taylor expanded in 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 38.9

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

   5. Applied rewrites 38.9%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+45} \lor \neg \left(z \leq 1.35 \cdot 10^{+156}\right):\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 33.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+124} \lor \neg \left(y \leq 1.1 \cdot 10^{+54}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;a + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.1e+124) (not (<= y 1.1e+54))) (* y b) (+ a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.1e+124) || !(y <= 1.1e+54)) {
		tmp = y * b;
	} else {
		tmp = a + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 <= (-2.1d+124)) .or. (.not. (y <= 1.1d+54))) then
        tmp = y * b
    else
        tmp = a + x
    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 <= -2.1e+124) || !(y <= 1.1e+54)) {
		tmp = y * b;
	} else {
		tmp = a + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.1e+124) or not (y <= 1.1e+54):
		tmp = y * b
	else:
		tmp = a + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.1e+124) || !(y <= 1.1e+54))
		tmp = Float64(y * b);
	else
		tmp = Float64(a + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.1e+124) || ~((y <= 1.1e+54)))
		tmp = y * b;
	else
		tmp = a + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.1e+124], N[Not[LessEqual[y, 1.1e+54]], $MachinePrecision]], N[(y * b), $MachinePrecision], N[(a + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000011e124 or 1.09999999999999995e54 < y

   1. Initial program 90.3%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 69.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 42.3%

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

   if -2.10000000000000011e124 < y < 1.09999999999999995e54

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

   5. Applied rewrites 78.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 43.2%

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

   9. Taylor expanded in b around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 30.7%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+124} \lor \neg \left(y \leq 1.1 \cdot 10^{+54}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;a + x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 24.6% accurate, 9.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 = a + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a + x), $MachinePrecision]

Derivation

1. Initial program 95.7%

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

3. Taylor expanded in z around 0

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

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

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

   2. +-commutative N/A

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

   3. mul-1-neg N/A

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

5. Applied rewrites 75.1%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 45.6%

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

9. Taylor expanded in b around 0

   \[\leadsto a + x \]
10. Step-by-step derivation

11. Applied rewrites 23.3%

    \[\leadsto a + x \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2025015 
(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)))