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

Percentage Accurate: 95.1% → 97.9%

Time: 5.0s

Alternatives: 19

Speedup: 0.5×

• 36.5% 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: 95.1% 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: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b))))
   (if (<= t_1 INFINITY) t_1 (* (- b a) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (b - a) * t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (b - a) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (b - a) * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(b - a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (b - a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 95.1%

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

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 95.1%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.8

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

   4. Applied rewrites 33.8%

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

Alternative 2: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ t_2 := t\_1 - \left(y - 1\right) \cdot z\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+156}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+126}:\\ \;\;\;\;t\_1 - \left(t - 1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)) (t_2 (- t_1 (* (- y 1.0) z))))
   (if (<= z -1.55e+156)
     t_2
     (if (<= z 1.9e+126) (- t_1 (* (- t 1.0) a)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double t_2 = t_1 - ((y - 1.0) * z);
	double tmp;
	if (z <= -1.55e+156) {
		tmp = t_2;
	} else if (z <= 1.9e+126) {
		tmp = t_1 - ((t - 1.0) * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	t_2 = Float64(t_1 - Float64(Float64(y - 1.0) * z))
	tmp = 0.0
	if (z <= -1.55e+156)
		tmp = t_2;
	elseif (z <= 1.9e+126)
		tmp = Float64(t_1 - Float64(Float64(t - 1.0) * a));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+156], t$95$2, If[LessEqual[z, 1.9e+126], N[(t$95$1 - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5500000000000001e156 or 1.90000000000000008e126 < z

   1. Initial program 95.1%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 72.8

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

   4. Applied rewrites 72.8%

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

   if -1.5500000000000001e156 < z < 1.90000000000000008e126

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.8

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

   4. Applied rewrites 73.8%

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

Alternative 3: 83.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + x\right) - z \cdot \left(y - 1\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a x) (* z (- y 1.0)))))
   (if (<= z -3.2e+156)
     t_1
     (if (<= z 2e+123) (- (fma (- (+ t y) 2.0) b x) (* (- t 1.0) a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + x) - (z * (y - 1.0));
	double tmp;
	if (z <= -3.2e+156) {
		tmp = t_1;
	} else if (z <= 2e+123) {
		tmp = fma(((t + y) - 2.0), b, x) - ((t - 1.0) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + x) - Float64(z * Float64(y - 1.0)))
	tmp = 0.0
	if (z <= -3.2e+156)
		tmp = t_1;
	elseif (z <= 2e+123)
		tmp = Float64(fma(Float64(Float64(t + y) - 2.0), b, x) - Float64(Float64(t - 1.0) * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + x), $MachinePrecision] - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+156], t$95$1, If[LessEqual[z, 2e+123], N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000002e156 or 1.99999999999999996e123 < z

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 50.4

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

   7. Applied rewrites 50.4%

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

   if -3.20000000000000002e156 < z < 1.99999999999999996e123

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.8

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

   4. Applied rewrites 73.8%

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

Alternative 4: 68.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + x\right) - z \cdot \left(y - 1\right)\\ \mathbf{if}\;b \leq -2.95 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-227}:\\ \;\;\;\;x - a \cdot \left(t - 1\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot t + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a x) (* z (- y 1.0)))))
   (if (<= b -2.95e-12)
     (fma (- (+ t y) 2.0) b x)
     (if (<= b -2.8e-223)
       t_1
       (if (<= b 3.8e-227)
         (- x (* a (- t 1.0)))
         (if (<= b 4.2e-28) t_1 (+ (* (- a) t) (* (- (+ y t) 2.0) b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + x) - (z * (y - 1.0));
	double tmp;
	if (b <= -2.95e-12) {
		tmp = fma(((t + y) - 2.0), b, x);
	} else if (b <= -2.8e-223) {
		tmp = t_1;
	} else if (b <= 3.8e-227) {
		tmp = x - (a * (t - 1.0));
	} else if (b <= 4.2e-28) {
		tmp = t_1;
	} else {
		tmp = (-a * t) + (((y + t) - 2.0) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + x) - Float64(z * Float64(y - 1.0)))
	tmp = 0.0
	if (b <= -2.95e-12)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, x);
	elseif (b <= -2.8e-223)
		tmp = t_1;
	elseif (b <= 3.8e-227)
		tmp = Float64(x - Float64(a * Float64(t - 1.0)));
	elseif (b <= 4.2e-28)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(-a) * t) + Float64(Float64(Float64(y + t) - 2.0) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + x), $MachinePrecision] - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.95e-12], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision], If[LessEqual[b, -2.8e-223], t$95$1, If[LessEqual[b, 3.8e-227], N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e-28], t$95$1, N[(N[((-a) * t), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.95e-12

   1. Initial program 95.1%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 45.4

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

   7. Applied rewrites 45.4%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-+.f64 51.0

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

   10. Applied rewrites 51.0%

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

   if -2.95e-12 < b < -2.80000000000000015e-223 or 3.8000000000000001e-227 < b < 4.20000000000000013e-28

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 50.4

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

   7. Applied rewrites 50.4%

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

   if -2.80000000000000015e-223 < b < 3.8000000000000001e-227

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.8

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

   4. Applied rewrites 73.8%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 42.5

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

   7. Applied rewrites 42.5%

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

   if 4.20000000000000013e-28 < b

   1. Initial program 95.1%

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

   2. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 51.2

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

   4. Applied rewrites 51.2%

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

Alternative 5: 67.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + x\right) - z \cdot \left(y - 1\right)\\ t_2 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -2.95 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-227}:\\ \;\;\;\;x - a \cdot \left(t - 1\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a x) (* z (- y 1.0)))) (t_2 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -2.95e-12)
     t_2
     (if (<= b -2.8e-223)
       t_1
       (if (<= b 3.8e-227)
         (- x (* a (- t 1.0)))
         (if (<= b 2.4e-30) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + x) - (z * (y - 1.0));
	double t_2 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -2.95e-12) {
		tmp = t_2;
	} else if (b <= -2.8e-223) {
		tmp = t_1;
	} else if (b <= 3.8e-227) {
		tmp = x - (a * (t - 1.0));
	} else if (b <= 2.4e-30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + x) - Float64(z * Float64(y - 1.0)))
	t_2 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -2.95e-12)
		tmp = t_2;
	elseif (b <= -2.8e-223)
		tmp = t_1;
	elseif (b <= 3.8e-227)
		tmp = Float64(x - Float64(a * Float64(t - 1.0)));
	elseif (b <= 2.4e-30)
		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[(a + x), $MachinePrecision] - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -2.95e-12], t$95$2, If[LessEqual[b, -2.8e-223], t$95$1, If[LessEqual[b, 3.8e-227], N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-30], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.95e-12 or 2.39999999999999985e-30 < b

   1. Initial program 95.1%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 45.4

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

   7. Applied rewrites 45.4%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-+.f64 51.0

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

   10. Applied rewrites 51.0%

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

   if -2.95e-12 < b < -2.80000000000000015e-223 or 3.8000000000000001e-227 < b < 2.39999999999999985e-30

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 50.4

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

   7. Applied rewrites 50.4%

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

   if -2.80000000000000015e-223 < b < 3.8000000000000001e-227

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.8

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

   4. Applied rewrites 73.8%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 42.5

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

   7. Applied rewrites 42.5%

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

Alternative 6: 67.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -3 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{-108}:\\ \;\;\;\;x - a \cdot \left(t - 1\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-47}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -3e-38)
     t_1
     (if (<= b 2.95e-108)
       (- x (* a (- t 1.0)))
       (if (<= b 6.8e-47) (* (- 1.0 y) z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -3e-38) {
		tmp = t_1;
	} else if (b <= 2.95e-108) {
		tmp = x - (a * (t - 1.0));
	} else if (b <= 6.8e-47) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -3e-38)
		tmp = t_1;
	elseif (b <= 2.95e-108)
		tmp = Float64(x - Float64(a * Float64(t - 1.0)));
	elseif (b <= 6.8e-47)
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -3e-38], t$95$1, If[LessEqual[b, 2.95e-108], N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e-47], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.99999999999999989e-38 or 6.8000000000000003e-47 < b

   1. Initial program 95.1%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 45.4

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

   7. Applied rewrites 45.4%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-+.f64 51.0

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

   10. Applied rewrites 51.0%

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

   if -2.99999999999999989e-38 < b < 2.94999999999999982e-108

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.8

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

   4. Applied rewrites 73.8%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 42.5

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

   7. Applied rewrites 42.5%

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

   if 2.94999999999999982e-108 < b < 6.8000000000000003e-47

   1. Initial program 95.1%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 27.9

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

   4. Applied rewrites 27.9%

      \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 63.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -23500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 70000000000:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -23500000000000.0)
     t_1
     (if (<= t 70000000000.0) (+ (fma (- y 2.0) b x) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -23500000000000.0) {
		tmp = t_1;
	} else if (t <= 70000000000.0) {
		tmp = fma((y - 2.0), b, x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -23500000000000.0)
		tmp = t_1;
	elseif (t <= 70000000000.0)
		tmp = Float64(fma(Float64(y - 2.0), b, x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -23500000000000.0], t$95$1, If[LessEqual[t, 70000000000.0], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.35e13 or 7e10 < t

   1. Initial program 95.1%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.8

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

   4. Applied rewrites 33.8%

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

   if -2.35e13 < t < 7e10

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + x\right) + a \]

      4. *-commutative N/A

         \[\leadsto \left(\left(y - 2\right) \cdot b + x\right) + a \]

      5. lift-fma.f64 N/A

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

      6. lift--.f64 46.6

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

   7. Applied rewrites 46.6%

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

Alternative 8: 58.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - 2, b, z\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+25}:\\ \;\;\;\;x - a \cdot \left(t - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- t 2.0) b z)))
   (if (<= b -3.1e+57) t_1 (if (<= b 7.2e+25) (- x (* a (- t 1.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((t - 2.0), b, z);
	double tmp;
	if (b <= -3.1e+57) {
		tmp = t_1;
	} else if (b <= 7.2e+25) {
		tmp = x - (a * (t - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(t - 2.0), b, z)
	tmp = 0.0
	if (b <= -3.1e+57)
		tmp = t_1;
	elseif (b <= 7.2e+25)
		tmp = Float64(x - Float64(a * Float64(t - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision]}, If[LessEqual[b, -3.1e+57], t$95$1, If[LessEqual[b, 7.2e+25], N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.10000000000000013e57 or 7.20000000000000031e25 < b

   1. Initial program 95.1%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 45.4

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

   7. Applied rewrites 45.4%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 32.2

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

   10. Applied rewrites 32.2%

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

   if -3.10000000000000013e57 < b < 7.20000000000000031e25

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.8

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

   4. Applied rewrites 73.8%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 42.5

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

   7. Applied rewrites 42.5%

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

Alternative 9: 58.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -23500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -23500000000000.0)
     t_1
     (if (<= t 1.3e+39) (fma (- y 2.0) b x) 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 <= -23500000000000.0) {
		tmp = t_1;
	} else if (t <= 1.3e+39) {
		tmp = fma((y - 2.0), b, x);
	} 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 <= -23500000000000.0)
		tmp = t_1;
	elseif (t <= 1.3e+39)
		tmp = fma(Float64(y - 2.0), b, x);
	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, -23500000000000.0], t$95$1, If[LessEqual[t, 1.3e+39], N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.35e13 or 1.3e39 < t

   1. Initial program 95.1%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.8

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

   4. Applied rewrites 33.8%

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

   if -2.35e13 < t < 1.3e39

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + x\right) + a \]

      4. *-commutative N/A

         \[\leadsto \left(\left(y - 2\right) \cdot b + x\right) + a \]

      5. lift-fma.f64 N/A

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

      6. lift--.f64 46.6

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

   7. Applied rewrites 46.6%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 24.3

         \[\leadsto a + x \]

   10. Applied rewrites 24.3%

       \[\leadsto a + x \]

   11. Taylor expanded in a around 0

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

       1. +-commutative N/A

          \[\leadsto b \cdot \left(y - 2\right) + x \]

       2. *-commutative N/A

          \[\leadsto \left(y - 2\right) \cdot b + x \]

       3. lower-fma.f64 N/A

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

       4. lower--.f64 37.4

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

   13. Applied rewrites 37.4%

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

Alternative 10: 53.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -920:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 240:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -920.0) t_1 (if (<= t 240.0) (fma (- y 2.0) b a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -920.0) {
		tmp = t_1;
	} else if (t <= 240.0) {
		tmp = fma((y - 2.0), b, a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -920.0)
		tmp = t_1;
	elseif (t <= 240.0)
		tmp = fma(Float64(y - 2.0), b, a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -920.0], t$95$1, If[LessEqual[t, 240.0], N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -920 or 240 < t

   1. Initial program 95.1%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.8

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

   4. Applied rewrites 33.8%

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

   if -920 < t < 240

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + x\right) + a \]

      4. *-commutative N/A

         \[\leadsto \left(\left(y - 2\right) \cdot b + x\right) + a \]

      5. lift-fma.f64 N/A

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

      6. lift--.f64 46.6

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

   7. Applied rewrites 46.6%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

         \[\leadsto b \cdot \left(y - 2\right) + a \]

      2. *-commutative N/A

         \[\leadsto \left(y - 2\right) \cdot b + a \]

      3. lower-fma.f64 N/A

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

      4. lift--.f64 33.3

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

   10. Applied rewrites 33.3%

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

Alternative 11: 49.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -8 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-251}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-112}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 240:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -8e-8)
     t_1
     (if (<= t 3.2e-251)
       (+ a x)
       (if (<= t 2e-112) (+ z x) (if (<= t 240.0) (* (- y 2.0) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -8e-8) {
		tmp = t_1;
	} else if (t <= 3.2e-251) {
		tmp = a + x;
	} else if (t <= 2e-112) {
		tmp = z + x;
	} else if (t <= 240.0) {
		tmp = (y - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-8d-8)) then
        tmp = t_1
    else if (t <= 3.2d-251) then
        tmp = a + x
    else if (t <= 2d-112) then
        tmp = z + x
    else if (t <= 240.0d0) then
        tmp = (y - 2.0d0) * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -8e-8) {
		tmp = t_1;
	} else if (t <= 3.2e-251) {
		tmp = a + x;
	} else if (t <= 2e-112) {
		tmp = z + x;
	} else if (t <= 240.0) {
		tmp = (y - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -8e-8:
		tmp = t_1
	elif t <= 3.2e-251:
		tmp = a + x
	elif t <= 2e-112:
		tmp = z + x
	elif t <= 240.0:
		tmp = (y - 2.0) * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -8e-8)
		tmp = t_1;
	elseif (t <= 3.2e-251)
		tmp = Float64(a + x);
	elseif (t <= 2e-112)
		tmp = Float64(z + x);
	elseif (t <= 240.0)
		tmp = Float64(Float64(y - 2.0) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -8e-8)
		tmp = t_1;
	elseif (t <= 3.2e-251)
		tmp = a + x;
	elseif (t <= 2e-112)
		tmp = z + x;
	elseif (t <= 240.0)
		tmp = (y - 2.0) * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -8e-8], t$95$1, If[LessEqual[t, 3.2e-251], N[(a + x), $MachinePrecision], If[LessEqual[t, 2e-112], N[(z + x), $MachinePrecision], If[LessEqual[t, 240.0], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.0000000000000002e-8 or 240 < t

   1. Initial program 95.1%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.8

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

   4. Applied rewrites 33.8%

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

   if -8.0000000000000002e-8 < t < 3.19999999999999982e-251

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + x\right) + a \]

      4. *-commutative N/A

         \[\leadsto \left(\left(y - 2\right) \cdot b + x\right) + a \]

      5. lift-fma.f64 N/A

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

      6. lift--.f64 46.6

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

   7. Applied rewrites 46.6%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 24.3

         \[\leadsto a + x \]

   10. Applied rewrites 24.3%

       \[\leadsto a + x \]

   if 3.19999999999999982e-251 < t < 1.9999999999999999e-112

   1. Initial program 95.1%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 45.4

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

   7. Applied rewrites 45.4%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

         \[\leadsto z + x \]

      2. lower-+.f64 23.7

         \[\leadsto z + x \]

   10. Applied rewrites 23.7%

       \[\leadsto z + x \]

   if 1.9999999999999999e-112 < t < 240

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + x\right) + a \]

      4. *-commutative N/A

         \[\leadsto \left(\left(y - 2\right) \cdot b + x\right) + a \]

      5. lift-fma.f64 N/A

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

      6. lift--.f64 46.6

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

   7. Applied rewrites 46.6%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 24.3

         \[\leadsto a + x \]

   10. Applied rewrites 24.3%

       \[\leadsto a + x \]

   11. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 24.2

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

   13. Applied rewrites 24.2%

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

Alternative 12: 40.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+63}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-112}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+106}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+63)
   (* b t)
   (if (<= b 8e-112)
     (- x (* a t))
     (if (<= b 2.1e+106) (* (- 1.0 y) z) (* (- y 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+63) {
		tmp = b * t;
	} else if (b <= 8e-112) {
		tmp = x - (a * t);
	} else if (b <= 2.1e+106) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = (y - 2.0) * b;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.25d+63)) then
        tmp = b * t
    else if (b <= 8d-112) then
        tmp = x - (a * t)
    else if (b <= 2.1d+106) then
        tmp = (1.0d0 - y) * z
    else
        tmp = (y - 2.0d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+63) {
		tmp = b * t;
	} else if (b <= 8e-112) {
		tmp = x - (a * t);
	} else if (b <= 2.1e+106) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = (y - 2.0) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e+63:
		tmp = b * t
	elif b <= 8e-112:
		tmp = x - (a * t)
	elif b <= 2.1e+106:
		tmp = (1.0 - y) * z
	else:
		tmp = (y - 2.0) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+63)
		tmp = Float64(b * t);
	elseif (b <= 8e-112)
		tmp = Float64(x - Float64(a * t));
	elseif (b <= 2.1e+106)
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = Float64(Float64(y - 2.0) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.25e+63)
		tmp = b * t;
	elseif (b <= 8e-112)
		tmp = x - (a * t);
	elseif (b <= 2.1e+106)
		tmp = (1.0 - y) * z;
	else
		tmp = (y - 2.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+63], N[(b * t), $MachinePrecision], If[LessEqual[b, 8e-112], N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+106], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.25000000000000003e63

   1. Initial program 95.1%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.8

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

   4. Applied rewrites 33.8%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 17.9%

      \[\leadsto b \cdot t \]

   if -1.25000000000000003e63 < b < 7.9999999999999996e-112

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.8

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

   4. Applied rewrites 73.8%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 42.5

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

   7. Applied rewrites 42.5%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 33.3

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

   10. Applied rewrites 33.3%

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

   if 7.9999999999999996e-112 < b < 2.10000000000000005e106

   1. Initial program 95.1%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 27.9

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

   4. Applied rewrites 27.9%

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

   if 2.10000000000000005e106 < b

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + x\right) + a \]

      4. *-commutative N/A

         \[\leadsto \left(\left(y - 2\right) \cdot b + x\right) + a \]

      5. lift-fma.f64 N/A

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

      6. lift--.f64 46.6

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

   7. Applied rewrites 46.6%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 24.3

         \[\leadsto a + x \]

   10. Applied rewrites 24.3%

       \[\leadsto a + x \]

   11. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 24.2

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

   13. Applied rewrites 24.2%

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

Alternative 13: 40.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+63}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-20}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+63)
   (* b t)
   (if (<= b 4.5e-20) (- x (* a t)) (* (- y 2.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+63) {
		tmp = b * t;
	} else if (b <= 4.5e-20) {
		tmp = x - (a * t);
	} else {
		tmp = (y - 2.0) * b;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.25d+63)) then
        tmp = b * t
    else if (b <= 4.5d-20) then
        tmp = x - (a * t)
    else
        tmp = (y - 2.0d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+63) {
		tmp = b * t;
	} else if (b <= 4.5e-20) {
		tmp = x - (a * t);
	} else {
		tmp = (y - 2.0) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e+63:
		tmp = b * t
	elif b <= 4.5e-20:
		tmp = x - (a * t)
	else:
		tmp = (y - 2.0) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+63)
		tmp = Float64(b * t);
	elseif (b <= 4.5e-20)
		tmp = Float64(x - Float64(a * t));
	else
		tmp = Float64(Float64(y - 2.0) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.25e+63)
		tmp = b * t;
	elseif (b <= 4.5e-20)
		tmp = x - (a * t);
	else
		tmp = (y - 2.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+63], N[(b * t), $MachinePrecision], If[LessEqual[b, 4.5e-20], N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.25000000000000003e63

   1. Initial program 95.1%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.8

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

   4. Applied rewrites 33.8%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 17.9%

      \[\leadsto b \cdot t \]

   if -1.25000000000000003e63 < b < 4.5000000000000001e-20

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.8

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

   4. Applied rewrites 73.8%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 42.5

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

   7. Applied rewrites 42.5%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 33.3

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

   10. Applied rewrites 33.3%

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

   if 4.5000000000000001e-20 < b

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + x\right) + a \]

      4. *-commutative N/A

         \[\leadsto \left(\left(y - 2\right) \cdot b + x\right) + a \]

      5. lift-fma.f64 N/A

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

      6. lift--.f64 46.6

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

   7. Applied rewrites 46.6%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 24.3

         \[\leadsto a + x \]

   10. Applied rewrites 24.3%

       \[\leadsto a + x \]

   11. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 24.2

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

   13. Applied rewrites 24.2%

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

Alternative 14: 34.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.44:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-142}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-21}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.44)
   (* b t)
   (if (<= b 1.8e-142) (+ a x) (if (<= b 1.25e-21) (+ z x) (* (- y 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.44) {
		tmp = b * t;
	} else if (b <= 1.8e-142) {
		tmp = a + x;
	} else if (b <= 1.25e-21) {
		tmp = z + x;
	} else {
		tmp = (y - 2.0) * b;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-0.44d0)) then
        tmp = b * t
    else if (b <= 1.8d-142) then
        tmp = a + x
    else if (b <= 1.25d-21) then
        tmp = z + x
    else
        tmp = (y - 2.0d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.44) {
		tmp = b * t;
	} else if (b <= 1.8e-142) {
		tmp = a + x;
	} else if (b <= 1.25e-21) {
		tmp = z + x;
	} else {
		tmp = (y - 2.0) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.44:
		tmp = b * t
	elif b <= 1.8e-142:
		tmp = a + x
	elif b <= 1.25e-21:
		tmp = z + x
	else:
		tmp = (y - 2.0) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.44)
		tmp = Float64(b * t);
	elseif (b <= 1.8e-142)
		tmp = Float64(a + x);
	elseif (b <= 1.25e-21)
		tmp = Float64(z + x);
	else
		tmp = Float64(Float64(y - 2.0) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.44)
		tmp = b * t;
	elseif (b <= 1.8e-142)
		tmp = a + x;
	elseif (b <= 1.25e-21)
		tmp = z + x;
	else
		tmp = (y - 2.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.44], N[(b * t), $MachinePrecision], If[LessEqual[b, 1.8e-142], N[(a + x), $MachinePrecision], If[LessEqual[b, 1.25e-21], N[(z + x), $MachinePrecision], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -0.440000000000000002

   1. Initial program 95.1%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.8

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

   4. Applied rewrites 33.8%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 17.9%

      \[\leadsto b \cdot t \]

   if -0.440000000000000002 < b < 1.8e-142

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + x\right) + a \]

      4. *-commutative N/A

         \[\leadsto \left(\left(y - 2\right) \cdot b + x\right) + a \]

      5. lift-fma.f64 N/A

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

      6. lift--.f64 46.6

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

   7. Applied rewrites 46.6%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 24.3

         \[\leadsto a + x \]

   10. Applied rewrites 24.3%

       \[\leadsto a + x \]

   if 1.8e-142 < b < 1.24999999999999993e-21

   1. Initial program 95.1%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 45.4

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

   7. Applied rewrites 45.4%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

         \[\leadsto z + x \]

      2. lower-+.f64 23.7

         \[\leadsto z + x \]

   10. Applied rewrites 23.7%

       \[\leadsto z + x \]

   if 1.24999999999999993e-21 < b

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + x\right) + a \]

      4. *-commutative N/A

         \[\leadsto \left(\left(y - 2\right) \cdot b + x\right) + a \]

      5. lift-fma.f64 N/A

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

      6. lift--.f64 46.6

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

   7. Applied rewrites 46.6%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 24.3

         \[\leadsto a + x \]

   10. Applied rewrites 24.3%

       \[\leadsto a + x \]

   11. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 24.2

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

   13. Applied rewrites 24.2%

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

Alternative 15: 32.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.44:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-142}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+45}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.44)
   (* b t)
   (if (<= b 1.8e-142) (+ a x) (if (<= b 3.6e+45) (+ z x) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.44) {
		tmp = b * t;
	} else if (b <= 1.8e-142) {
		tmp = a + x;
	} else if (b <= 3.6e+45) {
		tmp = z + x;
	} 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 (b <= (-0.44d0)) then
        tmp = b * t
    else if (b <= 1.8d-142) then
        tmp = a + x
    else if (b <= 3.6d+45) then
        tmp = z + x
    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 (b <= -0.44) {
		tmp = b * t;
	} else if (b <= 1.8e-142) {
		tmp = a + x;
	} else if (b <= 3.6e+45) {
		tmp = z + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.44:
		tmp = b * t
	elif b <= 1.8e-142:
		tmp = a + x
	elif b <= 3.6e+45:
		tmp = z + x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.44)
		tmp = Float64(b * t);
	elseif (b <= 1.8e-142)
		tmp = Float64(a + x);
	elseif (b <= 3.6e+45)
		tmp = Float64(z + x);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.44)
		tmp = b * t;
	elseif (b <= 1.8e-142)
		tmp = a + x;
	elseif (b <= 3.6e+45)
		tmp = z + x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.44], N[(b * t), $MachinePrecision], If[LessEqual[b, 1.8e-142], N[(a + x), $MachinePrecision], If[LessEqual[b, 3.6e+45], N[(z + x), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.440000000000000002 or 3.6e45 < b

   1. Initial program 95.1%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.8

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

   4. Applied rewrites 33.8%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 17.9%

      \[\leadsto b \cdot t \]

   if -0.440000000000000002 < b < 1.8e-142

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + x\right) + a \]

      4. *-commutative N/A

         \[\leadsto \left(\left(y - 2\right) \cdot b + x\right) + a \]

      5. lift-fma.f64 N/A

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

      6. lift--.f64 46.6

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

   7. Applied rewrites 46.6%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 24.3

         \[\leadsto a + x \]

   10. Applied rewrites 24.3%

       \[\leadsto a + x \]

   if 1.8e-142 < b < 3.6e45

   1. Initial program 95.1%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 45.4

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

   7. Applied rewrites 45.4%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

         \[\leadsto z + x \]

      2. lower-+.f64 23.7

         \[\leadsto z + x \]

   10. Applied rewrites 23.7%

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

Alternative 16: 29.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-50}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+141}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.5e-50) (+ z x) (if (<= z 1.8e+141) (+ a x) (+ z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.5e-50) {
		tmp = z + x;
	} else if (z <= 1.8e+141) {
		tmp = a + x;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 <= (-7.5d-50)) then
        tmp = z + x
    else if (z <= 1.8d+141) then
        tmp = a + x
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.5e-50) {
		tmp = z + x;
	} else if (z <= 1.8e+141) {
		tmp = a + x;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.5e-50:
		tmp = z + x
	elif z <= 1.8e+141:
		tmp = a + x
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.5e-50)
		tmp = Float64(z + x);
	elseif (z <= 1.8e+141)
		tmp = Float64(a + x);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -7.5e-50)
		tmp = z + x;
	elseif (z <= 1.8e+141)
		tmp = a + x;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.5e-50], N[(z + x), $MachinePrecision], If[LessEqual[z, 1.8e+141], N[(a + x), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e-50 or 1.8000000000000001e141 < z

   1. Initial program 95.1%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 45.4

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

   7. Applied rewrites 45.4%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

         \[\leadsto z + x \]

      2. lower-+.f64 23.7

         \[\leadsto z + x \]

   10. Applied rewrites 23.7%

       \[\leadsto z + x \]

   if -7.5e-50 < z < 1.8000000000000001e141

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + x\right) + a \]

      4. *-commutative N/A

         \[\leadsto \left(\left(y - 2\right) \cdot b + x\right) + a \]

      5. lift-fma.f64 N/A

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

      6. lift--.f64 46.6

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

   7. Applied rewrites 46.6%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 24.3

         \[\leadsto a + x \]

   10. Applied rewrites 24.3%

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

Alternative 17: 28.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+194}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+141}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.8e+194) z (if (<= z 1.8e+141) (+ a x) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.8e+194) {
		tmp = z;
	} else if (z <= 1.8e+141) {
		tmp = a + x;
	} else {
		tmp = z;
	}
	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 <= (-1.8d+194)) then
        tmp = z
    else if (z <= 1.8d+141) then
        tmp = a + x
    else
        tmp = z
    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 <= -1.8e+194) {
		tmp = z;
	} else if (z <= 1.8e+141) {
		tmp = a + x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.8e+194:
		tmp = z
	elif z <= 1.8e+141:
		tmp = a + x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.8e+194)
		tmp = z;
	elseif (z <= 1.8e+141)
		tmp = Float64(a + x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.8e+194)
		tmp = z;
	elseif (z <= 1.8e+141)
		tmp = a + x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.8e+194], z, If[LessEqual[z, 1.8e+141], N[(a + x), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e194 or 1.8000000000000001e141 < z

   1. Initial program 95.1%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 27.9

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

   4. Applied rewrites 27.9%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 10.6%

      \[\leadsto z \]

   if -1.8e194 < z < 1.8000000000000001e141

   1. Initial program 95.1%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + x\right) + a \]

      4. *-commutative N/A

         \[\leadsto \left(\left(y - 2\right) \cdot b + x\right) + a \]

      5. lift-fma.f64 N/A

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

      6. lift--.f64 46.6

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

   7. Applied rewrites 46.6%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 24.3

         \[\leadsto a + x \]

   10. Applied rewrites 24.3%

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

Alternative 18: 16.4% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-50}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+141}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7e-50) z (if (<= z 1.2e+141) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7e-50) {
		tmp = z;
	} else if (z <= 1.2e+141) {
		tmp = a;
	} else {
		tmp = z;
	}
	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 <= (-7d-50)) then
        tmp = z
    else if (z <= 1.2d+141) then
        tmp = a
    else
        tmp = z
    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 <= -7e-50) {
		tmp = z;
	} else if (z <= 1.2e+141) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7e-50:
		tmp = z
	elif z <= 1.2e+141:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7e-50)
		tmp = z;
	elseif (z <= 1.2e+141)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -7e-50)
		tmp = z;
	elseif (z <= 1.2e+141)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7e-50], z, If[LessEqual[z, 1.2e+141], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -6.99999999999999993e-50 or 1.19999999999999999e141 < z

   1. Initial program 95.1%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 27.9

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

   4. Applied rewrites 27.9%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 10.6%

      \[\leadsto z \]

   if -6.99999999999999993e-50 < z < 1.19999999999999999e141

   1. Initial program 95.1%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 29.3

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

   4. Applied rewrites 29.3%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 11.2%

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

Alternative 19: 11.2% accurate, 28.4× speedup

Math

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

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

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
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 95.1%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

2. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
3. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(1 - t\right) \cdot \color{blue}{a} \]

   2. lower-*.f64 N/A

      \[\leadsto \left(1 - t\right) \cdot \color{blue}{a} \]

   3. lower--.f64 29.3

      \[\leadsto \left(1 - t\right) \cdot a \]

4. Applied rewrites 29.3%

   \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

5. Taylor expanded in t around 0

   \[\leadsto a \]
6. Step-by-step derivation

7. Applied rewrites 11.2%

   \[\leadsto a \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025142 
(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)))