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

Percentage Accurate: 95.3% → 98.3%

Time: 5.4s

Alternatives: 23

Speedup: 0.5×

• 35.8% 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: 95.3% 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: 98.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)) (t_2 (* (- y 1.0) z)))
   (if (<= (+ (- (- x t_2) (* (- t 1.0) a)) t_1) INFINITY)
     (+ (- (fma (- 1.0 t) a x) t_2) t_1)
     (* (* (- (/ b a) 1.0) a) t))))

C

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_2 = Float64(Float64(y - 1.0) * z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - t_2) - Float64(Float64(t - 1.0) * a)) + t_1) <= Inf)
		tmp = Float64(Float64(fma(Float64(1.0 - t), a, x) - t_2) + t_1);
	else
		tmp = Float64(Float64(Float64(Float64(b / a) - 1.0) * a) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - t$95$2), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], Infinity], N[(N[(N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision] - t$95$2), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(N[(b / a), $MachinePrecision] - 1.0), $MachinePrecision] * 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 95.3%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 95.3

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

   4. Applied rewrites 95.3%

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

   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 95.3%

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

   2. 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 32.6

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

   4. Applied rewrites 32.6%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 32.9

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

   7. Applied rewrites 32.9%

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

Alternative 2: 92.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -130000000:\\ \;\;\;\;\left(\left(x - \left(\frac{-z}{y} + z\right) \cdot y\right) - \left(t - 1\right) \cdot a\right) + b \cdot y\\ \mathbf{elif}\;y \leq 1.7:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x\right) - \mathsf{fma}\left(t - 1, a, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b - a \cdot t\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -130000000.0)
   (+ (- (- x (* (+ (/ (- z) y) z) y)) (* (- t 1.0) a)) (* b y))
   (if (<= y 1.7)
     (- (fma (- t 2.0) b x) (fma (- t 1.0) a (- z)))
     (+ (fma (- b z) y (- (* (- t 2.0) b) (* a t))) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -130000000.0) {
		tmp = ((x - (((-z / y) + z) * y)) - ((t - 1.0) * a)) + (b * y);
	} else if (y <= 1.7) {
		tmp = fma((t - 2.0), b, x) - fma((t - 1.0), a, -z);
	} else {
		tmp = fma((b - z), y, (((t - 2.0) * b) - (a * t))) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -130000000.0)
		tmp = Float64(Float64(Float64(x - Float64(Float64(Float64(Float64(-z) / y) + z) * y)) - Float64(Float64(t - 1.0) * a)) + Float64(b * y));
	elseif (y <= 1.7)
		tmp = Float64(fma(Float64(t - 2.0), b, x) - fma(Float64(t - 1.0), a, Float64(-z)));
	else
		tmp = Float64(fma(Float64(b - z), y, Float64(Float64(Float64(t - 2.0) * b) - Float64(a * t))) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -130000000.0], N[(N[(N[(x - N[(N[(N[((-z) / y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7], N[(N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b - z), $MachinePrecision] * y + N[(N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e8

   1. Initial program 95.3%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 85.0

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

   4. Applied rewrites 85.0%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 70.3

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

   7. Applied rewrites 70.3%

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

   if -1.3e8 < y < 1.69999999999999996

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   if 1.69999999999999996 < y

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 77.5

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

   7. Applied rewrites 77.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 77.5

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

   9. Applied rewrites 77.8%

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

Alternative 3: 90.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(y - 1\right) \cdot z\\ \mathbf{elif}\;y \leq 1.7:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x\right) - \mathsf{fma}\left(t - 1, a, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b - a \cdot t\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.8e-8)
   (- (fma (- (+ t y) 2.0) b x) (* (- y 1.0) z))
   (if (<= y 1.7)
     (- (fma (- t 2.0) b x) (fma (- t 1.0) a (- z)))
     (+ (fma (- b z) y (- (* (- t 2.0) b) (* a t))) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.8e-8) {
		tmp = fma(((t + y) - 2.0), b, x) - ((y - 1.0) * z);
	} else if (y <= 1.7) {
		tmp = fma((t - 2.0), b, x) - fma((t - 1.0), a, -z);
	} else {
		tmp = fma((b - z), y, (((t - 2.0) * b) - (a * t))) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.8e-8)
		tmp = Float64(fma(Float64(Float64(t + y) - 2.0), b, x) - Float64(Float64(y - 1.0) * z));
	elseif (y <= 1.7)
		tmp = Float64(fma(Float64(t - 2.0), b, x) - fma(Float64(t - 1.0), a, Float64(-z)));
	else
		tmp = Float64(fma(Float64(b - z), y, Float64(Float64(Float64(t - 2.0) * b) - Float64(a * t))) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.8e-8], N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7], N[(N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b - z), $MachinePrecision] * y + N[(N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.7999999999999997e-8

   1. Initial program 95.3%

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

   2. 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 74.4

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

   4. Applied rewrites 74.4%

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

   if -7.7999999999999997e-8 < y < 1.69999999999999996

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

   if 1.69999999999999996 < y

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 77.5

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

   7. Applied rewrites 77.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 77.5

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

   9. Applied rewrites 77.8%

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

Alternative 4: 87.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(y - 1\right) \cdot z\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.039:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x\right) - \mathsf{fma}\left(t - 1, a, -z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (fma (- (+ t y) 2.0) b x) (* (- y 1.0) z))))
   (if (<= y -7.8e-8)
     t_1
     (if (<= y 0.039) (- (fma (- t 2.0) b x) (fma (- t 1.0) a (- 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) - ((y - 1.0) * z);
	double tmp;
	if (y <= -7.8e-8) {
		tmp = t_1;
	} else if (y <= 0.039) {
		tmp = fma((t - 2.0), b, x) - fma((t - 1.0), a, -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(Float64(t + y) - 2.0), b, x) - Float64(Float64(y - 1.0) * z))
	tmp = 0.0
	if (y <= -7.8e-8)
		tmp = t_1;
	elseif (y <= 0.039)
		tmp = Float64(fma(Float64(t - 2.0), b, x) - fma(Float64(t - 1.0), a, Float64(-z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.8e-8], t$95$1, If[LessEqual[y, 0.039], N[(N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.7999999999999997e-8 or 0.0389999999999999999 < y

   1. Initial program 95.3%

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

   2. 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 74.4

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

   4. Applied rewrites 74.4%

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

   if -7.7999999999999997e-8 < y < 0.0389999999999999999

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 68.8

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

   4. Applied rewrites 68.8%

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

Alternative 5: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ t_2 := t\_1 - \left(y - 1\right) \cdot z\\ \mathbf{if}\;z \leq -4 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+44}:\\ \;\;\;\;t\_1 - \left(t - 1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -4e+17) t_2 (if (<= z 1.25e+44) (- 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 <= -4e+17) {
		tmp = t_2;
	} else if (z <= 1.25e+44) {
		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 <= -4e+17)
		tmp = t_2;
	elseif (z <= 1.25e+44)
		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, -4e+17], t$95$2, If[LessEqual[z, 1.25e+44], 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 < -4e17 or 1.2499999999999999e44 < z

   1. Initial program 95.3%

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

   2. 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 74.4

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

   4. Applied rewrites 74.4%

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

   if -4e17 < z < 1.2499999999999999e44

   1. Initial program 95.3%

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

   2. 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 72.8

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

   4. Applied rewrites 72.8%

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

Alternative 6: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (fma a (- t 1.0) (* z (- y 1.0))))))
   (if (<= z -4.8e+17)
     t_1
     (if (<= z 1.8e+92) (- (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 = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	double tmp;
	if (z <= -4.8e+17) {
		tmp = t_1;
	} else if (z <= 1.8e+92) {
		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(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))))
	tmp = 0.0
	if (z <= -4.8e+17)
		tmp = t_1;
	elseif (z <= 1.8e+92)
		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[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+17], t$95$1, If[LessEqual[z, 1.8e+92], 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 < -4.8e17 or 1.8e92 < z

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 77.5

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

   7. Applied rewrites 77.5%

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

   8. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 67.7

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

   10. Applied rewrites 67.7%

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

   if -4.8e17 < z < 1.8e92

   1. Initial program 95.3%

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

   2. 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 72.8

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

   4. Applied rewrites 72.8%

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

Alternative 7: 83.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+80}:\\ \;\;\;\;\left(-a\right) \cdot t + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+95}:\\ \;\;\;\;x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.5e+80)
   (+ (* (- a) t) (* (- (+ y t) 2.0) b))
   (if (<= b 2.65e+95)
     (- x (fma a (- t 1.0) (* z (- y 1.0))))
     (fma (- (+ t y) 2.0) b (- x (- a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.5e+80) {
		tmp = (-a * t) + (((y + t) - 2.0) * b);
	} else if (b <= 2.65e+95) {
		tmp = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	} else {
		tmp = fma(((t + y) - 2.0), b, (x - -a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.5e+80)
		tmp = Float64(Float64(Float64(-a) * t) + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (b <= 2.65e+95)
		tmp = Float64(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))));
	else
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - Float64(-a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.5e+80], N[(N[((-a) * t), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.65e+95], N[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.50000000000000007e80

   1. Initial program 95.3%

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

   2. 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 49.8

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

   4. Applied rewrites 49.8%

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

   if -8.50000000000000007e80 < b < 2.6500000000000001e95

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 77.5

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

   7. Applied rewrites 77.5%

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

   8. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 67.7

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

   10. Applied rewrites 67.7%

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

   if 2.6500000000000001e95 < b

   1. Initial program 95.3%

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

   2. 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 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 60.3

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

   7. Applied rewrites 60.3%

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

      1. lift--.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate--l+ N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lower--.f64 60.3

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

   9. Applied rewrites 60.3%

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

Alternative 8: 71.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z \cdot y\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 44000:\\ \;\;\;\;x + \left(b \cdot t - \left(t - 1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (- (* z y)) (* (- (+ y t) 2.0) b))))
   (if (<= y -1.55e+28)
     t_1
     (if (<= y 44000.0) (+ x (- (* b t) (* (- t 1.0) a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -(z * y) + (((y + t) - 2.0) * b);
	double tmp;
	if (y <= -1.55e+28) {
		tmp = t_1;
	} else if (y <= 44000.0) {
		tmp = x + ((b * t) - ((t - 1.0) * a));
	} 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 = -(z * y) + (((y + t) - 2.0d0) * b)
    if (y <= (-1.55d+28)) then
        tmp = t_1
    else if (y <= 44000.0d0) then
        tmp = x + ((b * t) - ((t - 1.0d0) * a))
    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 = -(z * y) + (((y + t) - 2.0) * b);
	double tmp;
	if (y <= -1.55e+28) {
		tmp = t_1;
	} else if (y <= 44000.0) {
		tmp = x + ((b * t) - ((t - 1.0) * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -(z * y) + (((y + t) - 2.0) * b)
	tmp = 0
	if y <= -1.55e+28:
		tmp = t_1
	elif y <= 44000.0:
		tmp = x + ((b * t) - ((t - 1.0) * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-Float64(z * y)) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (y <= -1.55e+28)
		tmp = t_1;
	elseif (y <= 44000.0)
		tmp = Float64(x + Float64(Float64(b * t) - Float64(Float64(t - 1.0) * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -(z * y) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (y <= -1.55e+28)
		tmp = t_1;
	elseif (y <= 44000.0)
		tmp = x + ((b * t) - ((t - 1.0) * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-N[(z * y), $MachinePrecision]) + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+28], t$95$1, If[LessEqual[y, 44000.0], N[(x + N[(N[(b * t), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e28 or 44000 < y

   1. Initial program 95.3%

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

   2. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 50.8

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

   4. Applied rewrites 50.8%

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

   if -1.55e28 < y < 44000

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 62.4

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

   7. Applied rewrites 62.4%

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

   8. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 53.0

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

   10. Applied rewrites 53.0%

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

Alternative 9: 71.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ \mathbf{if}\;b \leq -6 \cdot 10^{-88}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x\right) - \left(-a\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+36}:\\ \;\;\;\;x + \left(\left(-y\right) \cdot z - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x - \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)))
   (if (<= b -6e-88)
     (- (fma t_1 b x) (- a))
     (if (<= b 1.2e+36)
       (+ x (- (* (- y) z) (* a t)))
       (fma t_1 b (- x (- a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) - 2.0;
	double tmp;
	if (b <= -6e-88) {
		tmp = fma(t_1, b, x) - -a;
	} else if (b <= 1.2e+36) {
		tmp = x + ((-y * z) - (a * t));
	} else {
		tmp = fma(t_1, b, (x - -a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	tmp = 0.0
	if (b <= -6e-88)
		tmp = Float64(fma(t_1, b, x) - Float64(-a));
	elseif (b <= 1.2e+36)
		tmp = Float64(x + Float64(Float64(Float64(-y) * z) - Float64(a * t)));
	else
		tmp = fma(t_1, b, Float64(x - Float64(-a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[b, -6e-88], N[(N[(t$95$1 * b + x), $MachinePrecision] - (-a)), $MachinePrecision], If[LessEqual[b, 1.2e+36], N[(x + N[(N[((-y) * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * b + N[(x - (-a)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.9999999999999999e-88

   1. Initial program 95.3%

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

   2. 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 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 60.3

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

   7. Applied rewrites 60.3%

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

   if -5.9999999999999999e-88 < b < 1.19999999999999996e36

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 77.5

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

   7. Applied rewrites 77.5%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 49.2

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

   10. Applied rewrites 49.2%

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

   if 1.19999999999999996e36 < b

   1. Initial program 95.3%

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

   2. 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 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 60.3

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

   7. Applied rewrites 60.3%

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

      1. lift--.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate--l+ N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lower--.f64 60.3

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

   9. Applied rewrites 60.3%

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

Alternative 10: 67.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(-a\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+36}:\\ \;\;\;\;x + \left(\left(-y\right) \cdot z - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (fma (- (+ t y) 2.0) b x) (- a))))
   (if (<= b -6e-88)
     t_1
     (if (<= b 1.2e+36) (+ x (- (* (- y) z) (* a t))) 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) - -a;
	double tmp;
	if (b <= -6e-88) {
		tmp = t_1;
	} else if (b <= 1.2e+36) {
		tmp = x + ((-y * z) - (a * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(Float64(t + y) - 2.0), b, x) - Float64(-a))
	tmp = 0.0
	if (b <= -6e-88)
		tmp = t_1;
	elseif (b <= 1.2e+36)
		tmp = Float64(x + Float64(Float64(Float64(-y) * z) - Float64(a * t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - (-a)), $MachinePrecision]}, If[LessEqual[b, -6e-88], t$95$1, If[LessEqual[b, 1.2e+36], N[(x + N[(N[((-y) * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.9999999999999999e-88 or 1.19999999999999996e36 < b

   1. Initial program 95.3%

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

   2. 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 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 60.3

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

   7. Applied rewrites 60.3%

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

   if -5.9999999999999999e-88 < b < 1.19999999999999996e36

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 77.5

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

   7. Applied rewrites 77.5%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 49.2

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

   10. Applied rewrites 49.2%

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

Alternative 11: 67.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+15}:\\ \;\;\;\;x + \left(b \cdot t - \left(t - 1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -4e+33)
     t_1
     (if (<= y 8e+15) (+ x (- (* b t) (* (- t 1.0) a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -4e+33) {
		tmp = t_1;
	} else if (y <= 8e+15) {
		tmp = x + ((b * t) - ((t - 1.0) * a));
	} 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 - z) * y
    if (y <= (-4d+33)) then
        tmp = t_1
    else if (y <= 8d+15) then
        tmp = x + ((b * t) - ((t - 1.0d0) * a))
    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 - z) * y;
	double tmp;
	if (y <= -4e+33) {
		tmp = t_1;
	} else if (y <= 8e+15) {
		tmp = x + ((b * t) - ((t - 1.0) * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -4e+33:
		tmp = t_1
	elif y <= 8e+15:
		tmp = x + ((b * t) - ((t - 1.0) * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -4e+33)
		tmp = t_1;
	elseif (y <= 8e+15)
		tmp = Float64(x + Float64(Float64(b * t) - Float64(Float64(t - 1.0) * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -4e+33)
		tmp = t_1;
	elseif (y <= 8e+15)
		tmp = x + ((b * t) - ((t - 1.0) * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4e+33], t$95$1, If[LessEqual[y, 8e+15], N[(x + N[(N[(b * t), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9999999999999998e33 or 8e15 < y

   1. Initial program 95.3%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.5

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

   4. Applied rewrites 33.5%

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

   if -3.9999999999999998e33 < y < 8e15

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 62.4

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

   7. Applied rewrites 62.4%

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

   8. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 53.0

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

   10. Applied rewrites 53.0%

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

Alternative 12: 66.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \left(\left(2 - t\right) - y\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+104}:\\ \;\;\;\;x + \left(\left(-y\right) \cdot z - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b) (- (- 2.0 t) y))))
   (if (<= b -1.25e+89)
     t_1
     (if (<= b 6e+104) (+ x (- (* (- y) z) (* a t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -b * ((2.0 - t) - y);
	double tmp;
	if (b <= -1.25e+89) {
		tmp = t_1;
	} else if (b <= 6e+104) {
		tmp = x + ((-y * z) - (a * t));
	} 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 * ((2.0d0 - t) - y)
    if (b <= (-1.25d+89)) then
        tmp = t_1
    else if (b <= 6d+104) then
        tmp = x + ((-y * z) - (a * t))
    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 * ((2.0 - t) - y);
	double tmp;
	if (b <= -1.25e+89) {
		tmp = t_1;
	} else if (b <= 6e+104) {
		tmp = x + ((-y * z) - (a * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -b * ((2.0 - t) - y)
	tmp = 0
	if b <= -1.25e+89:
		tmp = t_1
	elif b <= 6e+104:
		tmp = x + ((-y * z) - (a * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-b) * Float64(Float64(2.0 - t) - y))
	tmp = 0.0
	if (b <= -1.25e+89)
		tmp = t_1;
	elseif (b <= 6e+104)
		tmp = Float64(x + Float64(Float64(Float64(-y) * z) - Float64(a * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -b * ((2.0 - t) - y);
	tmp = 0.0;
	if (b <= -1.25e+89)
		tmp = t_1;
	elseif (b <= 6e+104)
		tmp = x + ((-y * z) - (a * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-b) * N[(N[(2.0 - t), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+89], t$95$1, If[LessEqual[b, 6e+104], N[(x + N[(N[((-y) * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.24999999999999996e89 or 5.99999999999999937e104 < b

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in b around -inf

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

      1. associate-*r* N/A

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

      2. distribute-lft-out N/A

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

      3. associate--l+ N/A

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

      4. +-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-+.f64 37.4

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

   7. Applied rewrites 37.4%

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

   8. Taylor expanded in b around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. associate--r+ N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 37.4

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

   10. Applied rewrites 37.4%

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

   if -1.24999999999999996e89 < b < 5.99999999999999937e104

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 77.5

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

   7. Applied rewrites 77.5%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 49.2

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

   10. Applied rewrites 49.2%

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

Alternative 13: 66.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -7 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+14}:\\ \;\;\;\;x + \left(b \cdot t - \left(\left(-a\right) - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -7e+32) t_1 (if (<= y 4e+14) (+ x (- (* b t) (- (- a) z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -7e+32) {
		tmp = t_1;
	} else if (y <= 4e+14) {
		tmp = x + ((b * t) - (-a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 - z) * y
    if (y <= (-7d+32)) then
        tmp = t_1
    else if (y <= 4d+14) then
        tmp = x + ((b * t) - (-a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -7e+32) {
		tmp = t_1;
	} else if (y <= 4e+14) {
		tmp = x + ((b * t) - (-a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -7e+32:
		tmp = t_1
	elif y <= 4e+14:
		tmp = x + ((b * t) - (-a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -7e+32)
		tmp = t_1;
	elseif (y <= 4e+14)
		tmp = Float64(x + Float64(Float64(b * t) - Float64(Float64(-a) - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -7e+32)
		tmp = t_1;
	elseif (y <= 4e+14)
		tmp = x + ((b * t) - (-a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -7e+32], t$95$1, If[LessEqual[y, 4e+14], N[(x + N[(N[(b * t), $MachinePrecision] - N[((-a) - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.0000000000000002e32 or 4e14 < y

   1. Initial program 95.3%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.5

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

   4. Applied rewrites 33.5%

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

   if -7.0000000000000002e32 < y < 4e14

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 62.4

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

   7. Applied rewrites 62.4%

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

   8. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-neg.f64 49.3

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

   10. Applied rewrites 49.3%

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

Alternative 14: 65.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+28}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 7000000000000:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -7.5e+71)
     t_1
     (if (<= t -8.5e+28)
       (* (- b z) y)
       (if (<= t 7000000000000.0) (- (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 <= -7.5e+71) {
		tmp = t_1;
	} else if (t <= -8.5e+28) {
		tmp = (b - z) * y;
	} else if (t <= 7000000000000.0) {
		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 <= -7.5e+71)
		tmp = t_1;
	elseif (t <= -8.5e+28)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 7000000000000.0)
		tmp = Float64(fma(Float64(y - 2.0), b, x) - Float64(-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, -7.5e+71], t$95$1, If[LessEqual[t, -8.5e+28], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 7000000000000.0], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - (-a)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.50000000000000007e71 or 7e12 < t

   1. Initial program 95.3%

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

   2. 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 32.6

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

   4. Applied rewrites 32.6%

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

   if -7.50000000000000007e71 < t < -8.49999999999999954e28

   1. Initial program 95.3%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.5

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

   4. Applied rewrites 33.5%

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

   if -8.49999999999999954e28 < t < 7e12

   1. Initial program 95.3%

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

   2. 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 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 46.7

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

   7. Applied rewrites 46.7%

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

Alternative 15: 64.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -7 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x\right) - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -7e+32) t_1 (if (<= y 4e+14) (- (fma (- t 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 - z) * y;
	double tmp;
	if (y <= -7e+32) {
		tmp = t_1;
	} else if (y <= 4e+14) {
		tmp = fma((t - 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 - z) * y)
	tmp = 0.0
	if (y <= -7e+32)
		tmp = t_1;
	elseif (y <= 4e+14)
		tmp = Float64(fma(Float64(t - 2.0), b, x) - Float64(-a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -7e+32], t$95$1, If[LessEqual[y, 4e+14], N[(N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - (-a)), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.0000000000000002e32 or 4e14 < y

   1. Initial program 95.3%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.5

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

   4. Applied rewrites 33.5%

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

   if -7.0000000000000002e32 < y < 4e14

   1. Initial program 95.3%

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

   2. 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 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 60.3

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

   7. Applied rewrites 60.3%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 46.4

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

   10. Applied rewrites 46.4%

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

Alternative 16: 57.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4800000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-97}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+14}:\\ \;\;\;\;x - a \cdot \left(t - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -4800000000000.0)
     t_1
     (if (<= y -5.4e-97)
       (* (- b a) t)
       (if (<= y 3.5e+14) (- 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 = (b - z) * y;
	double tmp;
	if (y <= -4800000000000.0) {
		tmp = t_1;
	} else if (y <= -5.4e-97) {
		tmp = (b - a) * t;
	} else if (y <= 3.5e+14) {
		tmp = x - (a * (t - 1.0));
	} 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 - z) * y
    if (y <= (-4800000000000.0d0)) then
        tmp = t_1
    else if (y <= (-5.4d-97)) then
        tmp = (b - a) * t
    else if (y <= 3.5d+14) then
        tmp = x - (a * (t - 1.0d0))
    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 - z) * y;
	double tmp;
	if (y <= -4800000000000.0) {
		tmp = t_1;
	} else if (y <= -5.4e-97) {
		tmp = (b - a) * t;
	} else if (y <= 3.5e+14) {
		tmp = x - (a * (t - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -4800000000000.0:
		tmp = t_1
	elif y <= -5.4e-97:
		tmp = (b - a) * t
	elif y <= 3.5e+14:
		tmp = x - (a * (t - 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -4800000000000.0)
		tmp = t_1;
	elseif (y <= -5.4e-97)
		tmp = Float64(Float64(b - a) * t);
	elseif (y <= 3.5e+14)
		tmp = Float64(x - Float64(a * Float64(t - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -4800000000000.0)
		tmp = t_1;
	elseif (y <= -5.4e-97)
		tmp = (b - a) * t;
	elseif (y <= 3.5e+14)
		tmp = x - (a * (t - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4800000000000.0], t$95$1, If[LessEqual[y, -5.4e-97], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 3.5e+14], N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8e12 or 3.5e14 < y

   1. Initial program 95.3%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.5

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

   4. Applied rewrites 33.5%

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

   if -4.8e12 < y < -5.3999999999999997e-97

   1. Initial program 95.3%

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

   2. 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 32.6

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

   4. Applied rewrites 32.6%

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

   if -5.3999999999999997e-97 < y < 3.5e14

   1. Initial program 95.3%

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

   2. 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 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 59.4

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

   7. Applied rewrites 59.4%

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

   8. Taylor expanded in b around 0

      \[\leadsto x - \color{blue}{a \cdot \left(t - 1\right)} \]
   9. 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 41.5

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

   10. Applied rewrites 41.5%

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

Alternative 17: 51.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4800000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 44000:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -4800000000000.0) t_1 (if (<= y 44000.0) (* (- b a) t) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -4800000000000.0) {
		tmp = t_1;
	} else if (y <= 44000.0) {
		tmp = (b - a) * t;
	} 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 - z) * y
    if (y <= (-4800000000000.0d0)) then
        tmp = t_1
    else if (y <= 44000.0d0) then
        tmp = (b - a) * t
    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 - z) * y;
	double tmp;
	if (y <= -4800000000000.0) {
		tmp = t_1;
	} else if (y <= 44000.0) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -4800000000000.0:
		tmp = t_1
	elif y <= 44000.0:
		tmp = (b - a) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -4800000000000.0)
		tmp = t_1;
	elseif (y <= 44000.0)
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -4800000000000.0)
		tmp = t_1;
	elseif (y <= 44000.0)
		tmp = (b - a) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4800000000000.0], t$95$1, If[LessEqual[y, 44000.0], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e12 or 44000 < y

   1. Initial program 95.3%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.5

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

   4. Applied rewrites 33.5%

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

   if -4.8e12 < y < 44000

   1. Initial program 95.3%

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

   2. 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 32.6

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

   4. Applied rewrites 32.6%

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

Alternative 18: 47.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+58}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -5.8e+71) t_1 (if (<= t 2.25e+58) (* (- 1.0 y) z) 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 <= -5.8e+71) {
		tmp = t_1;
	} else if (t <= 2.25e+58) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 <= (-5.8d+71)) then
        tmp = t_1
    else if (t <= 2.25d+58) then
        tmp = (1.0d0 - y) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -5.8e+71) {
		tmp = t_1;
	} else if (t <= 2.25e+58) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -5.8e+71:
		tmp = t_1
	elif t <= 2.25e+58:
		tmp = (1.0 - y) * z
	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 <= -5.8e+71)
		tmp = t_1;
	elseif (t <= 2.25e+58)
		tmp = Float64(Float64(1.0 - y) * z);
	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 <= -5.8e+71)
		tmp = t_1;
	elseif (t <= 2.25e+58)
		tmp = (1.0 - y) * z;
	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, -5.8e+71], t$95$1, If[LessEqual[t, 2.25e+58], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.80000000000000014e71 or 2.2499999999999999e58 < t

   1. Initial program 95.3%

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

   2. 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 32.6

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

   4. Applied rewrites 32.6%

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

   if -5.80000000000000014e71 < t < 2.2499999999999999e58

   1. Initial program 95.3%

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

   2. 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 29.0

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

   4. Applied rewrites 29.0%

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

Alternative 19: 43.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -1 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+21}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -1e+76) t_1 (if (<= z 2.6e+21) (* (- 1.0 t) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -1e+76) {
		tmp = t_1;
	} else if (z <= 2.6e+21) {
		tmp = (1.0 - t) * a;
	} 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 = (1.0d0 - y) * z
    if (z <= (-1d+76)) then
        tmp = t_1
    else if (z <= 2.6d+21) then
        tmp = (1.0d0 - t) * a
    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 = (1.0 - y) * z;
	double tmp;
	if (z <= -1e+76) {
		tmp = t_1;
	} else if (z <= 2.6e+21) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - y) * z
	tmp = 0
	if z <= -1e+76:
		tmp = t_1
	elif z <= 2.6e+21:
		tmp = (1.0 - t) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -1e+76)
		tmp = t_1;
	elseif (z <= 2.6e+21)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - y) * z;
	tmp = 0.0;
	if (z <= -1e+76)
		tmp = t_1;
	elseif (z <= 2.6e+21)
		tmp = (1.0 - t) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1e+76], t$95$1, If[LessEqual[z, 2.6e+21], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e76 or 2.6e21 < z

   1. Initial program 95.3%

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

   2. 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 29.0

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

   4. Applied rewrites 29.0%

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

   if -1e76 < z < 2.6e21

   1. Initial program 95.3%

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

   2. 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 27.3

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

   4. Applied rewrites 27.3%

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

Alternative 20: 33.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+14}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 2.85:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.25e+14) (* b y) (if (<= y 2.85) (* (- 1.0 t) a) (* b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.25e+14) {
		tmp = b * y;
	} else if (y <= 2.85) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.25d+14)) then
        tmp = b * y
    else if (y <= 2.85d0) then
        tmp = (1.0d0 - t) * a
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.25e+14) {
		tmp = b * y;
	} else if (y <= 2.85) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.25e+14:
		tmp = b * y
	elif y <= 2.85:
		tmp = (1.0 - t) * a
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.25e+14)
		tmp = Float64(b * y);
	elseif (y <= 2.85)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.25e+14)
		tmp = b * y;
	elseif (y <= 2.85)
		tmp = (1.0 - t) * a;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.25e+14], N[(b * y), $MachinePrecision], If[LessEqual[y, 2.85], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], N[(b * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.25e14 or 2.85000000000000009 < y

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in b around -inf

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

      1. associate-*r* N/A

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

      2. distribute-lft-out N/A

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

      3. associate--l+ N/A

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

      4. +-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-+.f64 37.4

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

   7. Applied rewrites 37.4%

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

   8. Taylor expanded in y around inf

      \[\leadsto b \cdot y \]
   9. Step-by-step derivation

      1. lower-*.f64 17.8

         \[\leadsto b \cdot y \]

   10. Applied rewrites 17.8%

       \[\leadsto b \cdot y \]

   if -2.25e14 < y < 2.85000000000000009

   1. Initial program 95.3%

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

   2. 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 27.3

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

   4. Applied rewrites 27.3%

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

Alternative 21: 27.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+14}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 2.85:\\ \;\;\;\;\left(-t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2e+14) (* b y) (if (<= y 2.85) (* (- t) a) (* b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2e+14) {
		tmp = b * y;
	} else if (y <= 2.85) {
		tmp = -t * a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2d+14)) then
        tmp = b * y
    else if (y <= 2.85d0) then
        tmp = -t * a
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2e+14) {
		tmp = b * y;
	} else if (y <= 2.85) {
		tmp = -t * a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2e+14:
		tmp = b * y
	elif y <= 2.85:
		tmp = -t * a
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2e+14)
		tmp = Float64(b * y);
	elseif (y <= 2.85)
		tmp = Float64(Float64(-t) * a);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2e+14)
		tmp = b * y;
	elseif (y <= 2.85)
		tmp = -t * a;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2e+14], N[(b * y), $MachinePrecision], If[LessEqual[y, 2.85], N[((-t) * a), $MachinePrecision], N[(b * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2e14 or 2.85000000000000009 < y

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in b around -inf

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

      1. associate-*r* N/A

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

      2. distribute-lft-out N/A

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

      3. associate--l+ N/A

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

      4. +-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-+.f64 37.4

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

   7. Applied rewrites 37.4%

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

   8. Taylor expanded in y around inf

      \[\leadsto b \cdot y \]
   9. Step-by-step derivation

      1. lower-*.f64 17.8

         \[\leadsto b \cdot y \]

   10. Applied rewrites 17.8%

       \[\leadsto b \cdot y \]

   if -2e14 < y < 2.85000000000000009

   1. Initial program 95.3%

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

   2. 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 27.3

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

   4. Applied rewrites 27.3%

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

   5. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 18.8

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

   7. Applied rewrites 18.8%

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

Alternative 22: 22.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-51}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 2.1:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.2e-51) (* b y) (if (<= y 2.1) a (* b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.2e-51) {
		tmp = b * y;
	} else if (y <= 2.1) {
		tmp = a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.2d-51)) then
        tmp = b * y
    else if (y <= 2.1d0) then
        tmp = a
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.2e-51) {
		tmp = b * y;
	} else if (y <= 2.1) {
		tmp = a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.2e-51:
		tmp = b * y
	elif y <= 2.1:
		tmp = a
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.2e-51)
		tmp = Float64(b * y);
	elseif (y <= 2.1)
		tmp = a;
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.2e-51)
		tmp = b * y;
	elseif (y <= 2.1)
		tmp = a;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.2e-51], N[(b * y), $MachinePrecision], If[LessEqual[y, 2.1], a, N[(b * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e-51 or 2.10000000000000009 < y

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in b around -inf

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

      1. associate-*r* N/A

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

      2. distribute-lft-out N/A

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

      3. associate--l+ N/A

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

      4. +-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-+.f64 37.4

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

   7. Applied rewrites 37.4%

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

   8. Taylor expanded in y around inf

      \[\leadsto b \cdot y \]
   9. Step-by-step derivation

      1. lower-*.f64 17.8

         \[\leadsto b \cdot y \]

   10. Applied rewrites 17.8%

       \[\leadsto b \cdot y \]

   if -3.2e-51 < y < 2.10000000000000009

   1. Initial program 95.3%

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

   2. 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 27.3

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

   4. Applied rewrites 27.3%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 10.6%

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

Alternative 23: 10.6% 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 95.3%

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

2. 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 27.3

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

4. Applied rewrites 27.3%

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

5. Taylor expanded in t around 0

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

7. Applied rewrites 10.6%

   \[\leadsto a \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025127 
(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)))