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

Percentage Accurate: 94.9% → 97.7%

Time: 5.6s

Alternatives: 25

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: 94.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - t$95$1), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(b - z), $MachinePrecision] * y), $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 94.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. *-commutative N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 95.3

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

   4. Applied rewrites 95.3%

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

   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 94.9%

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

   2. 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 33.1

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

   4. Applied rewrites 33.1%

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

Alternative 2: 90.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + b \cdot y\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x\right) - \left(a \cdot \left(t - 1\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* b y))))
   (if (<= y -1.1e+40)
     t_1
     (if (<= y 1e+21) (- (fma (- t 2.0) b x) (- (* a (- t 1.0)) z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (b * y);
	double tmp;
	if (y <= -1.1e+40) {
		tmp = t_1;
	} else if (y <= 1e+21) {
		tmp = fma((t - 2.0), b, x) - ((a * (t - 1.0)) - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(b * y))
	tmp = 0.0
	if (y <= -1.1e+40)
		tmp = t_1;
	elseif (y <= 1e+21)
		tmp = Float64(fma(Float64(t - 2.0), b, x) - Float64(Float64(a * Float64(t - 1.0)) - z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+40], t$95$1, If[LessEqual[y, 1e+21], N[(N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0999999999999999e40 or 1e21 < y

   1. Initial program 94.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 78.8

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

   4. Applied rewrites 78.8%

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

   if -1.0999999999999999e40 < y < 1e21

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lift-neg.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-flip-reverse N/A

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

      12. *-commutative N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift--.f64 69.1

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

   7. Applied rewrites 69.1%

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

Alternative 3: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+97}:\\ \;\;\;\;x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+92}:\\ \;\;\;\;t\_1 - \left(y - 1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \left(t - 1\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= a -7.5e+97)
     (- x (fma a (- t 1.0) (* z (- y 1.0))))
     (if (<= a 4.3e+92) (- t_1 (* (- y 1.0) z)) (- t_1 (* (- t 1.0) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (a <= -7.5e+97) {
		tmp = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	} else if (a <= 4.3e+92) {
		tmp = t_1 - ((y - 1.0) * z);
	} else {
		tmp = t_1 - ((t - 1.0) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (a <= -7.5e+97)
		tmp = Float64(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))));
	elseif (a <= 4.3e+92)
		tmp = Float64(t_1 - Float64(Float64(y - 1.0) * z));
	else
		tmp = Float64(t_1 - Float64(Float64(t - 1.0) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[a, -7.5e+97], N[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.3e+92], N[(t$95$1 - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.5000000000000004e97

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lift-neg.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-flip-reverse N/A

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

      12. *-commutative N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift--.f64 69.1

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

   7. Applied rewrites 69.1%

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

   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 68.5

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

   10. Applied rewrites 68.5%

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

   if -7.5000000000000004e97 < a < 4.2999999999999998e92

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 72.5

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

   4. Applied rewrites 72.5%

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

   if 4.2999999999999998e92 < a

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

Alternative 4: 86.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+89}:\\ \;\;\;\;x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \left(\mathsf{fma}\left(-y, z, z\right) - a \cdot \left(t - 1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.3e+89)
   (- x (fma a (- t 1.0) (* z (- y 1.0))))
   (if (<= z 4.7e+80)
     (- (fma (- (+ t y) 2.0) b x) (* (- t 1.0) a))
     (+ x (- (fma (- y) z z) (* a (- t 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3e+89) {
		tmp = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	} else if (z <= 4.7e+80) {
		tmp = fma(((t + y) - 2.0), b, x) - ((t - 1.0) * a);
	} else {
		tmp = x + (fma(-y, z, z) - (a * (t - 1.0)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.3e+89)
		tmp = Float64(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))));
	elseif (z <= 4.7e+80)
		tmp = Float64(fma(Float64(Float64(t + y) - 2.0), b, x) - Float64(Float64(t - 1.0) * a));
	else
		tmp = Float64(x + Float64(fma(Float64(-y), z, z) - Float64(a * Float64(t - 1.0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.3e+89], N[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e+80], N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[((-y) * z + z), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2999999999999999e89

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lift-neg.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-flip-reverse N/A

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

      12. *-commutative N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift--.f64 69.1

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

   7. Applied rewrites 69.1%

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

   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 68.5

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

   10. Applied rewrites 68.5%

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

   if -2.2999999999999999e89 < z < 4.70000000000000009e80

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   if 4.70000000000000009e80 < z

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 68.1

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

   7. Applied rewrites 68.1%

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

Alternative 5: 86.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(-a\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+41}:\\ \;\;\;\;x + \left(\mathsf{fma}\left(-y, z, z\right) - a \cdot \left(t - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (fma (- (+ t y) 2.0) b x) (- a))))
   (if (<= b -1.2e+48)
     t_1
     (if (<= b 2.4e+41) (+ x (- (fma (- y) z z) (* a (- t 1.0)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x) - -a;
	double tmp;
	if (b <= -1.2e+48) {
		tmp = t_1;
	} else if (b <= 2.4e+41) {
		tmp = x + (fma(-y, z, z) - (a * (t - 1.0)));
	} 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 <= -1.2e+48)
		tmp = t_1;
	elseif (b <= 2.4e+41)
		tmp = Float64(x + Float64(fma(Float64(-y), z, z) - Float64(a * Float64(t - 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - (-a)), $MachinePrecision]}, If[LessEqual[b, -1.2e+48], t$95$1, If[LessEqual[b, 2.4e+41], N[(x + N[(N[((-y) * z + z), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2000000000000001e48 or 2.4000000000000002e41 < b

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 59.9

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

   7. Applied rewrites 59.9%

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

   if -1.2000000000000001e48 < b < 2.4000000000000002e41

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 68.1

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

   7. Applied rewrites 68.1%

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

Alternative 6: 85.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(-a\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+41}:\\ \;\;\;\;x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (fma (- (+ t y) 2.0) b x) (- a))))
   (if (<= b -1.2e+48)
     t_1
     (if (<= b 2.4e+41) (- x (fma a (- t 1.0) (* z (- y 1.0)))) 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 <= -1.2e+48) {
		tmp = t_1;
	} else if (b <= 2.4e+41) {
		tmp = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	} 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 <= -1.2e+48)
		tmp = t_1;
	elseif (b <= 2.4e+41)
		tmp = Float64(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))));
	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, -1.2e+48], t$95$1, If[LessEqual[b, 2.4e+41], N[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2000000000000001e48 or 2.4000000000000002e41 < b

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 59.9

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

   7. Applied rewrites 59.9%

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

   if -1.2000000000000001e48 < b < 2.4000000000000002e41

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lift-neg.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-flip-reverse N/A

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

      12. *-commutative N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift--.f64 69.1

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

   7. Applied rewrites 69.1%

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

   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 68.5

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

   10. Applied rewrites 68.5%

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

Alternative 7: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\mathsf{fma}\left(-y, z, z\right) - a \cdot t\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-141}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(-a\right)\\ \mathbf{elif}\;z \leq 17:\\ \;\;\;\;\left(-a\right) \cdot t + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- (fma (- y) z z) (* a t)))))
   (if (<= z -3.5e+74)
     t_1
     (if (<= z 2.1e-141)
       (- (fma (- (+ t y) 2.0) b x) (- a))
       (if (<= z 17.0) (+ (* (- a) t) (* (- (+ y t) 2.0) b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (fma(-y, z, z) - (a * t));
	double tmp;
	if (z <= -3.5e+74) {
		tmp = t_1;
	} else if (z <= 2.1e-141) {
		tmp = fma(((t + y) - 2.0), b, x) - -a;
	} else if (z <= 17.0) {
		tmp = (-a * t) + (((y + t) - 2.0) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(fma(Float64(-y), z, z) - Float64(a * t)))
	tmp = 0.0
	if (z <= -3.5e+74)
		tmp = t_1;
	elseif (z <= 2.1e-141)
		tmp = Float64(fma(Float64(Float64(t + y) - 2.0), b, x) - Float64(-a));
	elseif (z <= 17.0)
		tmp = Float64(Float64(Float64(-a) * t) + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[((-y) * z + z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+74], t$95$1, If[LessEqual[z, 2.1e-141], N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - (-a)), $MachinePrecision], If[LessEqual[z, 17.0], N[(N[((-a) * t), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.50000000000000014e74 or 17 < z

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 68.1

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

   7. Applied rewrites 68.1%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 58.6

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

   10. Applied rewrites 58.6%

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

   if -3.50000000000000014e74 < z < 2.0999999999999999e-141

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 59.9

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

   7. Applied rewrites 59.9%

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

   if 2.0999999999999999e-141 < z < 17

   1. Initial program 94.9%

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

   2. 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 49.7

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

   4. Applied rewrites 49.7%

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

Alternative 8: 72.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\mathsf{fma}\left(-y, z, z\right) - a \cdot t\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- (fma (- y) z z) (* a t)))))
   (if (<= z -3.5e+74)
     t_1
     (if (<= z 1.6e+21) (- (fma (- (+ t 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 = x + (fma(-y, z, z) - (a * t));
	double tmp;
	if (z <= -3.5e+74) {
		tmp = t_1;
	} else if (z <= 1.6e+21) {
		tmp = fma(((t + y) - 2.0), b, x) - -a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(fma(Float64(-y), z, z) - Float64(a * t)))
	tmp = 0.0
	if (z <= -3.5e+74)
		tmp = t_1;
	elseif (z <= 1.6e+21)
		tmp = Float64(fma(Float64(Float64(t + 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[(x + N[(N[((-y) * z + z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+74], t$95$1, If[LessEqual[z, 1.6e+21], N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - (-a)), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000014e74 or 1.6e21 < z

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 68.1

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

   7. Applied rewrites 68.1%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 58.6

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

   10. Applied rewrites 58.6%

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

   if -3.50000000000000014e74 < z < 1.6e21

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 59.9

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

   7. Applied rewrites 59.9%

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

Alternative 9: 71.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\mathsf{fma}\left(-y, z, z\right) - \left(-a\right)\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- (fma (- y) z z) (- a)))))
   (if (<= z -1.7e+88)
     t_1
     (if (<= z 7.1e+139) (- (fma (- (+ t 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 = x + (fma(-y, z, z) - -a);
	double tmp;
	if (z <= -1.7e+88) {
		tmp = t_1;
	} else if (z <= 7.1e+139) {
		tmp = fma(((t + y) - 2.0), b, x) - -a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(fma(Float64(-y), z, z) - Float64(-a)))
	tmp = 0.0
	if (z <= -1.7e+88)
		tmp = t_1;
	elseif (z <= 7.1e+139)
		tmp = Float64(fma(Float64(Float64(t + 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[(x + N[(N[((-y) * z + z), $MachinePrecision] - (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+88], t$95$1, If[LessEqual[z, 7.1e+139], N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - (-a)), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000002e88 or 7.09999999999999964e139 < z

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 68.1

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

   7. Applied rewrites 68.1%

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

   8. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 51.8

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

   10. Applied rewrites 51.8%

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

   if -1.70000000000000002e88 < z < 7.09999999999999964e139

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 59.9

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

   7. Applied rewrites 59.9%

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

Alternative 10: 66.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+53}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, b \cdot y\right) + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.15e+41)
     t_1
     (if (<= t 1.1e+53) (+ (+ (fma -2.0 b (* b y)) 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 <= -1.15e+41) {
		tmp = t_1;
	} else if (t <= 1.1e+53) {
		tmp = (fma(-2.0, b, (b * y)) + 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 <= -1.15e+41)
		tmp = t_1;
	elseif (t <= 1.1e+53)
		tmp = Float64(Float64(fma(-2.0, b, Float64(b * y)) + x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.15e+41], t$95$1, If[LessEqual[t, 1.1e+53], N[(N[(N[(-2.0 * b + N[(b * y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1499999999999999e41 or 1.09999999999999999e53 < t

   1. Initial program 94.9%

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

   2. 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 32.9

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

   4. Applied rewrites 32.9%

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

   if -1.1499999999999999e41 < t < 1.09999999999999999e53

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 47.2

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

   10. Applied rewrites 47.2%

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

Alternative 11: 66.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.15e+41)
     t_1
     (if (<= t 1.1e+53) (+ (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 <= -1.15e+41) {
		tmp = t_1;
	} else if (t <= 1.1e+53) {
		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 <= -1.15e+41)
		tmp = t_1;
	elseif (t <= 1.1e+53)
		tmp = Float64(fma(Float64(y - 2.0), b, x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.15e+41], t$95$1, If[LessEqual[t, 1.1e+53], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1499999999999999e41 or 1.09999999999999999e53 < t

   1. Initial program 94.9%

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

   2. 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 32.9

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

   4. Applied rewrites 32.9%

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

   if -1.1499999999999999e41 < t < 1.09999999999999999e53

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-neg.f64 N/A

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

      5. add-flip-rev N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. lift-fma.f64 N/A

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

      12. lift--.f64 47.2

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

   9. Applied rewrites 47.2%

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

Alternative 12: 62.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \left(-\left(\left(t + y\right) - 2\right)\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+38}:\\ \;\;\;\;x - a \cdot \left(t - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b) (- (- (+ t y) 2.0)))))
   (if (<= b -4e+48) t_1 (if (<= b 2.3e+38) (- 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 * -((t + y) - 2.0);
	double tmp;
	if (b <= -4e+48) {
		tmp = t_1;
	} else if (b <= 2.3e+38) {
		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 * -((t + y) - 2.0d0)
    if (b <= (-4d+48)) then
        tmp = t_1
    else if (b <= 2.3d+38) 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 * -((t + y) - 2.0);
	double tmp;
	if (b <= -4e+48) {
		tmp = t_1;
	} else if (b <= 2.3e+38) {
		tmp = x - (a * (t - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -b * -((t + y) - 2.0)
	tmp = 0
	if b <= -4e+48:
		tmp = t_1
	elif b <= 2.3e+38:
		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) * Float64(-Float64(Float64(t + y) - 2.0)))
	tmp = 0.0
	if (b <= -4e+48)
		tmp = t_1;
	elseif (b <= 2.3e+38)
		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 * -((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -4e+48)
		tmp = t_1;
	elseif (b <= 2.3e+38)
		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[((-b) * (-N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[b, -4e+48], t$95$1, If[LessEqual[b, 2.3e+38], N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.00000000000000018e48 or 2.3000000000000001e38 < b

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   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 36.5

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

   7. Applied rewrites 36.5%

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

   if -4.00000000000000018e48 < b < 2.3000000000000001e38

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   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. lift--.f64 N/A

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

      3. lift-*.f64 43.0

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

   10. Applied rewrites 43.0%

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

Alternative 13: 56.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+53}:\\ \;\;\;\;x + \left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -3.7e+39)
     t_1
     (if (<= t 1.7e-20)
       (fma (- y 2.0) b a)
       (if (<= t 1.1e+53) (+ x (* (- 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 <= -3.7e+39) {
		tmp = t_1;
	} else if (t <= 1.7e-20) {
		tmp = fma((y - 2.0), b, a);
	} else if (t <= 1.1e+53) {
		tmp = x + (-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 <= -3.7e+39)
		tmp = t_1;
	elseif (t <= 1.7e-20)
		tmp = fma(Float64(y - 2.0), b, a);
	elseif (t <= 1.1e+53)
		tmp = Float64(x + Float64(Float64(-y) * z));
	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, -3.7e+39], t$95$1, If[LessEqual[t, 1.7e-20], N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision], If[LessEqual[t, 1.1e+53], N[(x + N[((-y) * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.70000000000000012e39 or 1.09999999999999999e53 < t

   1. Initial program 94.9%

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

   2. 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 32.9

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

   4. Applied rewrites 32.9%

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

   if -3.70000000000000012e39 < t < 1.6999999999999999e-20

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 33.0

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

   10. Applied rewrites 33.0%

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

   if 1.6999999999999999e-20 < t < 1.09999999999999999e53

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 68.1

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

   7. Applied rewrites 68.1%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 33.7

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

   10. Applied rewrites 33.7%

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

Alternative 14: 51.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2.35 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-105}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-20}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+53}:\\ \;\;\;\;x + \left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -2.35e+43)
     t_1
     (if (<= t -1.12e-105)
       (* (- b z) y)
       (if (<= t 1.7e-20)
         (+ a x)
         (if (<= t 1.1e+53) (+ x (* (- 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 <= -2.35e+43) {
		tmp = t_1;
	} else if (t <= -1.12e-105) {
		tmp = (b - z) * y;
	} else if (t <= 1.7e-20) {
		tmp = a + x;
	} else if (t <= 1.1e+53) {
		tmp = x + (-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 <= (-2.35d+43)) then
        tmp = t_1
    else if (t <= (-1.12d-105)) then
        tmp = (b - z) * y
    else if (t <= 1.7d-20) then
        tmp = a + x
    else if (t <= 1.1d+53) then
        tmp = x + (-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 <= -2.35e+43) {
		tmp = t_1;
	} else if (t <= -1.12e-105) {
		tmp = (b - z) * y;
	} else if (t <= 1.7e-20) {
		tmp = a + x;
	} else if (t <= 1.1e+53) {
		tmp = x + (-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 <= -2.35e+43:
		tmp = t_1
	elif t <= -1.12e-105:
		tmp = (b - z) * y
	elif t <= 1.7e-20:
		tmp = a + x
	elif t <= 1.1e+53:
		tmp = x + (-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 <= -2.35e+43)
		tmp = t_1;
	elseif (t <= -1.12e-105)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 1.7e-20)
		tmp = Float64(a + x);
	elseif (t <= 1.1e+53)
		tmp = Float64(x + Float64(Float64(-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 <= -2.35e+43)
		tmp = t_1;
	elseif (t <= -1.12e-105)
		tmp = (b - z) * y;
	elseif (t <= 1.7e-20)
		tmp = a + x;
	elseif (t <= 1.1e+53)
		tmp = x + (-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, -2.35e+43], t$95$1, If[LessEqual[t, -1.12e-105], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.7e-20], N[(a + x), $MachinePrecision], If[LessEqual[t, 1.1e+53], N[(x + N[((-y) * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.34999999999999999e43 or 1.09999999999999999e53 < t

   1. Initial program 94.9%

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

   2. 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 32.9

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

   4. Applied rewrites 32.9%

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

   if -2.34999999999999999e43 < t < -1.11999999999999995e-105

   1. Initial program 94.9%

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

   2. 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 33.1

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

   4. Applied rewrites 33.1%

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

   if -1.11999999999999995e-105 < t < 1.6999999999999999e-20

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 25.4

         \[\leadsto a + x \]

   10. Applied rewrites 25.4%

       \[\leadsto a + x \]

   if 1.6999999999999999e-20 < t < 1.09999999999999999e53

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 68.1

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

   7. Applied rewrites 68.1%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 33.7

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

   10. Applied rewrites 33.7%

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

Alternative 15: 51.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2.35 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-16}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)) (t_2 (* (- b a) t)))
   (if (<= t -2.35e+43)
     t_2
     (if (<= t -1.12e-105)
       t_1
       (if (<= t 2.05e-16) (+ a x) (if (<= t 5.8e+31) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -2.35e+43) {
		tmp = t_2;
	} else if (t <= -1.12e-105) {
		tmp = t_1;
	} else if (t <= 2.05e-16) {
		tmp = a + x;
	} else if (t <= 5.8e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b - z) * y
    t_2 = (b - a) * t
    if (t <= (-2.35d+43)) then
        tmp = t_2
    else if (t <= (-1.12d-105)) then
        tmp = t_1
    else if (t <= 2.05d-16) then
        tmp = a + x
    else if (t <= 5.8d+31) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -2.35e+43) {
		tmp = t_2;
	} else if (t <= -1.12e-105) {
		tmp = t_1;
	} else if (t <= 2.05e-16) {
		tmp = a + x;
	} else if (t <= 5.8e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	t_2 = (b - a) * t
	tmp = 0
	if t <= -2.35e+43:
		tmp = t_2
	elif t <= -1.12e-105:
		tmp = t_1
	elif t <= 2.05e-16:
		tmp = a + x
	elif t <= 5.8e+31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -2.35e+43)
		tmp = t_2;
	elseif (t <= -1.12e-105)
		tmp = t_1;
	elseif (t <= 2.05e-16)
		tmp = Float64(a + x);
	elseif (t <= 5.8e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	t_2 = (b - a) * t;
	tmp = 0.0;
	if (t <= -2.35e+43)
		tmp = t_2;
	elseif (t <= -1.12e-105)
		tmp = t_1;
	elseif (t <= 2.05e-16)
		tmp = a + x;
	elseif (t <= 5.8e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2.35e+43], t$95$2, If[LessEqual[t, -1.12e-105], t$95$1, If[LessEqual[t, 2.05e-16], N[(a + x), $MachinePrecision], If[LessEqual[t, 5.8e+31], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.34999999999999999e43 or 5.8000000000000001e31 < t

   1. Initial program 94.9%

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

   2. 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 32.9

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

   4. Applied rewrites 32.9%

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

   if -2.34999999999999999e43 < t < -1.11999999999999995e-105 or 2.05000000000000003e-16 < t < 5.8000000000000001e31

   1. Initial program 94.9%

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

   2. 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 33.1

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

   4. Applied rewrites 33.1%

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

   if -1.11999999999999995e-105 < t < 2.05000000000000003e-16

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 25.4

         \[\leadsto a + x \]

   10. Applied rewrites 25.4%

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

Alternative 16: 49.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-71}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+53}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -3.7e+39)
     t_1
     (if (<= t -4.6e-71) (* (- y 2.0) b) (if (<= t 1.02e+53) (+ a x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -3.7e+39) {
		tmp = t_1;
	} else if (t <= -4.6e-71) {
		tmp = (y - 2.0) * b;
	} else if (t <= 1.02e+53) {
		tmp = a + x;
	} 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 <= (-3.7d+39)) then
        tmp = t_1
    else if (t <= (-4.6d-71)) then
        tmp = (y - 2.0d0) * b
    else if (t <= 1.02d+53) then
        tmp = a + x
    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 <= -3.7e+39) {
		tmp = t_1;
	} else if (t <= -4.6e-71) {
		tmp = (y - 2.0) * b;
	} else if (t <= 1.02e+53) {
		tmp = a + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -3.7e+39:
		tmp = t_1
	elif t <= -4.6e-71:
		tmp = (y - 2.0) * b
	elif t <= 1.02e+53:
		tmp = a + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -3.7e+39)
		tmp = t_1;
	elseif (t <= -4.6e-71)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (t <= 1.02e+53)
		tmp = Float64(a + x);
	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 <= -3.7e+39)
		tmp = t_1;
	elseif (t <= -4.6e-71)
		tmp = (y - 2.0) * b;
	elseif (t <= 1.02e+53)
		tmp = a + x;
	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, -3.7e+39], t$95$1, If[LessEqual[t, -4.6e-71], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 1.02e+53], N[(a + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.70000000000000012e39 or 1.01999999999999999e53 < t

   1. Initial program 94.9%

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

   2. 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 32.9

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

   4. Applied rewrites 32.9%

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

   if -3.70000000000000012e39 < t < -4.5999999999999997e-71

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 25.4

         \[\leadsto a + x \]

   10. Applied rewrites 25.4%

       \[\leadsto a + x \]

   11. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 23.8

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

   13. Applied rewrites 23.8%

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

   if -4.5999999999999997e-71 < t < 1.01999999999999999e53

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 25.4

         \[\leadsto a + x \]

   10. Applied rewrites 25.4%

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

Alternative 17: 40.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -7.4 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-275}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+34}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+89}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -7.4e+56)
     t_1
     (if (<= a 8e-275)
       (* (- y 2.0) b)
       (if (<= a 1.2e+34) (* (- 1.0 y) z) (if (<= a 5.5e+89) (+ a x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -7.4e+56) {
		tmp = t_1;
	} else if (a <= 8e-275) {
		tmp = (y - 2.0) * b;
	} else if (a <= 1.2e+34) {
		tmp = (1.0 - y) * z;
	} else if (a <= 5.5e+89) {
		tmp = a + x;
	} 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 - t) * a
    if (a <= (-7.4d+56)) then
        tmp = t_1
    else if (a <= 8d-275) then
        tmp = (y - 2.0d0) * b
    else if (a <= 1.2d+34) then
        tmp = (1.0d0 - y) * z
    else if (a <= 5.5d+89) then
        tmp = a + x
    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 - t) * a;
	double tmp;
	if (a <= -7.4e+56) {
		tmp = t_1;
	} else if (a <= 8e-275) {
		tmp = (y - 2.0) * b;
	} else if (a <= 1.2e+34) {
		tmp = (1.0 - y) * z;
	} else if (a <= 5.5e+89) {
		tmp = a + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - t) * a
	tmp = 0
	if a <= -7.4e+56:
		tmp = t_1
	elif a <= 8e-275:
		tmp = (y - 2.0) * b
	elif a <= 1.2e+34:
		tmp = (1.0 - y) * z
	elif a <= 5.5e+89:
		tmp = a + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (a <= -7.4e+56)
		tmp = t_1;
	elseif (a <= 8e-275)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (a <= 1.2e+34)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (a <= 5.5e+89)
		tmp = Float64(a + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - t) * a;
	tmp = 0.0;
	if (a <= -7.4e+56)
		tmp = t_1;
	elseif (a <= 8e-275)
		tmp = (y - 2.0) * b;
	elseif (a <= 1.2e+34)
		tmp = (1.0 - y) * z;
	elseif (a <= 5.5e+89)
		tmp = a + x;
	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 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -7.4e+56], t$95$1, If[LessEqual[a, 8e-275], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[a, 1.2e+34], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, 5.5e+89], N[(a + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.39999999999999994e56 or 5.49999999999999976e89 < a

   1. Initial program 94.9%

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

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

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

      7. lower--.f64 28.8

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

   4. Applied rewrites 28.8%

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

   if -7.39999999999999994e56 < a < 7.99999999999999947e-275

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 25.4

         \[\leadsto a + x \]

   10. Applied rewrites 25.4%

       \[\leadsto a + x \]

   11. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 23.8

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

   13. Applied rewrites 23.8%

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

   if 7.99999999999999947e-275 < a < 1.19999999999999993e34

   1. Initial program 94.9%

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

   2. Taylor expanded in z around inf

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

      1. sub-negate-rev N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z \]

      6. sub-negate-rev N/A

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

      7. lower--.f64 28.4

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

   4. Applied rewrites 28.4%

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

   if 1.19999999999999993e34 < a < 5.49999999999999976e89

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 25.4

         \[\leadsto a + x \]

   10. Applied rewrites 25.4%

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

Alternative 18: 39.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -7.4 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-304}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+132}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -7.4e+56)
     t_1
     (if (<= a 5.8e-304) (* (- y 2.0) b) (if (<= a 9.5e+132) (+ z x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -7.4e+56) {
		tmp = t_1;
	} else if (a <= 5.8e-304) {
		tmp = (y - 2.0) * b;
	} else if (a <= 9.5e+132) {
		tmp = z + x;
	} 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 - t) * a
    if (a <= (-7.4d+56)) then
        tmp = t_1
    else if (a <= 5.8d-304) then
        tmp = (y - 2.0d0) * b
    else if (a <= 9.5d+132) then
        tmp = z + x
    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 - t) * a;
	double tmp;
	if (a <= -7.4e+56) {
		tmp = t_1;
	} else if (a <= 5.8e-304) {
		tmp = (y - 2.0) * b;
	} else if (a <= 9.5e+132) {
		tmp = z + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - t) * a
	tmp = 0
	if a <= -7.4e+56:
		tmp = t_1
	elif a <= 5.8e-304:
		tmp = (y - 2.0) * b
	elif a <= 9.5e+132:
		tmp = z + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (a <= -7.4e+56)
		tmp = t_1;
	elseif (a <= 5.8e-304)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (a <= 9.5e+132)
		tmp = Float64(z + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - t) * a;
	tmp = 0.0;
	if (a <= -7.4e+56)
		tmp = t_1;
	elseif (a <= 5.8e-304)
		tmp = (y - 2.0) * b;
	elseif (a <= 9.5e+132)
		tmp = z + x;
	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 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -7.4e+56], t$95$1, If[LessEqual[a, 5.8e-304], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[a, 9.5e+132], N[(z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.39999999999999994e56 or 9.5000000000000005e132 < a

   1. Initial program 94.9%

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

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

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

      7. lower--.f64 28.8

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

   4. Applied rewrites 28.8%

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

   if -7.39999999999999994e56 < a < 5.8e-304

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 25.4

         \[\leadsto a + x \]

   10. Applied rewrites 25.4%

       \[\leadsto a + x \]

   11. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 23.8

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

   13. Applied rewrites 23.8%

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

   if 5.8e-304 < a < 9.5000000000000005e132

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lift-neg.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-flip-reverse N/A

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

      12. *-commutative N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift--.f64 69.1

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

   7. Applied rewrites 69.1%

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

   8. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 46.0

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

   10. Applied rewrites 46.0%

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

   11. Taylor expanded in b around 0

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

       1. +-commutative N/A

          \[\leadsto z + x \]

       2. lower-+.f64 25.1

          \[\leadsto z + x \]

   13. Applied rewrites 25.1%

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

Alternative 19: 39.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-t\right) \cdot a\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+53}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t) a)))
   (if (<= t -8.5e+39)
     t_1
     (if (<= t 1.02e+53) (+ a x) (if (<= t 1.35e+190) t_1 (* b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -t * a;
	double tmp;
	if (t <= -8.5e+39) {
		tmp = t_1;
	} else if (t <= 1.02e+53) {
		tmp = a + x;
	} else if (t <= 1.35e+190) {
		tmp = t_1;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -t * a
    if (t <= (-8.5d+39)) then
        tmp = t_1
    else if (t <= 1.02d+53) then
        tmp = a + x
    else if (t <= 1.35d+190) then
        tmp = t_1
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -t * a;
	double tmp;
	if (t <= -8.5e+39) {
		tmp = t_1;
	} else if (t <= 1.02e+53) {
		tmp = a + x;
	} else if (t <= 1.35e+190) {
		tmp = t_1;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -t * a
	tmp = 0
	if t <= -8.5e+39:
		tmp = t_1
	elif t <= 1.02e+53:
		tmp = a + x
	elif t <= 1.35e+190:
		tmp = t_1
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-t) * a)
	tmp = 0.0
	if (t <= -8.5e+39)
		tmp = t_1;
	elseif (t <= 1.02e+53)
		tmp = Float64(a + x);
	elseif (t <= 1.35e+190)
		tmp = t_1;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -t * a;
	tmp = 0.0;
	if (t <= -8.5e+39)
		tmp = t_1;
	elseif (t <= 1.02e+53)
		tmp = a + x;
	elseif (t <= 1.35e+190)
		tmp = t_1;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-t) * a), $MachinePrecision]}, If[LessEqual[t, -8.5e+39], t$95$1, If[LessEqual[t, 1.02e+53], N[(a + x), $MachinePrecision], If[LessEqual[t, 1.35e+190], t$95$1, N[(b * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.49999999999999971e39 or 1.01999999999999999e53 < t < 1.35000000000000002e190

   1. Initial program 94.9%

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

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

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

      7. lower--.f64 28.8

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

   4. Applied rewrites 28.8%

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

   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 19.8

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

   7. Applied rewrites 19.8%

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

   if -8.49999999999999971e39 < t < 1.01999999999999999e53

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 25.4

         \[\leadsto a + x \]

   10. Applied rewrites 25.4%

       \[\leadsto a + x \]

   if 1.35000000000000002e190 < t

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lift-neg.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-flip-reverse N/A

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

      12. *-commutative N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift--.f64 69.1

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

   7. Applied rewrites 69.1%

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

   8. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 46.0

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

   10. Applied rewrites 46.0%

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

   11. Taylor expanded in t around inf

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

       1. lower-*.f64 17.0

          \[\leadsto b \cdot t \]

   13. Applied rewrites 17.0%

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

Alternative 20: 37.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 2\right) \cdot b\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+78}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 2.0) b)))
   (if (<= b -4.8e+64) t_1 (if (<= b 4e+78) (+ a x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 2.0) * b;
	double tmp;
	if (b <= -4.8e+64) {
		tmp = t_1;
	} else if (b <= 4e+78) {
		tmp = a + x;
	} 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 = (y - 2.0d0) * b
    if (b <= (-4.8d+64)) then
        tmp = t_1
    else if (b <= 4d+78) then
        tmp = a + x
    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 = (y - 2.0) * b;
	double tmp;
	if (b <= -4.8e+64) {
		tmp = t_1;
	} else if (b <= 4e+78) {
		tmp = a + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y - 2.0) * b
	tmp = 0
	if b <= -4.8e+64:
		tmp = t_1
	elif b <= 4e+78:
		tmp = a + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 2.0) * b)
	tmp = 0.0
	if (b <= -4.8e+64)
		tmp = t_1;
	elseif (b <= 4e+78)
		tmp = Float64(a + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y - 2.0) * b;
	tmp = 0.0;
	if (b <= -4.8e+64)
		tmp = t_1;
	elseif (b <= 4e+78)
		tmp = a + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -4.8e+64], t$95$1, If[LessEqual[b, 4e+78], N[(a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.79999999999999999e64 or 4.00000000000000003e78 < b

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 25.4

         \[\leadsto a + x \]

   10. Applied rewrites 25.4%

       \[\leadsto a + x \]

   11. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 23.8

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

   13. Applied rewrites 23.8%

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

   if -4.79999999999999999e64 < b < 4.00000000000000003e78

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 25.4

         \[\leadsto a + x \]

   10. Applied rewrites 25.4%

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

Alternative 21: 34.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+298}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b))))
   (if (<= t_1 -2e+298) (* b y) (if (<= t_1 1e+307) (+ a x) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -2e+298) {
		tmp = b * y;
	} else if (t_1 <= 1e+307) {
		tmp = a + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
    if (t_1 <= (-2d+298)) then
        tmp = b * y
    else if (t_1 <= 1d+307) then
        tmp = a + x
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -2e+298) {
		tmp = b * y;
	} else if (t_1 <= 1e+307) {
		tmp = a + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)
	tmp = 0
	if t_1 <= -2e+298:
		tmp = b * y
	elif t_1 <= 1e+307:
		tmp = a + x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (t_1 <= -2e+298)
		tmp = Float64(b * y);
	elseif (t_1 <= 1e+307)
		tmp = Float64(a + x);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (t_1 <= -2e+298)
		tmp = b * y;
	elseif (t_1 <= 1e+307)
		tmp = a + x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+298], N[(b * y), $MachinePrecision], If[LessEqual[t$95$1, 1e+307], N[(a + x), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 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)) < -1.9999999999999999e298

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 17.9

         \[\leadsto b \cdot y \]

   10. Applied rewrites 17.9%

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

   if -1.9999999999999999e298 < (+.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)) < 9.99999999999999986e306

   1. Initial program 94.9%

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

   2. 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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 73.3

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

   4. Applied rewrites 73.3%

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

   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 47.2

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

   7. Applied rewrites 47.2%

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

   8. Taylor expanded in b around 0

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

      1. lower-+.f64 25.4

         \[\leadsto a + x \]

   10. Applied rewrites 25.4%

       \[\leadsto a + x \]

   if 9.99999999999999986e306 < (+.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 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lift-neg.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-flip-reverse N/A

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

      12. *-commutative N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift--.f64 69.1

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

   7. Applied rewrites 69.1%

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

   8. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 46.0

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

   10. Applied rewrites 46.0%

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

   11. Taylor expanded in t around inf

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

       1. lower-*.f64 17.0

          \[\leadsto b \cdot t \]

   13. Applied rewrites 17.0%

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

Alternative 22: 32.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+229}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+53}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.8e+229) (* b t) (if (<= t 4.5e+53) (+ a x) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.8e+229) {
		tmp = b * t;
	} else if (t <= 4.5e+53) {
		tmp = a + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5.8d+229)) then
        tmp = b * t
    else if (t <= 4.5d+53) then
        tmp = a + x
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.8e+229) {
		tmp = b * t;
	} else if (t <= 4.5e+53) {
		tmp = a + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.8e+229:
		tmp = b * t
	elif t <= 4.5e+53:
		tmp = a + x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.8e+229)
		tmp = Float64(b * t);
	elseif (t <= 4.5e+53)
		tmp = Float64(a + x);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5.8e+229)
		tmp = b * t;
	elseif (t <= 4.5e+53)
		tmp = a + x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.8e+229], N[(b * t), $MachinePrecision], If[LessEqual[t, 4.5e+53], N[(a + x), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.79999999999999963e229 or 4.5000000000000002e53 < t

   1. Initial program 94.9%

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

   2. 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 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lift-neg.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-flip-reverse N/A

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

      12. *-commutative N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift--.f64 69.1

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

   7. Applied rewrites 69.1%

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

   8. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 46.0

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

   10. Applied rewrites 46.0%

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

   11. Taylor expanded in t around inf

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

       1. lower-*.f64 17.0

          \[\leadsto b \cdot t \]

   13. Applied rewrites 17.0%

       \[\leadsto b \cdot t \]

   if -5.79999999999999963e229 < t < 4.5000000000000002e53

   1. Initial program 94.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. 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

         \[\leadsto \left(\left(\left(t + y\right) - 2\right) \cdot b + x\right) - a \cdot \left(t - 1\right) \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - a \cdot \left(t - 1\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right) - \color{blue}{a} \cdot \left(t - 1\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right) - a \cdot \left(t - 1\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - a \cdot \left(t - 1\right) \]

      8. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - a \cdot \left(t - 1\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot \color{blue}{a} \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot a \]

      11. lift-*.f64 73.3

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot \color{blue}{a} \]

   4. Applied rewrites 73.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot a} \]

   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 47.2

         \[\leadsto \mathsf{fma}\left(y - 2, b, x\right) - \left(-a\right) \]

   7. Applied rewrites 47.2%

      \[\leadsto \mathsf{fma}\left(y - 2, b, x\right) - \color{blue}{\left(-a\right)} \]

   8. Taylor expanded in b around 0

      \[\leadsto a + x \]
   9. Step-by-step derivation

      1. lower-+.f64 25.4

         \[\leadsto a + x \]

   10. Applied rewrites 25.4%

       \[\leadsto a + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 31.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+91}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;a \leq 56000:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;a + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -8e+91) (+ a x) (if (<= a 56000.0) (+ z x) (+ a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8e+91) {
		tmp = a + x;
	} else if (a <= 56000.0) {
		tmp = z + x;
	} else {
		tmp = a + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-8d+91)) then
        tmp = a + x
    else if (a <= 56000.0d0) then
        tmp = z + x
    else
        tmp = a + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8e+91) {
		tmp = a + x;
	} else if (a <= 56000.0) {
		tmp = z + x;
	} else {
		tmp = a + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -8e+91:
		tmp = a + x
	elif a <= 56000.0:
		tmp = z + x
	else:
		tmp = a + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -8e+91)
		tmp = Float64(a + x);
	elseif (a <= 56000.0)
		tmp = Float64(z + x);
	else
		tmp = Float64(a + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -8e+91)
		tmp = a + x;
	elseif (a <= 56000.0)
		tmp = z + x;
	else
		tmp = a + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -8e+91], N[(a + x), $MachinePrecision], If[LessEqual[a, 56000.0], N[(z + x), $MachinePrecision], N[(a + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.00000000000000064e91 or 56000 < a

   1. Initial program 94.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. 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

         \[\leadsto \left(\left(\left(t + y\right) - 2\right) \cdot b + x\right) - a \cdot \left(t - 1\right) \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - a \cdot \left(t - 1\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right) - \color{blue}{a} \cdot \left(t - 1\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right) - a \cdot \left(t - 1\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - a \cdot \left(t - 1\right) \]

      8. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - a \cdot \left(t - 1\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot \color{blue}{a} \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot a \]

      11. lift-*.f64 73.3

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot \color{blue}{a} \]

   4. Applied rewrites 73.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot a} \]

   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 47.2

         \[\leadsto \mathsf{fma}\left(y - 2, b, x\right) - \left(-a\right) \]

   7. Applied rewrites 47.2%

      \[\leadsto \mathsf{fma}\left(y - 2, b, x\right) - \color{blue}{\left(-a\right)} \]

   8. Taylor expanded in b around 0

      \[\leadsto a + x \]
   9. Step-by-step derivation

      1. lower-+.f64 25.4

         \[\leadsto a + x \]

   10. Applied rewrites 25.4%

       \[\leadsto a + x \]

   if -8.00000000000000064e91 < a < 56000

   1. Initial program 94.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. 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 96.0

          \[\leadsto x + \left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) - \mathsf{fma}\left(t - 1, a, -z\right)\right) \]

   4. Applied rewrites 96.0%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) - \mathsf{fma}\left(t - 1, a, -z\right)\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(x + b \cdot \left(t - 2\right)\right) - \left(\left(\mathsf{neg}\left(z\right)\right) + \color{blue}{a} \cdot \left(t - 1\right)\right) \]

      2. lift-neg.f64 N/A

         \[\leadsto \left(x + b \cdot \left(t - 2\right)\right) - \left(\left(-z\right) + \color{blue}{a} \cdot \left(t - 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(t - 2\right)\right) - \left(a \cdot \left(t - 1\right) + \color{blue}{\left(-z\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(t - 2\right)\right) - \left(\left(t - 1\right) \cdot a + \left(-\color{blue}{z}\right)\right) \]

      5. lift-neg.f64 N/A

         \[\leadsto \left(x + b \cdot \left(t - 2\right)\right) - \left(\left(t - 1\right) \cdot a + \left(\mathsf{neg}\left(z\right)\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto \left(x + b \cdot \left(t - 2\right)\right) - \color{blue}{\left(\left(t - 1\right) \cdot a + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      7. +-commutative N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) + x\right) - \left(\color{blue}{\left(t - 1\right) \cdot a} + \left(\mathsf{neg}\left(z\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(\left(t - 2\right) \cdot b + x\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a + \left(\mathsf{neg}\left(z\right)\right)\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) - \left(\color{blue}{\left(t - 1\right) \cdot a} + \left(\mathsf{neg}\left(z\right)\right)\right) \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a + \left(\mathsf{neg}\left(z\right)\right)\right) \]

      11. sub-flip-reverse N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) - \left(\left(t - 1\right) \cdot a - \color{blue}{z}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) - \left(a \cdot \left(t - 1\right) - z\right) \]

      13. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) - \left(a \cdot \left(t - 1\right) - \color{blue}{z}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) - \left(a \cdot \left(t - 1\right) - z\right) \]

      15. lift--.f64 69.1

          \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) - \left(a \cdot \left(t - 1\right) - z\right) \]

   7. Applied rewrites 69.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, x\right) - \left(a \cdot \left(t - 1\right) - z\right)} \]

   8. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{\left(z + b \cdot \left(t - 2\right)\right)} \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(z + b \cdot \left(t - 2\right)\right) + x \]

      2. lower-+.f64 N/A

         \[\leadsto \left(z + b \cdot \left(t - 2\right)\right) + x \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) + z\right) + x \]

      4. *-commutative N/A

         \[\leadsto \left(\left(t - 2\right) \cdot b + z\right) + x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + x \]

      6. lift--.f64 46.0

         \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + x \]

   10. Applied rewrites 46.0%

       \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \color{blue}{x} \]

   11. Taylor expanded in b around 0

       \[\leadsto x + z \]
   12. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto z + x \]

       2. lower-+.f64 25.1

          \[\leadsto z + x \]

   13. Applied rewrites 25.1%

       \[\leadsto z + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 29.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.18 \cdot 10^{+92}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+166}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.18e+92) a (if (<= a 2.1e+166) (+ z x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.18e+92) {
		tmp = a;
	} else if (a <= 2.1e+166) {
		tmp = z + x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.18d+92)) then
        tmp = a
    else if (a <= 2.1d+166) then
        tmp = z + x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.18e+92) {
		tmp = a;
	} else if (a <= 2.1e+166) {
		tmp = z + x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.18e+92:
		tmp = a
	elif a <= 2.1e+166:
		tmp = z + x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.18e+92)
		tmp = a;
	elseif (a <= 2.1e+166)
		tmp = Float64(z + x);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.18e+92)
		tmp = a;
	elseif (a <= 2.1e+166)
		tmp = z + x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.18e+92], a, If[LessEqual[a, 2.1e+166], N[(z + x), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if a < -1.18e92 or 2.1000000000000001e166 < a

   1. Initial program 94.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   3. Step-by-step derivation

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(t - 1\right)\right) \cdot \color{blue}{a} \]

      4. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(t - 1\right)\right) \cdot \color{blue}{a} \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.8

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.8%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

   5. Taylor expanded in t around 0

      \[\leadsto a \]
   6. Step-by-step derivation

   7. Applied rewrites 11.2%

      \[\leadsto a \]

   if -1.18e92 < a < 2.1000000000000001e166

   1. Initial program 94.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. 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 96.0

          \[\leadsto x + \left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) - \mathsf{fma}\left(t - 1, a, -z\right)\right) \]

   4. Applied rewrites 96.0%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) - \mathsf{fma}\left(t - 1, a, -z\right)\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(x + b \cdot \left(t - 2\right)\right) - \left(\left(\mathsf{neg}\left(z\right)\right) + \color{blue}{a} \cdot \left(t - 1\right)\right) \]

      2. lift-neg.f64 N/A

         \[\leadsto \left(x + b \cdot \left(t - 2\right)\right) - \left(\left(-z\right) + \color{blue}{a} \cdot \left(t - 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(t - 2\right)\right) - \left(a \cdot \left(t - 1\right) + \color{blue}{\left(-z\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(t - 2\right)\right) - \left(\left(t - 1\right) \cdot a + \left(-\color{blue}{z}\right)\right) \]

      5. lift-neg.f64 N/A

         \[\leadsto \left(x + b \cdot \left(t - 2\right)\right) - \left(\left(t - 1\right) \cdot a + \left(\mathsf{neg}\left(z\right)\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto \left(x + b \cdot \left(t - 2\right)\right) - \color{blue}{\left(\left(t - 1\right) \cdot a + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      7. +-commutative N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) + x\right) - \left(\color{blue}{\left(t - 1\right) \cdot a} + \left(\mathsf{neg}\left(z\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(\left(t - 2\right) \cdot b + x\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a + \left(\mathsf{neg}\left(z\right)\right)\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) - \left(\color{blue}{\left(t - 1\right) \cdot a} + \left(\mathsf{neg}\left(z\right)\right)\right) \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a + \left(\mathsf{neg}\left(z\right)\right)\right) \]

      11. sub-flip-reverse N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) - \left(\left(t - 1\right) \cdot a - \color{blue}{z}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) - \left(a \cdot \left(t - 1\right) - z\right) \]

      13. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) - \left(a \cdot \left(t - 1\right) - \color{blue}{z}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) - \left(a \cdot \left(t - 1\right) - z\right) \]

      15. lift--.f64 69.1

          \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) - \left(a \cdot \left(t - 1\right) - z\right) \]

   7. Applied rewrites 69.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, x\right) - \left(a \cdot \left(t - 1\right) - z\right)} \]

   8. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{\left(z + b \cdot \left(t - 2\right)\right)} \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(z + b \cdot \left(t - 2\right)\right) + x \]

      2. lower-+.f64 N/A

         \[\leadsto \left(z + b \cdot \left(t - 2\right)\right) + x \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) + z\right) + x \]

      4. *-commutative N/A

         \[\leadsto \left(\left(t - 2\right) \cdot b + z\right) + x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + x \]

      6. lift--.f64 46.0

         \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + x \]

   10. Applied rewrites 46.0%

       \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \color{blue}{x} \]

   11. Taylor expanded in b around 0

       \[\leadsto x + z \]
   12. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto z + x \]

       2. lower-+.f64 25.1

          \[\leadsto z + x \]

   13. Applied rewrites 25.1%

       \[\leadsto z + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 11.2% accurate, 28.4× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 94.9%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

2. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
3. Step-by-step derivation

   1. sub-negate-rev N/A

      \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

   2. mul-1-neg N/A

      \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right) \]

   3. *-commutative N/A

      \[\leadsto \left(-1 \cdot \left(t - 1\right)\right) \cdot \color{blue}{a} \]

   4. lower-*.f64 N/A

      \[\leadsto \left(-1 \cdot \left(t - 1\right)\right) \cdot \color{blue}{a} \]

   5. mul-1-neg N/A

      \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

   6. sub-negate-rev N/A

      \[\leadsto \left(1 - t\right) \cdot a \]

   7. lower--.f64 28.8

      \[\leadsto \left(1 - t\right) \cdot a \]

4. Applied rewrites 28.8%

   \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

5. Taylor expanded in t around 0

   \[\leadsto a \]
6. Step-by-step derivation

7. Applied rewrites 11.2%

   \[\leadsto a \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025136 
(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)))