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

Percentage Accurate: 95.2% → 96.3%

Time: 5.8s

Alternatives: 23

Speedup: 1.1×

• 36.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2 \cdot 10^{-132}:\\ \;\;\;\;\left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(t - 1, a, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(y - 1, z, -a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 2e-132)
   (- (+ (fma (- b z) y (* (- t 2.0) b)) x) (fma (- t 1.0) a (- z)))
   (- (+ (fma (- b a) t (* (- y 2.0) b)) x) (fma (- y 1.0) z (- a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 2e-132) {
		tmp = (fma((b - z), y, ((t - 2.0) * b)) + x) - fma((t - 1.0), a, -z);
	} else {
		tmp = (fma((b - a), t, ((y - 2.0) * b)) + x) - fma((y - 1.0), z, -a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 2e-132)
		tmp = Float64(Float64(fma(Float64(b - z), y, Float64(Float64(t - 2.0) * b)) + x) - fma(Float64(t - 1.0), a, Float64(-z)));
	else
		tmp = Float64(Float64(fma(Float64(b - a), t, Float64(Float64(y - 2.0) * b)) + x) - fma(Float64(y - 1.0), z, Float64(-a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 2e-132], N[(N[(N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] - N[(N[(y - 1.0), $MachinePrecision] * z + (-a)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2e-132

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.8

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

   5. Applied rewrites 96.8%

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

   if 2e-132 < t

   1. Initial program 94.3%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 95.4

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

   5. Applied rewrites 95.4%

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

Alternative 2: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -6.1 \cdot 10^{+99}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-23}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -6.1e+99)
     (+ x t_1)
     (if (<= b 2.7e-23)
       (- x (fma (- t 1.0) a (* (- y 1.0) z)))
       (+ (fma (- 1.0 t) a x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -6.1e+99) {
		tmp = x + t_1;
	} else if (b <= 2.7e-23) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = fma((1.0 - t), a, x) + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -6.1e+99)
		tmp = Float64(x + t_1);
	elseif (b <= 2.7e-23)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = Float64(fma(Float64(1.0 - t), a, x) + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -6.1e+99], N[(x + t$95$1), $MachinePrecision], If[LessEqual[b, 2.7e-23], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.09999999999999973e99

   1. Initial program 90.6%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 82.4%

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

   if -6.09999999999999973e99 < b < 2.69999999999999985e-23

   1. Initial program 98.4%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. 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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 88.4

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

   5. Applied rewrites 88.4%

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

   if 2.69999999999999985e-23 < b

   1. Initial program 91.3%

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

   3. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift--.f64 91.3

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

   5. Applied rewrites 91.3%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift-fma.f64 N/A

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

      4. lift--.f64 80.9

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

   8. Applied rewrites 80.9%

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

Alternative 3: 55.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -155000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-80}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, z\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-86}:\\ \;\;\;\;x - \left(\left(-a\right) - z\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+19}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -155000000000.0)
     t_1
     (if (<= t -4.4e-80)
       (fma (- y) z z)
       (if (<= t 1.65e-86)
         (- x (- (- a) z))
         (if (<= t 1.05e+19) (* (- b z) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -155000000000.0) {
		tmp = t_1;
	} else if (t <= -4.4e-80) {
		tmp = fma(-y, z, z);
	} else if (t <= 1.65e-86) {
		tmp = x - (-a - z);
	} else if (t <= 1.05e+19) {
		tmp = (b - z) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -155000000000.0)
		tmp = t_1;
	elseif (t <= -4.4e-80)
		tmp = fma(Float64(-y), z, z);
	elseif (t <= 1.65e-86)
		tmp = Float64(x - Float64(Float64(-a) - z));
	elseif (t <= 1.05e+19)
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -155000000000.0], t$95$1, If[LessEqual[t, -4.4e-80], N[((-y) * z + z), $MachinePrecision], If[LessEqual[t, 1.65e-86], N[(x - N[((-a) - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+19], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.55e11 or 1.05e19 < t

   1. Initial program 92.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 65.7

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

   5. Applied rewrites 65.7%

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

   if -1.55e11 < t < -4.4000000000000002e-80

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 31.6

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

   5. Applied rewrites 31.6%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 31.6

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

   8. Applied rewrites 31.6%

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

   if -4.4000000000000002e-80 < t < 1.64999999999999993e-86

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 49.9%

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

   9. Taylor expanded in t around 0

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

       1. lower--.f64 N/A

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

       2. mul-1-neg N/A

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

       3. lower-neg.f64 49.9

          \[\leadsto x - \left(\left(-a\right) - z\right) \]

   11. Applied rewrites 49.9%

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

   if 1.64999999999999993e-86 < t < 1.05e19

   1. Initial program 97.2%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. 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 36.8

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

   5. Applied rewrites 36.8%

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

Alternative 4: 50.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-58}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-246}:\\ \;\;\;\;x - \left(-z\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+103}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -1.45e+15)
     t_1
     (if (<= y -2e-58)
       (* (- 1.0 t) a)
       (if (<= y -1.95e-246)
         (- x (- z))
         (if (<= y 4.8e+103) (* (- b a) t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -1.45e+15) {
		tmp = t_1;
	} else if (y <= -2e-58) {
		tmp = (1.0 - t) * a;
	} else if (y <= -1.95e-246) {
		tmp = x - -z;
	} else if (y <= 4.8e+103) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-1.45d+15)) then
        tmp = t_1
    else if (y <= (-2d-58)) then
        tmp = (1.0d0 - t) * a
    else if (y <= (-1.95d-246)) then
        tmp = x - -z
    else if (y <= 4.8d+103) then
        tmp = (b - a) * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -1.45e+15) {
		tmp = t_1;
	} else if (y <= -2e-58) {
		tmp = (1.0 - t) * a;
	} else if (y <= -1.95e-246) {
		tmp = x - -z;
	} else if (y <= 4.8e+103) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -1.45e+15:
		tmp = t_1
	elif y <= -2e-58:
		tmp = (1.0 - t) * a
	elif y <= -1.95e-246:
		tmp = x - -z
	elif y <= 4.8e+103:
		tmp = (b - a) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -1.45e+15)
		tmp = t_1;
	elseif (y <= -2e-58)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (y <= -1.95e-246)
		tmp = Float64(x - Float64(-z));
	elseif (y <= 4.8e+103)
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -1.45e+15)
		tmp = t_1;
	elseif (y <= -2e-58)
		tmp = (1.0 - t) * a;
	elseif (y <= -1.95e-246)
		tmp = x - -z;
	elseif (y <= 4.8e+103)
		tmp = (b - a) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.45e+15], t$95$1, If[LessEqual[y, -2e-58], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y, -1.95e-246], N[(x - (-z)), $MachinePrecision], If[LessEqual[y, 4.8e+103], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.45e15 or 4.7999999999999997e103 < y

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.0

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

   5. Applied rewrites 69.0%

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

   if -1.45e15 < y < -2.0000000000000001e-58

   1. Initial program 97.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 32.9

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

   5. Applied rewrites 32.9%

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

   if -2.0000000000000001e-58 < y < -1.94999999999999989e-246

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 98.3

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

   5. Applied rewrites 98.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 68.9%

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

   9. Taylor expanded in z around inf

      \[\leadsto x - -1 \cdot \color{blue}{z} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x - \left(\mathsf{neg}\left(z\right)\right) \]

       2. lift-neg.f64 39.1

          \[\leadsto x - \left(-z\right) \]

   11. Applied rewrites 39.1%

       \[\leadsto x - \left(-z\right) \]

   if -1.94999999999999989e-246 < y < 4.7999999999999997e103

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 38.8

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

   5. Applied rewrites 38.8%

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

Alternative 5: 68.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5.4 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.22 \cdot 10^{-54}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+33}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, -z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -5.4e+99)
     t_1
     (if (<= b -2.22e-54)
       (- x (fma z (- y 1.0) (- a)))
       (if (<= b 3.2e+33) (- x (fma (- t 1.0) a (- z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -5.4e+99) {
		tmp = t_1;
	} else if (b <= -2.22e-54) {
		tmp = x - fma(z, (y - 1.0), -a);
	} else if (b <= 3.2e+33) {
		tmp = x - fma((t - 1.0), a, -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -5.4e+99)
		tmp = t_1;
	elseif (b <= -2.22e-54)
		tmp = Float64(x - fma(z, Float64(y - 1.0), Float64(-a)));
	elseif (b <= 3.2e+33)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(-z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -5.4e+99], t$95$1, If[LessEqual[b, -2.22e-54], N[(x - N[(z * N[(y - 1.0), $MachinePrecision] + (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+33], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.39999999999999978e99 or 3.20000000000000017e33 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 73.0

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 73.0

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

   5. Applied rewrites 73.0%

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

   if -5.39999999999999978e99 < b < -2.2200000000000001e-54

   1. Initial program 95.3%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. 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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 67.4

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

   5. Applied rewrites 67.4%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 50.9

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

   8. Applied rewrites 50.9%

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

   if -2.2200000000000001e-54 < b < 3.20000000000000017e33

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.3

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 70.1%

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

Alternative 6: 83.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.1 \cdot 10^{+99}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 10^{+22}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(y - 2, b, b \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.1e+99)
   (+ x (* (- (+ y t) 2.0) b))
   (if (<= b 1e+22)
     (- x (fma (- t 1.0) a (* (- y 1.0) z)))
     (+ x (fma (- y 2.0) b (* b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.1e+99) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (b <= 1e+22) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = x + fma((y - 2.0), b, (b * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.1e+99)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (b <= 1e+22)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = Float64(x + fma(Float64(y - 2.0), b, Float64(b * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.1e+99], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+22], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - 2.0), $MachinePrecision] * b + N[(b * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.09999999999999973e99

   1. Initial program 90.6%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 82.4%

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

   if -6.09999999999999973e99 < b < 1e22

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. 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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 87.5

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

   5. Applied rewrites 87.5%

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

   if 1e22 < b

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 75.0%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. distribute-lft-out N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower-*.f64 73.2

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

   7. Applied rewrites 73.2%

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

Alternative 7: 97.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.2%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift--.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. lift-+.f64 N/A

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

   10. lift--.f64 N/A

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

   11. +-commutative N/A

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

   12. lower-fma.f64 N/A

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

   13. lift--.f64 N/A

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

   14. +-commutative N/A

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

   15. lower-+.f64 N/A

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

   16. associate--l- N/A

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

   17. *-commutative N/A

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

   18. *-commutative N/A

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

4. Applied rewrites 97.6%

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

Alternative 8: 76.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.7 \cdot 10^{+99}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+21}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(y - 2, b, b \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.7e+99)
   (+ x (* (- (+ y t) 2.0) b))
   (if (<= b 6.6e+21)
     (- x (fma (- t 1.0) a (* y z)))
     (+ x (fma (- y 2.0) b (* b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.7e+99) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (b <= 6.6e+21) {
		tmp = x - fma((t - 1.0), a, (y * z));
	} else {
		tmp = x + fma((y - 2.0), b, (b * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.7e+99)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (b <= 6.6e+21)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(y * z)));
	else
		tmp = Float64(x + fma(Float64(y - 2.0), b, Float64(b * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.7e+99], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.6e+21], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - 2.0), $MachinePrecision] * b + N[(b * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.70000000000000003e99

   1. Initial program 90.6%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 82.4%

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

   if -5.70000000000000003e99 < b < 6.6e21

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. 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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 87.5

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

   5. Applied rewrites 87.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 75.4%

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

   if 6.6e21 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 74.9%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. distribute-lft-out N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower-*.f64 73.2

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

   7. Applied rewrites 73.2%

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

Alternative 9: 76.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5.7 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+21}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -5.7e+99)
     t_1
     (if (<= b 6.6e+21) (- x (fma (- t 1.0) a (* y z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -5.7e+99) {
		tmp = t_1;
	} else if (b <= 6.6e+21) {
		tmp = x - fma((t - 1.0), a, (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -5.7e+99)
		tmp = t_1;
	elseif (b <= 6.6e+21)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.7e+99], t$95$1, If[LessEqual[b, 6.6e+21], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.70000000000000003e99 or 6.6e21 < b

   1. Initial program 90.3%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 78.2%

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

   if -5.70000000000000003e99 < b < 6.6e21

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. 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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 87.5

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

   5. Applied rewrites 87.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 75.4%

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

Alternative 10: 50.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-295}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+103}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -8.5e+14)
     t_1
     (if (<= y 3.4e-295)
       (- x (* a t))
       (if (<= y 4.8e+103) (* (- b a) t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -8.5e+14) {
		tmp = t_1;
	} else if (y <= 3.4e-295) {
		tmp = x - (a * t);
	} else if (y <= 4.8e+103) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-8.5d+14)) then
        tmp = t_1
    else if (y <= 3.4d-295) then
        tmp = x - (a * t)
    else if (y <= 4.8d+103) then
        tmp = (b - a) * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -8.5e+14) {
		tmp = t_1;
	} else if (y <= 3.4e-295) {
		tmp = x - (a * t);
	} else if (y <= 4.8e+103) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -8.5e+14:
		tmp = t_1
	elif y <= 3.4e-295:
		tmp = x - (a * t)
	elif y <= 4.8e+103:
		tmp = (b - a) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -8.5e+14)
		tmp = t_1;
	elseif (y <= 3.4e-295)
		tmp = Float64(x - Float64(a * t));
	elseif (y <= 4.8e+103)
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -8.5e+14)
		tmp = t_1;
	elseif (y <= 3.4e-295)
		tmp = x - (a * t);
	elseif (y <= 4.8e+103)
		tmp = (b - a) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -8.5e+14], t$95$1, If[LessEqual[y, 3.4e-295], N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+103], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5e14 or 4.7999999999999997e103 < y

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.0

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

   5. Applied rewrites 69.0%

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

   if -8.5e14 < y < 3.40000000000000007e-295

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 98.1

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

   5. Applied rewrites 98.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 68.2%

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

   9. Taylor expanded in t around inf

      \[\leadsto x - a \cdot \color{blue}{t} \]
   10. Step-by-step derivation

       1. lower-*.f64 38.2

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

   11. Applied rewrites 38.2%

       \[\leadsto x - a \cdot \color{blue}{t} \]

   if 3.40000000000000007e-295 < y < 4.7999999999999997e103

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 38.1

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

   5. Applied rewrites 38.1%

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

Alternative 11: 42.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, z, z\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+48}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- y) z z)))
   (if (<= z -2.2e+98)
     t_1
     (if (<= z -2.05e+30) (* b y) (if (<= z 1.5e+48) (* (- 1.0 t) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-y, z, z);
	double tmp;
	if (z <= -2.2e+98) {
		tmp = t_1;
	} else if (z <= -2.05e+30) {
		tmp = b * y;
	} else if (z <= 1.5e+48) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-y), z, z)
	tmp = 0.0
	if (z <= -2.2e+98)
		tmp = t_1;
	elseif (z <= -2.05e+30)
		tmp = Float64(b * y);
	elseif (z <= 1.5e+48)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-y) * z + z), $MachinePrecision]}, If[LessEqual[z, -2.2e+98], t$95$1, If[LessEqual[z, -2.05e+30], N[(b * y), $MachinePrecision], If[LessEqual[z, 1.5e+48], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000009e98 or 1.5e48 < z

   1. Initial program 91.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 58.8

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

   5. Applied rewrites 58.8%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 58.9

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

   8. Applied rewrites 58.9%

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

   if -2.20000000000000009e98 < z < -2.05000000000000003e30

   1. Initial program 96.6%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. 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 32.8

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

   5. Applied rewrites 32.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 14.1%

      \[\leadsto b \cdot y \]

   if -2.05000000000000003e30 < z < 1.5e48

   1. Initial program 97.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 34.5

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

   5. Applied rewrites 34.5%

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

Alternative 12: 71.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+34}:\\ \;\;\;\;a + t\_1\\ \mathbf{elif}\;b \leq 9.4 \cdot 10^{+20}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, -z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -5.8e+34)
     (+ a t_1)
     (if (<= b 9.4e+20) (- x (fma (- t 1.0) a (- z))) (+ x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -5.8e+34) {
		tmp = a + t_1;
	} else if (b <= 9.4e+20) {
		tmp = x - fma((t - 1.0), a, -z);
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -5.8e+34)
		tmp = Float64(a + t_1);
	elseif (b <= 9.4e+20)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(-z)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -5.8e+34], N[(a + t$95$1), $MachinePrecision], If[LessEqual[b, 9.4e+20], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.8000000000000003e34

   1. Initial program 91.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 76.5

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

   5. Applied rewrites 76.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 74.3%

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

   if -5.8000000000000003e34 < b < 9.4e20

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.1

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

   5. Applied rewrites 99.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 68.6%

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

   if 9.4e20 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 74.9%

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

Alternative 13: 71.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.48 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.4 \cdot 10^{+20}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, -z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1.48e+32)
     t_1
     (if (<= b 9.4e+20) (- x (fma (- t 1.0) a (- z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.48e+32) {
		tmp = t_1;
	} else if (b <= 9.4e+20) {
		tmp = x - fma((t - 1.0), a, -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.48e+32)
		tmp = t_1;
	elseif (b <= 9.4e+20)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(-z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.48e+32], t$95$1, If[LessEqual[b, 9.4e+20], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.4799999999999999e32 or 9.4e20 < b

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 75.5%

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

   if -1.4799999999999999e32 < b < 9.4e20

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.1

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

   5. Applied rewrites 99.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 68.7%

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

Alternative 14: 69.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5.4 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+33}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -5.4e+99)
     t_1
     (if (<= b 4.6e+33) (- x (fma z (- y 1.0) (- a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -5.4e+99) {
		tmp = t_1;
	} else if (b <= 4.6e+33) {
		tmp = x - fma(z, (y - 1.0), -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -5.4e+99)
		tmp = t_1;
	elseif (b <= 4.6e+33)
		tmp = Float64(x - fma(z, Float64(y - 1.0), Float64(-a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -5.4e+99], t$95$1, If[LessEqual[b, 4.6e+33], N[(x - N[(z * N[(y - 1.0), $MachinePrecision] + (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.39999999999999978e99 or 4.60000000000000021e33 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 73.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 73.1

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

   5. Applied rewrites 73.1%

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

   if -5.39999999999999978e99 < b < 4.60000000000000021e33

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. 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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 87.2

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

   5. Applied rewrites 87.2%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 66.5

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

   8. Applied rewrites 66.5%

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

Alternative 15: 35.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+83}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, z\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+212}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.6e+83)
   (* b t)
   (if (<= t 3.5e+19)
     (fma (- y) z z)
     (if (<= t 1.22e+212) (* (- a) t) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.6e+83) {
		tmp = b * t;
	} else if (t <= 3.5e+19) {
		tmp = fma(-y, z, z);
	} else if (t <= 1.22e+212) {
		tmp = -a * t;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.6e+83)
		tmp = Float64(b * t);
	elseif (t <= 3.5e+19)
		tmp = fma(Float64(-y), z, z);
	elseif (t <= 1.22e+212)
		tmp = Float64(Float64(-a) * t);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.6e+83], N[(b * t), $MachinePrecision], If[LessEqual[t, 3.5e+19], N[((-y) * z + z), $MachinePrecision], If[LessEqual[t, 1.22e+212], N[((-a) * t), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6000000000000001e83 or 1.22000000000000005e212 < t

   1. Initial program 89.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 74.8

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 41.0%

      \[\leadsto b \cdot t \]

   if -2.6000000000000001e83 < t < 3.5e19

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.3

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

   5. Applied rewrites 33.3%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 33.3

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

   8. Applied rewrites 33.3%

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

   if 3.5e19 < t < 1.22000000000000005e212

   1. Initial program 94.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 59.4

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

   5. Applied rewrites 59.4%

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

   6. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 34.2

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

   8. Applied rewrites 34.2%

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

Alternative 16: 35.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7200000000:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 0.046:\\ \;\;\;\;x - \left(-z\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+95}:\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7200000000.0)
   (* b y)
   (if (<= y 0.046) (- x (- z)) (if (<= y 2.45e+95) (* b t) (* b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7200000000.0) {
		tmp = b * y;
	} else if (y <= 0.046) {
		tmp = x - -z;
	} else if (y <= 2.45e+95) {
		tmp = b * t;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-7200000000.0d0)) then
        tmp = b * y
    else if (y <= 0.046d0) then
        tmp = x - -z
    else if (y <= 2.45d+95) then
        tmp = b * t
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7200000000.0) {
		tmp = b * y;
	} else if (y <= 0.046) {
		tmp = x - -z;
	} else if (y <= 2.45e+95) {
		tmp = b * t;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7200000000.0:
		tmp = b * y
	elif y <= 0.046:
		tmp = x - -z
	elif y <= 2.45e+95:
		tmp = b * t
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7200000000.0)
		tmp = Float64(b * y);
	elseif (y <= 0.046)
		tmp = Float64(x - Float64(-z));
	elseif (y <= 2.45e+95)
		tmp = Float64(b * t);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7200000000.0)
		tmp = b * y;
	elseif (y <= 0.046)
		tmp = x - -z;
	elseif (y <= 2.45e+95)
		tmp = b * t;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7200000000.0], N[(b * y), $MachinePrecision], If[LessEqual[y, 0.046], N[(x - (-z)), $MachinePrecision], If[LessEqual[y, 2.45e+95], N[(b * t), $MachinePrecision], N[(b * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.2e9 or 2.4499999999999999e95 < y

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. 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 68.2

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

   5. Applied rewrites 68.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 36.3%

      \[\leadsto b \cdot y \]

   if -7.2e9 < y < 0.045999999999999999

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 97.9

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

   5. Applied rewrites 97.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 68.6%

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

   9. Taylor expanded in z around inf

      \[\leadsto x - -1 \cdot \color{blue}{z} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x - \left(\mathsf{neg}\left(z\right)\right) \]

       2. lift-neg.f64 36.6

          \[\leadsto x - \left(-z\right) \]

   11. Applied rewrites 36.6%

       \[\leadsto x - \left(-z\right) \]

   if 0.045999999999999999 < y < 2.4499999999999999e95

   1. Initial program 97.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 34.2

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

   5. Applied rewrites 34.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 19.0%

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

Alternative 17: 25.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -134000000000:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-276}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -134000000000.0)
   (* b t)
   (if (<= t 1.55e-276) z (if (<= t 4e+37) x (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -134000000000.0) {
		tmp = b * t;
	} else if (t <= 1.55e-276) {
		tmp = z;
	} else if (t <= 4e+37) {
		tmp = 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 <= (-134000000000.0d0)) then
        tmp = b * t
    else if (t <= 1.55d-276) then
        tmp = z
    else if (t <= 4d+37) then
        tmp = 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 <= -134000000000.0) {
		tmp = b * t;
	} else if (t <= 1.55e-276) {
		tmp = z;
	} else if (t <= 4e+37) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -134000000000.0:
		tmp = b * t
	elif t <= 1.55e-276:
		tmp = z
	elif t <= 4e+37:
		tmp = x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -134000000000.0)
		tmp = Float64(b * t);
	elseif (t <= 1.55e-276)
		tmp = z;
	elseif (t <= 4e+37)
		tmp = 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 <= -134000000000.0)
		tmp = b * t;
	elseif (t <= 1.55e-276)
		tmp = z;
	elseif (t <= 4e+37)
		tmp = x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -134000000000.0], N[(b * t), $MachinePrecision], If[LessEqual[t, 1.55e-276], z, If[LessEqual[t, 4e+37], x, N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.34e11 or 3.99999999999999982e37 < t

   1. Initial program 92.1%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 66.4

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

   5. Applied rewrites 66.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 34.7%

      \[\leadsto b \cdot t \]

   if -1.34e11 < t < 1.54999999999999995e-276

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.9

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

   5. Applied rewrites 33.9%

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

   6. Taylor expanded in y around 0

      \[\leadsto z \]
   7. Step-by-step derivation

   8. Applied rewrites 14.8%

      \[\leadsto z \]

   if 1.54999999999999995e-276 < t < 3.99999999999999982e37

   1. Initial program 97.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Applied rewrites 20.1%

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

Alternative 18: 61.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+31}:\\ \;\;\;\;x - \mathsf{fma}\left(t, a, -z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -5.8e+34) t_1 (if (<= b 3.5e+31) (- x (fma t a (- z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -5.8e+34) {
		tmp = t_1;
	} else if (b <= 3.5e+31) {
		tmp = x - fma(t, a, -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -5.8e+34)
		tmp = t_1;
	elseif (b <= 3.5e+31)
		tmp = Float64(x - fma(t, a, Float64(-z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -5.8e+34], t$95$1, If[LessEqual[b, 3.5e+31], N[(x - N[(t * a + (-z)), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.8000000000000003e34 or 3.5e31 < b

   1. Initial program 90.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 69.3

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 69.3

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

   5. Applied rewrites 69.3%

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

   if -5.8000000000000003e34 < b < 3.5e31

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.1

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

   5. Applied rewrites 99.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 68.3%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 55.5%

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

Alternative 19: 56.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+31}:\\ \;\;\;\;x - \left(\left(-a\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -1.7e+33) t_1 (if (<= b 3.7e+31) (- x (- (- a) z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.7e+33) {
		tmp = t_1;
	} else if (b <= 3.7e+31) {
		tmp = x - (-a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-1.7d+33)) then
        tmp = t_1
    else if (b <= 3.7d+31) then
        tmp = x - (-a - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.7e+33) {
		tmp = t_1;
	} else if (b <= 3.7e+31) {
		tmp = x - (-a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -1.7e+33:
		tmp = t_1
	elif b <= 3.7e+31:
		tmp = x - (-a - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.7e+33)
		tmp = t_1;
	elseif (b <= 3.7e+31)
		tmp = Float64(x - Float64(Float64(-a) - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.7e+33)
		tmp = t_1;
	elseif (b <= 3.7e+31)
		tmp = x - (-a - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.7e+33], t$95$1, If[LessEqual[b, 3.7e+31], N[(x - N[((-a) - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7e33 or 3.6999999999999998e31 < b

   1. Initial program 90.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 69.3

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 69.3

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

   5. Applied rewrites 69.3%

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

   if -1.7e33 < b < 3.6999999999999998e31

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.1

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

   5. Applied rewrites 99.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 68.4%

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

   9. Taylor expanded in t around 0

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

       1. lower--.f64 N/A

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

       2. mul-1-neg N/A

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

       3. lower-neg.f64 46.0

          \[\leadsto x - \left(\left(-a\right) - z\right) \]

   11. Applied rewrites 46.0%

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

Alternative 20: 49.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -155000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.1 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -155000000000.0) t_1 (if (<= t 9.1e+18) (fma (- y) z 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 <= -155000000000.0) {
		tmp = t_1;
	} else if (t <= 9.1e+18) {
		tmp = fma(-y, z, 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 <= -155000000000.0)
		tmp = t_1;
	elseif (t <= 9.1e+18)
		tmp = fma(Float64(-y), z, 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, -155000000000.0], t$95$1, If[LessEqual[t, 9.1e+18], N[((-y) * z + z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.55e11 or 9.1e18 < t

   1. Initial program 92.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 65.7

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

   5. Applied rewrites 65.7%

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

   if -1.55e11 < t < 9.1e18

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.7

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

   5. Applied rewrites 33.7%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 33.7

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

   8. Applied rewrites 33.7%

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

Alternative 21: 27.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.00028:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+50}:\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -0.00028) (* b t) (if (<= t 1.15e+50) (* b y) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -0.00028) {
		tmp = b * t;
	} else if (t <= 1.15e+50) {
		tmp = b * y;
	} 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 <= (-0.00028d0)) then
        tmp = b * t
    else if (t <= 1.15d+50) then
        tmp = b * y
    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 <= -0.00028) {
		tmp = b * t;
	} else if (t <= 1.15e+50) {
		tmp = b * y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -0.00028:
		tmp = b * t
	elif t <= 1.15e+50:
		tmp = b * y
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -0.00028)
		tmp = Float64(b * t);
	elseif (t <= 1.15e+50)
		tmp = Float64(b * y);
	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 <= -0.00028)
		tmp = b * t;
	elseif (t <= 1.15e+50)
		tmp = b * y;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -0.00028], N[(b * t), $MachinePrecision], If[LessEqual[t, 1.15e+50], N[(b * y), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7999999999999998e-4 or 1.14999999999999998e50 < t

   1. Initial program 92.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 65.6

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

   5. Applied rewrites 65.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 34.3%

      \[\leadsto b \cdot t \]

   if -2.7999999999999998e-4 < t < 1.14999999999999998e50

   1. Initial program 98.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 38.5

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

   5. Applied rewrites 38.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 21.2%

      \[\leadsto b \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 19.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+220}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 450000000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.2e+220) x (if (<= x 450000000000.0) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.2e+220) {
		tmp = x;
	} else if (x <= 450000000000.0) {
		tmp = z;
	} else {
		tmp = 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 (x <= (-8.2d+220)) then
        tmp = x
    else if (x <= 450000000000.0d0) then
        tmp = z
    else
        tmp = 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 (x <= -8.2e+220) {
		tmp = x;
	} else if (x <= 450000000000.0) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.2e+220:
		tmp = x
	elif x <= 450000000000.0:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.2e+220)
		tmp = x;
	elseif (x <= 450000000000.0)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.2e+220)
		tmp = x;
	elseif (x <= 450000000000.0)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.2e+220], x, If[LessEqual[x, 450000000000.0], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.19999999999999962e220 or 4.5e11 < x

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Applied rewrites 32.9%

      \[\leadsto \color{blue}{x} \]

   if -8.19999999999999962e220 < x < 4.5e11

   1. Initial program 95.6%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 31.4

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

   5. Applied rewrites 31.4%

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

   6. Taylor expanded in y around 0

      \[\leadsto z \]
   7. Step-by-step derivation

   8. Applied rewrites 12.8%

      \[\leadsto z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 15.6% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 95.2%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Applied rewrites 15.6%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025089 
(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)))