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

Percentage Accurate: 95.2% → 97.6%

Time: 10.0s

Alternatives: 19

Speedup: 1.1×

• 36.7% 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: 97.6% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (- b a) t (fma (- 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) {
	return fma((b - a), t, fma((y - 2.0), b, (x - fma((y - 1.0), z, -a))));
}

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in t around 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. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. +-commutative N/A

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

   4. associate-+l+ N/A

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

   5. *-commutative N/A

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

   6. associate--l+ N/A

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

   7. +-commutative N/A

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

   8. lower-fma.f64 N/A

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

   9. lower--.f64 N/A

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

   10. +-commutative N/A

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

   11. associate--l+ N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lower--.f64 N/A

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

5. Applied rewrites 99.6%

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

Alternative 2: 43.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+302)))
     (* b y)
     (+ (+ z x) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+302)) {
		tmp = b * y;
	} else {
		tmp = (z + x) + a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+302)) {
		tmp = b * y;
	} else {
		tmp = (z + x) + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+302):
		tmp = b * y
	else:
		tmp = (z + x) + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+302))
		tmp = Float64(b * y);
	else
		tmp = Float64(Float64(z + x) + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+302)))
		tmp = b * y;
	else
		tmp = (z + x) + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+302]], $MachinePrecision]], N[(b * y), $MachinePrecision], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < -inf.0 or 5e302 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 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 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 98.9%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 51.8%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 34.2%

       \[\leadsto b \cdot y \]

   if -inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < 5e302

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 62.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 54.1%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq -\infty \lor \neg \left(\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.7:\\ \;\;\;\;\left(a + \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(-2, b, z\right)\right)\right) + x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+189}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, b \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a (fma (- z) (- y 1.0) x))))
   (if (<= y -2.7e+43)
     t_1
     (if (<= y 2.7)
       (+ (+ a (fma (- b a) t (fma -2.0 b z))) x)
       (if (<= y 1.9e+189) t_1 (fma (- z) y (* b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - t), a, fma(-z, (y - 1.0), x));
	double tmp;
	if (y <= -2.7e+43) {
		tmp = t_1;
	} else if (y <= 2.7) {
		tmp = (a + fma((b - a), t, fma(-2.0, b, z))) + x;
	} else if (y <= 1.9e+189) {
		tmp = t_1;
	} else {
		tmp = fma(-z, y, (b * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - t), a, fma(Float64(-z), Float64(y - 1.0), x))
	tmp = 0.0
	if (y <= -2.7e+43)
		tmp = t_1;
	elseif (y <= 2.7)
		tmp = Float64(Float64(a + fma(Float64(b - a), t, fma(-2.0, b, z))) + x);
	elseif (y <= 1.9e+189)
		tmp = t_1;
	else
		tmp = fma(Float64(-z), y, Float64(b * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a + N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+43], t$95$1, If[LessEqual[y, 2.7], N[(N[(a + N[(N[(b - a), $MachinePrecision] * t + N[(-2.0 * b + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 1.9e+189], t$95$1, N[((-z) * y + N[(b * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7000000000000002e43 or 2.7000000000000002 < y < 1.8999999999999999e189

   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 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 98.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 72.9%

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

   if -2.7000000000000002e43 < y < 2.7000000000000002

   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

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 97.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 98.5%

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

   if 1.8999999999999999e189 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.5

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

   5. Applied rewrites 79.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 79.5%

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

Alternative 4: 86.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+107} \lor \neg \left(z \leq 1.85 \cdot 10^{+27}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.8e+107) (not (<= z 1.85e+27)))
   (fma (- 1.0 t) a (fma (- z) (- y 1.0) x))
   (fma (- b a) t (+ (fma (- y 2.0) b x) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.8e+107) || !(z <= 1.85e+27)) {
		tmp = fma((1.0 - t), a, fma(-z, (y - 1.0), x));
	} else {
		tmp = fma((b - a), t, (fma((y - 2.0), b, x) + a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.8e+107) || !(z <= 1.85e+27))
		tmp = fma(Float64(1.0 - t), a, fma(Float64(-z), Float64(y - 1.0), x));
	else
		tmp = fma(Float64(b - a), t, Float64(fma(Float64(y - 2.0), b, x) + a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.8e+107], N[Not[LessEqual[z, 1.85e+27]], $MachinePrecision]], N[(N[(1.0 - t), $MachinePrecision] * a + N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t + N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999998e107 or 1.85000000000000001e27 < z

   1. Initial program 92.7%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 87.0%

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

   if -3.7999999999999998e107 < z < 1.85000000000000001e27

   1. Initial program 99.4%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.8%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+107} \lor \neg \left(z \leq 1.85 \cdot 10^{+27}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+107} \lor \neg \left(z \leq 1.85 \cdot 10^{+27}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.8e+107) (not (<= z 1.85e+27)))
   (fma (- 1.0 t) a (fma (- z) (- y 1.0) x))
   (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.8e+107) || !(z <= 1.85e+27)) {
		tmp = fma((1.0 - t), a, fma(-z, (y - 1.0), x));
	} else {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.8e+107) || !(z <= 1.85e+27))
		tmp = fma(Float64(1.0 - t), a, fma(Float64(-z), Float64(y - 1.0), x));
	else
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.8e+107], N[Not[LessEqual[z, 1.85e+27]], $MachinePrecision]], N[(N[(1.0 - t), $MachinePrecision] * a + N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999998e107 or 1.85000000000000001e27 < z

   1. Initial program 92.7%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 87.0%

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

   if -3.7999999999999998e107 < z < 1.85000000000000001e27

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 96.8%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+107} \lor \neg \left(z \leq 1.85 \cdot 10^{+27}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+107} \lor \neg \left(z \leq 1.6 \cdot 10^{+27}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.9e+107) (not (<= z 1.6e+27)))
   (fma (- 1.0 t) a (fma (- z) (- y 1.0) x))
   (fma (- a) t (+ (fma (- y 2.0) b x) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.9e+107) || !(z <= 1.6e+27)) {
		tmp = fma((1.0 - t), a, fma(-z, (y - 1.0), x));
	} else {
		tmp = fma(-a, t, (fma((y - 2.0), b, x) + a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.9e+107) || !(z <= 1.6e+27))
		tmp = fma(Float64(1.0 - t), a, fma(Float64(-z), Float64(y - 1.0), x));
	else
		tmp = fma(Float64(-a), t, Float64(fma(Float64(y - 2.0), b, x) + a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.9e+107], N[Not[LessEqual[z, 1.6e+27]], $MachinePrecision]], N[(N[(1.0 - t), $MachinePrecision] * a + N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[((-a) * t + N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.89999999999999988e107 or 1.60000000000000008e27 < z

   1. Initial program 92.7%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 87.0%

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

   if -2.89999999999999988e107 < z < 1.60000000000000008e27

   1. Initial program 99.4%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.8%

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

   9. Taylor expanded in a around inf

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

   11. Applied rewrites 82.8%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+107} \lor \neg \left(z \leq 1.6 \cdot 10^{+27}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+98} \lor \neg \left(b \leq 7.2 \cdot 10^{+67}\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9.8e+98) (not (<= b 7.2e+67)))
   (fma (- b a) t (fma (- y 2.0) b a))
   (fma (- 1.0 t) a (fma (- z) (- y 1.0) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9.8e+98) || !(b <= 7.2e+67)) {
		tmp = fma((b - a), t, fma((y - 2.0), b, a));
	} else {
		tmp = fma((1.0 - t), a, fma(-z, (y - 1.0), x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -9.8e+98) || !(b <= 7.2e+67))
		tmp = fma(Float64(b - a), t, fma(Float64(y - 2.0), b, a));
	else
		tmp = fma(Float64(1.0 - t), a, fma(Float64(-z), Float64(y - 1.0), x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -9.8e+98], N[Not[LessEqual[b, 7.2e+67]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.79999999999999958e98 or 7.1999999999999998e67 < b

   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 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 86.0%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 79.5%

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

   if -9.79999999999999958e98 < b < 7.1999999999999998e67

   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 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 86.5%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+98} \lor \neg \left(b \leq 7.2 \cdot 10^{+67}\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+107} \lor \neg \left(z \leq 7.5 \cdot 10^{+111}\right):\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.9e+107) (not (<= z 7.5e+111)))
   (- x (fma z (- y 1.0) (- a)))
   (fma (- b a) t (fma (- y 2.0) b a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.9e+107) || !(z <= 7.5e+111)) {
		tmp = x - fma(z, (y - 1.0), -a);
	} else {
		tmp = fma((b - a), t, fma((y - 2.0), b, a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.9e+107) || !(z <= 7.5e+111))
		tmp = Float64(x - fma(z, Float64(y - 1.0), Float64(-a)));
	else
		tmp = fma(Float64(b - a), t, fma(Float64(y - 2.0), b, a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.9e+107], N[Not[LessEqual[z, 7.5e+111]], $MachinePrecision]], N[(x - N[(z * N[(y - 1.0), $MachinePrecision] + (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.89999999999999988e107 or 7.49999999999999948e111 < z

   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 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 98.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 41.4%

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

   9. Taylor expanded in b around 0

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

       1. lower--.f64 N/A

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

       2. lower-fma.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-*.f64 N/A

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

       5. lower--.f64 88.5

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

   11. Applied rewrites 88.5%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 80.3%

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

   if -2.89999999999999988e107 < z < 7.49999999999999948e111

   1. Initial program 99.4%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 95.3%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 74.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+107} \lor \neg \left(z \leq 7.5 \cdot 10^{+111}\right):\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-67}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 175000:\\ \;\;\;\;\mathsf{fma}\left(-2, b, a\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.02e+125)
     t_1
     (if (<= t -3.5e-67)
       (* (- b z) y)
       (if (<= t 175000.0) (+ (fma -2.0 b a) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -1.02e+125) {
		tmp = t_1;
	} else if (t <= -3.5e-67) {
		tmp = (b - z) * y;
	} else if (t <= 175000.0) {
		tmp = fma(-2.0, b, a) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -1.02e+125)
		tmp = t_1;
	elseif (t <= -3.5e-67)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 175000.0)
		tmp = Float64(fma(-2.0, b, a) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.02e+125], t$95$1, If[LessEqual[t, -3.5e-67], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 175000.0], N[(N[(-2.0 * b + a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.02e125 or 175000 < t

   1. Initial program 92.9%

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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.3

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

   5. Applied rewrites 72.3%

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

   if -1.02e125 < t < -3.5e-67

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 49.4

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

   5. Applied rewrites 49.4%

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

   if -3.5e-67 < t < 175000

   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

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 66.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 66.2%

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

   10. Applied rewrites 66.2%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 56.0%

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

Alternative 10: 66.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+125} \lor \neg \left(t \leq 3.4 \cdot 10^{+41}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.02e+125) (not (<= t 3.4e+41)))
   (* (- b a) t)
   (- x (fma z (- y 1.0) (- a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.02e+125) || !(t <= 3.4e+41)) {
		tmp = (b - a) * t;
	} else {
		tmp = x - fma(z, (y - 1.0), -a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.02e+125) || !(t <= 3.4e+41))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = Float64(x - fma(z, Float64(y - 1.0), Float64(-a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.02e+125], N[Not[LessEqual[t, 3.4e+41]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(x - N[(z * N[(y - 1.0), $MachinePrecision] + (-a)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.02e125 or 3.39999999999999998e41 < t

   1. Initial program 93.5%

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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.0

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

   5. Applied rewrites 75.0%

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

   if -1.02e125 < t < 3.39999999999999998e41

   1. Initial program 98.8%

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

   3. Taylor expanded in t around 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 72.2%

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

   9. Taylor expanded in b around 0

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

       1. lower--.f64 N/A

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

       2. lower-fma.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-*.f64 N/A

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

       5. lower--.f64 72.8

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

   11. Applied rewrites 72.8%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 68.4%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+125} \lor \neg \left(t \leq 3.4 \cdot 10^{+41}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-67}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+28}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.02e+125)
     t_1
     (if (<= t -3.5e-67)
       (* (- b z) y)
       (if (<= t 1.56e+28) (+ (+ z x) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -1.02e+125) {
		tmp = t_1;
	} else if (t <= -3.5e-67) {
		tmp = (b - z) * y;
	} else if (t <= 1.56e+28) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-1.02d+125)) then
        tmp = t_1
    else if (t <= (-3.5d-67)) then
        tmp = (b - z) * y
    else if (t <= 1.56d+28) then
        tmp = (z + x) + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -1.02e+125) {
		tmp = t_1;
	} else if (t <= -3.5e-67) {
		tmp = (b - z) * y;
	} else if (t <= 1.56e+28) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -1.02e+125:
		tmp = t_1
	elif t <= -3.5e-67:
		tmp = (b - z) * y
	elif t <= 1.56e+28:
		tmp = (z + x) + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -1.02e+125)
		tmp = t_1;
	elseif (t <= -3.5e-67)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 1.56e+28)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -1.02e+125)
		tmp = t_1;
	elseif (t <= -3.5e-67)
		tmp = (b - z) * y;
	elseif (t <= 1.56e+28)
		tmp = (z + x) + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.02e+125], t$95$1, If[LessEqual[t, -3.5e-67], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.56e+28], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.02e125 or 1.5599999999999999e28 < t

   1. Initial program 92.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.9

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

   5. Applied rewrites 72.9%

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

   if -1.02e125 < t < -3.5e-67

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 49.4

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

   5. Applied rewrites 49.4%

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

   if -3.5e-67 < t < 1.5599999999999999e28

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 67.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 66.0%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 55.4%

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

Alternative 12: 65.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+85}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, b \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3e+85)
   (* (- b z) y)
   (if (<= y 1.1e+37) (+ (fma (- t 2.0) b z) x) (fma (- z) y (* b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3e+85) {
		tmp = (b - z) * y;
	} else if (y <= 1.1e+37) {
		tmp = fma((t - 2.0), b, z) + x;
	} else {
		tmp = fma(-z, y, (b * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3e+85)
		tmp = Float64(Float64(b - z) * y);
	elseif (y <= 1.1e+37)
		tmp = Float64(fma(Float64(t - 2.0), b, z) + x);
	else
		tmp = fma(Float64(-z), y, Float64(b * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3e+85], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 1.1e+37], N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + x), $MachinePrecision], N[((-z) * y + N[(b * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3e85

   1. Initial program 86.0%

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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.5

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

   5. Applied rewrites 68.5%

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

   if -3e85 < y < 1.1e37

   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

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 95.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 63.9%

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

   if 1.1e37 < y

   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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.6

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

   5. Applied rewrites 68.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 68.6%

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

Alternative 13: 65.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+85} \lor \neg \left(y \leq 1.1 \cdot 10^{+37}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3e+85) (not (<= y 1.1e+37)))
   (* (- b z) y)
   (+ (fma (- t 2.0) b z) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3e+85) || !(y <= 1.1e+37)) {
		tmp = (b - z) * y;
	} else {
		tmp = fma((t - 2.0), b, z) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3e+85) || !(y <= 1.1e+37))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = Float64(fma(Float64(t - 2.0), b, z) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3e+85], N[Not[LessEqual[y, 1.1e+37]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e85 or 1.1e37 < y

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.5

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

   5. Applied rewrites 68.5%

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

   if -3e85 < y < 1.1e37

   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

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 95.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 63.9%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+85} \lor \neg \left(y \leq 1.1 \cdot 10^{+37}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2700 \lor \neg \left(t \leq 1.56 \cdot 10^{+28}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(a + \mathsf{fma}\left(-2, b, z\right)\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2700.0) (not (<= t 1.56e+28)))
   (* (- b a) t)
   (+ (+ a (fma -2.0 b z)) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2700.0) || !(t <= 1.56e+28)) {
		tmp = (b - a) * t;
	} else {
		tmp = (a + fma(-2.0, b, z)) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2700.0) || !(t <= 1.56e+28))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = Float64(Float64(a + fma(-2.0, b, z)) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2700.0], N[Not[LessEqual[t, 1.56e+28]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(a + N[(-2.0 * b + z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2700 or 1.5599999999999999e28 < t

   1. Initial program 94.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 65.9

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

   5. Applied rewrites 65.9%

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

   if -2700 < t < 1.5599999999999999e28

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 63.4%

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

   10. Applied rewrites 63.4%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2700 \lor \neg \left(t \leq 1.56 \cdot 10^{+28}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(a + \mathsf{fma}\left(-2, b, z\right)\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2700 \lor \neg \left(t \leq 1.56 \cdot 10^{+28}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2700.0) (not (<= t 1.56e+28))) (* (- b a) t) (+ (+ z x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2700.0) || !(t <= 1.56e+28)) {
		tmp = (b - a) * t;
	} else {
		tmp = (z + x) + a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2700.0d0)) .or. (.not. (t <= 1.56d+28))) then
        tmp = (b - a) * t
    else
        tmp = (z + x) + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2700.0) || !(t <= 1.56e+28)) {
		tmp = (b - a) * t;
	} else {
		tmp = (z + x) + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2700.0) or not (t <= 1.56e+28):
		tmp = (b - a) * t
	else:
		tmp = (z + x) + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2700.0) || !(t <= 1.56e+28))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = Float64(Float64(z + x) + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2700.0) || ~((t <= 1.56e+28)))
		tmp = (b - a) * t;
	else
		tmp = (z + x) + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2700.0], N[Not[LessEqual[t, 1.56e+28]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2700 or 1.5599999999999999e28 < t

   1. Initial program 94.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 65.9

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

   5. Applied rewrites 65.9%

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

   if -2700 < t < 1.5599999999999999e28

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 63.4%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 52.9%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2700 \lor \neg \left(t \leq 1.56 \cdot 10^{+28}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 43.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1300:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;t \leq 1.86 \cdot 10^{+28}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1300.0)
   (* (- 1.0 t) a)
   (if (<= t 1.86e+28) (+ (+ z x) a) (* (- t) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1300.0) {
		tmp = (1.0 - t) * a;
	} else if (t <= 1.86e+28) {
		tmp = (z + x) + a;
	} else {
		tmp = -t * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1300.0d0)) then
        tmp = (1.0d0 - t) * a
    else if (t <= 1.86d+28) then
        tmp = (z + x) + a
    else
        tmp = -t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1300.0) {
		tmp = (1.0 - t) * a;
	} else if (t <= 1.86e+28) {
		tmp = (z + x) + a;
	} else {
		tmp = -t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1300.0:
		tmp = (1.0 - t) * a
	elif t <= 1.86e+28:
		tmp = (z + x) + a
	else:
		tmp = -t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1300.0)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (t <= 1.86e+28)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = Float64(Float64(-t) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1300.0)
		tmp = (1.0 - t) * a;
	elseif (t <= 1.86e+28)
		tmp = (z + x) + a;
	else
		tmp = -t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1300.0], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, 1.86e+28], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], N[((-t) * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1300

   1. Initial program 96.4%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.8

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

   5. Applied rewrites 33.8%

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

   if -1300 < t < 1.86000000000000009e28

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 63.4%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 52.9%

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

   if 1.86000000000000009e28 < 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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 49.8

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

   5. Applied rewrites 49.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 49.8%

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

Alternative 17: 42.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+131}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 1.86 \cdot 10^{+28}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.8e+131) (* b t) (if (<= t 1.86e+28) (+ (+ z x) a) (* (- t) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.8e+131) {
		tmp = b * t;
	} else if (t <= 1.86e+28) {
		tmp = (z + x) + a;
	} else {
		tmp = -t * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.8d+131)) then
        tmp = b * t
    else if (t <= 1.86d+28) then
        tmp = (z + x) + a
    else
        tmp = -t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.8e+131) {
		tmp = b * t;
	} else if (t <= 1.86e+28) {
		tmp = (z + x) + a;
	} else {
		tmp = -t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.8e+131:
		tmp = b * t
	elif t <= 1.86e+28:
		tmp = (z + x) + a
	else:
		tmp = -t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.8e+131)
		tmp = Float64(b * t);
	elseif (t <= 1.86e+28)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = Float64(Float64(-t) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.8e+131)
		tmp = b * t;
	elseif (t <= 1.86e+28)
		tmp = (z + x) + a;
	else
		tmp = -t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.8e+131], N[(b * t), $MachinePrecision], If[LessEqual[t, 1.86e+28], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], N[((-t) * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000004e131

   1. Initial program 93.1%

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

   3. Taylor expanded in t around 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 43.4%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 43.6%

       \[\leadsto b \cdot t \]

   if -3.8000000000000004e131 < t < 1.86000000000000009e28

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 64.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 56.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 48.0%

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

   if 1.86000000000000009e28 < 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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 49.8

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

   5. Applied rewrites 49.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 49.8%

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

Alternative 18: 27.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+14} \lor \neg \left(y \leq 3.1 \cdot 10^{+36}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.1e+14) (not (<= y 3.1e+36))) (* b y) (* b t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.1e+14) || !(y <= 3.1e+36)) {
		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 ((y <= (-5.1d+14)) .or. (.not. (y <= 3.1d+36))) 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 ((y <= -5.1e+14) || !(y <= 3.1e+36)) {
		tmp = b * y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.1e+14) or not (y <= 3.1e+36):
		tmp = b * y
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.1e+14) || !(y <= 3.1e+36))
		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 ((y <= -5.1e+14) || ~((y <= 3.1e+36)))
		tmp = b * y;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.1e+14], N[Not[LessEqual[y, 3.1e+36]], $MachinePrecision]], N[(b * y), $MachinePrecision], N[(b * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1e14 or 3.0999999999999999e36 < y

   1. Initial program 94.0%

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

   3. Taylor expanded in t around 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.1%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 39.9%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 35.6%

       \[\leadsto b \cdot y \]

   if -5.1e14 < y < 3.0999999999999999e36

   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 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 31.9%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 21.9%

       \[\leadsto b \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+14} \lor \neg \left(y \leq 3.1 \cdot 10^{+36}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 17.2% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ b \cdot t \end{array} \]

FPCore

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

C

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

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 = b * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(b * t), $MachinePrecision]

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in t around 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. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. +-commutative N/A

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

   4. associate-+l+ N/A

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

   5. *-commutative N/A

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

   6. associate--l+ N/A

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

   7. +-commutative N/A

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

   8. lower-fma.f64 N/A

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

   9. lower--.f64 N/A

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

   10. +-commutative N/A

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

   11. associate--l+ N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lower--.f64 N/A

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

5. Applied rewrites 99.6%

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

6. Taylor expanded in b around -inf

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

8. Applied rewrites 35.6%

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

9. Taylor expanded in t around inf

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

11. Applied rewrites 16.0%

    \[\leadsto b \cdot t \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024363 
(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)))