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

Percentage Accurate: 95.1% → 97.5%

Time: 9.4s

Alternatives: 23

Speedup: 0.5×

• 37.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. associate--l- N/A

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

      17. *-commutative N/A

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

      18. *-commutative N/A

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

   3. Applied rewrites 100.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 50.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 50.1

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

   4. Applied rewrites 50.1%

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

Alternative 2: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(1 - y\right) \cdot z\right)\\ \mathbf{if}\;b \leq -0.068:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2400000000000:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b (* (- 1.0 y) z))))
   (if (<= b -0.068)
     t_1
     (if (<= b 2400000000000.0)
       (- x (fma (- t 1.0) a (* (- y 1.0) z)))
       (if (<= b 1.85e+166) t_1 (+ x (* (- (+ y t) 2.0) b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, ((1.0 - y) * z));
	double tmp;
	if (b <= -0.068) {
		tmp = t_1;
	} else if (b <= 2400000000000.0) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else if (b <= 1.85e+166) {
		tmp = t_1;
	} else {
		tmp = x + (((y + t) - 2.0) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, Float64(Float64(1.0 - y) * z))
	tmp = 0.0
	if (b <= -0.068)
		tmp = t_1;
	elseif (b <= 2400000000000.0)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	elseif (b <= 1.85e+166)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.068], t$95$1, If[LessEqual[b, 2400000000000.0], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.85e+166], t$95$1, N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.068000000000000005 or 2.4e12 < b < 1.85000000000000011e166

   1. Initial program 91.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. associate--l- N/A

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

      17. *-commutative N/A

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

      18. *-commutative N/A

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

   3. Applied rewrites 96.0%

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

   4. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. associate--l- N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 73.7

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

   6. Applied rewrites 73.7%

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

   if -0.068000000000000005 < b < 2.4e12

   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. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 91.3

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

   4. Applied rewrites 91.3%

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

   if 1.85000000000000011e166 < b

   1. Initial program 89.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 89.2%

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

Alternative 3: 84.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.06 \cdot 10^{+64}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -3.6e+44)
     t_1
     (if (<= b 2.06e+64) (- x (fma (- t 1.0) a (* (- y 1.0) z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.6e+44) {
		tmp = t_1;
	} else if (b <= 2.06e+64) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -3.6e+44)
		tmp = t_1;
	elseif (b <= 2.06e+64)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.6e+44], t$95$1, If[LessEqual[b, 2.06e+64], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.6e44 or 2.05999999999999986e64 < b

   1. Initial program 89.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 77.6%

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

   if -3.6e44 < b < 2.05999999999999986e64

   1. Initial program 99.0%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 88.6

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

   4. Applied rewrites 88.6%

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

Alternative 4: 64.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) - 2\\ t_2 := t\_1 \cdot b\\ \mathbf{if}\;b \leq -7.6 \cdot 10^{+95}:\\ \;\;\;\;x + t\_2\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-32}:\\ \;\;\;\;\left(-a\right) \cdot t + t\_2\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+56}:\\ \;\;\;\;x + \mathsf{fma}\left(-y, z, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ y t) 2.0)) (t_2 (* t_1 b)))
   (if (<= b -7.6e+95)
     (+ x t_2)
     (if (<= b -2e-32)
       (+ (* (- a) t) t_2)
       (if (<= b 2.05e+56) (+ x (fma (- y) z z)) (fma t_1 b a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) - 2.0;
	double t_2 = t_1 * b;
	double tmp;
	if (b <= -7.6e+95) {
		tmp = x + t_2;
	} else if (b <= -2e-32) {
		tmp = (-a * t) + t_2;
	} else if (b <= 2.05e+56) {
		tmp = x + fma(-y, z, z);
	} else {
		tmp = fma(t_1, b, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) - 2.0)
	t_2 = Float64(t_1 * b)
	tmp = 0.0
	if (b <= -7.6e+95)
		tmp = Float64(x + t_2);
	elseif (b <= -2e-32)
		tmp = Float64(Float64(Float64(-a) * t) + t_2);
	elseif (b <= 2.05e+56)
		tmp = Float64(x + fma(Float64(-y), z, z));
	else
		tmp = fma(t_1, b, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * b), $MachinePrecision]}, If[LessEqual[b, -7.6e+95], N[(x + t$95$2), $MachinePrecision], If[LessEqual[b, -2e-32], N[(N[((-a) * t), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[b, 2.05e+56], N[(x + N[((-y) * z + z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * b + a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.5999999999999999e95

   1. Initial program 88.5%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 81.8%

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

   if -7.5999999999999999e95 < b < -2.00000000000000011e-32

   1. Initial program 95.7%

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

   2. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 49.1

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

   4. Applied rewrites 49.1%

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

   if -2.00000000000000011e-32 < b < 2.0500000000000002e56

   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. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.2

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

   4. Applied rewrites 99.2%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 90.3

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

   7. Applied rewrites 90.3%

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

   8. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. distribute-lft1-in N/A

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

      6. lift-fma.f64 56.8

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

   10. Applied rewrites 56.8%

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

   if 2.0500000000000002e56 < b

   1. Initial program 90.5%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.1

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

   4. Applied rewrites 79.1%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 77.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 77.5

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

   9. Applied rewrites 77.5%

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

Alternative 5: 64.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) - 2\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{+55}:\\ \;\;\;\;x + t\_1 \cdot b\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-31}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+56}:\\ \;\;\;\;x + \mathsf{fma}\left(-y, z, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ y t) 2.0)))
   (if (<= b -3.8e+55)
     (+ x (* t_1 b))
     (if (<= b -6.5e-31)
       (* (- b a) t)
       (if (<= b 2.05e+56) (+ x (fma (- y) z z)) (fma t_1 b a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) - 2.0;
	double tmp;
	if (b <= -3.8e+55) {
		tmp = x + (t_1 * b);
	} else if (b <= -6.5e-31) {
		tmp = (b - a) * t;
	} else if (b <= 2.05e+56) {
		tmp = x + fma(-y, z, z);
	} else {
		tmp = fma(t_1, b, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) - 2.0)
	tmp = 0.0
	if (b <= -3.8e+55)
		tmp = Float64(x + Float64(t_1 * b));
	elseif (b <= -6.5e-31)
		tmp = Float64(Float64(b - a) * t);
	elseif (b <= 2.05e+56)
		tmp = Float64(x + fma(Float64(-y), z, z));
	else
		tmp = fma(t_1, b, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[b, -3.8e+55], N[(x + N[(t$95$1 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.5e-31], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[b, 2.05e+56], N[(x + N[((-y) * z + z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * b + a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.8e55

   1. Initial program 89.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 78.1%

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

   if -3.8e55 < b < -6.49999999999999967e-31

   1. Initial program 97.5%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.5

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

   4. Applied rewrites 33.5%

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

   if -6.49999999999999967e-31 < b < 2.0500000000000002e56

   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. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.2

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

   4. Applied rewrites 99.2%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 90.2

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

   7. Applied rewrites 90.2%

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

   8. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. distribute-lft1-in N/A

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

      6. lift-fma.f64 56.7

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

   10. Applied rewrites 56.7%

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

   if 2.0500000000000002e56 < b

   1. Initial program 90.5%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.1

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

   4. Applied rewrites 79.1%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 77.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 77.5

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

   9. Applied rewrites 77.5%

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

Alternative 6: 63.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(y + t\right) - 2, b, a\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-31}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+56}:\\ \;\;\;\;x + \mathsf{fma}\left(-y, z, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ y t) 2.0) b a)))
   (if (<= b -4.2e+55)
     t_1
     (if (<= b -6.5e-31)
       (* (- b a) t)
       (if (<= b 2.05e+56) (+ x (fma (- y) z z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((y + t) - 2.0), b, a);
	double tmp;
	if (b <= -4.2e+55) {
		tmp = t_1;
	} else if (b <= -6.5e-31) {
		tmp = (b - a) * t;
	} else if (b <= 2.05e+56) {
		tmp = x + fma(-y, z, z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(y + t) - 2.0), b, a)
	tmp = 0.0
	if (b <= -4.2e+55)
		tmp = t_1;
	elseif (b <= -6.5e-31)
		tmp = Float64(Float64(b - a) * t);
	elseif (b <= 2.05e+56)
		tmp = Float64(x + fma(Float64(-y), z, z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b + a), $MachinePrecision]}, If[LessEqual[b, -4.2e+55], t$95$1, If[LessEqual[b, -6.5e-31], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[b, 2.05e+56], N[(x + N[((-y) * z + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.2000000000000001e55 or 2.0500000000000002e56 < b

   1. Initial program 89.7%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 78.3

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

   4. Applied rewrites 78.3%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 77.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 77.6

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

   9. Applied rewrites 77.6%

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

   if -4.2000000000000001e55 < b < -6.49999999999999967e-31

   1. Initial program 97.5%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.5

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

   4. Applied rewrites 33.5%

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

   if -6.49999999999999967e-31 < b < 2.0500000000000002e56

   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. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.2

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

   4. Applied rewrites 99.2%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 90.2

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

   7. Applied rewrites 90.2%

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

   8. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. distribute-lft1-in N/A

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

      6. lift-fma.f64 56.7

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

   10. Applied rewrites 56.7%

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

Alternative 7: 61.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-31}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;b \leq 2.06 \cdot 10^{+64}:\\ \;\;\;\;x + \mathsf{fma}\left(-y, z, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -4.2e+55)
     t_1
     (if (<= b -6.5e-31)
       (* (- b a) t)
       (if (<= b 2.06e+64) (+ x (fma (- y) z z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -4.2e+55) {
		tmp = t_1;
	} else if (b <= -6.5e-31) {
		tmp = (b - a) * t;
	} else if (b <= 2.06e+64) {
		tmp = x + fma(-y, z, z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -4.2e+55)
		tmp = t_1;
	elseif (b <= -6.5e-31)
		tmp = Float64(Float64(b - a) * t);
	elseif (b <= 2.06e+64)
		tmp = Float64(x + fma(Float64(-y), z, z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -4.2e+55], t$95$1, If[LessEqual[b, -6.5e-31], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[b, 2.06e+64], N[(x + N[((-y) * z + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.2000000000000001e55 or 2.05999999999999986e64 < b

   1. Initial program 89.6%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 72.8

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 72.8

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

   4. Applied rewrites 72.8%

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

   if -4.2000000000000001e55 < b < -6.49999999999999967e-31

   1. Initial program 97.5%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.5

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

   4. Applied rewrites 33.5%

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

   if -6.49999999999999967e-31 < b < 2.05999999999999986e64

   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. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.2

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

   4. Applied rewrites 99.2%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 89.9

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

   7. Applied rewrites 89.9%

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

   8. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. distribute-lft1-in N/A

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

      6. lift-fma.f64 56.5

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

   10. Applied rewrites 56.5%

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

Alternative 8: 61.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+66}:\\ \;\;\;\;x + \left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -5.6e-25) t_1 (if (<= t 4.4e+66) (+ x (* (- b z) y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -5.6e-25) {
		tmp = t_1;
	} else if (t <= 4.4e+66) {
		tmp = x + ((b - z) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-5.6d-25)) then
        tmp = t_1
    else if (t <= 4.4d+66) then
        tmp = x + ((b - z) * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -5.6e-25) {
		tmp = t_1;
	} else if (t <= 4.4e+66) {
		tmp = x + ((b - z) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -5.6e-25:
		tmp = t_1
	elif t <= 4.4e+66:
		tmp = x + ((b - z) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -5.6e-25)
		tmp = t_1;
	elseif (t <= 4.4e+66)
		tmp = Float64(x + Float64(Float64(b - z) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -5.6e-25)
		tmp = t_1;
	elseif (t <= 4.4e+66)
		tmp = x + ((b - z) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -5.6e-25], t$95$1, If[LessEqual[t, 4.4e+66], N[(x + N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.59999999999999976e-25 or 4.3999999999999997e66 < t

   1. Initial program 92.3%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 63.9

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

   4. Applied rewrites 63.9%

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

   if -5.59999999999999976e-25 < t < 4.3999999999999997e66

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 55.8

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

   7. Applied rewrites 55.8%

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

Alternative 9: 59.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 23000000000000:\\ \;\;\;\;x + \left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -3.6e+44)
     t_1
     (if (<= b 23000000000000.0) (+ x (* (- 1.0 t) a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -3.6e+44) {
		tmp = t_1;
	} else if (b <= 23000000000000.0) {
		tmp = x + ((1.0 - t) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-3.6d+44)) then
        tmp = t_1
    else if (b <= 23000000000000.0d0) then
        tmp = x + ((1.0d0 - t) * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -3.6e+44) {
		tmp = t_1;
	} else if (b <= 23000000000000.0) {
		tmp = x + ((1.0 - t) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -3.6e+44:
		tmp = t_1
	elif b <= 23000000000000.0:
		tmp = x + ((1.0 - t) * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -3.6e+44)
		tmp = t_1;
	elseif (b <= 23000000000000.0)
		tmp = Float64(x + Float64(Float64(1.0 - t) * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -3.6e+44)
		tmp = t_1;
	elseif (b <= 23000000000000.0)
		tmp = x + ((1.0 - t) * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -3.6e+44], t$95$1, If[LessEqual[b, 23000000000000.0], N[(x + N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.6e44 or 2.3e13 < b

   1. Initial program 90.4%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 68.6

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 68.6

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

   4. Applied rewrites 68.6%

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

   if -3.6e44 < b < 2.3e13

   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. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.1

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 56.2

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

   7. Applied rewrites 56.2%

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

Alternative 10: 55.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-31}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+64}:\\ \;\;\;\;x + \left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -4.2e+55)
     t_1
     (if (<= b -6.5e-31)
       (* (- b a) t)
       (if (<= b 2.05e+64) (+ x (* (- y) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -4.2e+55) {
		tmp = t_1;
	} else if (b <= -6.5e-31) {
		tmp = (b - a) * t;
	} else if (b <= 2.05e+64) {
		tmp = x + (-y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-4.2d+55)) then
        tmp = t_1
    else if (b <= (-6.5d-31)) then
        tmp = (b - a) * t
    else if (b <= 2.05d+64) then
        tmp = x + (-y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -4.2e+55) {
		tmp = t_1;
	} else if (b <= -6.5e-31) {
		tmp = (b - a) * t;
	} else if (b <= 2.05e+64) {
		tmp = x + (-y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -4.2e+55:
		tmp = t_1
	elif b <= -6.5e-31:
		tmp = (b - a) * t
	elif b <= 2.05e+64:
		tmp = x + (-y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -4.2e+55)
		tmp = t_1;
	elseif (b <= -6.5e-31)
		tmp = Float64(Float64(b - a) * t);
	elseif (b <= 2.05e+64)
		tmp = Float64(x + Float64(Float64(-y) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -4.2e+55)
		tmp = t_1;
	elseif (b <= -6.5e-31)
		tmp = (b - a) * t;
	elseif (b <= 2.05e+64)
		tmp = x + (-y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -4.2e+55], t$95$1, If[LessEqual[b, -6.5e-31], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[b, 2.05e+64], N[(x + N[((-y) * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.2000000000000001e55 or 2.04999999999999989e64 < b

   1. Initial program 89.6%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 72.8

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 72.8

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

   4. Applied rewrites 72.8%

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

   if -4.2000000000000001e55 < b < -6.49999999999999967e-31

   1. Initial program 97.5%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.5

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

   4. Applied rewrites 33.5%

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

   if -6.49999999999999967e-31 < b < 2.04999999999999989e64

   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. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.2

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

   4. Applied rewrites 99.2%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 89.9

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

   7. Applied rewrites 89.9%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 43.9

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

   10. Applied rewrites 43.9%

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

Alternative 11: 52.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -19:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-141}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+54}:\\ \;\;\;\;x + \left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -19.0)
     t_1
     (if (<= t -1.8e-141)
       (fma (- y 2.0) b a)
       (if (<= t 2.6e+54) (+ x (* (- y) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -19.0) {
		tmp = t_1;
	} else if (t <= -1.8e-141) {
		tmp = fma((y - 2.0), b, a);
	} else if (t <= 2.6e+54) {
		tmp = x + (-y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -19.0)
		tmp = t_1;
	elseif (t <= -1.8e-141)
		tmp = fma(Float64(y - 2.0), b, a);
	elseif (t <= 2.6e+54)
		tmp = Float64(x + Float64(Float64(-y) * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -19.0], t$95$1, If[LessEqual[t, -1.8e-141], N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision], If[LessEqual[t, 2.6e+54], N[(x + N[((-y) * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -19 or 2.60000000000000007e54 < 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. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.0

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

   4. Applied rewrites 66.0%

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

   if -19 < t < -1.80000000000000007e-141

   1. Initial program 98.1%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.9

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

   4. Applied rewrites 51.9%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 51.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 51.1

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

   9. Applied rewrites 51.1%

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

   10. Taylor expanded in y around inf

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

   12. Applied rewrites 50.3%

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

   if -1.80000000000000007e-141 < t < 2.60000000000000007e54

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 69.5

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

   7. Applied rewrites 69.5%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 39.0

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

   10. Applied rewrites 39.0%

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

Alternative 12: 50.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{-10}:\\ \;\;\;\;x + y \cdot b\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)) (t_2 (* (- b a) t)))
   (if (<= t -4.3e-22)
     t_2
     (if (<= t -1.1e-211)
       t_1
       (if (<= t 1.66e-10) (+ x (* y b)) (if (<= t 1.75e+53) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -4.3e-22) {
		tmp = t_2;
	} else if (t <= -1.1e-211) {
		tmp = t_1;
	} else if (t <= 1.66e-10) {
		tmp = x + (y * b);
	} else if (t <= 1.75e+53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (1.0d0 - y) * z
    t_2 = (b - a) * t
    if (t <= (-4.3d-22)) then
        tmp = t_2
    else if (t <= (-1.1d-211)) then
        tmp = t_1
    else if (t <= 1.66d-10) then
        tmp = x + (y * b)
    else if (t <= 1.75d+53) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -4.3e-22) {
		tmp = t_2;
	} else if (t <= -1.1e-211) {
		tmp = t_1;
	} else if (t <= 1.66e-10) {
		tmp = x + (y * b);
	} else if (t <= 1.75e+53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - y) * z
	t_2 = (b - a) * t
	tmp = 0
	if t <= -4.3e-22:
		tmp = t_2
	elif t <= -1.1e-211:
		tmp = t_1
	elif t <= 1.66e-10:
		tmp = x + (y * b)
	elif t <= 1.75e+53:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -4.3e-22)
		tmp = t_2;
	elseif (t <= -1.1e-211)
		tmp = t_1;
	elseif (t <= 1.66e-10)
		tmp = Float64(x + Float64(y * b));
	elseif (t <= 1.75e+53)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - y) * z;
	t_2 = (b - a) * t;
	tmp = 0.0;
	if (t <= -4.3e-22)
		tmp = t_2;
	elseif (t <= -1.1e-211)
		tmp = t_1;
	elseif (t <= 1.66e-10)
		tmp = x + (y * b);
	elseif (t <= 1.75e+53)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.3e-22], t$95$2, If[LessEqual[t, -1.1e-211], t$95$1, If[LessEqual[t, 1.66e-10], N[(x + N[(y * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+53], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.30000000000000037e-22 or 1.75000000000000009e53 < t

   1. Initial program 92.4%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 63.7

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

   4. Applied rewrites 63.7%

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

   if -4.30000000000000037e-22 < t < -1.09999999999999999e-211 or 1.66e-10 < t < 1.75000000000000009e53

   1. Initial program 97.9%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 32.3

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

   4. Applied rewrites 32.3%

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

   if -1.09999999999999999e-211 < t < 1.66e-10

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.6%

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

   5. Taylor expanded in y around inf

      \[\leadsto x + \color{blue}{y} \cdot b \]
   6. Step-by-step derivation

   7. Applied rewrites 38.7%

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

Alternative 13: 49.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+54}:\\ \;\;\;\;x + \left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -2.7e-34) t_1 (if (<= t 2.6e+54) (+ x (* (- y) z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -2.7e-34) {
		tmp = t_1;
	} else if (t <= 2.6e+54) {
		tmp = x + (-y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-2.7d-34)) then
        tmp = t_1
    else if (t <= 2.6d+54) then
        tmp = x + (-y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -2.7e-34) {
		tmp = t_1;
	} else if (t <= 2.6e+54) {
		tmp = x + (-y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -2.7e-34:
		tmp = t_1
	elif t <= 2.6e+54:
		tmp = x + (-y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -2.7e-34)
		tmp = t_1;
	elseif (t <= 2.6e+54)
		tmp = Float64(x + Float64(Float64(-y) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -2.7e-34)
		tmp = t_1;
	elseif (t <= 2.6e+54)
		tmp = x + (-y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2.7e-34], t$95$1, If[LessEqual[t, 2.6e+54], N[(x + N[((-y) * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.70000000000000017e-34 or 2.60000000000000007e54 < t

   1. Initial program 92.6%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 62.6

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

   4. Applied rewrites 62.6%

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

   if -2.70000000000000017e-34 < t < 2.60000000000000007e54

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 69.6

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

   7. Applied rewrites 69.6%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 39.3

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

   10. Applied rewrites 39.3%

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

Alternative 14: 48.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+53}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -4.3e-22) t_1 (if (<= t 1.75e+53) (* (- 1.0 y) z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -4.3e-22) {
		tmp = t_1;
	} else if (t <= 1.75e+53) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-4.3d-22)) then
        tmp = t_1
    else if (t <= 1.75d+53) then
        tmp = (1.0d0 - y) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -4.3e-22) {
		tmp = t_1;
	} else if (t <= 1.75e+53) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -4.3e-22:
		tmp = t_1
	elif t <= 1.75e+53:
		tmp = (1.0 - y) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -4.3e-22)
		tmp = t_1;
	elseif (t <= 1.75e+53)
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -4.3e-22)
		tmp = t_1;
	elseif (t <= 1.75e+53)
		tmp = (1.0 - y) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.3e-22], t$95$1, If[LessEqual[t, 1.75e+53], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.30000000000000037e-22 or 1.75000000000000009e53 < t

   1. Initial program 92.4%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 63.7

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

   4. Applied rewrites 63.7%

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

   if -4.30000000000000037e-22 < t < 1.75000000000000009e53

   1. Initial program 97.5%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.9

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

   4. Applied rewrites 33.9%

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

Alternative 15: 41.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -7 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(t, b, a\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+116}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -7e-7)
     t_1
     (if (<= z 1.1e-135)
       (fma t b a)
       (if (<= z 7.5e+116) (* (- 1.0 t) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -7e-7) {
		tmp = t_1;
	} else if (z <= 1.1e-135) {
		tmp = fma(t, b, a);
	} else if (z <= 7.5e+116) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -7e-7)
		tmp = t_1;
	elseif (z <= 1.1e-135)
		tmp = fma(t, b, a);
	elseif (z <= 7.5e+116)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -7e-7], t$95$1, If[LessEqual[z, 1.1e-135], N[(t * b + a), $MachinePrecision], If[LessEqual[z, 7.5e+116], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999968e-7 or 7.5e116 < z

   1. Initial program 91.4%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 54.2

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

   4. Applied rewrites 54.2%

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

   if -6.99999999999999968e-7 < z < 1.1e-135

   1. Initial program 97.9%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.8

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

   4. Applied rewrites 75.8%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 59.3%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 59.3

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

   9. Applied rewrites 59.3%

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

   10. Taylor expanded in t around inf

       \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, a\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 32.9%

       \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, a\right) \]

   if 1.1e-135 < z < 7.5e116

   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. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 30.0

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

   4. Applied rewrites 30.0%

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

Alternative 16: 34.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot t\\ \mathbf{if}\;t \leq -19:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-195}:\\ \;\;\;\;\mathsf{fma}\left(y, b, a\right)\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+55}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a) t)))
   (if (<= t -19.0)
     t_1
     (if (<= t 2e-195)
       (fma y b a)
       (if (<= t 1.66e-10)
         x
         (if (<= t 3.2e+55) (* (- z) y) (if (<= t 5e+196) t_1 (* b t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a * t;
	double tmp;
	if (t <= -19.0) {
		tmp = t_1;
	} else if (t <= 2e-195) {
		tmp = fma(y, b, a);
	} else if (t <= 1.66e-10) {
		tmp = x;
	} else if (t <= 3.2e+55) {
		tmp = -z * y;
	} else if (t <= 5e+196) {
		tmp = t_1;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) * t)
	tmp = 0.0
	if (t <= -19.0)
		tmp = t_1;
	elseif (t <= 2e-195)
		tmp = fma(y, b, a);
	elseif (t <= 1.66e-10)
		tmp = x;
	elseif (t <= 3.2e+55)
		tmp = Float64(Float64(-z) * y);
	elseif (t <= 5e+196)
		tmp = t_1;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) * t), $MachinePrecision]}, If[LessEqual[t, -19.0], t$95$1, If[LessEqual[t, 2e-195], N[(y * b + a), $MachinePrecision], If[LessEqual[t, 1.66e-10], x, If[LessEqual[t, 3.2e+55], N[((-z) * y), $MachinePrecision], If[LessEqual[t, 5e+196], t$95$1, N[(b * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -19 or 3.2000000000000003e55 < t < 4.9999999999999998e196

   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. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 61.6

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

   4. Applied rewrites 61.6%

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

   5. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 35.2

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

   7. Applied rewrites 35.2%

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

   if -19 < t < 2.0000000000000002e-195

   1. Initial program 97.5%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.0

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

   4. Applied rewrites 52.0%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 51.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 51.7

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

   9. Applied rewrites 51.7%

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

   10. Taylor expanded in y around inf

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

   12. Applied rewrites 38.9%

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

   if 2.0000000000000002e-195 < t < 1.66e-10

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 19.8%

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

   if 1.66e-10 < t < 3.2000000000000003e55

   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. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 34.8

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

   4. Applied rewrites 34.8%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 20.6

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

   7. Applied rewrites 20.6%

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

   if 4.9999999999999998e196 < t

   1. Initial program 88.1%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.5

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

   4. Applied rewrites 83.5%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 44.0%

      \[\leadsto b \cdot t \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 17: 34.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot y\\ t_2 := \left(-a\right) \cdot t\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+196}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- z) y)) (t_2 (* (- a) t)))
   (if (<= t -2.7e-34)
     t_2
     (if (<= t 1.85e-256)
       t_1
       (if (<= t 1.66e-10)
         x
         (if (<= t 3.2e+55) t_1 (if (<= t 5e+196) t_2 (* b t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -z * y;
	double t_2 = -a * t;
	double tmp;
	if (t <= -2.7e-34) {
		tmp = t_2;
	} else if (t <= 1.85e-256) {
		tmp = t_1;
	} else if (t <= 1.66e-10) {
		tmp = x;
	} else if (t <= 3.2e+55) {
		tmp = t_1;
	} else if (t <= 5e+196) {
		tmp = t_2;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -z * y
    t_2 = -a * t
    if (t <= (-2.7d-34)) then
        tmp = t_2
    else if (t <= 1.85d-256) then
        tmp = t_1
    else if (t <= 1.66d-10) then
        tmp = x
    else if (t <= 3.2d+55) then
        tmp = t_1
    else if (t <= 5d+196) then
        tmp = t_2
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -z * y;
	double t_2 = -a * t;
	double tmp;
	if (t <= -2.7e-34) {
		tmp = t_2;
	} else if (t <= 1.85e-256) {
		tmp = t_1;
	} else if (t <= 1.66e-10) {
		tmp = x;
	} else if (t <= 3.2e+55) {
		tmp = t_1;
	} else if (t <= 5e+196) {
		tmp = t_2;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -z * y
	t_2 = -a * t
	tmp = 0
	if t <= -2.7e-34:
		tmp = t_2
	elif t <= 1.85e-256:
		tmp = t_1
	elif t <= 1.66e-10:
		tmp = x
	elif t <= 3.2e+55:
		tmp = t_1
	elif t <= 5e+196:
		tmp = t_2
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-z) * y)
	t_2 = Float64(Float64(-a) * t)
	tmp = 0.0
	if (t <= -2.7e-34)
		tmp = t_2;
	elseif (t <= 1.85e-256)
		tmp = t_1;
	elseif (t <= 1.66e-10)
		tmp = x;
	elseif (t <= 3.2e+55)
		tmp = t_1;
	elseif (t <= 5e+196)
		tmp = t_2;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -z * y;
	t_2 = -a * t;
	tmp = 0.0;
	if (t <= -2.7e-34)
		tmp = t_2;
	elseif (t <= 1.85e-256)
		tmp = t_1;
	elseif (t <= 1.66e-10)
		tmp = x;
	elseif (t <= 3.2e+55)
		tmp = t_1;
	elseif (t <= 5e+196)
		tmp = t_2;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-z) * y), $MachinePrecision]}, Block[{t$95$2 = N[((-a) * t), $MachinePrecision]}, If[LessEqual[t, -2.7e-34], t$95$2, If[LessEqual[t, 1.85e-256], t$95$1, If[LessEqual[t, 1.66e-10], x, If[LessEqual[t, 3.2e+55], t$95$1, If[LessEqual[t, 5e+196], t$95$2, N[(b * t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.70000000000000017e-34 or 3.2000000000000003e55 < t < 4.9999999999999998e196

   1. Initial program 93.6%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 57.7

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

   4. Applied rewrites 57.7%

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

   5. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 33.0

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

   7. Applied rewrites 33.0%

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

   if -2.70000000000000017e-34 < t < 1.85000000000000014e-256 or 1.66e-10 < t < 3.2000000000000003e55

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 38.3

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

   4. Applied rewrites 38.3%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 21.5

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

   7. Applied rewrites 21.5%

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

   if 1.85000000000000014e-256 < t < 1.66e-10

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 19.8%

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

   if 4.9999999999999998e196 < t

   1. Initial program 88.1%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.5

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

   4. Applied rewrites 83.5%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 44.0%

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

Alternative 18: 33.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot y\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+241}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(t, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- z) y)))
   (if (<= z -5.2e+241)
     z
     (if (<= z -1.55e+39) t_1 (if (<= z 3.05e+38) (fma t b a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -z * y;
	double tmp;
	if (z <= -5.2e+241) {
		tmp = z;
	} else if (z <= -1.55e+39) {
		tmp = t_1;
	} else if (z <= 3.05e+38) {
		tmp = fma(t, b, a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-z) * y)
	tmp = 0.0
	if (z <= -5.2e+241)
		tmp = z;
	elseif (z <= -1.55e+39)
		tmp = t_1;
	elseif (z <= 3.05e+38)
		tmp = fma(t, b, a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-z) * y), $MachinePrecision]}, If[LessEqual[z, -5.2e+241], z, If[LessEqual[z, -1.55e+39], t$95$1, If[LessEqual[z, 3.05e+38], N[(t * b + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.20000000000000015e241

   1. Initial program 90.1%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 78.9

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 35.2%

      \[\leadsto z \]

   if -5.20000000000000015e241 < z < -1.5500000000000001e39 or 3.05e38 < z

   1. Initial program 91.7%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.4

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

   4. Applied rewrites 41.4%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 34.4

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

   7. Applied rewrites 34.4%

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

   if -1.5500000000000001e39 < z < 3.05e38

   1. Initial program 97.9%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.3

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

   4. Applied rewrites 73.3%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 57.3%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 57.3

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

   9. Applied rewrites 57.3%

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

   10. Taylor expanded in t around inf

       \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, a\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 31.8%

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

Alternative 19: 27.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot y\\ \mathbf{if}\;y \leq -5.7 \cdot 10^{+194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+67}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- z) y)))
   (if (<= y -5.7e+194) t_1 (if (<= y 4.6e+67) (* (- 1.0 t) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -z * y;
	double tmp;
	if (y <= -5.7e+194) {
		tmp = t_1;
	} else if (y <= 4.6e+67) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -z * y
    if (y <= (-5.7d+194)) then
        tmp = t_1
    else if (y <= 4.6d+67) then
        tmp = (1.0d0 - t) * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -z * y;
	double tmp;
	if (y <= -5.7e+194) {
		tmp = t_1;
	} else if (y <= 4.6e+67) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -z * y
	tmp = 0
	if y <= -5.7e+194:
		tmp = t_1
	elif y <= 4.6e+67:
		tmp = (1.0 - t) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-z) * y)
	tmp = 0.0
	if (y <= -5.7e+194)
		tmp = t_1;
	elseif (y <= 4.6e+67)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -z * y;
	tmp = 0.0;
	if (y <= -5.7e+194)
		tmp = t_1;
	elseif (y <= 4.6e+67)
		tmp = (1.0 - t) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-z) * y), $MachinePrecision]}, If[LessEqual[y, -5.7e+194], t$95$1, If[LessEqual[y, 4.6e+67], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.69999999999999983e194 or 4.5999999999999997e67 < y

   1. Initial program 89.4%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.8

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

   4. Applied rewrites 73.8%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 42.4

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

   7. Applied rewrites 42.4%

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

   if -5.69999999999999983e194 < y < 4.5999999999999997e67

   1. Initial program 97.3%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 31.9

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

   4. Applied rewrites 31.9%

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

Alternative 20: 26.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot t\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a) t)))
   (if (<= t -3.2e-36)
     t_1
     (if (<= t 7.5e+67) x (if (<= t 5e+196) t_1 (* b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a * t;
	double tmp;
	if (t <= -3.2e-36) {
		tmp = t_1;
	} else if (t <= 7.5e+67) {
		tmp = x;
	} else if (t <= 5e+196) {
		tmp = t_1;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a * t
    if (t <= (-3.2d-36)) then
        tmp = t_1
    else if (t <= 7.5d+67) then
        tmp = x
    else if (t <= 5d+196) then
        tmp = t_1
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a * t;
	double tmp;
	if (t <= -3.2e-36) {
		tmp = t_1;
	} else if (t <= 7.5e+67) {
		tmp = x;
	} else if (t <= 5e+196) {
		tmp = t_1;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a * t
	tmp = 0
	if t <= -3.2e-36:
		tmp = t_1
	elif t <= 7.5e+67:
		tmp = x
	elif t <= 5e+196:
		tmp = t_1
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) * t)
	tmp = 0.0
	if (t <= -3.2e-36)
		tmp = t_1;
	elseif (t <= 7.5e+67)
		tmp = x;
	elseif (t <= 5e+196)
		tmp = t_1;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a * t;
	tmp = 0.0;
	if (t <= -3.2e-36)
		tmp = t_1;
	elseif (t <= 7.5e+67)
		tmp = x;
	elseif (t <= 5e+196)
		tmp = t_1;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) * t), $MachinePrecision]}, If[LessEqual[t, -3.2e-36], t$95$1, If[LessEqual[t, 7.5e+67], x, If[LessEqual[t, 5e+196], t$95$1, N[(b * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.20000000000000021e-36 or 7.5000000000000005e67 < t < 4.9999999999999998e196

   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. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 57.7

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

   4. Applied rewrites 57.7%

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

   5. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 33.0

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

   7. Applied rewrites 33.0%

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

   if -3.20000000000000021e-36 < t < 7.5000000000000005e67

   1. Initial program 97.5%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 19.2%

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

   if 4.9999999999999998e196 < t

   1. Initial program 88.1%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.5

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

   4. Applied rewrites 83.5%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 44.0%

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

Alternative 21: 25.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+73}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-44}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 850000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.8e+73)
   (* b t)
   (if (<= t -1.3e-44) z (if (<= t 850000000000.0) x (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.8e+73) {
		tmp = b * t;
	} else if (t <= -1.3e-44) {
		tmp = z;
	} else if (t <= 850000000000.0) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-9.8d+73)) then
        tmp = b * t
    else if (t <= (-1.3d-44)) then
        tmp = z
    else if (t <= 850000000000.0d0) then
        tmp = x
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.8e+73) {
		tmp = b * t;
	} else if (t <= -1.3e-44) {
		tmp = z;
	} else if (t <= 850000000000.0) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.8e+73:
		tmp = b * t
	elif t <= -1.3e-44:
		tmp = z
	elif t <= 850000000000.0:
		tmp = x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.8e+73)
		tmp = Float64(b * t);
	elseif (t <= -1.3e-44)
		tmp = z;
	elseif (t <= 850000000000.0)
		tmp = x;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.8e+73)
		tmp = b * t;
	elseif (t <= -1.3e-44)
		tmp = z;
	elseif (t <= 850000000000.0)
		tmp = x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.8e+73], N[(b * t), $MachinePrecision], If[LessEqual[t, -1.3e-44], z, If[LessEqual[t, 850000000000.0], x, N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.7999999999999998e73 or 8.5e11 < t

   1. Initial program 92.0%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.2

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

   4. Applied rewrites 68.2%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 35.9%

      \[\leadsto b \cdot t \]

   if -9.7999999999999998e73 < t < -1.2999999999999999e-44

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

         \[\leadsto \left(1 - y\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(1 - y\right) \cdot \color{blue}{z} \]

      3. lower--.f64 30.0

         \[\leadsto \left(1 - y\right) \cdot z \]

   4. Applied rewrites 30.0%

      \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]

   5. Taylor expanded in y around 0

      \[\leadsto z \]
   6. Step-by-step derivation

   7. Applied rewrites 12.3%

      \[\leadsto z \]

   if -1.2999999999999999e-44 < t < 8.5e11

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 19.2%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 19.8% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+233}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.5e+233) z (if (<= z 2e+120) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.5e+233) {
		tmp = z;
	} else if (z <= 2e+120) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-7.5d+233)) then
        tmp = z
    else if (z <= 2d+120) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.5e+233) {
		tmp = z;
	} else if (z <= 2e+120) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.5e+233:
		tmp = z
	elif z <= 2e+120:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.5e+233)
		tmp = z;
	elseif (z <= 2e+120)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -7.5e+233)
		tmp = z;
	elseif (z <= 2e+120)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.5e+233], z, If[LessEqual[z, 2e+120], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4999999999999997e233 or 2e120 < z

   1. Initial program 89.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(1 - y\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(1 - y\right) \cdot \color{blue}{z} \]

      3. lower--.f64 67.6

         \[\leadsto \left(1 - y\right) \cdot z \]

   4. Applied rewrites 67.6%

      \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]

   5. Taylor expanded in y around 0

      \[\leadsto z \]
   6. Step-by-step derivation

   7. Applied rewrites 27.4%

      \[\leadsto z \]

   if -7.4999999999999997e233 < z < 2e120

   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. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 17.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 15.4% accurate, 28.4× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 95.1%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

2. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
3. Step-by-step derivation

4. Applied rewrites 15.4%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025093 
(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)))