Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.1% → 92.7%

Time: 16.3s

Alternatives: 18

Speedup: 0.3×

Specification

Math

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

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* (- y z) (/ (- t x) (- a z)))))

C

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

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)
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
    code = x + ((y - z) * ((t - x) / (a - z)))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x + ((y - z) * ((t - x) / (a - z)))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.1% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* (- y z) (/ (- t x) (- a z)))))

C

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

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)
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
    code = x + ((y - z) * ((t - x) / (a - z)))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x + ((y - z) * ((t - x) / (a - z)))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - y}{z - a}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-86}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{z - a} \cdot \left(z - y\right), t - x, x\right)\\ \mathbf{elif}\;t\_2 \leq 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-1, t\_1, \frac{z}{z - a}\right) - \frac{a}{z - a}, \frac{t \cdot \left(z - y\right)}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1 \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z y) (- z a))) (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -5e-86)
     (fma (* (/ 1.0 (- z a)) (- z y)) (- t x) x)
     (if (<= t_2 1e-7)
       (fma
        x
        (- (fma -1.0 t_1 (/ z (- z a))) (/ a (- z a)))
        (/ (* t (- z y)) (- z a)))
       (+ x (* t_1 (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - y) / (z - a);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e-86) {
		tmp = fma(((1.0 / (z - a)) * (z - y)), (t - x), x);
	} else if (t_2 <= 1e-7) {
		tmp = fma(x, (fma(-1.0, t_1, (z / (z - a))) - (a / (z - a))), ((t * (z - y)) / (z - a)));
	} else {
		tmp = x + (t_1 * (t - x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - y) / Float64(z - a))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -5e-86)
		tmp = fma(Float64(Float64(1.0 / Float64(z - a)) * Float64(z - y)), Float64(t - x), x);
	elseif (t_2 <= 1e-7)
		tmp = fma(x, Float64(fma(-1.0, t_1, Float64(z / Float64(z - a))) - Float64(a / Float64(z - a))), Float64(Float64(t * Float64(z - y)) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(t_1 * Float64(t - x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-86], N[(N[(N[(1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 1e-7], N[(x * N[(N[(-1.0 * t$95$1 + N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999999e-86

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

   5. Applied rewrites 84.1%

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

   if -4.9999999999999999e-86 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.9999999999999995e-8

   1. Initial program 80.1%

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

   3. Applied rewrites 63.4%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 78.9%

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

   if 9.9999999999999995e-8 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

Alternative 2: 91.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-254}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{z - a} \cdot \left(z - y\right), t - x, x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{z - a} \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -4e-254)
     (fma (* (/ 1.0 (- z a)) (- z y)) (- t x) x)
     (if (<= t_1 0.0)
       (+ t (* -1.0 (/ (- (* y (- t x)) (* a (- t x))) z)))
       (+ x (* (/ (- z y) (- z a)) (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -4e-254) {
		tmp = fma(((1.0 / (z - a)) * (z - y)), (t - x), x);
	} else if (t_1 <= 0.0) {
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z));
	} else {
		tmp = x + (((z - y) / (z - a)) * (t - x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -4e-254)
		tmp = fma(Float64(Float64(1.0 / Float64(z - a)) * Float64(z - y)), Float64(t - x), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(-1.0 * Float64(Float64(Float64(y * Float64(t - x)) - Float64(a * Float64(t - x))) / z)));
	else
		tmp = Float64(x + Float64(Float64(Float64(z - y) / Float64(z - a)) * Float64(t - x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-254], N[(N[(N[(1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(-1.0 * N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -3.9999999999999996e-254

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

   5. Applied rewrites 84.1%

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

   if -3.9999999999999996e-254 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 80.1%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 45.8%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

Alternative 3: 87.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-254}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{z - a} \cdot \left(z - y\right), t - x, x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{z - a} \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -4e-254)
     (fma (* (/ 1.0 (- z a)) (- z y)) (- t x) x)
     (if (<= t_1 0.0)
       (* t (- (/ y (- a z)) (/ z (- a z))))
       (+ x (* (/ (- z y) (- z a)) (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -4e-254) {
		tmp = fma(((1.0 / (z - a)) * (z - y)), (t - x), x);
	} else if (t_1 <= 0.0) {
		tmp = t * ((y / (a - z)) - (z / (a - z)));
	} else {
		tmp = x + (((z - y) / (z - a)) * (t - x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -4e-254)
		tmp = fma(Float64(Float64(1.0 / Float64(z - a)) * Float64(z - y)), Float64(t - x), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t * Float64(Float64(y / Float64(a - z)) - Float64(z / Float64(a - z))));
	else
		tmp = Float64(x + Float64(Float64(Float64(z - y) / Float64(z - a)) * Float64(t - x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-254], N[(N[(N[(1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -3.9999999999999996e-254

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

   5. Applied rewrites 84.1%

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

   if -3.9999999999999996e-254 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 80.1%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 50.8%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

Alternative 4: 87.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - y}{z - a}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-254}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, t - x, x\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1 \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z y) (- z a))) (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -4e-254)
     (fma t_1 (- t x) x)
     (if (<= t_2 0.0)
       (* t (- (/ y (- a z)) (/ z (- a z))))
       (+ x (* t_1 (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - y) / (z - a);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-254) {
		tmp = fma(t_1, (t - x), x);
	} else if (t_2 <= 0.0) {
		tmp = t * ((y / (a - z)) - (z / (a - z)));
	} else {
		tmp = x + (t_1 * (t - x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - y) / Float64(z - a))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -4e-254)
		tmp = fma(t_1, Float64(t - x), x);
	elseif (t_2 <= 0.0)
		tmp = Float64(t * Float64(Float64(y / Float64(a - z)) - Float64(z / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t_1 * Float64(t - x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-254], N[(t$95$1 * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -3.9999999999999996e-254

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

   if -3.9999999999999996e-254 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 80.1%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 50.8%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

Alternative 5: 86.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - y}{z - a}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-289}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, t - x, x\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{-1 \cdot \left(a \cdot x\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1 \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z y) (- z a))) (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -5e-289)
     (fma t_1 (- t x) x)
     (if (<= t_2 0.0) (/ (* -1.0 (* a x)) (- z a)) (+ x (* t_1 (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - y) / (z - a);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e-289) {
		tmp = fma(t_1, (t - x), x);
	} else if (t_2 <= 0.0) {
		tmp = (-1.0 * (a * x)) / (z - a);
	} else {
		tmp = x + (t_1 * (t - x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - y) / Float64(z - a))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -5e-289)
		tmp = fma(t_1, Float64(t - x), x);
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(-1.0 * Float64(a * x)) / Float64(z - a));
	else
		tmp = Float64(x + Float64(t_1 * Float64(t - x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-289], N[(t$95$1 * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(-1.0 * N[(a * x), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000029e-289

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

   if -5.00000000000000029e-289 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 80.1%

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

   3. Applied rewrites 63.4%

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

   4. Taylor expanded in a around inf

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

   6. Applied rewrites 21.3%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

Alternative 6: 86.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{z - a}, t - x, x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{-1 \cdot \left(a \cdot x\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) (- z a)) (- t x) x))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -5e-289)
     t_1
     (if (<= t_2 0.0) (/ (* -1.0 (* a x)) (- z a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - y) / (z - a)), (t - x), x);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e-289) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = (-1.0 * (a * x)) / (z - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / Float64(z - a)), Float64(t - x), x)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -5e-289)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(-1.0 * Float64(a * x)) / Float64(z - a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-289], t$95$1, If[LessEqual[t$95$2, 0.0], N[(N[(-1.0 * N[(a * x), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000029e-289 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

   if -5.00000000000000029e-289 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 80.1%

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

   3. Applied rewrites 63.4%

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

   4. Taylor expanded in a around inf

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

   6. Applied rewrites 21.3%

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

Alternative 7: 82.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t - x}{z - a}, z - y, x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-274}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t x) (- z a)) (- z y) x))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -1e-146)
     t_1
     (if (<= t_2 4e-274) (/ (* t (- y z)) (- a z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((t - x) / (z - a)), (z - y), x);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -1e-146) {
		tmp = t_1;
	} else if (t_2 <= 4e-274) {
		tmp = (t * (y - z)) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(t - x) / Float64(z - a)), Float64(z - y), x)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-146)
		tmp = t_1;
	elseif (t_2 <= 4e-274)
		tmp = Float64(Float64(t * Float64(y - z)) / Float64(a - z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-146], t$95$1, If[LessEqual[t$95$2, 4e-274], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000003e-146 or 3.99999999999999986e-274 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.1%

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

   3. Applied rewrites 80.2%

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

   if -1.00000000000000003e-146 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 3.99999999999999986e-274

   1. Initial program 80.1%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 39.0%

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

Alternative 8: 72.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+114}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z - a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \left(\frac{1}{z - a} \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.7e+114)
   (* (/ y (- z a)) (- x t))
   (if (<= y 5.4e+46)
     (fma (/ (- z y) (- z a)) t x)
     (* (- t x) (* (/ 1.0 (- z a)) (- y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.7e+114) {
		tmp = (y / (z - a)) * (x - t);
	} else if (y <= 5.4e+46) {
		tmp = fma(((z - y) / (z - a)), t, x);
	} else {
		tmp = (t - x) * ((1.0 / (z - a)) * -y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.7e+114)
		tmp = Float64(Float64(y / Float64(z - a)) * Float64(x - t));
	elseif (y <= 5.4e+46)
		tmp = fma(Float64(Float64(z - y) / Float64(z - a)), t, x);
	else
		tmp = Float64(Float64(t - x) * Float64(Float64(1.0 / Float64(z - a)) * Float64(-y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.7e+114], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+46], N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(N[(1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision] * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e114

   1. Initial program 80.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 42.1%

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

   6. Applied rewrites 44.0%

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

   if -1.7e114 < y < 5.4000000000000003e46

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 67.0%

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

   if 5.4000000000000003e46 < y

   1. Initial program 80.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 42.1%

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

   6. Applied rewrites 38.4%

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

   8. Applied rewrites 44.0%

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

Alternative 9: 72.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z - a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- z a)) (- x t))))
   (if (<= y -1.7e+114)
     t_1
     (if (<= y 5.4e+46) (fma (/ (- z y) (- z a)) t x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * (x - t);
	double tmp;
	if (y <= -1.7e+114) {
		tmp = t_1;
	} else if (y <= 5.4e+46) {
		tmp = fma(((z - y) / (z - a)), t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(z - a)) * Float64(x - t))
	tmp = 0.0
	if (y <= -1.7e+114)
		tmp = t_1;
	elseif (y <= 5.4e+46)
		tmp = fma(Float64(Float64(z - y) / Float64(z - a)), t, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+114], t$95$1, If[LessEqual[y, 5.4e+46], N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e114 or 5.4000000000000003e46 < y

   1. Initial program 80.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 42.1%

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

   6. Applied rewrites 44.0%

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

   if -1.7e114 < y < 5.4000000000000003e46

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 67.0%

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

Alternative 10: 70.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{z - a}, z - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- z a)) (- x t))))
   (if (<= y -1.7e+114)
     t_1
     (if (<= y 1.65e+45) (fma (/ t (- z a)) (- z y) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * (x - t);
	double tmp;
	if (y <= -1.7e+114) {
		tmp = t_1;
	} else if (y <= 1.65e+45) {
		tmp = fma((t / (z - a)), (z - y), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(z - a)) * Float64(x - t))
	tmp = 0.0
	if (y <= -1.7e+114)
		tmp = t_1;
	elseif (y <= 1.65e+45)
		tmp = fma(Float64(t / Float64(z - a)), Float64(z - y), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+114], t$95$1, If[LessEqual[y, 1.65e+45], N[(N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e114 or 1.65e45 < y

   1. Initial program 80.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 42.1%

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

   6. Applied rewrites 44.0%

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

   if -1.7e114 < y < 1.65e45

   1. Initial program 80.1%

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

   3. Applied rewrites 80.2%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 63.6%

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

Alternative 11: 59.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+154}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.7e+154)
   (fma (/ y a) (- t x) x)
   (if (<= a 4.7e+17) (* (/ y (- z a)) (- x t)) (+ x (* (- y z) (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e+154) {
		tmp = fma((y / a), (t - x), x);
	} else if (a <= 4.7e+17) {
		tmp = (y / (z - a)) * (x - t);
	} else {
		tmp = x + ((y - z) * (t / a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.7e+154)
		tmp = fma(Float64(y / a), Float64(t - x), x);
	elseif (a <= 4.7e+17)
		tmp = Float64(Float64(y / Float64(z - a)) * Float64(x - t));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.7e+154], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 4.7e+17], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.69999999999999987e154

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 49.2%

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

   if -1.69999999999999987e154 < a < 4.7e17

   1. Initial program 80.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 42.1%

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

   6. Applied rewrites 44.0%

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

   if 4.7e17 < a

   1. Initial program 80.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 51.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 43.9%

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

Alternative 12: 59.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1020000:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y a) (- t x) x)))
   (if (<= a -1.7e+154)
     t_1
     (if (<= a 1020000.0) (* (/ y (- z a)) (- x t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / a), (t - x), x);
	double tmp;
	if (a <= -1.7e+154) {
		tmp = t_1;
	} else if (a <= 1020000.0) {
		tmp = (y / (z - a)) * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / a), Float64(t - x), x)
	tmp = 0.0
	if (a <= -1.7e+154)
		tmp = t_1;
	elseif (a <= 1020000.0)
		tmp = Float64(Float64(y / Float64(z - a)) * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.7e+154], t$95$1, If[LessEqual[a, 1020000.0], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.69999999999999987e154 or 1.02e6 < a

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 49.2%

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

   if -1.69999999999999987e154 < a < 1.02e6

   1. Initial program 80.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 42.1%

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

   6. Applied rewrites 44.0%

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

Alternative 13: 55.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{if}\;a \leq -2 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-184}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-59}:\\ \;\;\;\;\frac{t \cdot z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y a) (- t x) x)))
   (if (<= a -2e-92)
     t_1
     (if (<= a 8.5e-184)
       (/ (* y (- x t)) z)
       (if (<= a 1.05e-59) (/ (* t z) (- z a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / a), (t - x), x);
	double tmp;
	if (a <= -2e-92) {
		tmp = t_1;
	} else if (a <= 8.5e-184) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 1.05e-59) {
		tmp = (t * z) / (z - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / a), Float64(t - x), x)
	tmp = 0.0
	if (a <= -2e-92)
		tmp = t_1;
	elseif (a <= 8.5e-184)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 1.05e-59)
		tmp = Float64(Float64(t * z) / Float64(z - a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2e-92], t$95$1, If[LessEqual[a, 8.5e-184], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.05e-59], N[(N[(t * z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.99999999999999998e-92 or 1.04999999999999998e-59 < a

   1. Initial program 80.1%

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

   3. Applied rewrites 84.2%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 49.2%

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

   if -1.99999999999999998e-92 < a < 8.50000000000000036e-184

   1. Initial program 80.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 42.1%

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

   6. Applied rewrites 38.4%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 24.0%

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

   if 8.50000000000000036e-184 < a < 1.04999999999999998e-59

   1. Initial program 80.1%

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

   3. Applied rewrites 63.4%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 21.0%

      \[\leadsto \frac{\color{blue}{t \cdot z}}{z - a} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 45.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-105}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-109}:\\ \;\;\;\;\frac{t \cdot z}{z - a}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 (- INFINITY))
     (/ (* x y) (- z a))
     (if (<= t_1 -5e-105)
       (+ x t)
       (if (<= t_1 2e-109)
         (/ (* t z) (- z a))
         (if (<= t_1 2e+307) (+ x t) (/ (* y (- x t)) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x * y) / (z - a);
	} else if (t_1 <= -5e-105) {
		tmp = x + t;
	} else if (t_1 <= 2e-109) {
		tmp = (t * z) / (z - a);
	} else if (t_1 <= 2e+307) {
		tmp = x + t;
	} else {
		tmp = (y * (x - t)) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * y) / (z - a);
	} else if (t_1 <= -5e-105) {
		tmp = x + t;
	} else if (t_1 <= 2e-109) {
		tmp = (t * z) / (z - a);
	} else if (t_1 <= 2e+307) {
		tmp = x + t;
	} else {
		tmp = (y * (x - t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x * y) / (z - a)
	elif t_1 <= -5e-105:
		tmp = x + t
	elif t_1 <= 2e-109:
		tmp = (t * z) / (z - a)
	elif t_1 <= 2e+307:
		tmp = x + t
	else:
		tmp = (y * (x - t)) / z
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x * y) / Float64(z - a));
	elseif (t_1 <= -5e-105)
		tmp = Float64(x + t);
	elseif (t_1 <= 2e-109)
		tmp = Float64(Float64(t * z) / Float64(z - a));
	elseif (t_1 <= 2e+307)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x * y) / (z - a);
	elseif (t_1 <= -5e-105)
		tmp = x + t;
	elseif (t_1 <= 2e-109)
		tmp = (t * z) / (z - a);
	elseif (t_1 <= 2e+307)
		tmp = x + t;
	else
		tmp = (y * (x - t)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-105], N[(x + t), $MachinePrecision], If[LessEqual[t$95$1, 2e-109], N[(N[(t * z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+307], N[(x + t), $MachinePrecision], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0

   1. Initial program 80.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 42.1%

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

   6. Applied rewrites 38.4%

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

   7. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{\color{blue}{z} - a} \]

   9. Applied rewrites 21.9%

      \[\leadsto \frac{x \cdot y}{\color{blue}{z} - a} \]

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999963e-105 or 2e-109 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.99999999999999997e307

   1. Initial program 80.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 19.1%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]

   7. Applied rewrites 34.1%

      \[\leadsto x + t \]

   if -4.99999999999999963e-105 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e-109

   1. Initial program 80.1%

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

   3. Applied rewrites 63.4%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 21.0%

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

   if 1.99999999999999997e307 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 42.1%

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

   6. Applied rewrites 38.4%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 24.0%

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

Alternative 15: 43.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 (- INFINITY))
     (/ (* x y) (- z a))
     (if (<= t_1 2e+307) (+ x t) (/ (* y (- x t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x * y) / (z - a);
	} else if (t_1 <= 2e+307) {
		tmp = x + t;
	} else {
		tmp = (y * (x - t)) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * y) / (z - a);
	} else if (t_1 <= 2e+307) {
		tmp = x + t;
	} else {
		tmp = (y * (x - t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x * y) / (z - a)
	elif t_1 <= 2e+307:
		tmp = x + t
	else:
		tmp = (y * (x - t)) / z
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x * y) / Float64(z - a));
	elseif (t_1 <= 2e+307)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x * y) / (z - a);
	elseif (t_1 <= 2e+307)
		tmp = x + t;
	else
		tmp = (y * (x - t)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+307], N[(x + t), $MachinePrecision], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0

   1. Initial program 80.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 42.1%

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

   6. Applied rewrites 38.4%

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

   7. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{\color{blue}{z} - a} \]

   9. Applied rewrites 21.9%

      \[\leadsto \frac{x \cdot y}{\color{blue}{z} - a} \]

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.99999999999999997e307

   1. Initial program 80.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 19.1%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]

   7. Applied rewrites 34.1%

      \[\leadsto x + t \]

   if 1.99999999999999997e307 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 42.1%

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

   6. Applied rewrites 38.4%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 24.0%

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

Alternative 16: 42.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(x - t\right)}{z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- x t)) z)) (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 2e+307) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (x - t)) / z;
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 2e+307) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (x - t)) / z;
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 2e+307) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (x - t)) / z
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 2e+307:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(x - t)) / z)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 2e+307)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (x - t)) / z;
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 2e+307)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 2e+307], N[(x + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0 or 1.99999999999999997e307 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 42.1%

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

   6. Applied rewrites 38.4%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 24.0%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.99999999999999997e307

   1. Initial program 80.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 19.1%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]

   7. Applied rewrites 34.1%

      \[\leadsto x + t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 37.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / (a - z);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t * y) / (a - z)
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= math.inf:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t * y) / (a - z);
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= Inf)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0 or +inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 80.1%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 42.1%

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

   5. Taylor expanded in x around 0

      \[\leadsto \frac{t \cdot y}{\color{blue}{a - z}} \]

   7. Applied rewrites 21.2%

      \[\leadsto \frac{t \cdot y}{\color{blue}{a - z}} \]

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < +inf.0

   1. Initial program 80.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 19.1%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]

   7. Applied rewrites 34.1%

      \[\leadsto x + t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 34.1% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ x + t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x t))

C

double code(double x, double y, double z, double t, double a) {
	return x + t;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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
    code = x + t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + t;
}

Python

def code(x, y, z, t, a):
	return x + t

Julia

function code(x, y, z, t, a)
	return Float64(x + t)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + t;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + t), $MachinePrecision]

Derivation

1. Initial program 80.1%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 19.1%

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

5. Taylor expanded in x around 0

   \[\leadsto x + t \]

7. Applied rewrites 34.1%

   \[\leadsto x + t \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025153 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))