Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Percentage Accurate: 97.2% → 99.7%

Time: 17.5s

Alternatives: 13

Speedup: 1.1×

Specification

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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 - z) + 1.0d0) / a))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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 - z) + 1.0d0) / a))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (x y z t a) :precision binary64 (fma (/ (- z y) (- 1.0 (- z t))) a x))

C

double code(double x, double y, double z, double t, double a) {
	return fma(((z - y) / (1.0 - (z - t))), a, x);
}

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

3. Applied rewrites 99.7%

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

Alternative 2: 97.5% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (x y z t a) :precision binary64 (fma (/ a (- (- z 1.0) t)) (- y z) x))

C

double code(double x, double y, double z, double t, double a) {
	return fma((a / ((z - 1.0) - t)), (y - z), x);
}

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

3. Applied rewrites 97.5%

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

Alternative 3: 91.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{if}\;t \leq -1.18 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.85 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{1 - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) t) a x)))
   (if (<= t -1.18e+98)
     t_1
     (if (<= t 3.85e+68) (fma (/ (- z y) (- 1.0 z)) a x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - y) / t), a, x);
	double tmp;
	if (t <= -1.18e+98) {
		tmp = t_1;
	} else if (t <= 3.85e+68) {
		tmp = fma(((z - y) / (1.0 - z)), a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / t), a, x)
	tmp = 0.0
	if (t <= -1.18e+98)
		tmp = t_1;
	elseif (t <= 3.85e+68)
		tmp = fma(Float64(Float64(z - y) / Float64(1.0 - z)), a, x);
	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] / t), $MachinePrecision] * a + x), $MachinePrecision]}, If[LessEqual[t, -1.18e+98], t$95$1, If[LessEqual[t, 3.85e+68], N[(N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.18000000000000002e98 or 3.8499999999999999e68 < t

   1. Initial program 97.2%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 53.3%

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

   if -1.18000000000000002e98 < t < 3.8499999999999999e68

   1. Initial program 97.2%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 80.8%

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

Alternative 4: 90.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{if}\;t \leq -1.18 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.85 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{z - 1}, y - z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) t) a x)))
   (if (<= t -1.18e+98)
     t_1
     (if (<= t 3.85e+68) (fma (/ a (- z 1.0)) (- y z) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - y) / t), a, x);
	double tmp;
	if (t <= -1.18e+98) {
		tmp = t_1;
	} else if (t <= 3.85e+68) {
		tmp = fma((a / (z - 1.0)), (y - z), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / t), a, x)
	tmp = 0.0
	if (t <= -1.18e+98)
		tmp = t_1;
	elseif (t <= 3.85e+68)
		tmp = fma(Float64(a / Float64(z - 1.0)), Float64(y - z), x);
	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] / t), $MachinePrecision] * a + x), $MachinePrecision]}, If[LessEqual[t, -1.18e+98], t$95$1, If[LessEqual[t, 3.85e+68], N[(N[(a / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.18000000000000002e98 or 3.8499999999999999e68 < t

   1. Initial program 97.2%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 53.3%

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

   if -1.18000000000000002e98 < t < 3.8499999999999999e68

   1. Initial program 97.2%

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

   3. Applied rewrites 97.5%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 79.1%

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

Alternative 5: 87.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{a}{z}, y - z, x\right)\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{a}{1 + t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ a z) (- y z) x)))
   (if (<= z -1.26e+26)
     t_1
     (if (<= z 6.7e+38) (- x (* (/ a (+ 1.0 t)) y)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((a / z), (y - z), x);
	double tmp;
	if (z <= -1.26e+26) {
		tmp = t_1;
	} else if (z <= 6.7e+38) {
		tmp = x - ((a / (1.0 + t)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(a / z), Float64(y - z), x)
	tmp = 0.0
	if (z <= -1.26e+26)
		tmp = t_1;
	elseif (z <= 6.7e+38)
		tmp = Float64(x - Float64(Float64(a / Float64(1.0 + t)) * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a / z), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.26e+26], t$95$1, If[LessEqual[z, 6.7e+38], N[(x - N[(N[(a / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25999999999999995e26 or 6.70000000000000025e38 < z

   1. Initial program 97.2%

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

   3. Applied rewrites 97.5%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 57.7%

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

   if -1.25999999999999995e26 < z < 6.70000000000000025e38

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]

   4. Applied rewrites 69.4%

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]

   6. Applied rewrites 71.8%

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

Alternative 6: 79.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 255:\\ \;\;\;\;x - \frac{y}{1 - z} \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) t) a x)))
   (if (<= t -1.15e+35)
     t_1
     (if (<= t 255.0) (- x (* (/ y (- 1.0 z)) a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - y) / t), a, x);
	double tmp;
	if (t <= -1.15e+35) {
		tmp = t_1;
	} else if (t <= 255.0) {
		tmp = x - ((y / (1.0 - z)) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / t), a, x)
	tmp = 0.0
	if (t <= -1.15e+35)
		tmp = t_1;
	elseif (t <= 255.0)
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 - 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] / t), $MachinePrecision] * a + x), $MachinePrecision]}, If[LessEqual[t, -1.15e+35], t$95$1, If[LessEqual[t, 255.0], N[(x - N[(N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1499999999999999e35 or 255 < t

   1. Initial program 97.2%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 53.3%

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

   if -1.1499999999999999e35 < t < 255

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 70.6%

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

   5. Taylor expanded in y around inf

      \[\leadsto x - \frac{a \cdot y}{\color{blue}{1 - z}} \]

   7. Applied rewrites 64.1%

      \[\leadsto x - \frac{a \cdot y}{\color{blue}{1 - z}} \]

   9. Applied rewrites 65.6%

      \[\leadsto x - \frac{y}{1 - z} \cdot a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 77.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{a}{z}, y - z, x\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(-1 \cdot a, y - z, x\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{y}{t} \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ a z) (- y z) x)))
   (if (<= z -1.0)
     t_1
     (if (<= z 6.2e-85)
       (fma (* -1.0 a) (- y z) x)
       (if (<= z 8.5e+38) (- x (* (/ y t) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((a / z), (y - z), x);
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 6.2e-85) {
		tmp = fma((-1.0 * a), (y - z), x);
	} else if (z <= 8.5e+38) {
		tmp = x - ((y / t) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(a / z), Float64(y - z), x)
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= 6.2e-85)
		tmp = fma(Float64(-1.0 * a), Float64(y - z), x);
	elseif (z <= 8.5e+38)
		tmp = Float64(x - Float64(Float64(y / t) * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a / z), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$1, If[LessEqual[z, 6.2e-85], N[(N[(-1.0 * a), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 8.5e+38], N[(x - N[(N[(y / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 8.4999999999999997e38 < z

   1. Initial program 97.2%

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

   3. Applied rewrites 97.5%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 57.7%

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

   if -1 < z < 6.2000000000000005e-85

   1. Initial program 97.2%

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

   3. Applied rewrites 97.5%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 79.1%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 51.4%

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

   if 6.2000000000000005e-85 < z < 8.4999999999999997e38

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]

   4. Applied rewrites 69.4%

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 54.1%

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

   9. Applied rewrites 55.8%

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

Alternative 8: 74.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -900000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(-1 \cdot a, y - z, x\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{y}{t} \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -900000.0)
   (- x a)
   (if (<= z 6.2e-85)
     (fma (* -1.0 a) (- y z) x)
     (if (<= z 3.3e+38) (- x (* (/ y t) a)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -900000.0) {
		tmp = x - a;
	} else if (z <= 6.2e-85) {
		tmp = fma((-1.0 * a), (y - z), x);
	} else if (z <= 3.3e+38) {
		tmp = x - ((y / t) * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -900000.0)
		tmp = Float64(x - a);
	elseif (z <= 6.2e-85)
		tmp = fma(Float64(-1.0 * a), Float64(y - z), x);
	elseif (z <= 3.3e+38)
		tmp = Float64(x - Float64(Float64(y / t) * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -900000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 6.2e-85], N[(N[(-1.0 * a), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 3.3e+38], N[(x - N[(N[(y / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9e5 or 3.2999999999999999e38 < z

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.0%

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

   if -9e5 < z < 6.2000000000000005e-85

   1. Initial program 97.2%

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

   3. Applied rewrites 97.5%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 79.1%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 51.4%

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

   if 6.2000000000000005e-85 < z < 3.2999999999999999e38

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]

   4. Applied rewrites 69.4%

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 54.1%

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

   9. Applied rewrites 55.8%

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

Alternative 9: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1050000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-85}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{y}{t} \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1050000.0)
   (- x a)
   (if (<= z 6.2e-85)
     (- x (* a y))
     (if (<= z 3.3e+38) (- x (* (/ y t) a)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1050000.0) {
		tmp = x - a;
	} else if (z <= 6.2e-85) {
		tmp = x - (a * y);
	} else if (z <= 3.3e+38) {
		tmp = x - ((y / t) * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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) :: tmp
    if (z <= (-1050000.0d0)) then
        tmp = x - a
    else if (z <= 6.2d-85) then
        tmp = x - (a * y)
    else if (z <= 3.3d+38) then
        tmp = x - ((y / t) * a)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1050000.0) {
		tmp = x - a;
	} else if (z <= 6.2e-85) {
		tmp = x - (a * y);
	} else if (z <= 3.3e+38) {
		tmp = x - ((y / t) * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1050000.0:
		tmp = x - a
	elif z <= 6.2e-85:
		tmp = x - (a * y)
	elif z <= 3.3e+38:
		tmp = x - ((y / t) * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1050000.0)
		tmp = Float64(x - a);
	elseif (z <= 6.2e-85)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 3.3e+38)
		tmp = Float64(x - Float64(Float64(y / t) * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1050000.0)
		tmp = x - a;
	elseif (z <= 6.2e-85)
		tmp = x - (a * y);
	elseif (z <= 3.3e+38)
		tmp = x - ((y / t) * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1050000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 6.2e-85], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+38], N[(x - N[(N[(y / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e6 or 3.2999999999999999e38 < z

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.0%

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

   if -1.05e6 < z < 6.2000000000000005e-85

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 70.6%

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

   5. Taylor expanded in y around inf

      \[\leadsto x - \frac{a \cdot y}{\color{blue}{1 - z}} \]

   7. Applied rewrites 64.1%

      \[\leadsto x - \frac{a \cdot y}{\color{blue}{1 - z}} \]

   9. Applied rewrites 65.6%

      \[\leadsto x - \frac{y}{1 - z} \cdot a \]

   10. Taylor expanded in z around 0

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

   12. Applied rewrites 57.4%

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

   if 6.2000000000000005e-85 < z < 3.2999999999999999e38

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]

   4. Applied rewrites 69.4%

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 54.1%

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

   9. Applied rewrites 55.8%

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

Alternative 10: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1050000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-85}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{a}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1050000.0)
   (- x a)
   (if (<= z 6.2e-85)
     (- x (* a y))
     (if (<= z 3.3e+38) (- x (* (/ a t) y)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1050000.0) {
		tmp = x - a;
	} else if (z <= 6.2e-85) {
		tmp = x - (a * y);
	} else if (z <= 3.3e+38) {
		tmp = x - ((a / t) * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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) :: tmp
    if (z <= (-1050000.0d0)) then
        tmp = x - a
    else if (z <= 6.2d-85) then
        tmp = x - (a * y)
    else if (z <= 3.3d+38) then
        tmp = x - ((a / t) * y)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1050000.0) {
		tmp = x - a;
	} else if (z <= 6.2e-85) {
		tmp = x - (a * y);
	} else if (z <= 3.3e+38) {
		tmp = x - ((a / t) * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1050000.0:
		tmp = x - a
	elif z <= 6.2e-85:
		tmp = x - (a * y)
	elif z <= 3.3e+38:
		tmp = x - ((a / t) * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1050000.0)
		tmp = Float64(x - a);
	elseif (z <= 6.2e-85)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 3.3e+38)
		tmp = Float64(x - Float64(Float64(a / t) * y));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1050000.0)
		tmp = x - a;
	elseif (z <= 6.2e-85)
		tmp = x - (a * y);
	elseif (z <= 3.3e+38)
		tmp = x - ((a / t) * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1050000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 6.2e-85], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+38], N[(x - N[(N[(a / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e6 or 3.2999999999999999e38 < z

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.0%

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

   if -1.05e6 < z < 6.2000000000000005e-85

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 70.6%

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

   5. Taylor expanded in y around inf

      \[\leadsto x - \frac{a \cdot y}{\color{blue}{1 - z}} \]

   7. Applied rewrites 64.1%

      \[\leadsto x - \frac{a \cdot y}{\color{blue}{1 - z}} \]

   9. Applied rewrites 65.6%

      \[\leadsto x - \frac{y}{1 - z} \cdot a \]

   10. Taylor expanded in z around 0

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

   12. Applied rewrites 57.4%

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

   if 6.2000000000000005e-85 < z < 3.2999999999999999e38

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]

   4. Applied rewrites 69.4%

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 54.1%

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

   9. Applied rewrites 55.6%

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

Alternative 11: 73.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1050000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+16}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1050000.0) (- x a) (if (<= z 9.2e+16) (- x (* a y)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1050000.0) {
		tmp = x - a;
	} else if (z <= 9.2e+16) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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) :: tmp
    if (z <= (-1050000.0d0)) then
        tmp = x - a
    else if (z <= 9.2d+16) then
        tmp = x - (a * y)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1050000.0) {
		tmp = x - a;
	} else if (z <= 9.2e+16) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1050000.0:
		tmp = x - a
	elif z <= 9.2e+16:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1050000.0)
		tmp = Float64(x - a);
	elseif (z <= 9.2e+16)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1050000.0)
		tmp = x - a;
	elseif (z <= 9.2e+16)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1050000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 9.2e+16], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e6 or 9.2e16 < z

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.0%

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

   if -1.05e6 < z < 9.2e16

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 70.6%

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

   5. Taylor expanded in y around inf

      \[\leadsto x - \frac{a \cdot y}{\color{blue}{1 - z}} \]

   7. Applied rewrites 64.1%

      \[\leadsto x - \frac{a \cdot y}{\color{blue}{1 - z}} \]

   9. Applied rewrites 65.6%

      \[\leadsto x - \frac{y}{1 - z} \cdot a \]

   10. Taylor expanded in z around 0

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

   12. Applied rewrites 57.4%

       \[\leadsto x - a \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 66.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-59}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+17}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e-59) (- x a) (if (<= z 1.02e+17) (* x 1.0) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e-59) {
		tmp = x - a;
	} else if (z <= 1.02e+17) {
		tmp = x * 1.0;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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) :: tmp
    if (z <= (-8d-59)) then
        tmp = x - a
    else if (z <= 1.02d+17) then
        tmp = x * 1.0d0
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e-59) {
		tmp = x - a;
	} else if (z <= 1.02e+17) {
		tmp = x * 1.0;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e-59:
		tmp = x - a
	elif z <= 1.02e+17:
		tmp = x * 1.0
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e-59)
		tmp = Float64(x - a);
	elseif (z <= 1.02e+17)
		tmp = Float64(x * 1.0);
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e-59)
		tmp = x - a;
	elseif (z <= 1.02e+17)
		tmp = x * 1.0;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e-59], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.02e+17], N[(x * 1.0), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000002e-59 or 1.02e17 < z

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.0%

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

   if -8.0000000000000002e-59 < z < 1.02e17

   1. Initial program 97.2%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 80.6%

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

   7. Taylor expanded in x around inf

      \[\leadsto x \cdot 1 \]

   9. Applied rewrites 53.8%

      \[\leadsto x \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 60.0% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ x - a \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 60.0%

   \[\leadsto x - \color{blue}{a} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025153 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64
  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))