Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 76.7% → 98.1%

Time: 14.1s

Alternatives: 7

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.7%

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

3. Applied rewrites 89.2%

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

4. Taylor expanded in z around 0

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

6. Applied rewrites 98.1%

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

Alternative 2: 87.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y}{a} \cdot z\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (* (/ y a) z))))
   (if (<= a -1.45e+34) t_1 (if (<= a 2.2e+101) (fma y (/ z (- t a)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y / a) * z);
	double tmp;
	if (a <= -1.45e+34) {
		tmp = t_1;
	} else if (a <= 2.2e+101) {
		tmp = fma(y, (z / (t - a)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y / a) * z))
	tmp = 0.0
	if (a <= -1.45e+34)
		tmp = t_1;
	elseif (a <= 2.2e+101)
		tmp = fma(y, Float64(z / Float64(t - a)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e+34], t$95$1, If[LessEqual[a, 2.2e+101], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4500000000000001e34 or 2.2000000000000001e101 < a

   1. Initial program 76.7%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 64.5%

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

   6. Applied rewrites 66.1%

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

   if -1.4500000000000001e34 < a < 2.2000000000000001e101

   1. Initial program 76.7%

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

   3. Applied rewrites 89.2%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 76.5%

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

Alternative 3: 84.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+134}:\\ \;\;\;\;\mathsf{fma}\left(y, 1, x\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.1e+134)
   (fma y 1.0 x)
   (if (<= a 3.8e+106) (fma y (/ z (- t a)) x) (fma y 1.0 x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e+134) {
		tmp = fma(y, 1.0, x);
	} else if (a <= 3.8e+106) {
		tmp = fma(y, (z / (t - a)), x);
	} else {
		tmp = fma(y, 1.0, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e+134)
		tmp = fma(y, 1.0, x);
	elseif (a <= 3.8e+106)
		tmp = fma(y, Float64(z / Float64(t - a)), x);
	else
		tmp = fma(y, 1.0, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e+134], N[(y * 1.0 + x), $MachinePrecision], If[LessEqual[a, 3.8e+106], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * 1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.1000000000000001e134 or 3.7999999999999998e106 < a

   1. Initial program 76.7%

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

   3. Applied rewrites 89.2%

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

   4. Taylor expanded in a around inf

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

   6. Applied rewrites 60.1%

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

   if -2.1000000000000001e134 < a < 3.7999999999999998e106

   1. Initial program 76.7%

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

   3. Applied rewrites 89.2%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 76.5%

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

Alternative 4: 77.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+107}:\\ \;\;\;\;\mathsf{fma}\left(y, 1, x\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+102}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.2e+107)
   (fma y 1.0 x)
   (if (<= a 8.2e+102) (fma (/ y t) (- z a) x) (fma y 1.0 x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.2e+107) {
		tmp = fma(y, 1.0, x);
	} else if (a <= 8.2e+102) {
		tmp = fma((y / t), (z - a), x);
	} else {
		tmp = fma(y, 1.0, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.2e+107)
		tmp = fma(y, 1.0, x);
	elseif (a <= 8.2e+102)
		tmp = fma(Float64(y / t), Float64(z - a), x);
	else
		tmp = fma(y, 1.0, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.2e+107], N[(y * 1.0 + x), $MachinePrecision], If[LessEqual[a, 8.2e+102], N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + x), $MachinePrecision], N[(y * 1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.2000000000000002e107 or 8.1999999999999999e102 < a

   1. Initial program 76.7%

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

   3. Applied rewrites 89.2%

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

   4. Taylor expanded in a around inf

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

   6. Applied rewrites 60.1%

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

   if -5.2000000000000002e107 < a < 8.1999999999999999e102

   1. Initial program 76.7%

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

   2. Taylor expanded in t around -inf

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

   4. Applied rewrites 57.6%

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

   6. Applied rewrites 61.4%

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

Alternative 5: 75.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+107}:\\ \;\;\;\;\mathsf{fma}\left(y, 1, x\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+102}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.5e+107)
   (fma y 1.0 x)
   (if (<= a 8e+102) (fma y (/ z t) x) (fma y 1.0 x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+107) {
		tmp = fma(y, 1.0, x);
	} else if (a <= 8e+102) {
		tmp = fma(y, (z / t), x);
	} else {
		tmp = fma(y, 1.0, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.5e+107)
		tmp = fma(y, 1.0, x);
	elseif (a <= 8e+102)
		tmp = fma(y, Float64(z / t), x);
	else
		tmp = fma(y, 1.0, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.5e+107], N[(y * 1.0 + x), $MachinePrecision], If[LessEqual[a, 8e+102], N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision], N[(y * 1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.5000000000000001e107 or 7.99999999999999982e102 < a

   1. Initial program 76.7%

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

   3. Applied rewrites 89.2%

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

   4. Taylor expanded in a around inf

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

   6. Applied rewrites 60.1%

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

   if -2.5000000000000001e107 < a < 7.99999999999999982e102

   1. Initial program 76.7%

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

   3. Applied rewrites 89.2%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 76.5%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 62.1%

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

Alternative 6: 62.6% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (+ x y) (/ (* (- z t) y) (- a t))) (- INFINITY))
   (* (/ y t) z)
   (fma y 1.0 x)))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 76.7%

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

   2. Taylor expanded in t around -inf

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

   4. Applied rewrites 57.6%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 18.6%

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

   9. Applied rewrites 20.3%

      \[\leadsto \frac{y}{t} \cdot z \]

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

   1. Initial program 76.7%

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

   3. Applied rewrites 89.2%

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

   4. Taylor expanded in a around inf

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

   6. Applied rewrites 60.1%

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

Alternative 7: 60.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, 1, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.7%

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

3. Applied rewrites 89.2%

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

4. Taylor expanded in a around inf

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

6. Applied rewrites 60.1%

   \[\leadsto \mathsf{fma}\left(y, \color{blue}{1}, x\right) \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025153 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64
  (- (+ x y) (/ (* (- z t) y) (- a t))))