Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 67.7% → 67.7%

Time: 2.0s

Alternatives: 9

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

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

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

real(8) function code(x, y, z, t, a)
    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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 67.7% accurate, 1.0× speedup

Math

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

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

real(8) function code(x, y, z, t, a)
    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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 67.7% accurate, 1.0× speedup

Math

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

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

real(8) function code(x, y, z, t, a)
    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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 64.7%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 53.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (- a z)))))
   (if (<= a -1.7e+92)
     t_1
     (if (<= a 1.5e+77) (/ (* (- y z) (- t x)) (- a z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a - z));
	double tmp;
	if (a <= -1.7e+92) {
		tmp = t_1;
	} else if (a <= 1.5e+77) {
		tmp = ((y - z) * (t - x)) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) / (a - z))
    if (a <= (-1.7d+92)) then
        tmp = t_1
    else if (a <= 1.5d+77) then
        tmp = ((y - z) * (t - x)) / (a - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a - z));
	double tmp;
	if (a <= -1.7e+92) {
		tmp = t_1;
	} else if (a <= 1.5e+77) {
		tmp = ((y - z) * (t - x)) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / (a - z))
	tmp = 0
	if a <= -1.7e+92:
		tmp = t_1
	elif a <= 1.5e+77:
		tmp = ((y - z) * (t - x)) / (a - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -1.7e+92)
		tmp = t_1;
	elseif (a <= 1.5e+77)
		tmp = Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -1.7e+92)
		tmp = t_1;
	elseif (a <= 1.5e+77)
		tmp = ((y - z) * (t - x)) / (a - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+92], t$95$1, If[LessEqual[a, 1.5e+77], N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6999999999999999e92 or 1.4999999999999999e77 < a

   1. Initial program 67.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 52.4%

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

   if -1.6999999999999999e92 < a < 1.4999999999999999e77

   1. Initial program 63.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 54.8%

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

Alternative 3: 24.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+140}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.4e+140) (+ x (* (- y z) (- t x))) (+ x (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+140) {
		tmp = x + ((y - z) * (t - x));
	} else {
		tmp = x + ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 (t <= (-3.4d+140)) then
        tmp = x + ((y - z) * (t - x))
    else
        tmp = x + ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+140) {
		tmp = x + ((y - z) * (t - x));
	} else {
		tmp = x + ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.4e+140:
		tmp = x + ((y - z) * (t - x))
	else:
		tmp = x + ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.4e+140)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t - x)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.4e+140)
		tmp = x + ((y - z) * (t - x));
	else
		tmp = x + ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.4e+140], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4e140

   1. Initial program 64.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 24.3%

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

   if -3.4e140 < t

   1. Initial program 64.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 29.5%

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

Alternative 4: 19.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.4 \cdot 10^{+25}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 1.4e+25) (+ x (* (- y z) (- t x))) (+ x (/ (- a z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.4e+25) {
		tmp = x + ((y - z) * (t - x));
	} else {
		tmp = x + ((a - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 (x <= 1.4d+25) then
        tmp = x + ((y - z) * (t - x))
    else
        tmp = x + ((a - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.4e+25) {
		tmp = x + ((y - z) * (t - x));
	} else {
		tmp = x + ((a - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 1.4e+25:
		tmp = x + ((y - z) * (t - x))
	else:
		tmp = x + ((a - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 1.4e+25)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t - x)));
	else
		tmp = Float64(x + Float64(Float64(a - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 1.4e+25)
		tmp = x + ((y - z) * (t - x));
	else
		tmp = x + ((a - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 1.4e+25], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.4000000000000001e25

   1. Initial program 70.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 16.8%

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

   if 1.4000000000000001e25 < x

   1. Initial program 50.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 37.2%

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

Alternative 5: 18.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3 \cdot 10^{+41}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 3e+41) (+ x (* (- y z) (- t x))) (+ x (- y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 3e+41) {
		tmp = x + ((y - z) * (t - x));
	} else {
		tmp = x + (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 (x <= 3d+41) then
        tmp = x + ((y - z) * (t - x))
    else
        tmp = x + (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 3e+41) {
		tmp = x + ((y - z) * (t - x));
	} else {
		tmp = x + (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 3e+41:
		tmp = x + ((y - z) * (t - x))
	else:
		tmp = x + (y - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 3e+41)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t - x)));
	else
		tmp = Float64(x + Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 3e+41)
		tmp = x + ((y - z) * (t - x));
	else
		tmp = x + (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 3e+41], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.9999999999999998e41

   1. Initial program 70.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 17.0%

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

   if 2.9999999999999998e41 < x

   1. Initial program 49.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 23.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 32.8%

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

Alternative 6: 18.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+153}:\\ \;\;\;\;\left(y - z\right) \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.8e+153) (* (- y z) (- y z)) (+ x (- y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.8e+153) {
		tmp = (y - z) * (y - z);
	} else {
		tmp = x + (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 (y <= (-3.8d+153)) then
        tmp = (y - z) * (y - z)
    else
        tmp = x + (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.8e+153) {
		tmp = (y - z) * (y - z);
	} else {
		tmp = x + (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.8e+153:
		tmp = (y - z) * (y - z)
	else:
		tmp = x + (y - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.8e+153)
		tmp = Float64(Float64(y - z) * Float64(y - z));
	else
		tmp = Float64(x + Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.8e+153)
		tmp = (y - z) * (y - z);
	else
		tmp = x + (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.8e+153], N[(N[(y - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.79999999999999966e153

   1. Initial program 64.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 60.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 18.0%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 26.7%

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

   if -3.79999999999999966e153 < y

   1. Initial program 64.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 18.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 20.0%

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

Alternative 7: 17.0% accurate, 4.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.7%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 18.7%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 18.0%

   \[\leadsto x + \left(y - \color{blue}{z}\right) \]
9. Add Preprocessing

Alternative 8: 9.9% accurate, 4.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.7%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 18.7%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 18.0%

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

9. Taylor expanded in x around 0

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

11. Applied rewrites 10.3%

    \[\leadsto x + \left(a - \color{blue}{z}\right) \]
12. Add Preprocessing

Alternative 9: 3.3% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ y - z \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.7%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 18.7%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 18.0%

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

9. Taylor expanded in x around 0

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

11. Applied rewrites 3.1%

    \[\leadsto \color{blue}{y - z} \]
12. Add Preprocessing

Developer Target 1: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64
  :pre (TRUE)

  :alt
  (! :herbie-platform default (if (< z -125361310560950360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- t (* (/ y z) (- t x))) (if (< z 44467023691138110000000000000000000000000000000000000000000000000) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x))))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))