Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 94.4%

Time: 14.0s

Alternatives: 20

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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(y - z) * Float64(Float64(t - x) / Float64(a - z))))
end

MATLAB

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

Wolfram

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

Initial Program: 80.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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(y - z) * Float64(Float64(t - x) / Float64(a - z))))
end

MATLAB

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

Wolfram

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

Alternative 1: 94.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{\frac{y - z}{a - z}}{\frac{-1}{x - t}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - z}{y - z}}{x - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -2e-262)
     (+ x (/ (/ (- y z) (- a z)) (/ -1.0 (- x t))))
     (if (<= t_1 0.0)
       (+ t (* (/ (- t x) z) (- a y)))
       (+ x (/ -1.0 (/ (/ (- a z) (- y z)) (- x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-262) {
		tmp = x + (((y - z) / (a - z)) / (-1.0 / (x - t)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)));
	}
	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) * ((t - x) / (a - z)))
    if (t_1 <= (-2d-262)) then
        tmp = x + (((y - z) / (a - z)) / ((-1.0d0) / (x - t)))
    else if (t_1 <= 0.0d0) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x + ((-1.0d0) / (((a - z) / (y - z)) / (x - t)))
    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) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-262) {
		tmp = x + (((y - z) / (a - z)) / (-1.0 / (x - t)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -2e-262:
		tmp = x + (((y - z) / (a - z)) / (-1.0 / (x - t)))
	elif t_1 <= 0.0:
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -2e-262)
		tmp = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) / Float64(-1.0 / Float64(x - t))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(Float64(a - z) / Float64(y - z)) / Float64(x - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -2e-262)
		tmp = x + (((y - z) / (a - z)) / (-1.0 / (x - t)));
	elseif (t_1 <= 0.0)
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-262], N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] / N[(-1.0 / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 / N[(N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000002e-262

   1. Initial program 90.7%

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

      1. clear-num 90.5%

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

      2. un-div-inv 90.5%

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

   4. Applied egg-rr 90.5%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 46.6%

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

      2. div-inv 46.6%

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

      3. times-frac 44.3%

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

   6. Applied egg-rr 44.3%

      \[\leadsto x + \color{blue}{\frac{\sqrt{y - z}}{a - z} \cdot \frac{\sqrt{y - z}}{\frac{1}{t - x}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 48.2%

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

      2. *-commutative 48.2%

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

      3. associate-*r/ 48.2%

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

      4. rem-square-sqrt 93.9%

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

   8. Simplified 93.9%

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

   if -2.00000000000000002e-262 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

      1. +-commutative 3.5%

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

      2. fma-define 3.7%

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

   3. Simplified 3.7%

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

   5. Taylor expanded in z around inf 83.0%

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

      1. associate--l+ 83.0%

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

      2. distribute-lft-out-- 83.0%

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

      3. div-sub 83.0%

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

      4. mul-1-neg 83.0%

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

      5. unsub-neg 83.0%

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

      6. div-sub 83.0%

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

      7. associate-/l* 85.9%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

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

   1. Initial program 92.4%

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

      1. associate-*r/ 76.0%

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

      2. clear-num 75.8%

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

   4. Applied egg-rr 75.8%

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

      1. associate-/r* 93.8%

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

      2. div-inv 93.7%

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

   6. Applied egg-rr 93.7%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{a - z}{y - z} \cdot \frac{1}{t - x}}} \]
   7. Step-by-step derivation

      1. un-div-inv 93.8%

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

   8. Applied egg-rr 93.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{\frac{y - z}{a - z}}{\frac{-1}{x - t}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - z}{y - z}}{x - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-262} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - z}{y - z}}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-262) (not (<= t_1 0.0)))
     (+ x (/ -1.0 (/ (/ (- a z) (- y z)) (- x t))))
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-262) || !(t_1 <= 0.0)) {
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	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) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-262)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((-1.0d0) / (((a - z) / (y - z)) / (x - t)))
    else
        tmp = t + (((t - x) / z) * (a - y))
    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) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-262) || !(t_1 <= 0.0)) {
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-262) or not (t_1 <= 0.0):
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-262) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(Float64(a - z) / Float64(y - z)) / Float64(x - t))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-262) || ~((t_1 <= 0.0)))
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-262], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(-1.0 / N[(N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000002e-262 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.5%

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

      1. associate-*r/ 75.5%

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

      2. clear-num 75.4%

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

   4. Applied egg-rr 75.4%

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

      1. associate-/r* 93.8%

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

      2. div-inv 93.8%

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

   6. Applied egg-rr 93.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{a - z}{y - z} \cdot \frac{1}{t - x}}} \]
   7. Step-by-step derivation

      1. un-div-inv 93.8%

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

   8. Applied egg-rr 93.8%

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

   if -2.00000000000000002e-262 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

      1. +-commutative 3.5%

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

      2. fma-define 3.7%

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

   3. Simplified 3.7%

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

   5. Taylor expanded in z around inf 83.0%

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

      1. associate--l+ 83.0%

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

      2. distribute-lft-out-- 83.0%

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

      3. div-sub 83.0%

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

      4. mul-1-neg 83.0%

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

      5. unsub-neg 83.0%

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

      6. div-sub 83.0%

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

      7. associate-/l* 85.9%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-262} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - z}{y - z}}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-262} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-303}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-262) (not (<= t_1 2e-303)))
     t_1
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-262) || !(t_1 <= 2e-303)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	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) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-262)) .or. (.not. (t_1 <= 2d-303))) then
        tmp = t_1
    else
        tmp = t + (((t - x) / z) * (a - y))
    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) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-262) || !(t_1 <= 2e-303)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-262) or not (t_1 <= 2e-303):
		tmp = t_1
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-262) || !(t_1 <= 2e-303))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-262) || ~((t_1 <= 2e-303)))
		tmp = t_1;
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-262], N[Not[LessEqual[t$95$1, 2e-303]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000002e-262 or 1.99999999999999986e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.3%

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

   if -2.00000000000000002e-262 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.99999999999999986e-303

   1. Initial program 3.8%

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

      1. +-commutative 3.8%

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

      2. fma-define 4.0%

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

   3. Simplified 4.0%

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

   5. Taylor expanded in z around inf 81.2%

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

      1. associate--l+ 81.2%

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

      2. distribute-lft-out-- 81.2%

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

      3. div-sub 81.3%

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

      4. mul-1-neg 81.3%

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

      5. unsub-neg 81.3%

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

      6. div-sub 81.2%

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

      7. associate-/l* 84.0%

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

      8. associate-/l* 97.1%

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

      9. distribute-rgt-out-- 97.1%

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

   7. Simplified 97.1%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-262} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-303}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-303}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -2e-262)
     t_1
     (if (<= t_1 2e-303)
       (+ t (* (/ (- t x) z) (- a y)))
       (+ x (/ (- y z) (/ (- a z) (- t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-262) {
		tmp = t_1;
	} else if (t_1 <= 2e-303) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	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) * ((t - x) / (a - z)))
    if (t_1 <= (-2d-262)) then
        tmp = t_1
    else if (t_1 <= 2d-303) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    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) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-262) {
		tmp = t_1;
	} else if (t_1 <= 2e-303) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -2e-262:
		tmp = t_1
	elif t_1 <= 2e-303:
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -2e-262)
		tmp = t_1;
	elseif (t_1 <= 2e-303)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -2e-262)
		tmp = t_1;
	elseif (t_1 <= 2e-303)
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-262], t$95$1, If[LessEqual[t$95$1, 2e-303], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000002e-262

   1. Initial program 90.7%

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

   if -2.00000000000000002e-262 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.99999999999999986e-303

   1. Initial program 3.8%

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

      1. +-commutative 3.8%

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

      2. fma-define 4.0%

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

   3. Simplified 4.0%

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

   5. Taylor expanded in z around inf 81.2%

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

      1. associate--l+ 81.2%

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

      2. distribute-lft-out-- 81.2%

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

      3. div-sub 81.3%

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

      4. mul-1-neg 81.3%

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

      5. unsub-neg 81.3%

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

      6. div-sub 81.2%

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

      7. associate-/l* 84.0%

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

      8. associate-/l* 97.1%

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

      9. distribute-rgt-out-- 97.1%

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

   7. Simplified 97.1%

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

   if 1.99999999999999986e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.0%

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

      1. clear-num 94.1%

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

      2. un-div-inv 94.2%

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

   4. Applied egg-rr 94.2%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-262}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-303}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{x \cdot a}{z}\\ \mathbf{if}\;z \leq -1.48 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+17}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+229}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* x a) z))))
   (if (<= z -1.48e+82)
     t_1
     (if (<= z 1.35e+17)
       (+ x (* t (/ y a)))
       (if (<= z 4.5e+229) (* y (/ (- x t) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((x * a) / z);
	double tmp;
	if (z <= -1.48e+82) {
		tmp = t_1;
	} else if (z <= 1.35e+17) {
		tmp = x + (t * (y / a));
	} else if (z <= 4.5e+229) {
		tmp = y * ((x - t) / 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 = t - ((x * a) / z)
    if (z <= (-1.48d+82)) then
        tmp = t_1
    else if (z <= 1.35d+17) then
        tmp = x + (t * (y / a))
    else if (z <= 4.5d+229) then
        tmp = y * ((x - t) / 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 = t - ((x * a) / z);
	double tmp;
	if (z <= -1.48e+82) {
		tmp = t_1;
	} else if (z <= 1.35e+17) {
		tmp = x + (t * (y / a));
	} else if (z <= 4.5e+229) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((x * a) / z)
	tmp = 0
	if z <= -1.48e+82:
		tmp = t_1
	elif z <= 1.35e+17:
		tmp = x + (t * (y / a))
	elif z <= 4.5e+229:
		tmp = y * ((x - t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(x * a) / z))
	tmp = 0.0
	if (z <= -1.48e+82)
		tmp = t_1;
	elseif (z <= 1.35e+17)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 4.5e+229)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((x * a) / z);
	tmp = 0.0;
	if (z <= -1.48e+82)
		tmp = t_1;
	elseif (z <= 1.35e+17)
		tmp = x + (t * (y / a));
	elseif (z <= 4.5e+229)
		tmp = y * ((x - t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.48e+82], t$95$1, If[LessEqual[z, 1.35e+17], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+229], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.48e82 or 4.50000000000000023e229 < z

   1. Initial program 52.0%

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

      1. +-commutative 52.0%

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

      2. fma-define 52.0%

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

   3. Simplified 52.0%

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

   5. Taylor expanded in z around inf 65.8%

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

      1. associate--l+ 65.8%

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

      2. distribute-lft-out-- 65.8%

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

      3. div-sub 65.8%

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

      4. mul-1-neg 65.8%

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

      5. unsub-neg 65.8%

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

      6. div-sub 65.8%

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

      7. associate-/l* 74.4%

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

      8. associate-/l* 88.5%

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

      9. distribute-rgt-out-- 88.5%

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

   7. Simplified 88.5%

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

   8. Taylor expanded in y around 0 58.7%

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

      1. associate-*r/ 58.7%

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

      2. associate-*r* 58.7%

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

      3. neg-mul-1 58.7%

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

   10. Simplified 58.7%

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

   11. Taylor expanded in t around 0 64.4%

       \[\leadsto t - \color{blue}{\frac{a \cdot x}{z}} \]
   12. Step-by-step derivation

       1. *-commutative 64.4%

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

   13. Simplified 64.4%

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

   if -1.48e82 < z < 1.35e17

   1. Initial program 90.6%

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

   3. Taylor expanded in t around inf 65.6%

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

   4. Taylor expanded in z around 0 53.1%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 57.5%

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

   6. Simplified 57.5%

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

   if 1.35e17 < z < 4.50000000000000023e229

   1. Initial program 74.3%

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

      1. +-commutative 74.3%

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

      2. fma-define 74.2%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in z around inf 52.5%

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

      1. associate--l+ 52.5%

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

      2. distribute-lft-out-- 52.5%

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

      3. div-sub 52.5%

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

      4. mul-1-neg 52.5%

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

      5. unsub-neg 52.5%

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

      6. div-sub 52.5%

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

      7. associate-/l* 59.7%

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

      8. associate-/l* 71.3%

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

      9. distribute-rgt-out-- 73.6%

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

   7. Simplified 73.6%

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

   8. Taylor expanded in y around -inf 33.3%

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

      1. associate-*r/ 33.3%

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

      2. neg-mul-1 33.3%

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

      3. distribute-lft-neg-in 33.3%

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

   10. Simplified 33.3%

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

   11. Taylor expanded in y around 0 33.3%

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

       1. mul-1-neg 33.3%

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

       2. associate-*r/ 44.9%

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

       3. distribute-lft-neg-in 44.9%

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

   13. Simplified 44.9%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+82}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+17}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+229}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+82} \lor \neg \left(z \leq 1.06 \cdot 10^{+80}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.48e+82) (not (<= z 1.06e+80)))
   (+ t (* (/ (- t x) z) (- a y)))
   (+ x (/ y (/ (- a z) (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.48e+82) || !(z <= 1.06e+80)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + (y / ((a - z) / (t - x)));
	}
	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 ((z <= (-1.48d+82)) .or. (.not. (z <= 1.06d+80))) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x + (y / ((a - z) / (t - x)))
    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 <= -1.48e+82) || !(z <= 1.06e+80)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + (y / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.48e+82) or not (z <= 1.06e+80):
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x + (y / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.48e+82) || !(z <= 1.06e+80))
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.48e+82) || ~((z <= 1.06e+80)))
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x + (y / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.48e+82], N[Not[LessEqual[z, 1.06e+80]], $MachinePrecision]], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.48e82 or 1.05999999999999996e80 < z

   1. Initial program 56.3%

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

      1. +-commutative 56.3%

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

      2. fma-define 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in z around inf 60.6%

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

      1. associate--l+ 60.6%

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

      2. distribute-lft-out-- 60.6%

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

      3. div-sub 60.6%

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

      4. mul-1-neg 60.6%

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

      5. unsub-neg 60.6%

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

      6. div-sub 60.6%

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

      7. associate-/l* 68.8%

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

      8. associate-/l* 83.8%

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

      9. distribute-rgt-out-- 83.8%

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

   7. Simplified 83.8%

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

   if -1.48e82 < z < 1.05999999999999996e80

   1. Initial program 91.2%

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

      1. clear-num 91.1%

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

      2. un-div-inv 91.2%

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

   4. Applied egg-rr 91.2%

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

   5. Taylor expanded in y around inf 83.9%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+82} \lor \neg \left(z \leq 1.06 \cdot 10^{+80}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+82} \lor \neg \left(z \leq 2.55 \cdot 10^{+79}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.15e+82) (not (<= z 2.55e+79)))
   (+ t (* y (/ (- x t) z)))
   (+ x (/ y (/ (- a z) (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.15e+82) || !(z <= 2.55e+79)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y / ((a - z) / (t - x)));
	}
	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 ((z <= (-2.15d+82)) .or. (.not. (z <= 2.55d+79))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + (y / ((a - z) / (t - x)))
    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 <= -2.15e+82) || !(z <= 2.55e+79)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.15e+82) or not (z <= 2.55e+79):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + (y / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.15e+82) || !(z <= 2.55e+79))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.15e+82) || ~((z <= 2.55e+79)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + (y / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.15e+82], N[Not[LessEqual[z, 2.55e+79]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15000000000000007e82 or 2.5500000000000001e79 < z

   1. Initial program 56.3%

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

      1. +-commutative 56.3%

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

      2. fma-define 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in z around inf 60.6%

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

      1. associate--l+ 60.6%

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

      2. distribute-lft-out-- 60.6%

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

      3. div-sub 60.6%

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

      4. mul-1-neg 60.6%

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

      5. unsub-neg 60.6%

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

      6. div-sub 60.6%

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

      7. associate-/l* 68.8%

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

      8. associate-/l* 83.8%

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

      9. distribute-rgt-out-- 83.8%

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

   7. Simplified 83.8%

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

   8. Taylor expanded in y around inf 72.7%

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

   if -2.15000000000000007e82 < z < 2.5500000000000001e79

   1. Initial program 91.2%

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

      1. clear-num 91.1%

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

      2. un-div-inv 91.2%

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

   4. Applied egg-rr 91.2%

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

   5. Taylor expanded in y around inf 83.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+82} \lor \neg \left(z \leq 2.55 \cdot 10^{+79}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+82} \lor \neg \left(z \leq 2.15 \cdot 10^{+79}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.48e+82) (not (<= z 2.15e+79)))
   (+ t (* y (/ (- x t) z)))
   (+ x (* y (/ (- t x) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.48e+82) || !(z <= 2.15e+79)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y * ((t - x) / (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 ((z <= (-1.48d+82)) .or. (.not. (z <= 2.15d+79))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + (y * ((t - x) / (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 ((z <= -1.48e+82) || !(z <= 2.15e+79)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y * ((t - x) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.48e+82) or not (z <= 2.15e+79):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + (y * ((t - x) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.48e+82) || !(z <= 2.15e+79))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.48e+82) || ~((z <= 2.15e+79)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + (y * ((t - x) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.48e+82], N[Not[LessEqual[z, 2.15e+79]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.48e82 or 2.1500000000000002e79 < z

   1. Initial program 56.3%

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

      1. +-commutative 56.3%

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

      2. fma-define 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in z around inf 60.6%

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

      1. associate--l+ 60.6%

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

      2. distribute-lft-out-- 60.6%

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

      3. div-sub 60.6%

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

      4. mul-1-neg 60.6%

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

      5. unsub-neg 60.6%

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

      6. div-sub 60.6%

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

      7. associate-/l* 68.8%

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

      8. associate-/l* 83.8%

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

      9. distribute-rgt-out-- 83.8%

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

   7. Simplified 83.8%

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

   8. Taylor expanded in y around inf 72.7%

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

   if -1.48e82 < z < 2.1500000000000002e79

   1. Initial program 91.2%

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

   3. Taylor expanded in y around inf 83.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+82} \lor \neg \left(z \leq 2.15 \cdot 10^{+79}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-67} \lor \neg \left(a \leq 4.4 \cdot 10^{-40}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7e-67) (not (<= a 4.4e-40)))
   (+ x (* t (/ (- y z) (- a z))))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7e-67) || !(a <= 4.4e-40)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t + (y * ((x - t) / 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 ((a <= (-7d-67)) .or. (.not. (a <= 4.4d-40))) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = t + (y * ((x - t) / 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 ((a <= -7e-67) || !(a <= 4.4e-40)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7e-67) or not (a <= 4.4e-40):
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7e-67) || !(a <= 4.4e-40))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7e-67) || ~((a <= 4.4e-40)))
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7e-67], N[Not[LessEqual[a, 4.4e-40]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.0000000000000001e-67 or 4.40000000000000018e-40 < a

   1. Initial program 86.2%

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

   3. Taylor expanded in t around inf 60.9%

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

      1. associate-/l* 73.9%

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

   5. Simplified 73.9%

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

   if -7.0000000000000001e-67 < a < 4.40000000000000018e-40

   1. Initial program 70.8%

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

      1. +-commutative 70.8%

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

      2. fma-define 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in z around inf 73.9%

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

      1. associate--l+ 73.9%

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

      2. distribute-lft-out-- 73.9%

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

      3. div-sub 73.9%

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

      4. mul-1-neg 73.9%

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

      5. unsub-neg 73.9%

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

      6. div-sub 73.9%

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

      7. associate-/l* 77.1%

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

      8. associate-/l* 74.1%

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

      9. distribute-rgt-out-- 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in y around inf 75.8%

      \[\leadsto t - \frac{t - x}{z} \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-67} \lor \neg \left(a \leq 4.4 \cdot 10^{-40}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-295}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6e-67)
   x
   (if (<= a -7e-295) t (if (<= a 1.28e-55) (* x (/ y z)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e-67) {
		tmp = x;
	} else if (a <= -7e-295) {
		tmp = t;
	} else if (a <= 1.28e-55) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	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 (a <= (-6d-67)) then
        tmp = x
    else if (a <= (-7d-295)) then
        tmp = t
    else if (a <= 1.28d-55) then
        tmp = x * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e-67) {
		tmp = x;
	} else if (a <= -7e-295) {
		tmp = t;
	} else if (a <= 1.28e-55) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6e-67:
		tmp = x
	elif a <= -7e-295:
		tmp = t
	elif a <= 1.28e-55:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6e-67)
		tmp = x;
	elseif (a <= -7e-295)
		tmp = t;
	elseif (a <= 1.28e-55)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6e-67)
		tmp = x;
	elseif (a <= -7e-295)
		tmp = t;
	elseif (a <= 1.28e-55)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6e-67], x, If[LessEqual[a, -7e-295], t, If[LessEqual[a, 1.28e-55], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.00000000000000065e-67 or 1.27999999999999994e-55 < a

   1. Initial program 85.5%

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

      1. +-commutative 85.5%

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

      2. fma-define 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in a around inf 41.1%

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

   if -6.00000000000000065e-67 < a < -6.99999999999999977e-295

   1. Initial program 69.1%

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

   3. Taylor expanded in t around inf 43.7%

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

   4. Taylor expanded in z around inf 31.4%

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

   5. Taylor expanded in x around 0 49.2%

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

   if -6.99999999999999977e-295 < a < 1.27999999999999994e-55

   1. Initial program 72.5%

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

      1. +-commutative 72.5%

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

      2. fma-define 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in t around 0 34.5%

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

      1. mul-1-neg 34.5%

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

      2. *-rgt-identity 34.5%

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

      3. associate-/l* 39.3%

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

      4. distribute-rgt-neg-in 39.3%

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

      5. mul-1-neg 39.3%

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

      6. distribute-lft-in 39.3%

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

      7. mul-1-neg 39.3%

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

      8. unsub-neg 39.3%

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

   7. Simplified 39.3%

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

   8. Taylor expanded in a around 0 43.3%

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

Alternative 11: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.001633 \lor \neg \left(a \leq 1.02 \cdot 10^{-53}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.001633) (not (<= a 1.02e-53)))
   (+ x (* y (/ (- t x) a)))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.001633) || !(a <= 1.02e-53)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t + (y * ((x - t) / 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 ((a <= (-0.001633d0)) .or. (.not. (a <= 1.02d-53))) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t + (y * ((x - t) / 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 ((a <= -0.001633) || !(a <= 1.02e-53)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.001633) or not (a <= 1.02e-53):
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.001633) || !(a <= 1.02e-53))
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -0.001633) || ~((a <= 1.02e-53)))
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.001633], N[Not[LessEqual[a, 1.02e-53]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.0016329999999999999 or 1.02000000000000002e-53 < a

   1. Initial program 85.2%

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

   3. Taylor expanded in z around 0 58.2%

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

      1. associate-/l* 69.1%

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

   5. Simplified 69.1%

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

   if -0.0016329999999999999 < a < 1.02000000000000002e-53

   1. Initial program 73.4%

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

      1. +-commutative 73.4%

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

      2. fma-define 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in z around inf 71.9%

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

      1. associate--l+ 71.9%

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

      2. distribute-lft-out-- 71.9%

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

      3. div-sub 72.7%

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

      4. mul-1-neg 72.7%

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

      5. unsub-neg 72.7%

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

      6. div-sub 71.9%

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

      7. associate-/l* 75.5%

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

      8. associate-/l* 72.9%

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

      9. distribute-rgt-out-- 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in y around inf 75.6%

      \[\leadsto t - \frac{t - x}{z} \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.001633 \lor \neg \left(a \leq 1.02 \cdot 10^{-53}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+82}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + t \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e+82)
   (- t (/ (* x a) z))
   (if (<= z 1.4e+17) (+ x (* y (/ (- t x) a))) (+ t (* t (/ (- a y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+82) {
		tmp = t - ((x * a) / z);
	} else if (z <= 1.4e+17) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t + (t * ((a - 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 (z <= (-2.2d+82)) then
        tmp = t - ((x * a) / z)
    else if (z <= 1.4d+17) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t + (t * ((a - 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 (z <= -2.2e+82) {
		tmp = t - ((x * a) / z);
	} else if (z <= 1.4e+17) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t + (t * ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e+82:
		tmp = t - ((x * a) / z)
	elif z <= 1.4e+17:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t + (t * ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e+82)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	elseif (z <= 1.4e+17)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t + Float64(t * Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e+82)
		tmp = t - ((x * a) / z);
	elseif (z <= 1.4e+17)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t + (t * ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e+82], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+17], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(t * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e82

   1. Initial program 55.1%

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

      1. +-commutative 55.1%

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

      2. fma-define 55.4%

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

   3. Simplified 55.4%

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

   5. Taylor expanded in z around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. distribute-lft-out-- 66.6%

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

      3. div-sub 66.6%

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

      4. mul-1-neg 66.6%

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

      5. unsub-neg 66.6%

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

      6. div-sub 66.6%

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

      7. associate-/l* 75.0%

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

      8. associate-/l* 88.9%

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

      9. distribute-rgt-out-- 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in y around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. associate-*r* 57.9%

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

      3. neg-mul-1 57.9%

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

   10. Simplified 57.9%

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

   11. Taylor expanded in t around 0 64.9%

       \[\leadsto t - \color{blue}{\frac{a \cdot x}{z}} \]
   12. Step-by-step derivation

       1. *-commutative 64.9%

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

   13. Simplified 64.9%

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

   if -2.2000000000000001e82 < z < 1.4e17

   1. Initial program 90.6%

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

   3. Taylor expanded in z around 0 64.7%

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

      1. associate-/l* 70.6%

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

   5. Simplified 70.6%

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

   if 1.4e17 < z

   1. Initial program 67.5%

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

      1. +-commutative 67.5%

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

      2. fma-define 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in z around inf 54.4%

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

      1. associate--l+ 54.4%

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

      2. distribute-lft-out-- 54.4%

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

      3. div-sub 54.4%

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

      4. mul-1-neg 54.4%

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

      5. unsub-neg 54.4%

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

      6. div-sub 54.4%

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

      7. associate-/l* 62.0%

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

      8. associate-/l* 74.1%

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

      9. distribute-rgt-out-- 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in t around inf 43.9%

      \[\leadsto t - \color{blue}{\frac{t \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 47.3%

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

   10. Simplified 47.3%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+82}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + t \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+82}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+81}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.48e+82)
   (- t (/ (* x a) z))
   (if (<= z 2.6e+81) (+ x (* y (/ (- t x) a))) (* x (/ (- y a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.48e+82) {
		tmp = t - ((x * a) / z);
	} else if (z <= 2.6e+81) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = x * ((y - 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 (z <= (-1.48d+82)) then
        tmp = t - ((x * a) / z)
    else if (z <= 2.6d+81) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = x * ((y - 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 (z <= -1.48e+82) {
		tmp = t - ((x * a) / z);
	} else if (z <= 2.6e+81) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.48e+82:
		tmp = t - ((x * a) / z)
	elif z <= 2.6e+81:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.48e+82)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	elseif (z <= 2.6e+81)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.48e+82)
		tmp = t - ((x * a) / z);
	elseif (z <= 2.6e+81)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.48e+82], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+81], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.48e82

   1. Initial program 55.1%

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

      1. +-commutative 55.1%

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

      2. fma-define 55.4%

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

   3. Simplified 55.4%

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

   5. Taylor expanded in z around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. distribute-lft-out-- 66.6%

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

      3. div-sub 66.6%

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

      4. mul-1-neg 66.6%

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

      5. unsub-neg 66.6%

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

      6. div-sub 66.6%

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

      7. associate-/l* 75.0%

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

      8. associate-/l* 88.9%

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

      9. distribute-rgt-out-- 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in y around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. associate-*r* 57.9%

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

      3. neg-mul-1 57.9%

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

   10. Simplified 57.9%

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

   11. Taylor expanded in t around 0 64.9%

       \[\leadsto t - \color{blue}{\frac{a \cdot x}{z}} \]
   12. Step-by-step derivation

       1. *-commutative 64.9%

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

   13. Simplified 64.9%

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

   if -1.48e82 < z < 2.59999999999999992e81

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 62.9%

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

      1. associate-/l* 68.9%

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

   5. Simplified 68.9%

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

   if 2.59999999999999992e81 < z

   1. Initial program 57.5%

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

      1. +-commutative 57.5%

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

      2. fma-define 57.2%

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

   3. Simplified 57.2%

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

   5. Taylor expanded in z around inf 54.2%

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

      1. associate--l+ 54.2%

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

      2. distribute-lft-out-- 54.2%

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

      3. div-sub 54.2%

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

      4. mul-1-neg 54.2%

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

      5. unsub-neg 54.2%

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

      6. div-sub 54.2%

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

      7. associate-/l* 62.1%

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

      8. associate-/l* 78.2%

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

      9. distribute-rgt-out-- 78.2%

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

   7. Simplified 78.2%

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

   8. Taylor expanded in t around 0 23.3%

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

      1. associate-/l* 41.0%

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

   10. Simplified 41.0%

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

Alternative 14: 53.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+82}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+101}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.35e+82)
   (- t (/ (* x a) z))
   (if (<= z 1.1e+101) (+ x (* t (/ y (- a z)))) (* x (/ (- y a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.35e+82) {
		tmp = t - ((x * a) / z);
	} else if (z <= 1.1e+101) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x * ((y - 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 (z <= (-2.35d+82)) then
        tmp = t - ((x * a) / z)
    else if (z <= 1.1d+101) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x * ((y - 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 (z <= -2.35e+82) {
		tmp = t - ((x * a) / z);
	} else if (z <= 1.1e+101) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.35e+82:
		tmp = t - ((x * a) / z)
	elif z <= 1.1e+101:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.35e+82)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	elseif (z <= 1.1e+101)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.35e+82)
		tmp = t - ((x * a) / z);
	elseif (z <= 1.1e+101)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.35e+82], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+101], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.35e82

   1. Initial program 55.1%

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

      1. +-commutative 55.1%

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

      2. fma-define 55.4%

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

   3. Simplified 55.4%

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

   5. Taylor expanded in z around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. distribute-lft-out-- 66.6%

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

      3. div-sub 66.6%

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

      4. mul-1-neg 66.6%

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

      5. unsub-neg 66.6%

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

      6. div-sub 66.6%

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

      7. associate-/l* 75.0%

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

      8. associate-/l* 88.9%

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

      9. distribute-rgt-out-- 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in y around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. associate-*r* 57.9%

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

      3. neg-mul-1 57.9%

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

   10. Simplified 57.9%

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

   11. Taylor expanded in t around 0 64.9%

       \[\leadsto t - \color{blue}{\frac{a \cdot x}{z}} \]
   12. Step-by-step derivation

       1. *-commutative 64.9%

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

   13. Simplified 64.9%

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

   if -2.35e82 < z < 1.1e101

   1. Initial program 91.3%

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

   3. Taylor expanded in t around inf 65.4%

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

   4. Taylor expanded in y around inf 58.8%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a - z}} \]
   5. Step-by-step derivation

      1. associate-/l* 63.8%

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

   6. Simplified 63.8%

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

   if 1.1e101 < z

   1. Initial program 54.0%

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

      1. +-commutative 54.0%

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

      2. fma-define 53.8%

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

   3. Simplified 53.8%

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

   5. Taylor expanded in z around inf 50.5%

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

      1. associate--l+ 50.5%

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

      2. distribute-lft-out-- 50.5%

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

      3. div-sub 50.5%

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

      4. mul-1-neg 50.5%

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

      5. unsub-neg 50.5%

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

      6. div-sub 50.5%

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

      7. associate-/l* 59.0%

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

      8. associate-/l* 76.4%

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

      9. distribute-rgt-out-- 76.4%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in t around 0 24.8%

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

      1. associate-/l* 44.0%

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

   10. Simplified 44.0%

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

Alternative 15: 50.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+82}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+99}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+82)
   (- t (/ (* x a) z))
   (if (<= z 2.8e+99) (+ x (* t (/ y a))) (* x (/ (- y a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+82) {
		tmp = t - ((x * a) / z);
	} else if (z <= 2.8e+99) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x * ((y - 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 (z <= (-1.8d+82)) then
        tmp = t - ((x * a) / z)
    else if (z <= 2.8d+99) then
        tmp = x + (t * (y / a))
    else
        tmp = x * ((y - 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 (z <= -1.8e+82) {
		tmp = t - ((x * a) / z);
	} else if (z <= 2.8e+99) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+82:
		tmp = t - ((x * a) / z)
	elif z <= 2.8e+99:
		tmp = x + (t * (y / a))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+82)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	elseif (z <= 2.8e+99)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+82)
		tmp = t - ((x * a) / z);
	elseif (z <= 2.8e+99)
		tmp = x + (t * (y / a));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+82], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+99], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.80000000000000007e82

   1. Initial program 55.1%

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

      1. +-commutative 55.1%

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

      2. fma-define 55.4%

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

   3. Simplified 55.4%

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

   5. Taylor expanded in z around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. distribute-lft-out-- 66.6%

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

      3. div-sub 66.6%

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

      4. mul-1-neg 66.6%

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

      5. unsub-neg 66.6%

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

      6. div-sub 66.6%

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

      7. associate-/l* 75.0%

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

      8. associate-/l* 88.9%

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

      9. distribute-rgt-out-- 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in y around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. associate-*r* 57.9%

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

      3. neg-mul-1 57.9%

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

   10. Simplified 57.9%

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

   11. Taylor expanded in t around 0 64.9%

       \[\leadsto t - \color{blue}{\frac{a \cdot x}{z}} \]
   12. Step-by-step derivation

       1. *-commutative 64.9%

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

   13. Simplified 64.9%

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

   if -1.80000000000000007e82 < z < 2.8e99

   1. Initial program 91.3%

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

   3. Taylor expanded in t around inf 65.2%

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

   4. Taylor expanded in z around 0 50.4%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 55.0%

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

   6. Simplified 55.0%

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

   if 2.8e99 < z

   1. Initial program 55.3%

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

      1. +-commutative 55.3%

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

      2. fma-define 55.0%

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

   3. Simplified 55.0%

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

   5. Taylor expanded in z around inf 51.8%

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

      1. associate--l+ 51.8%

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

      2. distribute-lft-out-- 51.8%

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

      3. div-sub 51.8%

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

      4. mul-1-neg 51.8%

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

      5. unsub-neg 51.8%

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

      6. div-sub 51.8%

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

      7. associate-/l* 60.1%

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

      8. associate-/l* 77.1%

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

      9. distribute-rgt-out-- 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in t around 0 24.4%

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

      1. associate-/l* 43.1%

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

   10. Simplified 43.1%

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

Alternative 16: 49.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+94}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e+82)
   t
   (if (<= z 8.2e+94) (+ x (* t (/ y a))) (* x (/ (- y a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+82) {
		tmp = t;
	} else if (z <= 8.2e+94) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x * ((y - 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 (z <= (-1.7d+82)) then
        tmp = t
    else if (z <= 8.2d+94) then
        tmp = x + (t * (y / a))
    else
        tmp = x * ((y - 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 (z <= -1.7e+82) {
		tmp = t;
	} else if (z <= 8.2e+94) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e+82:
		tmp = t
	elif z <= 8.2e+94:
		tmp = x + (t * (y / a))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e+82)
		tmp = t;
	elseif (z <= 8.2e+94)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.7e+82)
		tmp = t;
	elseif (z <= 8.2e+94)
		tmp = x + (t * (y / a));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e+82], t, If[LessEqual[z, 8.2e+94], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.69999999999999997e82

   1. Initial program 55.1%

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

   3. Taylor expanded in t around inf 20.5%

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

   4. Taylor expanded in z around inf 42.2%

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

   5. Taylor expanded in x around 0 57.3%

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

   if -1.69999999999999997e82 < z < 8.20000000000000061e94

   1. Initial program 91.3%

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

   3. Taylor expanded in t around inf 65.2%

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

   4. Taylor expanded in z around 0 50.4%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 55.0%

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

   6. Simplified 55.0%

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

   if 8.20000000000000061e94 < z

   1. Initial program 55.3%

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

      1. +-commutative 55.3%

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

      2. fma-define 55.0%

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

   3. Simplified 55.0%

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

   5. Taylor expanded in z around inf 51.8%

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

      1. associate--l+ 51.8%

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

      2. distribute-lft-out-- 51.8%

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

      3. div-sub 51.8%

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

      4. mul-1-neg 51.8%

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

      5. unsub-neg 51.8%

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

      6. div-sub 51.8%

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

      7. associate-/l* 60.1%

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

      8. associate-/l* 77.1%

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

      9. distribute-rgt-out-- 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in t around 0 24.4%

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

      1. associate-/l* 43.1%

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

   10. Simplified 43.1%

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

Alternative 17: 45.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e+82)
   t
   (if (<= z 2.9e+96) (* x (- 1.0 (/ y a))) (* x (/ (- y a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+82) {
		tmp = t;
	} else if (z <= 2.9e+96) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = x * ((y - 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 (z <= (-1.95d+82)) then
        tmp = t
    else if (z <= 2.9d+96) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = x * ((y - 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 (z <= -1.95e+82) {
		tmp = t;
	} else if (z <= 2.9e+96) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e+82:
		tmp = t
	elif z <= 2.9e+96:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e+82)
		tmp = t;
	elseif (z <= 2.9e+96)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.95e+82)
		tmp = t;
	elseif (z <= 2.9e+96)
		tmp = x * (1.0 - (y / a));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e+82], t, If[LessEqual[z, 2.9e+96], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.94999999999999988e82

   1. Initial program 55.1%

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

   3. Taylor expanded in t around inf 20.5%

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

   4. Taylor expanded in z around inf 42.2%

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

   5. Taylor expanded in x around 0 57.3%

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

   if -1.94999999999999988e82 < z < 2.89999999999999978e96

   1. Initial program 91.3%

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

      1. +-commutative 91.3%

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

      2. fma-define 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in t around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. *-rgt-identity 58.2%

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

      3. associate-/l* 62.4%

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

      4. distribute-rgt-neg-in 62.4%

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

      5. mul-1-neg 62.4%

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

      6. distribute-lft-in 62.4%

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

      7. mul-1-neg 62.4%

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

      8. unsub-neg 62.4%

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

   7. Simplified 62.4%

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

   8. Taylor expanded in z around 0 53.1%

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

   if 2.89999999999999978e96 < z

   1. Initial program 55.3%

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

      1. +-commutative 55.3%

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

      2. fma-define 55.0%

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

   3. Simplified 55.0%

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

   5. Taylor expanded in z around inf 51.8%

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

      1. associate--l+ 51.8%

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

      2. distribute-lft-out-- 51.8%

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

      3. div-sub 51.8%

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

      4. mul-1-neg 51.8%

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

      5. unsub-neg 51.8%

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

      6. div-sub 51.8%

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

      7. associate-/l* 60.1%

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

      8. associate-/l* 77.1%

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

      9. distribute-rgt-out-- 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in t around 0 24.4%

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

      1. associate-/l* 43.1%

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

   10. Simplified 43.1%

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

Alternative 18: 48.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e+82) t (if (<= z 1.25e+17) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+82) {
		tmp = t;
	} else if (z <= 1.25e+17) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	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 (z <= (-1.7d+82)) then
        tmp = t
    else if (z <= 1.25d+17) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t
    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 <= -1.7e+82) {
		tmp = t;
	} else if (z <= 1.25e+17) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e+82:
		tmp = t
	elif z <= 1.25e+17:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e+82)
		tmp = t;
	elseif (z <= 1.25e+17)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.7e+82)
		tmp = t;
	elseif (z <= 1.25e+17)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e+82], t, If[LessEqual[z, 1.25e+17], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.69999999999999997e82 or 1.25e17 < z

   1. Initial program 62.0%

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

   3. Taylor expanded in t around inf 30.6%

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

   4. Taylor expanded in z around inf 34.0%

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

   5. Taylor expanded in x around 0 44.0%

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

   if -1.69999999999999997e82 < z < 1.25e17

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. fma-define 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in t around 0 61.0%

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

      1. mul-1-neg 61.0%

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

      2. *-rgt-identity 61.0%

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

      3. associate-/l* 65.6%

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

      4. distribute-rgt-neg-in 65.6%

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

      5. mul-1-neg 65.6%

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

      6. distribute-lft-in 65.6%

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

      7. mul-1-neg 65.6%

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

      8. unsub-neg 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in z around 0 55.4%

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

Alternative 19: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.65e+82) t (if (<= z 7.6e+16) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e+82) {
		tmp = t;
	} else if (z <= 7.6e+16) {
		tmp = x;
	} else {
		tmp = t;
	}
	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 (z <= (-1.65d+82)) then
        tmp = t
    else if (z <= 7.6d+16) then
        tmp = x
    else
        tmp = t
    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 <= -1.65e+82) {
		tmp = t;
	} else if (z <= 7.6e+16) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.65e+82:
		tmp = t
	elif z <= 7.6e+16:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.65e+82)
		tmp = t;
	elseif (z <= 7.6e+16)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.65e+82)
		tmp = t;
	elseif (z <= 7.6e+16)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.65e+82], t, If[LessEqual[z, 7.6e+16], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6499999999999999e82 or 7.6e16 < z

   1. Initial program 62.0%

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

   3. Taylor expanded in t around inf 30.6%

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

   4. Taylor expanded in z around inf 34.0%

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

   5. Taylor expanded in x around 0 44.0%

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

   if -1.6499999999999999e82 < z < 7.6e16

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. fma-define 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in a around inf 38.7%

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

Alternative 20: 24.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

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 = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 79.8%

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

3. Taylor expanded in t around inf 52.5%

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

4. Taylor expanded in z around inf 31.8%

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

5. Taylor expanded in x around 0 21.7%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))