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

Percentage Accurate: 67.8% → 89.2%

Time: 16.7s

Alternatives: 26

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - z) * (t - x)) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - z) * (t - x)) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+155} \lor \neg \left(z \leq 6.2 \cdot 10^{+154}\right):\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2e+155) (not (<= z 6.2e+154)))
   (+ t (* (/ (- y a) z) (- x t)))
   (+ x (/ (- t x) (/ (- a z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e+155) || !(z <= 6.2e+154)) {
		tmp = t + (((y - a) / z) * (x - t));
	} else {
		tmp = x + ((t - x) / ((a - z) / (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 <= (-2d+155)) .or. (.not. (z <= 6.2d+154))) then
        tmp = t + (((y - a) / z) * (x - t))
    else
        tmp = x + ((t - x) / ((a - z) / (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 <= -2e+155) || !(z <= 6.2e+154)) {
		tmp = t + (((y - a) / z) * (x - t));
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2e+155) or not (z <= 6.2e+154):
		tmp = t + (((y - a) / z) * (x - t))
	else:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2e+155) || !(z <= 6.2e+154))
		tmp = Float64(t + Float64(Float64(Float64(y - a) / z) * Float64(x - t)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2e+155) || ~((z <= 6.2e+154)))
		tmp = t + (((y - a) / z) * (x - t));
	else
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2e+155], N[Not[LessEqual[z, 6.2e+154]], $MachinePrecision]], N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000001e155 or 6.2000000000000003e154 < z

   1. Initial program 27.4%

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

      1. +-commutative 27.4%

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

      2. associate-*l/ 61.1%

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

      3. fma-def 61.1%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in z around inf 66.2%

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

      1. +-commutative 66.2%

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

      2. associate-/l* 92.1%

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

      3. distribute-lft-out-- 92.1%

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

      4. mul-1-neg 92.1%

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

      5. distribute-neg-frac 92.1%

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

      6. associate-/l* 66.2%

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

      7. *-commutative 66.2%

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

      8. distribute-rgt-out-- 65.9%

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

      9. unsub-neg 65.9%

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

      10. distribute-rgt-out-- 66.2%

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

      11. *-commutative 66.2%

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

      12. associate-/l* 92.1%

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

   6. Simplified 92.1%

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

      1. associate-/r/ 92.4%

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

   8. Applied egg-rr 92.4%

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

   if -2.00000000000000001e155 < z < 6.2000000000000003e154

   1. Initial program 78.6%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

      1. *-commutative 91.3%

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

      2. clear-num 91.3%

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

      3. un-div-inv 91.3%

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

   5. Applied egg-rr 91.3%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+155} \lor \neg \left(z \leq 6.2 \cdot 10^{+154}\right):\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 2: 53.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-151}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y z) (- x t))))
   (if (<= z -2.3e+33)
     (- t (* t (/ y z)))
     (if (<= z -1.95e-59)
       t_1
       (if (<= z 5.5e-151)
         (+ x (/ y (/ a t)))
         (if (<= z 2.5e-71)
           (* x (- 1.0 (/ y a)))
           (if (<= z 2.3e+81) t_1 (- t (* a (/ x z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / z) * (x - t);
	double tmp;
	if (z <= -2.3e+33) {
		tmp = t - (t * (y / z));
	} else if (z <= -1.95e-59) {
		tmp = t_1;
	} else if (z <= 5.5e-151) {
		tmp = x + (y / (a / t));
	} else if (z <= 2.5e-71) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.3e+81) {
		tmp = t_1;
	} else {
		tmp = t - (a * (x / 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) :: t_1
    real(8) :: tmp
    t_1 = (y / z) * (x - t)
    if (z <= (-2.3d+33)) then
        tmp = t - (t * (y / z))
    else if (z <= (-1.95d-59)) then
        tmp = t_1
    else if (z <= 5.5d-151) then
        tmp = x + (y / (a / t))
    else if (z <= 2.5d-71) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 2.3d+81) then
        tmp = t_1
    else
        tmp = t - (a * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / z) * (x - t);
	double tmp;
	if (z <= -2.3e+33) {
		tmp = t - (t * (y / z));
	} else if (z <= -1.95e-59) {
		tmp = t_1;
	} else if (z <= 5.5e-151) {
		tmp = x + (y / (a / t));
	} else if (z <= 2.5e-71) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.3e+81) {
		tmp = t_1;
	} else {
		tmp = t - (a * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / z) * (x - t)
	tmp = 0
	if z <= -2.3e+33:
		tmp = t - (t * (y / z))
	elif z <= -1.95e-59:
		tmp = t_1
	elif z <= 5.5e-151:
		tmp = x + (y / (a / t))
	elif z <= 2.5e-71:
		tmp = x * (1.0 - (y / a))
	elif z <= 2.3e+81:
		tmp = t_1
	else:
		tmp = t - (a * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / z) * Float64(x - t))
	tmp = 0.0
	if (z <= -2.3e+33)
		tmp = Float64(t - Float64(t * Float64(y / z)));
	elseif (z <= -1.95e-59)
		tmp = t_1;
	elseif (z <= 5.5e-151)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 2.5e-71)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 2.3e+81)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(a * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / z) * (x - t);
	tmp = 0.0;
	if (z <= -2.3e+33)
		tmp = t - (t * (y / z));
	elseif (z <= -1.95e-59)
		tmp = t_1;
	elseif (z <= 5.5e-151)
		tmp = x + (y / (a / t));
	elseif (z <= 2.5e-71)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 2.3e+81)
		tmp = t_1;
	else
		tmp = t - (a * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+33], N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-59], t$95$1, If[LessEqual[z, 5.5e-151], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-71], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+81], t$95$1, N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.30000000000000011e33

   1. Initial program 51.5%

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

      1. +-commutative 51.5%

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

      2. associate-*l/ 73.6%

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

      3. fma-def 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in z around inf 65.8%

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

      1. +-commutative 65.8%

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

      2. associate-/l* 82.5%

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

      3. distribute-lft-out-- 82.5%

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

      4. mul-1-neg 82.5%

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

      5. distribute-neg-frac 82.5%

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

      6. associate-/l* 65.8%

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

      7. *-commutative 65.8%

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

      8. distribute-rgt-out-- 65.5%

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

      9. unsub-neg 65.5%

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

      10. distribute-rgt-out-- 65.8%

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

      11. *-commutative 65.8%

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

      12. associate-/l* 82.5%

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

   6. Simplified 82.5%

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

   7. Taylor expanded in y around inf 60.8%

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

      1. associate-/l* 74.7%

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

      2. associate-/r/ 74.6%

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

   9. Simplified 74.6%

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

   10. Taylor expanded in t around inf 49.4%

       \[\leadsto t - \color{blue}{\frac{y \cdot t}{z}} \]
   11. Step-by-step derivation

       1. associate-*l/ 57.8%

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

       2. *-commutative 57.8%

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

   12. Simplified 57.8%

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

   if -2.30000000000000011e33 < z < -1.95000000000000009e-59 or 2.49999999999999999e-71 < z < 2.2999999999999999e81

   1. Initial program 75.5%

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

      1. +-commutative 75.5%

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

      2. associate-*l/ 86.6%

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

      3. fma-def 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in y around -inf 57.0%

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

   5. Taylor expanded in a around 0 54.5%

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

      1. mul-1-neg 54.5%

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

      2. associate-/l* 54.5%

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

      3. associate-/r/ 54.6%

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

      4. distribute-lft-neg-in 54.6%

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

      5. distribute-frac-neg 54.6%

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

   7. Simplified 54.6%

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

   if -1.95000000000000009e-59 < z < 5.4999999999999998e-151

   1. Initial program 89.8%

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

      1. +-commutative 89.8%

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

      2. associate-*l/ 98.7%

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

      3. fma-def 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. associate-/l* 85.8%

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

   6. Simplified 85.8%

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

   7. Taylor expanded in t around inf 67.2%

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

      1. associate-/l* 70.5%

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

   9. Simplified 70.5%

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

   if 5.4999999999999998e-151 < z < 2.49999999999999999e-71

   1. Initial program 77.3%

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

      1. +-commutative 77.3%

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

      2. associate-*l/ 92.4%

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

      3. fma-def 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 70.4%

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

      1. +-commutative 70.4%

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

      2. associate-/l* 85.1%

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

   6. Simplified 85.1%

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

   7. Taylor expanded in x around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

   9. Simplified 78.5%

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

   if 2.2999999999999999e81 < z

   1. Initial program 33.8%

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

      1. +-commutative 33.8%

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

      2. associate-*l/ 68.0%

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

      3. fma-def 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in z around inf 65.3%

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

      1. +-commutative 65.3%

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

      2. associate-/l* 84.7%

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

      3. distribute-lft-out-- 84.7%

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

      4. mul-1-neg 84.7%

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

      5. distribute-neg-frac 84.7%

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

      6. associate-/l* 65.3%

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

      7. *-commutative 65.3%

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

      8. distribute-rgt-out-- 65.3%

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

      9. unsub-neg 65.3%

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

      10. distribute-rgt-out-- 65.3%

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

      11. *-commutative 65.3%

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

      12. associate-/l* 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in t around 0 82.9%

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

      1. mul-1-neg 82.9%

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

      2. distribute-neg-frac 82.9%

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

   9. Simplified 82.9%

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

   10. Taylor expanded in y around 0 54.5%

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

       1. associate-*r/ 58.5%

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

   12. Simplified 58.5%

       \[\leadsto t - \color{blue}{a \cdot \frac{x}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-59}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-151}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+81}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-10}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.02e-10)
   (+ t (/ (- x t) (/ z y)))
   (if (<= z -8e-83)
     (* x (+ (/ (- z y) (- a z)) 1.0))
     (if (<= z -1.16e-89)
       (* t (/ (- y z) (- a z)))
       (if (<= z 7.8e-26)
         (+ x (/ y (/ a (- t x))))
         (+ t (* (- y a) (/ x z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.02e-10) {
		tmp = t + ((x - t) / (z / y));
	} else if (z <= -8e-83) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else if (z <= -1.16e-89) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 7.8e-26) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + ((y - a) * (x / 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 <= (-1.02d-10)) then
        tmp = t + ((x - t) / (z / y))
    else if (z <= (-8d-83)) then
        tmp = x * (((z - y) / (a - z)) + 1.0d0)
    else if (z <= (-1.16d-89)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 7.8d-26) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t + ((y - a) * (x / 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 <= -1.02e-10) {
		tmp = t + ((x - t) / (z / y));
	} else if (z <= -8e-83) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else if (z <= -1.16e-89) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 7.8e-26) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + ((y - a) * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.02e-10:
		tmp = t + ((x - t) / (z / y))
	elif z <= -8e-83:
		tmp = x * (((z - y) / (a - z)) + 1.0)
	elif z <= -1.16e-89:
		tmp = t * ((y - z) / (a - z))
	elif z <= 7.8e-26:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t + ((y - a) * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.02e-10)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif (z <= -8e-83)
		tmp = Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) + 1.0));
	elseif (z <= -1.16e-89)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 7.8e-26)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.02e-10)
		tmp = t + ((x - t) / (z / y));
	elseif (z <= -8e-83)
		tmp = x * (((z - y) / (a - z)) + 1.0);
	elseif (z <= -1.16e-89)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 7.8e-26)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t + ((y - a) * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.02e-10], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8e-83], N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.16e-89], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e-26], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.01999999999999997e-10

   1. Initial program 55.8%

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

      1. +-commutative 55.8%

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

      2. associate-*l/ 75.4%

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

      3. fma-def 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in z around inf 68.4%

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

      1. +-commutative 68.4%

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

      2. associate-/l* 83.2%

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

      3. distribute-lft-out-- 83.2%

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

      4. mul-1-neg 83.2%

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

      5. distribute-neg-frac 83.2%

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

      6. associate-/l* 68.4%

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

      7. *-commutative 68.4%

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

      8. distribute-rgt-out-- 68.2%

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

      9. unsub-neg 68.2%

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

      10. distribute-rgt-out-- 68.4%

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

      11. *-commutative 68.4%

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

      12. associate-/l* 83.2%

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

   6. Simplified 83.2%

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

   7. Taylor expanded in y around inf 62.9%

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

      1. associate-/l* 75.1%

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

      2. associate-/r/ 75.1%

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

   9. Simplified 75.1%

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

       1. *-commutative 75.1%

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

       2. clear-num 75.1%

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

       3. un-div-inv 75.2%

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

   11. Applied egg-rr 75.2%

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

   if -1.01999999999999997e-10 < z < -8.0000000000000003e-83

   1. Initial program 80.9%

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

      1. +-commutative 80.9%

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

      2. associate-*l/ 86.9%

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

      3. fma-def 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in x around inf 74.1%

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

      1. *-commutative 74.1%

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

      2. mul-1-neg 74.1%

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

      3. unsub-neg 74.1%

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

   6. Simplified 74.1%

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

   if -8.0000000000000003e-83 < z < -1.15999999999999993e-89

   1. Initial program 66.7%

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

      1. +-commutative 66.7%

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

      2. associate-*l/ 66.7%

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

      3. fma-def 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in t around inf 83.1%

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

      1. div-sub 83.1%

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

   6. Simplified 83.1%

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

   if -1.15999999999999993e-89 < z < 7.79999999999999973e-26

   1. Initial program 87.2%

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

      1. +-commutative 87.2%

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

      2. associate-*l/ 98.8%

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

      3. fma-def 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 78.7%

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

      1. +-commutative 78.7%

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

      2. associate-/l* 86.4%

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

   6. Simplified 86.4%

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

   if 7.79999999999999973e-26 < z

   1. Initial program 42.5%

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

      1. +-commutative 42.5%

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

      2. associate-*l/ 71.5%

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

      3. fma-def 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in z around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-/l* 83.7%

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

      3. distribute-lft-out-- 83.7%

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

      4. mul-1-neg 83.7%

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

      5. distribute-neg-frac 83.7%

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

      6. associate-/l* 69.0%

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

      7. *-commutative 69.0%

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

      8. distribute-rgt-out-- 69.0%

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

      9. unsub-neg 69.0%

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

      10. distribute-rgt-out-- 69.0%

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

      11. *-commutative 69.0%

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

      12. associate-/l* 83.7%

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

   6. Simplified 83.7%

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

      1. associate-/r/ 84.0%

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

   8. Applied egg-rr 84.0%

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

   9. Taylor expanded in t around 0 63.0%

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

       1. mul-1-neg 63.0%

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

       2. associate-*r/ 74.6%

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

       3. distribute-lft-neg-out 74.6%

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

       4. *-commutative 74.6%

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

   11. Simplified 74.6%

       \[\leadsto t - \color{blue}{\frac{x}{z} \cdot \left(-\left(y - a\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-10}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 4: 73.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-53}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-75}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e-53)
   (+ t (/ (- x t) (/ z y)))
   (if (<= z 5e-75)
     (- x (/ (- x t) (/ a (- y z))))
     (if (<= z 5.8e+153)
       (+ x (/ (- y z) (/ (- a z) t)))
       (+ t (* (- y a) (/ x z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e-53) {
		tmp = t + ((x - t) / (z / y));
	} else if (z <= 5e-75) {
		tmp = x - ((x - t) / (a / (y - z)));
	} else if (z <= 5.8e+153) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + ((y - a) * (x / 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 <= (-1.9d-53)) then
        tmp = t + ((x - t) / (z / y))
    else if (z <= 5d-75) then
        tmp = x - ((x - t) / (a / (y - z)))
    else if (z <= 5.8d+153) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = t + ((y - a) * (x / 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 <= -1.9e-53) {
		tmp = t + ((x - t) / (z / y));
	} else if (z <= 5e-75) {
		tmp = x - ((x - t) / (a / (y - z)));
	} else if (z <= 5.8e+153) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + ((y - a) * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e-53:
		tmp = t + ((x - t) / (z / y))
	elif z <= 5e-75:
		tmp = x - ((x - t) / (a / (y - z)))
	elif z <= 5.8e+153:
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t + ((y - a) * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e-53)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif (z <= 5e-75)
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / Float64(y - z))));
	elseif (z <= 5.8e+153)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e-53)
		tmp = t + ((x - t) / (z / y));
	elseif (z <= 5e-75)
		tmp = x - ((x - t) / (a / (y - z)));
	elseif (z <= 5.8e+153)
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t + ((y - a) * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e-53], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-75], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+153], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8999999999999999e-53

   1. Initial program 57.1%

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

      1. +-commutative 57.1%

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

      2. associate-*l/ 75.7%

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

      3. fma-def 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in z around inf 69.5%

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

      1. +-commutative 69.5%

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

      2. associate-/l* 82.7%

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

      3. distribute-lft-out-- 82.7%

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

      4. mul-1-neg 82.7%

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

      5. distribute-neg-frac 82.7%

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

      6. associate-/l* 69.5%

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

      7. *-commutative 69.5%

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

      8. distribute-rgt-out-- 69.2%

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

      9. unsub-neg 69.2%

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

      10. distribute-rgt-out-- 69.5%

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

      11. *-commutative 69.5%

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

      12. associate-/l* 82.7%

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

   6. Simplified 82.7%

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

   7. Taylor expanded in y around inf 62.4%

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

      1. associate-/l* 73.3%

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

      2. associate-/r/ 73.3%

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

   9. Simplified 73.3%

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

       1. *-commutative 73.3%

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

       2. clear-num 73.3%

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

       3. un-div-inv 73.4%

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

   11. Applied egg-rr 73.4%

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

   if -1.8999999999999999e-53 < z < 4.99999999999999979e-75

   1. Initial program 89.2%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

      1. *-commutative 97.8%

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

      2. clear-num 97.8%

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

      3. un-div-inv 97.8%

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

   5. Applied egg-rr 97.8%

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

   6. Taylor expanded in a around inf 92.7%

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

   if 4.99999999999999979e-75 < z < 5.80000000000000004e153

   1. Initial program 60.6%

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

      1. associate-/l* 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in t around inf 70.7%

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

   if 5.80000000000000004e153 < z

   1. Initial program 24.1%

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

      1. +-commutative 24.1%

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

      2. associate-*l/ 57.2%

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

      3. fma-def 57.2%

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

   3. Simplified 57.2%

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

   4. Taylor expanded in z around inf 73.7%

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

      1. +-commutative 73.7%

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

      2. associate-/l* 95.9%

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

      3. distribute-lft-out-- 95.9%

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

      4. mul-1-neg 95.9%

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

      5. distribute-neg-frac 95.9%

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

      6. associate-/l* 73.7%

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

      7. *-commutative 73.7%

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

      8. distribute-rgt-out-- 73.7%

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

      9. unsub-neg 73.7%

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

      10. distribute-rgt-out-- 73.7%

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

      11. *-commutative 73.7%

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

      12. associate-/l* 95.9%

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

   6. Simplified 95.9%

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

      1. associate-/r/ 96.5%

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

   8. Applied egg-rr 96.5%

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

   9. Taylor expanded in t around 0 80.1%

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

       1. mul-1-neg 80.1%

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

       2. associate-*r/ 95.9%

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

       3. distribute-lft-neg-out 95.9%

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

       4. *-commutative 95.9%

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

   11. Simplified 95.9%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-53}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-75}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 5: 89.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+157} \lor \neg \left(z \leq 4 \cdot 10^{+153}\right):\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{a - z} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e+157) (not (<= z 4e+153)))
   (+ t (* (/ (- y a) z) (- x t)))
   (+ x (* (/ (- z y) (- a z)) (- x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+157) || !(z <= 4e+153)) {
		tmp = t + (((y - a) / z) * (x - t));
	} else {
		tmp = x + (((z - y) / (a - 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) :: tmp
    if ((z <= (-1.2d+157)) .or. (.not. (z <= 4d+153))) then
        tmp = t + (((y - a) / z) * (x - t))
    else
        tmp = x + (((z - y) / (a - 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 tmp;
	if ((z <= -1.2e+157) || !(z <= 4e+153)) {
		tmp = t + (((y - a) / z) * (x - t));
	} else {
		tmp = x + (((z - y) / (a - z)) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e+157) or not (z <= 4e+153):
		tmp = t + (((y - a) / z) * (x - t))
	else:
		tmp = x + (((z - y) / (a - z)) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e+157) || !(z <= 4e+153))
		tmp = Float64(t + Float64(Float64(Float64(y - a) / z) * Float64(x - t)));
	else
		tmp = Float64(x + Float64(Float64(Float64(z - y) / Float64(a - z)) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.2e+157) || ~((z <= 4e+153)))
		tmp = t + (((y - a) / z) * (x - t));
	else
		tmp = x + (((z - y) / (a - z)) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e+157], N[Not[LessEqual[z, 4e+153]], $MachinePrecision]], N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e157 or 4e153 < z

   1. Initial program 27.4%

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

      1. +-commutative 27.4%

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

      2. associate-*l/ 61.1%

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

      3. fma-def 61.1%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in z around inf 66.2%

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

      1. +-commutative 66.2%

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

      2. associate-/l* 92.1%

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

      3. distribute-lft-out-- 92.1%

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

      4. mul-1-neg 92.1%

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

      5. distribute-neg-frac 92.1%

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

      6. associate-/l* 66.2%

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

      7. *-commutative 66.2%

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

      8. distribute-rgt-out-- 65.9%

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

      9. unsub-neg 65.9%

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

      10. distribute-rgt-out-- 66.2%

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

      11. *-commutative 66.2%

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

      12. associate-/l* 92.1%

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

   6. Simplified 92.1%

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

      1. associate-/r/ 92.4%

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

   8. Applied egg-rr 92.4%

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

   if -1.2e157 < z < 4e153

   1. Initial program 78.6%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+157} \lor \neg \left(z \leq 4 \cdot 10^{+153}\right):\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{a - z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 6: 51.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+53}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.85 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))))
   (if (<= z -5e+53)
     t
     (if (<= z 8.8e-156)
       t_1
       (if (<= z 5e-75) (* x (- 1.0 (/ y a))) (if (<= z 3.85e+80) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (z <= -5e+53) {
		tmp = t;
	} else if (z <= 8.8e-156) {
		tmp = t_1;
	} else if (z <= 5e-75) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.85e+80) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    if (z <= (-5d+53)) then
        tmp = t
    else if (z <= 8.8d-156) then
        tmp = t_1
    else if (z <= 5d-75) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 3.85d+80) then
        tmp = t_1
    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 t_1 = x + (y / (a / t));
	double tmp;
	if (z <= -5e+53) {
		tmp = t;
	} else if (z <= 8.8e-156) {
		tmp = t_1;
	} else if (z <= 5e-75) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.85e+80) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	tmp = 0
	if z <= -5e+53:
		tmp = t
	elif z <= 8.8e-156:
		tmp = t_1
	elif z <= 5e-75:
		tmp = x * (1.0 - (y / a))
	elif z <= 3.85e+80:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (z <= -5e+53)
		tmp = t;
	elseif (z <= 8.8e-156)
		tmp = t_1;
	elseif (z <= 5e-75)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 3.85e+80)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	tmp = 0.0;
	if (z <= -5e+53)
		tmp = t;
	elseif (z <= 8.8e-156)
		tmp = t_1;
	elseif (z <= 5e-75)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 3.85e+80)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+53], t, If[LessEqual[z, 8.8e-156], t$95$1, If[LessEqual[z, 5e-75], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.85e+80], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.0000000000000004e53 or 3.84999999999999998e80 < z

   1. Initial program 41.4%

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

      1. +-commutative 41.4%

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

      2. associate-*l/ 70.8%

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

      3. fma-def 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in z around inf 50.3%

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

   if -5.0000000000000004e53 < z < 8.7999999999999996e-156 or 4.99999999999999979e-75 < z < 3.84999999999999998e80

   1. Initial program 84.0%

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

      1. +-commutative 84.0%

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

      2. associate-*l/ 93.6%

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

      3. fma-def 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in z around 0 62.2%

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

      1. +-commutative 62.2%

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

      2. associate-/l* 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in t around inf 54.4%

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

      1. associate-/l* 57.8%

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

   9. Simplified 57.8%

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

   if 8.7999999999999996e-156 < z < 4.99999999999999979e-75

   1. Initial program 83.7%

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

      1. +-commutative 83.7%

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

      2. associate-*l/ 91.8%

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

      3. fma-def 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around 0 76.2%

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

      1. +-commutative 76.2%

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

      2. associate-/l* 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in x around inf 76.7%

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

      1. *-commutative 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

   9. Simplified 76.7%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+53}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-156}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.85 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 54.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ t_2 := t - a \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -0.0128:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))) (t_2 (- t (* a (/ x z)))))
   (if (<= z -0.0128)
     t_2
     (if (<= z 6.8e-152)
       t_1
       (if (<= z 3.8e-75)
         (* x (- 1.0 (/ y a)))
         (if (<= z 1.25e+81) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double t_2 = t - (a * (x / z));
	double tmp;
	if (z <= -0.0128) {
		tmp = t_2;
	} else if (z <= 6.8e-152) {
		tmp = t_1;
	} else if (z <= 3.8e-75) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.25e+81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    t_2 = t - (a * (x / z))
    if (z <= (-0.0128d0)) then
        tmp = t_2
    else if (z <= 6.8d-152) then
        tmp = t_1
    else if (z <= 3.8d-75) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.25d+81) then
        tmp = t_1
    else
        tmp = t_2
    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 / (a / t));
	double t_2 = t - (a * (x / z));
	double tmp;
	if (z <= -0.0128) {
		tmp = t_2;
	} else if (z <= 6.8e-152) {
		tmp = t_1;
	} else if (z <= 3.8e-75) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.25e+81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	t_2 = t - (a * (x / z))
	tmp = 0
	if z <= -0.0128:
		tmp = t_2
	elif z <= 6.8e-152:
		tmp = t_1
	elif z <= 3.8e-75:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.25e+81:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	t_2 = Float64(t - Float64(a * Float64(x / z)))
	tmp = 0.0
	if (z <= -0.0128)
		tmp = t_2;
	elseif (z <= 6.8e-152)
		tmp = t_1;
	elseif (z <= 3.8e-75)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.25e+81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	t_2 = t - (a * (x / z));
	tmp = 0.0;
	if (z <= -0.0128)
		tmp = t_2;
	elseif (z <= 6.8e-152)
		tmp = t_1;
	elseif (z <= 3.8e-75)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.25e+81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0128], t$95$2, If[LessEqual[z, 6.8e-152], t$95$1, If[LessEqual[z, 3.8e-75], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+81], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0128000000000000006 or 1.25e81 < z

   1. Initial program 46.7%

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

      1. +-commutative 46.7%

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

      2. associate-*l/ 72.2%

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

      3. fma-def 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in z around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. associate-/l* 83.5%

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

      3. distribute-lft-out-- 83.5%

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

      4. mul-1-neg 83.5%

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

      5. distribute-neg-frac 83.5%

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

      6. associate-/l* 66.7%

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

      7. *-commutative 66.7%

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

      8. distribute-rgt-out-- 66.6%

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

      9. unsub-neg 66.6%

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

      10. distribute-rgt-out-- 66.7%

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

      11. *-commutative 66.7%

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

      12. associate-/l* 83.5%

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

   6. Simplified 83.5%

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

   7. Taylor expanded in t around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. distribute-neg-frac 76.7%

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

   9. Simplified 76.7%

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

   10. Taylor expanded in y around 0 53.2%

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

       1. associate-*r/ 56.1%

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

   12. Simplified 56.1%

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

   if -0.0128000000000000006 < z < 6.79999999999999968e-152 or 3.79999999999999994e-75 < z < 1.25e81

   1. Initial program 84.3%

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

      1. +-commutative 84.3%

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

      2. associate-*l/ 95.2%

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

      3. fma-def 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 66.9%

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

      1. +-commutative 66.9%

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

      2. associate-/l* 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in t around inf 58.0%

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

      1. associate-/l* 61.9%

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

   9. Simplified 61.9%

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

   if 6.79999999999999968e-152 < z < 3.79999999999999994e-75

   1. Initial program 83.7%

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

      1. +-commutative 83.7%

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

      2. associate-*l/ 91.8%

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

      3. fma-def 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around 0 76.2%

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

      1. +-commutative 76.2%

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

      2. associate-/l* 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in x around inf 76.7%

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

      1. *-commutative 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

   9. Simplified 76.7%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0128:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-152}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]

Alternative 8: 54.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;z \leq -0.0128:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))))
   (if (<= z -0.0128)
     (- t (* a (/ x z)))
     (if (<= z 8e-154)
       t_1
       (if (<= z 5.4e-75)
         (* x (- 1.0 (/ y a)))
         (if (<= z 1.02e-25) t_1 (- t (* t (/ y z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (z <= -0.0128) {
		tmp = t - (a * (x / z));
	} else if (z <= 8e-154) {
		tmp = t_1;
	} else if (z <= 5.4e-75) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.02e-25) {
		tmp = t_1;
	} else {
		tmp = t - (t * (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) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    if (z <= (-0.0128d0)) then
        tmp = t - (a * (x / z))
    else if (z <= 8d-154) then
        tmp = t_1
    else if (z <= 5.4d-75) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.02d-25) then
        tmp = t_1
    else
        tmp = t - (t * (y / z))
    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 / (a / t));
	double tmp;
	if (z <= -0.0128) {
		tmp = t - (a * (x / z));
	} else if (z <= 8e-154) {
		tmp = t_1;
	} else if (z <= 5.4e-75) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.02e-25) {
		tmp = t_1;
	} else {
		tmp = t - (t * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	tmp = 0
	if z <= -0.0128:
		tmp = t - (a * (x / z))
	elif z <= 8e-154:
		tmp = t_1
	elif z <= 5.4e-75:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.02e-25:
		tmp = t_1
	else:
		tmp = t - (t * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (z <= -0.0128)
		tmp = Float64(t - Float64(a * Float64(x / z)));
	elseif (z <= 8e-154)
		tmp = t_1;
	elseif (z <= 5.4e-75)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.02e-25)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(t * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	tmp = 0.0;
	if (z <= -0.0128)
		tmp = t - (a * (x / z));
	elseif (z <= 8e-154)
		tmp = t_1;
	elseif (z <= 5.4e-75)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.02e-25)
		tmp = t_1;
	else
		tmp = t - (t * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0128], N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-154], t$95$1, If[LessEqual[z, 5.4e-75], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-25], t$95$1, N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.0128000000000000006

   1. Initial program 54.7%

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

      1. +-commutative 54.7%

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

      2. associate-*l/ 74.7%

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

      3. fma-def 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in z around inf 67.6%

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

      1. +-commutative 67.6%

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

      2. associate-/l* 82.8%

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

      3. distribute-lft-out-- 82.8%

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

      4. mul-1-neg 82.8%

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

      5. distribute-neg-frac 82.8%

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

      6. associate-/l* 67.6%

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

      7. *-commutative 67.6%

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

      8. distribute-rgt-out-- 67.3%

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

      9. unsub-neg 67.3%

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

      10. distribute-rgt-out-- 67.6%

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

      11. *-commutative 67.6%

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

      12. associate-/l* 82.8%

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

   6. Simplified 82.8%

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

   7. Taylor expanded in t around 0 72.8%

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

      1. mul-1-neg 72.8%

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

      2. distribute-neg-frac 72.8%

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

   9. Simplified 72.8%

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

   10. Taylor expanded in y around 0 52.5%

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

       1. associate-*r/ 54.6%

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

   12. Simplified 54.6%

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

   if -0.0128000000000000006 < z < 7.9999999999999998e-154 or 5.3999999999999996e-75 < z < 1.01999999999999998e-25

   1. Initial program 86.4%

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

      1. +-commutative 86.4%

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

      2. associate-*l/ 97.1%

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

      3. fma-def 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in z around 0 72.2%

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

      1. +-commutative 72.2%

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

      2. associate-/l* 77.6%

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

   6. Simplified 77.6%

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

   7. Taylor expanded in t around inf 61.1%

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

      1. associate-/l* 65.5%

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

   9. Simplified 65.5%

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

   if 7.9999999999999998e-154 < z < 5.3999999999999996e-75

   1. Initial program 83.7%

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

      1. +-commutative 83.7%

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

      2. associate-*l/ 91.8%

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

      3. fma-def 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around 0 76.2%

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

      1. +-commutative 76.2%

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

      2. associate-/l* 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in x around inf 76.7%

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

      1. *-commutative 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

   9. Simplified 76.7%

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

   if 1.01999999999999998e-25 < z

   1. Initial program 42.5%

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

      1. +-commutative 42.5%

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

      2. associate-*l/ 71.5%

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

      3. fma-def 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in z around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-/l* 83.7%

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

      3. distribute-lft-out-- 83.7%

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

      4. mul-1-neg 83.7%

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

      5. distribute-neg-frac 83.7%

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

      6. associate-/l* 69.0%

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

      7. *-commutative 69.0%

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

      8. distribute-rgt-out-- 69.0%

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

      9. unsub-neg 69.0%

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

      10. distribute-rgt-out-- 69.0%

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

      11. *-commutative 69.0%

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

      12. associate-/l* 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in y around inf 65.2%

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

      1. associate-/l* 73.7%

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

      2. associate-/r/ 74.1%

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

   9. Simplified 74.1%

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

   10. Taylor expanded in t around inf 54.8%

       \[\leadsto t - \color{blue}{\frac{y \cdot t}{z}} \]
   11. Step-by-step derivation

       1. associate-*l/ 53.4%

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

       2. *-commutative 53.4%

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

   12. Simplified 53.4%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0128:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-154}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \end{array} \]

Alternative 9: 56.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-158}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{+81}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ x z)))))
   (if (<= z -1.45e-57)
     t_1
     (if (<= z 8e-158)
       (+ x (/ y (/ a t)))
       (if (<= z 6e-73)
         (* x (- 1.0 (/ y a)))
         (if (<= z 1.48e+81) (* (/ y z) (- x t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double tmp;
	if (z <= -1.45e-57) {
		tmp = t_1;
	} else if (z <= 8e-158) {
		tmp = x + (y / (a / t));
	} else if (z <= 6e-73) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.48e+81) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (y * (x / z))
    if (z <= (-1.45d-57)) then
        tmp = t_1
    else if (z <= 8d-158) then
        tmp = x + (y / (a / t))
    else if (z <= 6d-73) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.48d+81) then
        tmp = (y / z) * (x - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double tmp;
	if (z <= -1.45e-57) {
		tmp = t_1;
	} else if (z <= 8e-158) {
		tmp = x + (y / (a / t));
	} else if (z <= 6e-73) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.48e+81) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * (x / z))
	tmp = 0
	if z <= -1.45e-57:
		tmp = t_1
	elif z <= 8e-158:
		tmp = x + (y / (a / t))
	elif z <= 6e-73:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.48e+81:
		tmp = (y / z) * (x - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(x / z)))
	tmp = 0.0
	if (z <= -1.45e-57)
		tmp = t_1;
	elseif (z <= 8e-158)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 6e-73)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.48e+81)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * (x / z));
	tmp = 0.0;
	if (z <= -1.45e-57)
		tmp = t_1;
	elseif (z <= 8e-158)
		tmp = x + (y / (a / t));
	elseif (z <= 6e-73)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.48e+81)
		tmp = (y / z) * (x - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e-57], t$95$1, If[LessEqual[z, 8e-158], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-73], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.48e+81], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.45000000000000013e-57 or 1.47999999999999998e81 < z

   1. Initial program 49.3%

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

      1. +-commutative 49.3%

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

      2. associate-*l/ 73.2%

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

      3. fma-def 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in z around inf 67.5%

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

      1. +-commutative 67.5%

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

      2. associate-/l* 82.8%

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

      3. distribute-lft-out-- 82.8%

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

      4. mul-1-neg 82.8%

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

      5. distribute-neg-frac 82.8%

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

      6. associate-/l* 67.5%

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

      7. *-commutative 67.5%

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

      8. distribute-rgt-out-- 67.4%

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

      9. unsub-neg 67.4%

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

      10. distribute-rgt-out-- 67.5%

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

      11. *-commutative 67.5%

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

      12. associate-/l* 82.8%

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

   6. Simplified 82.8%

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

   7. Taylor expanded in y around inf 61.9%

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

      1. associate-/l* 72.9%

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

      2. associate-/r/ 73.0%

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

   9. Simplified 73.0%

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

   10. Taylor expanded in t around 0 56.7%

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

       1. mul-1-neg 56.7%

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

       2. associate-*r/ 65.8%

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

   12. Simplified 65.8%

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

   if -1.45000000000000013e-57 < z < 8.00000000000000052e-158

   1. Initial program 89.8%

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

      1. +-commutative 89.8%

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

      2. associate-*l/ 98.7%

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

      3. fma-def 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. associate-/l* 85.8%

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

   6. Simplified 85.8%

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

   7. Taylor expanded in t around inf 67.2%

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

      1. associate-/l* 70.5%

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

   9. Simplified 70.5%

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

   if 8.00000000000000052e-158 < z < 6e-73

   1. Initial program 77.3%

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

      1. +-commutative 77.3%

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

      2. associate-*l/ 92.4%

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

      3. fma-def 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 70.4%

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

      1. +-commutative 70.4%

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

      2. associate-/l* 85.1%

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

   6. Simplified 85.1%

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

   7. Taylor expanded in x around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

   9. Simplified 78.5%

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

   if 6e-73 < z < 1.47999999999999998e81

   1. Initial program 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-*l/ 88.4%

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

      3. fma-def 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in y around -inf 54.7%

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

   5. Taylor expanded in a around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. associate-/l* 54.3%

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

      3. associate-/r/ 54.5%

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

      4. distribute-lft-neg-in 54.5%

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

      5. distribute-frac-neg 54.5%

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

   7. Simplified 54.5%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-57}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-158}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{+81}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 10: 56.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -7 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-151}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+81}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ y z)))))
   (if (<= z -7e-60)
     t_1
     (if (<= z 5.5e-151)
       (+ x (/ y (/ a t)))
       (if (<= z 3.1e-71)
         (* x (- 1.0 (/ y a)))
         (if (<= z 7.4e+81) (* (/ y z) (- x t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double tmp;
	if (z <= -7e-60) {
		tmp = t_1;
	} else if (z <= 5.5e-151) {
		tmp = x + (y / (a / t));
	} else if (z <= 3.1e-71) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 7.4e+81) {
		tmp = (y / z) * (x - t);
	} 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 * (y / z))
    if (z <= (-7d-60)) then
        tmp = t_1
    else if (z <= 5.5d-151) then
        tmp = x + (y / (a / t))
    else if (z <= 3.1d-71) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 7.4d+81) then
        tmp = (y / z) * (x - t)
    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 * (y / z));
	double tmp;
	if (z <= -7e-60) {
		tmp = t_1;
	} else if (z <= 5.5e-151) {
		tmp = x + (y / (a / t));
	} else if (z <= 3.1e-71) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 7.4e+81) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * (y / z))
	tmp = 0
	if z <= -7e-60:
		tmp = t_1
	elif z <= 5.5e-151:
		tmp = x + (y / (a / t))
	elif z <= 3.1e-71:
		tmp = x * (1.0 - (y / a))
	elif z <= 7.4e+81:
		tmp = (y / z) * (x - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(y / z)))
	tmp = 0.0
	if (z <= -7e-60)
		tmp = t_1;
	elseif (z <= 5.5e-151)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 3.1e-71)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 7.4e+81)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * (y / z));
	tmp = 0.0;
	if (z <= -7e-60)
		tmp = t_1;
	elseif (z <= 5.5e-151)
		tmp = x + (y / (a / t));
	elseif (z <= 3.1e-71)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 7.4e+81)
		tmp = (y / z) * (x - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e-60], t$95$1, If[LessEqual[z, 5.5e-151], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-71], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e+81], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.99999999999999952e-60 or 7.4000000000000001e81 < z

   1. Initial program 49.3%

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

      1. +-commutative 49.3%

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

      2. associate-*l/ 73.2%

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

      3. fma-def 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in z around inf 67.5%

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

      1. +-commutative 67.5%

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

      2. associate-/l* 82.8%

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

      3. distribute-lft-out-- 82.8%

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

      4. mul-1-neg 82.8%

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

      5. distribute-neg-frac 82.8%

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

      6. associate-/l* 67.5%

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

      7. *-commutative 67.5%

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

      8. distribute-rgt-out-- 67.4%

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

      9. unsub-neg 67.4%

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

      10. distribute-rgt-out-- 67.5%

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

      11. *-commutative 67.5%

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

      12. associate-/l* 82.8%

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

   6. Simplified 82.8%

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

   7. Taylor expanded in y around inf 61.9%

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

      1. associate-/l* 72.9%

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

      2. associate-/r/ 73.0%

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

   9. Simplified 73.0%

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

   10. Taylor expanded in t around 0 56.7%

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

       1. associate-*l/ 66.0%

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

       2. neg-mul-1 66.0%

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

       3. distribute-rgt-neg-out 66.0%

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

   12. Simplified 66.0%

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

   if -6.99999999999999952e-60 < z < 5.4999999999999998e-151

   1. Initial program 89.8%

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

      1. +-commutative 89.8%

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

      2. associate-*l/ 98.7%

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

      3. fma-def 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. associate-/l* 85.8%

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

   6. Simplified 85.8%

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

   7. Taylor expanded in t around inf 67.2%

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

      1. associate-/l* 70.5%

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

   9. Simplified 70.5%

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

   if 5.4999999999999998e-151 < z < 3.10000000000000002e-71

   1. Initial program 77.3%

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

      1. +-commutative 77.3%

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

      2. associate-*l/ 92.4%

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

      3. fma-def 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 70.4%

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

      1. +-commutative 70.4%

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

      2. associate-/l* 85.1%

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

   6. Simplified 85.1%

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

   7. Taylor expanded in x around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

   9. Simplified 78.5%

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

   if 3.10000000000000002e-71 < z < 7.4000000000000001e81

   1. Initial program 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-*l/ 88.4%

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

      3. fma-def 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in y around -inf 54.7%

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

   5. Taylor expanded in a around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. associate-/l* 54.3%

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

      3. associate-/r/ 54.5%

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

      4. distribute-lft-neg-in 54.5%

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

      5. distribute-frac-neg 54.5%

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

   7. Simplified 54.5%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-60}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-151}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+81}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 11: 76.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-53} \lor \neg \left(z \leq 1.85 \cdot 10^{-25}\right):\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e-53) (not (<= z 1.85e-25)))
   (+ t (* (/ (- y a) z) (- x t)))
   (- x (/ (- x t) (/ a (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e-53) || !(z <= 1.85e-25)) {
		tmp = t + (((y - a) / z) * (x - t));
	} else {
		tmp = x - ((x - 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 <= (-7.2d-53)) .or. (.not. (z <= 1.85d-25))) then
        tmp = t + (((y - a) / z) * (x - t))
    else
        tmp = x - ((x - 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 <= -7.2e-53) || !(z <= 1.85e-25)) {
		tmp = t + (((y - a) / z) * (x - t));
	} else {
		tmp = x - ((x - t) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e-53) or not (z <= 1.85e-25):
		tmp = t + (((y - a) / z) * (x - t))
	else:
		tmp = x - ((x - t) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e-53) || !(z <= 1.85e-25))
		tmp = Float64(t + Float64(Float64(Float64(y - a) / z) * Float64(x - t)));
	else
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.2e-53) || ~((z <= 1.85e-25)))
		tmp = t + (((y - a) / z) * (x - t));
	else
		tmp = x - ((x - t) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e-53], N[Not[LessEqual[z, 1.85e-25]], $MachinePrecision]], N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.1999999999999998e-53 or 1.85000000000000004e-25 < z

   1. Initial program 51.0%

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

      1. +-commutative 51.0%

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

      2. associate-*l/ 73.9%

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

      3. fma-def 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in z around inf 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-/l* 83.1%

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

      3. distribute-lft-out-- 83.1%

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

      4. mul-1-neg 83.1%

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

      5. distribute-neg-frac 83.1%

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

      6. associate-/l* 69.3%

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

      7. *-commutative 69.3%

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

      8. distribute-rgt-out-- 69.1%

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

      9. unsub-neg 69.1%

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

      10. distribute-rgt-out-- 69.3%

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

      11. *-commutative 69.3%

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

      12. associate-/l* 83.1%

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

   6. Simplified 83.1%

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

      1. associate-/r/ 83.2%

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

   8. Applied egg-rr 83.2%

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

   if -7.1999999999999998e-53 < z < 1.85000000000000004e-25

   1. Initial program 87.3%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

      1. *-commutative 98.0%

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

      2. clear-num 97.9%

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

      3. un-div-inv 98.0%

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

   5. Applied egg-rr 98.0%

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

   6. Taylor expanded in a around inf 91.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-53} \lor \neg \left(z \leq 1.85 \cdot 10^{-25}\right):\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \end{array} \]

Alternative 12: 71.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-53}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-25}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e-53)
   (+ t (/ (- x t) (/ z y)))
   (if (<= z 3.5e-25)
     (- x (/ (- x t) (/ a (- y z))))
     (+ t (* (- y a) (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e-53) {
		tmp = t + ((x - t) / (z / y));
	} else if (z <= 3.5e-25) {
		tmp = x - ((x - t) / (a / (y - z)));
	} else {
		tmp = t + ((y - a) * (x / 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 <= (-9d-53)) then
        tmp = t + ((x - t) / (z / y))
    else if (z <= 3.5d-25) then
        tmp = x - ((x - t) / (a / (y - z)))
    else
        tmp = t + ((y - a) * (x / 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 <= -9e-53) {
		tmp = t + ((x - t) / (z / y));
	} else if (z <= 3.5e-25) {
		tmp = x - ((x - t) / (a / (y - z)));
	} else {
		tmp = t + ((y - a) * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9e-53:
		tmp = t + ((x - t) / (z / y))
	elif z <= 3.5e-25:
		tmp = x - ((x - t) / (a / (y - z)))
	else:
		tmp = t + ((y - a) * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e-53)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif (z <= 3.5e-25)
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9e-53)
		tmp = t + ((x - t) / (z / y));
	elseif (z <= 3.5e-25)
		tmp = x - ((x - t) / (a / (y - z)));
	else
		tmp = t + ((y - a) * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e-53], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-25], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999997e-53

   1. Initial program 57.1%

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

      1. +-commutative 57.1%

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

      2. associate-*l/ 75.7%

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

      3. fma-def 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in z around inf 69.5%

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

      1. +-commutative 69.5%

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

      2. associate-/l* 82.7%

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

      3. distribute-lft-out-- 82.7%

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

      4. mul-1-neg 82.7%

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

      5. distribute-neg-frac 82.7%

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

      6. associate-/l* 69.5%

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

      7. *-commutative 69.5%

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

      8. distribute-rgt-out-- 69.2%

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

      9. unsub-neg 69.2%

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

      10. distribute-rgt-out-- 69.5%

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

      11. *-commutative 69.5%

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

      12. associate-/l* 82.7%

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

   6. Simplified 82.7%

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

   7. Taylor expanded in y around inf 62.4%

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

      1. associate-/l* 73.3%

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

      2. associate-/r/ 73.3%

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

   9. Simplified 73.3%

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

       1. *-commutative 73.3%

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

       2. clear-num 73.3%

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

       3. un-div-inv 73.4%

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

   11. Applied egg-rr 73.4%

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

   if -8.9999999999999997e-53 < z < 3.5000000000000002e-25

   1. Initial program 87.3%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

      1. *-commutative 98.0%

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

      2. clear-num 97.9%

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

      3. un-div-inv 98.0%

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

   5. Applied egg-rr 98.0%

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

   6. Taylor expanded in a around inf 91.0%

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

   if 3.5000000000000002e-25 < z

   1. Initial program 42.5%

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

      1. +-commutative 42.5%

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

      2. associate-*l/ 71.5%

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

      3. fma-def 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in z around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-/l* 83.7%

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

      3. distribute-lft-out-- 83.7%

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

      4. mul-1-neg 83.7%

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

      5. distribute-neg-frac 83.7%

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

      6. associate-/l* 69.0%

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

      7. *-commutative 69.0%

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

      8. distribute-rgt-out-- 69.0%

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

      9. unsub-neg 69.0%

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

      10. distribute-rgt-out-- 69.0%

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

      11. *-commutative 69.0%

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

      12. associate-/l* 83.7%

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

   6. Simplified 83.7%

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

      1. associate-/r/ 84.0%

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

   8. Applied egg-rr 84.0%

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

   9. Taylor expanded in t around 0 63.0%

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

       1. mul-1-neg 63.0%

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

       2. associate-*r/ 74.6%

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

       3. distribute-lft-neg-out 74.6%

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

       4. *-commutative 74.6%

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

   11. Simplified 74.6%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-53}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-25}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 13: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-26}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e-53)
   (+ t (/ (- a y) (/ z (- t x))))
   (if (<= z 5.8e-26)
     (- x (/ (- x t) (/ a (- y z))))
     (+ t (* (/ (- y a) z) (- x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e-53) {
		tmp = t + ((a - y) / (z / (t - x)));
	} else if (z <= 5.8e-26) {
		tmp = x - ((x - t) / (a / (y - z)));
	} else {
		tmp = t + (((y - a) / 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) :: tmp
    if (z <= (-1.15d-53)) then
        tmp = t + ((a - y) / (z / (t - x)))
    else if (z <= 5.8d-26) then
        tmp = x - ((x - t) / (a / (y - z)))
    else
        tmp = t + (((y - a) / 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 tmp;
	if (z <= -1.15e-53) {
		tmp = t + ((a - y) / (z / (t - x)));
	} else if (z <= 5.8e-26) {
		tmp = x - ((x - t) / (a / (y - z)));
	} else {
		tmp = t + (((y - a) / z) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e-53:
		tmp = t + ((a - y) / (z / (t - x)))
	elif z <= 5.8e-26:
		tmp = x - ((x - t) / (a / (y - z)))
	else:
		tmp = t + (((y - a) / z) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e-53)
		tmp = Float64(t + Float64(Float64(a - y) / Float64(z / Float64(t - x))));
	elseif (z <= 5.8e-26)
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(y - a) / z) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e-53)
		tmp = t + ((a - y) / (z / (t - x)));
	elseif (z <= 5.8e-26)
		tmp = x - ((x - t) / (a / (y - z)));
	else
		tmp = t + (((y - a) / z) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e-53], N[(t + N[(N[(a - y), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-26], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1500000000000001e-53

   1. Initial program 57.1%

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

      1. +-commutative 57.1%

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

      2. associate-*l/ 75.7%

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

      3. fma-def 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in z around inf 69.5%

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

      1. +-commutative 69.5%

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

      2. associate-/l* 82.7%

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

      3. distribute-lft-out-- 82.7%

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

      4. mul-1-neg 82.7%

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

      5. distribute-neg-frac 82.7%

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

      6. associate-/l* 69.5%

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

      7. *-commutative 69.5%

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

      8. distribute-rgt-out-- 69.2%

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

      9. unsub-neg 69.2%

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

      10. distribute-rgt-out-- 69.5%

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

      11. *-commutative 69.5%

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

      12. associate-/l* 82.7%

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

   6. Simplified 82.7%

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

   if -1.1500000000000001e-53 < z < 5.7999999999999996e-26

   1. Initial program 87.3%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

      1. *-commutative 98.0%

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

      2. clear-num 97.9%

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

      3. un-div-inv 98.0%

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

   5. Applied egg-rr 98.0%

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

   6. Taylor expanded in a around inf 91.0%

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

   if 5.7999999999999996e-26 < z

   1. Initial program 42.5%

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

      1. +-commutative 42.5%

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

      2. associate-*l/ 71.5%

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

      3. fma-def 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in z around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-/l* 83.7%

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

      3. distribute-lft-out-- 83.7%

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

      4. mul-1-neg 83.7%

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

      5. distribute-neg-frac 83.7%

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

      6. associate-/l* 69.0%

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

      7. *-commutative 69.0%

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

      8. distribute-rgt-out-- 69.0%

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

      9. unsub-neg 69.0%

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

      10. distribute-rgt-out-- 69.0%

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

      11. *-commutative 69.0%

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

      12. associate-/l* 83.7%

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

   6. Simplified 83.7%

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

      1. associate-/r/ 84.0%

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

   8. Applied egg-rr 84.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-26}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 14: 34.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-68}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-146}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-72}:\\ \;\;\;\;-y \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(-\frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e-68)
   t
   (if (<= z 1.55e-146)
     (* t (/ y a))
     (if (<= z 1.05e-72)
       (- (* y (/ x a)))
       (if (<= z 3.3e+80) (* t (- (/ y z))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e-68) {
		tmp = t;
	} else if (z <= 1.55e-146) {
		tmp = t * (y / a);
	} else if (z <= 1.05e-72) {
		tmp = -(y * (x / a));
	} else if (z <= 3.3e+80) {
		tmp = t * -(y / z);
	} 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 <= (-6.5d-68)) then
        tmp = t
    else if (z <= 1.55d-146) then
        tmp = t * (y / a)
    else if (z <= 1.05d-72) then
        tmp = -(y * (x / a))
    else if (z <= 3.3d+80) then
        tmp = t * -(y / z)
    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 <= -6.5e-68) {
		tmp = t;
	} else if (z <= 1.55e-146) {
		tmp = t * (y / a);
	} else if (z <= 1.05e-72) {
		tmp = -(y * (x / a));
	} else if (z <= 3.3e+80) {
		tmp = t * -(y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e-68:
		tmp = t
	elif z <= 1.55e-146:
		tmp = t * (y / a)
	elif z <= 1.05e-72:
		tmp = -(y * (x / a))
	elif z <= 3.3e+80:
		tmp = t * -(y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e-68)
		tmp = t;
	elseif (z <= 1.55e-146)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 1.05e-72)
		tmp = Float64(-Float64(y * Float64(x / a)));
	elseif (z <= 3.3e+80)
		tmp = Float64(t * Float64(-Float64(y / z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e-68)
		tmp = t;
	elseif (z <= 1.55e-146)
		tmp = t * (y / a);
	elseif (z <= 1.05e-72)
		tmp = -(y * (x / a));
	elseif (z <= 3.3e+80)
		tmp = t * -(y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e-68], t, If[LessEqual[z, 1.55e-146], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-72], (-N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), If[LessEqual[z, 3.3e+80], N[(t * (-N[(y / z), $MachinePrecision])), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.4999999999999997e-68 or 3.29999999999999991e80 < z

   1. Initial program 50.8%

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

      1. +-commutative 50.8%

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

      2. associate-*l/ 74.0%

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

      3. fma-def 74.0%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in z around inf 43.0%

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

   if -6.4999999999999997e-68 < z < 1.5499999999999999e-146

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-*l/ 98.6%

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

      3. fma-def 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in y around -inf 52.4%

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

   5. Taylor expanded in t around inf 38.4%

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

   6. Taylor expanded in a around inf 37.2%

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

      1. associate-/l* 39.3%

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

   8. Simplified 39.3%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}}} \]
   9. Step-by-step derivation

      1. associate-/r/ 40.7%

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

   10. Applied egg-rr 40.7%

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

   if 1.5499999999999999e-146 < z < 1.05e-72

   1. Initial program 75.4%

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

      1. +-commutative 75.4%

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

      2. associate-*l/ 91.8%

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

      3. fma-def 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around 0 67.9%

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

      1. +-commutative 67.9%

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

      2. associate-/l* 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in y around inf 59.0%

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

      1. div-sub 59.0%

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

      2. *-commutative 59.0%

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

   9. Simplified 59.0%

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

   10. Taylor expanded in t around 0 51.3%

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

       1. neg-mul-1 51.3%

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

       2. distribute-neg-frac 51.3%

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

   12. Simplified 51.3%

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

   if 1.05e-72 < z < 3.29999999999999991e80

   1. Initial program 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-*l/ 88.4%

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

      3. fma-def 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in y around -inf 54.7%

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

   5. Taylor expanded in t around inf 37.3%

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

   6. Taylor expanded in a around 0 37.0%

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

      1. mul-1-neg 37.0%

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

      2. associate-*l/ 37.1%

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

      3. *-commutative 37.1%

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

      4. distribute-rgt-neg-in 37.1%

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

      5. distribute-frac-neg 37.1%

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

   8. Simplified 37.1%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-68}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-146}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-72}:\\ \;\;\;\;-y \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(-\frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 47.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \left(-\frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+57)
   t
   (if (<= z 8.2e-71)
     (* x (- 1.0 (/ y a)))
     (if (<= z 9e+52)
       (* t (/ (- y z) a))
       (if (<= z 3.5e+82) (* t (- (/ y z))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+57) {
		tmp = t;
	} else if (z <= 8.2e-71) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 9e+52) {
		tmp = t * ((y - z) / a);
	} else if (z <= 3.5e+82) {
		tmp = t * -(y / z);
	} 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 <= (-1.9d+57)) then
        tmp = t
    else if (z <= 8.2d-71) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 9d+52) then
        tmp = t * ((y - z) / a)
    else if (z <= 3.5d+82) then
        tmp = t * -(y / z)
    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 <= -1.9e+57) {
		tmp = t;
	} else if (z <= 8.2e-71) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 9e+52) {
		tmp = t * ((y - z) / a);
	} else if (z <= 3.5e+82) {
		tmp = t * -(y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+57:
		tmp = t
	elif z <= 8.2e-71:
		tmp = x * (1.0 - (y / a))
	elif z <= 9e+52:
		tmp = t * ((y - z) / a)
	elif z <= 3.5e+82:
		tmp = t * -(y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+57)
		tmp = t;
	elseif (z <= 8.2e-71)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 9e+52)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 3.5e+82)
		tmp = Float64(t * Float64(-Float64(y / z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e+57)
		tmp = t;
	elseif (z <= 8.2e-71)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 9e+52)
		tmp = t * ((y - z) / a);
	elseif (z <= 3.5e+82)
		tmp = t * -(y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+57], t, If[LessEqual[z, 8.2e-71], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+52], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+82], N[(t * (-N[(y / z), $MachinePrecision])), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8999999999999999e57 or 3.5e82 < z

   1. Initial program 41.4%

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

      1. +-commutative 41.4%

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

      2. associate-*l/ 70.8%

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

      3. fma-def 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in z around inf 50.3%

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

   if -1.8999999999999999e57 < z < 8.19999999999999987e-71

   1. Initial program 86.2%

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

      1. +-commutative 86.2%

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

      2. associate-*l/ 94.4%

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

      3. fma-def 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around 0 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-/l* 72.8%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 72.8%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   7. Taylor expanded in x around inf 55.0%

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{y}{a}\right) \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 55.0%

         \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]

      2. mul-1-neg 55.0%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y}{a}\right)}\right) \]

      3. unsub-neg 55.0%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   9. Simplified 55.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]

   if 8.19999999999999987e-71 < z < 8.9999999999999999e52

   1. Initial program 75.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 75.9%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 91.0%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 91.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in t around inf 64.5%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 64.5%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

   6. Simplified 64.5%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Taylor expanded in a around inf 42.4%

      \[\leadsto t \cdot \color{blue}{\frac{y - z}{a}} \]

   if 8.9999999999999999e52 < z < 3.5e82

   1. Initial program 52.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 52.9%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 76.0%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 76.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in y around -inf 76.9%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

   5. Taylor expanded in t around inf 51.6%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a - z}} \]

   6. Taylor expanded in a around 0 51.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot t}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 51.8%

         \[\leadsto \color{blue}{-\frac{y \cdot t}{z}} \]

      2. associate-*l/ 51.8%

         \[\leadsto -\color{blue}{\frac{y}{z} \cdot t} \]

      3. *-commutative 51.8%

         \[\leadsto -\color{blue}{t \cdot \frac{y}{z}} \]

      4. distribute-rgt-neg-in 51.8%

         \[\leadsto \color{blue}{t \cdot \left(-\frac{y}{z}\right)} \]

      5. distribute-frac-neg 51.8%

         \[\leadsto t \cdot \color{blue}{\frac{-y}{z}} \]

   8. Simplified 51.8%

      \[\leadsto \color{blue}{t \cdot \frac{-y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \left(-\frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 64.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-57} \lor \neg \left(z \leq 2.1 \cdot 10^{-25}\right):\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.6e-57) (not (<= z 2.1e-25)))
   (+ t (* x (/ y z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.6e-57) || !(z <= 2.1e-25)) {
		tmp = t + (x * (y / z));
	} else {
		tmp = x + (y / (a / (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 <= (-8.6d-57)) .or. (.not. (z <= 2.1d-25))) then
        tmp = t + (x * (y / z))
    else
        tmp = x + (y / (a / (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 <= -8.6e-57) || !(z <= 2.1e-25)) {
		tmp = t + (x * (y / z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.6e-57) or not (z <= 2.1e-25):
		tmp = t + (x * (y / z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.6e-57) || !(z <= 2.1e-25))
		tmp = Float64(t + Float64(x * Float64(y / z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.6e-57) || ~((z <= 2.1e-25)))
		tmp = t + (x * (y / z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.6e-57], N[Not[LessEqual[z, 2.1e-25]], $MachinePrecision]], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.60000000000000043e-57 or 2.10000000000000002e-25 < z

   1. Initial program 51.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 51.4%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 74.1%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 74.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 68.8%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 68.8%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 82.6%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 82.6%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 82.6%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 82.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 68.8%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 68.8%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 68.7%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 68.7%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 68.8%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 68.8%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 82.6%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 82.6%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in y around inf 63.1%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 73.0%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

      2. associate-/r/ 73.2%

         \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

   9. Simplified 73.2%

      \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

   10. Taylor expanded in t around 0 55.3%

       \[\leadsto t - \color{blue}{-1 \cdot \frac{y \cdot x}{z}} \]
   11. Step-by-step derivation

       1. associate-*l/ 63.6%

          \[\leadsto t - -1 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} \]

       2. neg-mul-1 63.6%

          \[\leadsto t - \color{blue}{\left(-\frac{y}{z} \cdot x\right)} \]

       3. distribute-rgt-neg-out 63.6%

          \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(-x\right)} \]

   12. Simplified 63.6%

       \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(-x\right)} \]

   if -8.60000000000000043e-57 < z < 2.10000000000000002e-25

   1. Initial program 87.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 87.2%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 98.0%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 98.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around 0 77.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 77.7%

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

      2. associate-/l* 84.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 84.0%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-57} \lor \neg \left(z \leq 2.1 \cdot 10^{-25}\right):\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 17: 69.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-57} \lor \neg \left(z \leq 4.8 \cdot 10^{-26}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e-57) (not (<= z 4.8e-26)))
   (+ t (* (/ y z) (- x t)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e-57) || !(z <= 4.8e-26)) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = x + (y / (a / (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 <= (-1.3d-57)) .or. (.not. (z <= 4.8d-26))) then
        tmp = t + ((y / z) * (x - t))
    else
        tmp = x + (y / (a / (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 <= -1.3e-57) || !(z <= 4.8e-26)) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.3e-57) or not (z <= 4.8e-26):
		tmp = t + ((y / z) * (x - t))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.3e-57) || !(z <= 4.8e-26))
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.3e-57) || ~((z <= 4.8e-26)))
		tmp = t + ((y / z) * (x - t));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.3e-57], N[Not[LessEqual[z, 4.8e-26]], $MachinePrecision]], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.29999999999999993e-57 or 4.8000000000000002e-26 < z

   1. Initial program 51.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 51.4%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 74.1%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 74.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 68.8%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 68.8%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 82.6%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 82.6%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 82.6%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 82.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 68.8%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 68.8%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 68.7%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 68.7%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 68.8%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 68.8%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 82.6%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 82.6%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in y around inf 63.1%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 73.0%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

      2. associate-/r/ 73.2%

         \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

   9. Simplified 73.2%

      \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

   if -1.29999999999999993e-57 < z < 4.8000000000000002e-26

   1. Initial program 87.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 87.2%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 98.0%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 98.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around 0 77.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 77.7%

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

      2. associate-/l* 84.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 84.0%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-57} \lor \neg \left(z \leq 4.8 \cdot 10^{-26}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 18: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-58} \lor \neg \left(z \leq 5.1 \cdot 10^{-26}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1e-58) (not (<= z 5.1e-26)))
   (+ t (/ (- x t) (/ z y)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e-58) || !(z <= 5.1e-26)) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x + (y / (a / (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 <= (-1d-58)) .or. (.not. (z <= 5.1d-26))) then
        tmp = t + ((x - t) / (z / y))
    else
        tmp = x + (y / (a / (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 <= -1e-58) || !(z <= 5.1e-26)) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1e-58) or not (z <= 5.1e-26):
		tmp = t + ((x - t) / (z / y))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1e-58) || !(z <= 5.1e-26))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1e-58) || ~((z <= 5.1e-26)))
		tmp = t + ((x - t) / (z / y));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1e-58], N[Not[LessEqual[z, 5.1e-26]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e-58 or 5.09999999999999991e-26 < z

   1. Initial program 51.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 51.4%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 74.1%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 74.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 68.8%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 68.8%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 82.6%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 82.6%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 82.6%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 82.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 68.8%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 68.8%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 68.7%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 68.7%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 68.8%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 68.8%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 82.6%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 82.6%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in y around inf 63.1%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 73.0%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

      2. associate-/r/ 73.2%

         \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

   9. Simplified 73.2%

      \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 73.2%

          \[\leadsto t - \color{blue}{\left(t - x\right) \cdot \frac{y}{z}} \]

       2. clear-num 73.2%

          \[\leadsto t - \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{z}{y}}} \]

       3. un-div-inv 73.2%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y}}} \]

   11. Applied egg-rr 73.2%

       \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y}}} \]

   if -1e-58 < z < 5.09999999999999991e-26

   1. Initial program 87.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 87.2%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 98.0%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 98.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around 0 77.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 77.7%

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

      2. associate-/l* 84.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 84.0%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-58} \lor \neg \left(z \leq 5.1 \cdot 10^{-26}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 19: 57.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-82}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.8e-82)
   (+ t (* x (/ y z)))
   (if (<= x 2.55e+94) (* t (/ (- y z) (- a z))) (* x (- 1.0 (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e-82) {
		tmp = t + (x * (y / z));
	} else if (x <= 2.55e+94) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-6.8d-82)) then
        tmp = t + (x * (y / z))
    else if (x <= 2.55d+94) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e-82) {
		tmp = t + (x * (y / z));
	} else if (x <= 2.55e+94) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.8e-82:
		tmp = t + (x * (y / z))
	elif x <= 2.55e+94:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.8e-82)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (x <= 2.55e+94)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.8e-82)
		tmp = t + (x * (y / z));
	elseif (x <= 2.55e+94)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.8e-82], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.55e+94], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.7999999999999995e-82

   1. Initial program 54.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 54.5%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 72.7%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 72.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 72.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 55.1%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 55.1%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 66.8%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 66.8%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 66.8%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 66.8%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 55.1%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 55.1%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 53.8%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 53.8%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 55.1%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 55.1%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 66.8%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 66.8%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in y around inf 46.8%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 56.2%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

      2. associate-/r/ 57.3%

         \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

   9. Simplified 57.3%

      \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

   10. Taylor expanded in t around 0 45.6%

       \[\leadsto t - \color{blue}{-1 \cdot \frac{y \cdot x}{z}} \]
   11. Step-by-step derivation

       1. associate-*l/ 55.8%

          \[\leadsto t - -1 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} \]

       2. neg-mul-1 55.8%

          \[\leadsto t - \color{blue}{\left(-\frac{y}{z} \cdot x\right)} \]

       3. distribute-rgt-neg-out 55.8%

          \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(-x\right)} \]

   12. Simplified 55.8%

       \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(-x\right)} \]

   if -6.7999999999999995e-82 < x < 2.5500000000000002e94

   1. Initial program 76.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 76.7%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 92.7%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 92.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 92.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in t around inf 72.0%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 72.0%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

   6. Simplified 72.0%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if 2.5500000000000002e94 < x

   1. Initial program 58.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 58.0%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 80.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 80.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 80.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around 0 47.9%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 47.9%

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

      2. associate-/l* 55.6%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 55.6%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   7. Taylor expanded in x around inf 52.7%

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{y}{a}\right) \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 52.7%

         \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]

      2. mul-1-neg 52.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y}{a}\right)}\right) \]

      3. unsub-neg 52.7%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   9. Simplified 52.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-82}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 20: 57.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.2e-82)
   (* y (/ (- t x) (- a z)))
   (if (<= x 3.8e+95) (* t (/ (- y z) (- a z))) (* x (- 1.0 (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.2e-82) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 3.8e+95) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-4.2d-82)) then
        tmp = y * ((t - x) / (a - z))
    else if (x <= 3.8d+95) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.2e-82) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 3.8e+95) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.2e-82:
		tmp = y * ((t - x) / (a - z))
	elif x <= 3.8e+95:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.2e-82)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (x <= 3.8e+95)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.2e-82)
		tmp = y * ((t - x) / (a - z));
	elseif (x <= 3.8e+95)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.2e-82], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+95], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2000000000000001e-82

   1. Initial program 54.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 54.5%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 72.7%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 72.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 72.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in y around inf 56.0%

      \[\leadsto \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 56.0%

         \[\leadsto \color{blue}{\frac{t - x}{a - z}} \cdot y \]

      2. *-commutative 56.0%

         \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Simplified 56.0%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -4.2000000000000001e-82 < x < 3.7999999999999999e95

   1. Initial program 76.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 76.7%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 92.7%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 92.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 92.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in t around inf 72.0%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 72.0%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

   6. Simplified 72.0%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if 3.7999999999999999e95 < x

   1. Initial program 58.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 58.0%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 80.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 80.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 80.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around 0 47.9%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 47.9%

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

      2. associate-/l* 55.6%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 55.6%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   7. Taylor expanded in x around inf 52.7%

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{y}{a}\right) \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 52.7%

         \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]

      2. mul-1-neg 52.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y}{a}\right)}\right) \]

      3. unsub-neg 52.7%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   9. Simplified 52.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 21: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{-57}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.7e-57)
   (+ t (/ (- x t) (/ z y)))
   (if (<= z 1.2e-25) (+ x (/ y (/ a (- t x)))) (+ t (* (- y a) (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e-57) {
		tmp = t + ((x - t) / (z / y));
	} else if (z <= 1.2e-25) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + ((y - a) * (x / 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 <= (-4.7d-57)) then
        tmp = t + ((x - t) / (z / y))
    else if (z <= 1.2d-25) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t + ((y - a) * (x / 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 <= -4.7e-57) {
		tmp = t + ((x - t) / (z / y));
	} else if (z <= 1.2e-25) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + ((y - a) * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.7e-57:
		tmp = t + ((x - t) / (z / y))
	elif z <= 1.2e-25:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t + ((y - a) * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.7e-57)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif (z <= 1.2e-25)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.7e-57)
		tmp = t + ((x - t) / (z / y));
	elseif (z <= 1.2e-25)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t + ((y - a) * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.7e-57], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-25], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6999999999999998e-57

   1. Initial program 57.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 57.6%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 75.9%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 75.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 68.7%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 68.7%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 81.8%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 81.8%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 81.8%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 81.8%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 68.7%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 68.7%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 68.5%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 68.5%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 68.7%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 68.7%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 81.8%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 81.8%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in y around inf 61.7%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 72.6%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

      2. associate-/r/ 72.5%

         \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

   9. Simplified 72.5%

      \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 72.5%

          \[\leadsto t - \color{blue}{\left(t - x\right) \cdot \frac{y}{z}} \]

       2. clear-num 72.5%

          \[\leadsto t - \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{z}{y}}} \]

       3. un-div-inv 72.6%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y}}} \]

   11. Applied egg-rr 72.6%

       \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y}}} \]

   if -4.6999999999999998e-57 < z < 1.20000000000000005e-25

   1. Initial program 87.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 87.2%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 98.0%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 98.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around 0 77.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 77.7%

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

      2. associate-/l* 84.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 84.0%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   if 1.20000000000000005e-25 < z

   1. Initial program 42.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 42.5%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 71.5%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 71.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 71.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 69.0%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 69.0%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 83.7%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 83.7%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 83.7%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 83.7%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 69.0%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 69.0%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 69.0%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 69.0%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 69.0%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 69.0%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 83.7%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 83.7%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 84.0%

         \[\leadsto t - \color{blue}{\frac{y - a}{z} \cdot \left(t - x\right)} \]

   8. Applied egg-rr 84.0%

      \[\leadsto t - \color{blue}{\frac{y - a}{z} \cdot \left(t - x\right)} \]

   9. Taylor expanded in t around 0 63.0%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{\left(y - a\right) \cdot x}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 63.0%

          \[\leadsto t - \color{blue}{\left(-\frac{\left(y - a\right) \cdot x}{z}\right)} \]

       2. associate-*r/ 74.6%

          \[\leadsto t - \left(-\color{blue}{\left(y - a\right) \cdot \frac{x}{z}}\right) \]

       3. distribute-lft-neg-out 74.6%

          \[\leadsto t - \color{blue}{\left(-\left(y - a\right)\right) \cdot \frac{x}{z}} \]

       4. *-commutative 74.6%

          \[\leadsto t - \color{blue}{\frac{x}{z} \cdot \left(-\left(y - a\right)\right)} \]

   11. Simplified 74.6%

       \[\leadsto t - \color{blue}{\frac{x}{z} \cdot \left(-\left(y - a\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{-57}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 22: 36.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-71}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e-71) t (if (<= z 2.05e+89) (* t (/ (- y z) a)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e-71) {
		tmp = t;
	} else if (z <= 2.05e+89) {
		tmp = t * ((y - z) / 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 <= (-2.3d-71)) then
        tmp = t
    else if (z <= 2.05d+89) then
        tmp = t * ((y - z) / 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 <= -2.3e-71) {
		tmp = t;
	} else if (z <= 2.05e+89) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e-71:
		tmp = t
	elif z <= 2.05e+89:
		tmp = t * ((y - z) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e-71)
		tmp = t;
	elseif (z <= 2.05e+89)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.3e-71)
		tmp = t;
	elseif (z <= 2.05e+89)
		tmp = t * ((y - z) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e-71], t, If[LessEqual[z, 2.05e+89], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999998e-71 or 2.04999999999999993e89 < z

   1. Initial program 51.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 51.1%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 73.4%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 73.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 43.2%

      \[\leadsto \color{blue}{t} \]

   if -2.2999999999999998e-71 < z < 2.04999999999999993e89

   1. Initial program 83.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 83.3%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 96.0%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 96.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 96.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in t around inf 49.5%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 49.5%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

   6. Simplified 49.5%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Taylor expanded in a around inf 40.3%

      \[\leadsto t \cdot \color{blue}{\frac{y - z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-71}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 23: 33.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-76}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e-76) t (if (<= z 3.1e+80) (* y (/ t a)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e-76) {
		tmp = t;
	} else if (z <= 3.1e+80) {
		tmp = y * (t / 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 <= (-1.2d-76)) then
        tmp = t
    else if (z <= 3.1d+80) then
        tmp = y * (t / 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 <= -1.2e-76) {
		tmp = t;
	} else if (z <= 3.1e+80) {
		tmp = y * (t / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e-76:
		tmp = t
	elif z <= 3.1e+80:
		tmp = y * (t / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e-76)
		tmp = t;
	elseif (z <= 3.1e+80)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e-76)
		tmp = t;
	elseif (z <= 3.1e+80)
		tmp = y * (t / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e-76], t, If[LessEqual[z, 3.1e+80], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000007e-76 or 3.09999999999999988e80 < z

   1. Initial program 50.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 50.8%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 74.0%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 74.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 43.0%

      \[\leadsto \color{blue}{t} \]

   if -1.20000000000000007e-76 < z < 3.09999999999999988e80

   1. Initial program 84.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 84.5%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 95.9%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 95.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in y around -inf 52.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

   5. Taylor expanded in t around inf 35.7%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a - z}} \]

   6. Taylor expanded in a around inf 31.7%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 34.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}}} \]

   8. Simplified 34.9%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}}} \]
   9. Step-by-step derivation

      1. clear-num 34.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{a}{t}}{y}}} \]

      2. associate-/r/ 34.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{t}} \cdot y} \]

      3. clear-num 34.9%

         \[\leadsto \color{blue}{\frac{t}{a}} \cdot y \]

   10. Applied egg-rr 34.9%

       \[\leadsto \color{blue}{\frac{t}{a} \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-76}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 24: 34.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-67}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e-67) t (if (<= z 3e+80) (* t (/ y a)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e-67) {
		tmp = t;
	} else if (z <= 3e+80) {
		tmp = t * (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 <= (-1.45d-67)) then
        tmp = t
    else if (z <= 3d+80) then
        tmp = t * (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 <= -1.45e-67) {
		tmp = t;
	} else if (z <= 3e+80) {
		tmp = t * (y / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e-67:
		tmp = t
	elif z <= 3e+80:
		tmp = t * (y / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e-67)
		tmp = t;
	elseif (z <= 3e+80)
		tmp = Float64(t * 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 <= -1.45e-67)
		tmp = t;
	elseif (z <= 3e+80)
		tmp = t * (y / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e-67], t, If[LessEqual[z, 3e+80], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45000000000000002e-67 or 2.99999999999999987e80 < z

   1. Initial program 50.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 50.8%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 74.0%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 74.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 43.0%

      \[\leadsto \color{blue}{t} \]

   if -1.45000000000000002e-67 < z < 2.99999999999999987e80

   1. Initial program 84.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 84.5%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 95.9%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 95.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in y around -inf 52.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

   5. Taylor expanded in t around inf 35.7%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a - z}} \]

   6. Taylor expanded in a around inf 31.7%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 34.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}}} \]

   8. Simplified 34.9%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}}} \]
   9. Step-by-step derivation

      1. associate-/r/ 36.6%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot t} \]

   10. Applied egg-rr 36.6%

       \[\leadsto \color{blue}{\frac{y}{a} \cdot t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-67}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 25: 39.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.95 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.95e+15) t (if (<= z 6.6e+53) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.95e+15) {
		tmp = t;
	} else if (z <= 6.6e+53) {
		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 <= (-3.95d+15)) then
        tmp = t
    else if (z <= 6.6d+53) 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 <= -3.95e+15) {
		tmp = t;
	} else if (z <= 6.6e+53) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.95e+15:
		tmp = t
	elif z <= 6.6e+53:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.95e+15)
		tmp = t;
	elseif (z <= 6.6e+53)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.95e+15)
		tmp = t;
	elseif (z <= 6.6e+53)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.95e+15], t, If[LessEqual[z, 6.6e+53], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.95e15 or 6.6000000000000004e53 < z

   1. Initial program 46.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 46.7%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 72.2%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 72.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 72.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 45.9%

      \[\leadsto \color{blue}{t} \]

   if -3.95e15 < z < 6.6000000000000004e53

   1. Initial program 84.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 84.3%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 94.9%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 94.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in a around inf 31.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.95 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 26: 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 66.2%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. +-commutative 66.2%

      \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

   2. associate-*l/ 84.0%

      \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

   3. fma-def 84.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

3. Simplified 84.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

4. Taylor expanded in z around inf 26.7%

   \[\leadsto \color{blue}{t} \]

5. Final simplification 26.7%

   \[\leadsto t \]

Developer target: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023229 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))