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

Percentage Accurate: 68.1% → 88.6%

Time: 19.1s

Alternatives: 29

Speedup: 0.8×

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: 68.1% 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: 88.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+202} \lor \neg \left(z \leq 3.15 \cdot 10^{+170}\right):\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.22e+202) (not (<= z 3.15e+170)))
   (+ t (* (- y a) (/ x z)))
   (fma (/ (- y z) (- a z)) (- t x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.22e+202) || !(z <= 3.15e+170)) {
		tmp = t + ((y - a) * (x / z));
	} else {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.22e+202) || !(z <= 3.15e+170))
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	else
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.22e+202], N[Not[LessEqual[z, 3.15e+170]], $MachinePrecision]], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.22e202 or 3.1500000000000001e170 < z

   1. Initial program 27.8%

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

      1. +-commutative 27.8%

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

      2. associate-*l/ 60.7%

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

      3. fma-def 61.0%

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

   3. Simplified 61.0%

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

   4. Taylor expanded in z around inf 63.2%

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

      1. +-commutative 63.2%

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

      2. associate-/l* 87.3%

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

      3. distribute-lft-out-- 87.3%

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

      4. mul-1-neg 87.3%

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

      5. distribute-neg-frac 87.3%

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

      6. associate-/l* 63.2%

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

      7. *-commutative 63.2%

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

      8. distribute-rgt-out-- 60.7%

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

      9. unsub-neg 60.7%

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

      10. distribute-rgt-out-- 63.2%

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

      11. *-commutative 63.2%

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

      12. associate-/l* 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in t around 0 87.6%

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

      1. associate-*r/ 87.6%

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

      2. neg-mul-1 87.6%

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

   9. Simplified 87.6%

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

   10. Taylor expanded in z around 0 78.9%

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

       1. associate-/l* 87.6%

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

       2. associate-*r/ 87.6%

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

       3. associate-*l/ 87.6%

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

       4. metadata-eval 87.6%

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

       5. distribute-neg-frac 87.6%

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

       6. *-commutative 87.6%

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

       7. associate-/r/ 90.5%

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

       8. associate-*l/ 90.6%

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

       9. *-lft-identity 90.6%

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

   12. Simplified 90.6%

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

   if -1.22e202 < z < 3.1500000000000001e170

   1. Initial program 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-*l/ 90.8%

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

      3. fma-def 90.8%

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

   3. Simplified 90.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+202} \lor \neg \left(z \leq 3.15 \cdot 10^{+170}\right):\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \end{array} \]

Alternative 2: 68.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + \left(y - a\right) \cdot \frac{x}{z}\\ t_3 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-129}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z))))
        (t_2 (+ t (* (- y a) (/ x z))))
        (t_3 (+ x (* (- t x) (/ y a)))))
   (if (<= z -2.3e+202)
     t_2
     (if (<= z -2.6e+124)
       t_1
       (if (<= z -1.06e+63)
         t_2
         (if (<= z -2.05e-129)
           t_3
           (if (<= z -7.7e-205)
             (* y (/ (- t x) (- a z)))
             (if (<= z 1.8e+30)
               t_3
               (if (<= z 6.2e+76)
                 t_1
                 (if (<= z 8e+82)
                   (* x (+ (/ (- z y) (- a z)) 1.0))
                   t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = t + ((y - a) * (x / z));
	double t_3 = x + ((t - x) * (y / a));
	double tmp;
	if (z <= -2.3e+202) {
		tmp = t_2;
	} else if (z <= -2.6e+124) {
		tmp = t_1;
	} else if (z <= -1.06e+63) {
		tmp = t_2;
	} else if (z <= -2.05e-129) {
		tmp = t_3;
	} else if (z <= -7.7e-205) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.8e+30) {
		tmp = t_3;
	} else if (z <= 6.2e+76) {
		tmp = t_1;
	} else if (z <= 8e+82) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} 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) :: t_3
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = t + ((y - a) * (x / z))
    t_3 = x + ((t - x) * (y / a))
    if (z <= (-2.3d+202)) then
        tmp = t_2
    else if (z <= (-2.6d+124)) then
        tmp = t_1
    else if (z <= (-1.06d+63)) then
        tmp = t_2
    else if (z <= (-2.05d-129)) then
        tmp = t_3
    else if (z <= (-7.7d-205)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.8d+30) then
        tmp = t_3
    else if (z <= 6.2d+76) then
        tmp = t_1
    else if (z <= 8d+82) then
        tmp = x * (((z - y) / (a - z)) + 1.0d0)
    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 = t * ((y - z) / (a - z));
	double t_2 = t + ((y - a) * (x / z));
	double t_3 = x + ((t - x) * (y / a));
	double tmp;
	if (z <= -2.3e+202) {
		tmp = t_2;
	} else if (z <= -2.6e+124) {
		tmp = t_1;
	} else if (z <= -1.06e+63) {
		tmp = t_2;
	} else if (z <= -2.05e-129) {
		tmp = t_3;
	} else if (z <= -7.7e-205) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.8e+30) {
		tmp = t_3;
	} else if (z <= 6.2e+76) {
		tmp = t_1;
	} else if (z <= 8e+82) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = t + ((y - a) * (x / z))
	t_3 = x + ((t - x) * (y / a))
	tmp = 0
	if z <= -2.3e+202:
		tmp = t_2
	elif z <= -2.6e+124:
		tmp = t_1
	elif z <= -1.06e+63:
		tmp = t_2
	elif z <= -2.05e-129:
		tmp = t_3
	elif z <= -7.7e-205:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.8e+30:
		tmp = t_3
	elif z <= 6.2e+76:
		tmp = t_1
	elif z <= 8e+82:
		tmp = x * (((z - y) / (a - z)) + 1.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(t + Float64(Float64(y - a) * Float64(x / z)))
	t_3 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (z <= -2.3e+202)
		tmp = t_2;
	elseif (z <= -2.6e+124)
		tmp = t_1;
	elseif (z <= -1.06e+63)
		tmp = t_2;
	elseif (z <= -2.05e-129)
		tmp = t_3;
	elseif (z <= -7.7e-205)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.8e+30)
		tmp = t_3;
	elseif (z <= 6.2e+76)
		tmp = t_1;
	elseif (z <= 8e+82)
		tmp = Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) + 1.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = t + ((y - a) * (x / z));
	t_3 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (z <= -2.3e+202)
		tmp = t_2;
	elseif (z <= -2.6e+124)
		tmp = t_1;
	elseif (z <= -1.06e+63)
		tmp = t_2;
	elseif (z <= -2.05e-129)
		tmp = t_3;
	elseif (z <= -7.7e-205)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.8e+30)
		tmp = t_3;
	elseif (z <= 6.2e+76)
		tmp = t_1;
	elseif (z <= 8e+82)
		tmp = x * (((z - y) / (a - z)) + 1.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+202], t$95$2, If[LessEqual[z, -2.6e+124], t$95$1, If[LessEqual[z, -1.06e+63], t$95$2, If[LessEqual[z, -2.05e-129], t$95$3, If[LessEqual[z, -7.7e-205], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+30], t$95$3, If[LessEqual[z, 6.2e+76], t$95$1, If[LessEqual[z, 8e+82], N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.29999999999999999e202 or -2.6e124 < z < -1.0600000000000001e63 or 7.9999999999999997e82 < z

   1. Initial program 38.5%

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

      1. +-commutative 38.5%

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

      2. associate-*l/ 67.0%

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

      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 z around inf 64.4%

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

      1. +-commutative 64.4%

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

      2. associate-/l* 80.4%

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

      3. distribute-lft-out-- 80.4%

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

      4. mul-1-neg 80.4%

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

      5. distribute-neg-frac 80.4%

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

      6. associate-/l* 64.4%

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

      7. *-commutative 64.4%

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

      8. distribute-rgt-out-- 62.9%

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

      9. unsub-neg 62.9%

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

      10. distribute-rgt-out-- 64.4%

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

      11. *-commutative 64.4%

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

      12. associate-/l* 80.4%

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

   6. Simplified 80.4%

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

   7. Taylor expanded in t around 0 78.3%

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

      1. associate-*r/ 78.3%

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

      2. neg-mul-1 78.3%

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

   9. Simplified 78.3%

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

   10. Taylor expanded in z around 0 71.5%

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

       1. associate-/l* 78.3%

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

       2. associate-*r/ 78.3%

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

       3. associate-*l/ 78.2%

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

       4. metadata-eval 78.2%

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

       5. distribute-neg-frac 78.2%

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

       6. *-commutative 78.2%

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

       7. associate-/r/ 79.8%

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

       8. associate-*l/ 79.9%

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

       9. *-lft-identity 79.9%

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

   12. Simplified 79.9%

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

   if -2.29999999999999999e202 < z < -2.6e124 or 1.8000000000000001e30 < z < 6.20000000000000023e76

   1. Initial program 45.1%

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

      1. +-commutative 45.1%

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

      2. associate-*l/ 87.4%

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

      3. fma-def 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in t around inf 78.0%

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

      1. div-sub 78.0%

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

   6. Simplified 78.0%

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

   if -1.0600000000000001e63 < z < -2.05e-129 or -7.7000000000000001e-205 < z < 1.8000000000000001e30

   1. Initial program 91.2%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around 0 78.3%

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

   if -2.05e-129 < z < -7.7000000000000001e-205

   1. Initial program 83.1%

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

      1. +-commutative 83.1%

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

      2. associate-*l/ 87.4%

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

      3. fma-def 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in y around inf 81.0%

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

      1. div-sub 81.0%

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

      2. *-commutative 81.0%

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

   6. Simplified 81.0%

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

   if 6.20000000000000023e76 < z < 7.9999999999999997e82

   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/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   6. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+202}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+124}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+63}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-129}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+30}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3: 68.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + \left(y - a\right) \cdot \frac{x}{z}\\ t_3 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-128}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z))))
        (t_2 (+ t (* (- y a) (/ x z))))
        (t_3 (+ x (* (- t x) (/ y a)))))
   (if (<= z -2.3e+202)
     t_2
     (if (<= z -7.2e+122)
       t_1
       (if (<= z -1.85e+64)
         t_2
         (if (<= z -8.2e-128)
           t_3
           (if (<= z -7.7e-205)
             (* y (/ (- t x) (- a z)))
             (if (<= z 2e+29)
               t_3
               (if (<= z 5.4e+72)
                 t_1
                 (if (<= z 1.06e+77) (+ x (/ (* t y) a)) t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = t + ((y - a) * (x / z));
	double t_3 = x + ((t - x) * (y / a));
	double tmp;
	if (z <= -2.3e+202) {
		tmp = t_2;
	} else if (z <= -7.2e+122) {
		tmp = t_1;
	} else if (z <= -1.85e+64) {
		tmp = t_2;
	} else if (z <= -8.2e-128) {
		tmp = t_3;
	} else if (z <= -7.7e-205) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 2e+29) {
		tmp = t_3;
	} else if (z <= 5.4e+72) {
		tmp = t_1;
	} else if (z <= 1.06e+77) {
		tmp = x + ((t * y) / a);
	} 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) :: t_3
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = t + ((y - a) * (x / z))
    t_3 = x + ((t - x) * (y / a))
    if (z <= (-2.3d+202)) then
        tmp = t_2
    else if (z <= (-7.2d+122)) then
        tmp = t_1
    else if (z <= (-1.85d+64)) then
        tmp = t_2
    else if (z <= (-8.2d-128)) then
        tmp = t_3
    else if (z <= (-7.7d-205)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 2d+29) then
        tmp = t_3
    else if (z <= 5.4d+72) then
        tmp = t_1
    else if (z <= 1.06d+77) then
        tmp = x + ((t * y) / a)
    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 = t * ((y - z) / (a - z));
	double t_2 = t + ((y - a) * (x / z));
	double t_3 = x + ((t - x) * (y / a));
	double tmp;
	if (z <= -2.3e+202) {
		tmp = t_2;
	} else if (z <= -7.2e+122) {
		tmp = t_1;
	} else if (z <= -1.85e+64) {
		tmp = t_2;
	} else if (z <= -8.2e-128) {
		tmp = t_3;
	} else if (z <= -7.7e-205) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 2e+29) {
		tmp = t_3;
	} else if (z <= 5.4e+72) {
		tmp = t_1;
	} else if (z <= 1.06e+77) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = t + ((y - a) * (x / z))
	t_3 = x + ((t - x) * (y / a))
	tmp = 0
	if z <= -2.3e+202:
		tmp = t_2
	elif z <= -7.2e+122:
		tmp = t_1
	elif z <= -1.85e+64:
		tmp = t_2
	elif z <= -8.2e-128:
		tmp = t_3
	elif z <= -7.7e-205:
		tmp = y * ((t - x) / (a - z))
	elif z <= 2e+29:
		tmp = t_3
	elif z <= 5.4e+72:
		tmp = t_1
	elif z <= 1.06e+77:
		tmp = x + ((t * y) / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(t + Float64(Float64(y - a) * Float64(x / z)))
	t_3 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (z <= -2.3e+202)
		tmp = t_2;
	elseif (z <= -7.2e+122)
		tmp = t_1;
	elseif (z <= -1.85e+64)
		tmp = t_2;
	elseif (z <= -8.2e-128)
		tmp = t_3;
	elseif (z <= -7.7e-205)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 2e+29)
		tmp = t_3;
	elseif (z <= 5.4e+72)
		tmp = t_1;
	elseif (z <= 1.06e+77)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = t + ((y - a) * (x / z));
	t_3 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (z <= -2.3e+202)
		tmp = t_2;
	elseif (z <= -7.2e+122)
		tmp = t_1;
	elseif (z <= -1.85e+64)
		tmp = t_2;
	elseif (z <= -8.2e-128)
		tmp = t_3;
	elseif (z <= -7.7e-205)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 2e+29)
		tmp = t_3;
	elseif (z <= 5.4e+72)
		tmp = t_1;
	elseif (z <= 1.06e+77)
		tmp = x + ((t * y) / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+202], t$95$2, If[LessEqual[z, -7.2e+122], t$95$1, If[LessEqual[z, -1.85e+64], t$95$2, If[LessEqual[z, -8.2e-128], t$95$3, If[LessEqual[z, -7.7e-205], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+29], t$95$3, If[LessEqual[z, 5.4e+72], t$95$1, If[LessEqual[z, 1.06e+77], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.29999999999999999e202 or -7.2000000000000005e122 < z < -1.84999999999999992e64 or 1.06000000000000003e77 < z

   1. Initial program 38.8%

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

      1. +-commutative 38.8%

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

      2. associate-*l/ 67.8%

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

      3. fma-def 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in z around inf 64.1%

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

      1. +-commutative 64.1%

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

      2. associate-/l* 79.8%

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

      3. distribute-lft-out-- 79.8%

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

      4. mul-1-neg 79.8%

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

      5. distribute-neg-frac 79.8%

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

      6. associate-/l* 64.1%

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

      7. *-commutative 64.1%

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

      8. distribute-rgt-out-- 62.7%

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

      9. unsub-neg 62.7%

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

      10. distribute-rgt-out-- 64.1%

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

      11. *-commutative 64.1%

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

      12. associate-/l* 79.8%

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

   6. Simplified 79.8%

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

   7. Taylor expanded in t around 0 77.7%

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

      1. associate-*r/ 77.7%

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

      2. neg-mul-1 77.7%

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

   9. Simplified 77.7%

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

   10. Taylor expanded in z around 0 71.1%

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

       1. associate-/l* 77.7%

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

       2. associate-*r/ 77.7%

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

       3. associate-*l/ 77.7%

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

       4. metadata-eval 77.7%

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

       5. distribute-neg-frac 77.7%

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

       6. *-commutative 77.7%

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

       7. associate-/r/ 79.2%

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

       8. associate-*l/ 79.2%

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

       9. *-lft-identity 79.2%

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

   12. Simplified 79.2%

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

   if -2.29999999999999999e202 < z < -7.2000000000000005e122 or 1.99999999999999983e29 < z < 5.4000000000000001e72

   1. Initial program 43.3%

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

      1. +-commutative 43.3%

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

      2. associate-*l/ 87.0%

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

      3. fma-def 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in t around inf 77.2%

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

      1. div-sub 77.2%

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

   6. Simplified 77.2%

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

   if -1.84999999999999992e64 < z < -8.1999999999999999e-128 or -7.7000000000000001e-205 < z < 1.99999999999999983e29

   1. Initial program 91.2%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around 0 78.3%

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

   if -8.1999999999999999e-128 < z < -7.7000000000000001e-205

   1. Initial program 83.1%

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

      1. +-commutative 83.1%

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

      2. associate-*l/ 87.4%

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

      3. fma-def 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in y around inf 81.0%

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

      1. div-sub 81.0%

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

      2. *-commutative 81.0%

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

   6. Simplified 81.0%

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

   if 5.4000000000000001e72 < z < 1.06000000000000003e77

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+202}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+122}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+64}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-128}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+29}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 4: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ t_2 := t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-175}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) t)))) (t_2 (+ t (* (- y a) (/ x z)))))
   (if (<= z -4.1e+197)
     t_2
     (if (<= z -2.5e+123)
       t_1
       (if (<= z -1.6e+67)
         t_2
         (if (<= z -1.6e-184)
           t_1
           (if (<= z 8e-175)
             (+ x (* (- t x) (/ y a)))
             (if (<= z 1.25e+113) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / t));
	double t_2 = t + ((y - a) * (x / z));
	double tmp;
	if (z <= -4.1e+197) {
		tmp = t_2;
	} else if (z <= -2.5e+123) {
		tmp = t_1;
	} else if (z <= -1.6e+67) {
		tmp = t_2;
	} else if (z <= -1.6e-184) {
		tmp = t_1;
	} else if (z <= 8e-175) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 1.25e+113) {
		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 - z) / ((a - z) / t))
    t_2 = t + ((y - a) * (x / z))
    if (z <= (-4.1d+197)) then
        tmp = t_2
    else if (z <= (-2.5d+123)) then
        tmp = t_1
    else if (z <= (-1.6d+67)) then
        tmp = t_2
    else if (z <= (-1.6d-184)) then
        tmp = t_1
    else if (z <= 8d-175) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 1.25d+113) 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 - z) / ((a - z) / t));
	double t_2 = t + ((y - a) * (x / z));
	double tmp;
	if (z <= -4.1e+197) {
		tmp = t_2;
	} else if (z <= -2.5e+123) {
		tmp = t_1;
	} else if (z <= -1.6e+67) {
		tmp = t_2;
	} else if (z <= -1.6e-184) {
		tmp = t_1;
	} else if (z <= 8e-175) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 1.25e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / t))
	t_2 = t + ((y - a) * (x / z))
	tmp = 0
	if z <= -4.1e+197:
		tmp = t_2
	elif z <= -2.5e+123:
		tmp = t_1
	elif z <= -1.6e+67:
		tmp = t_2
	elif z <= -1.6e-184:
		tmp = t_1
	elif z <= 8e-175:
		tmp = x + ((t - x) * (y / a))
	elif z <= 1.25e+113:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)))
	t_2 = Float64(t + Float64(Float64(y - a) * Float64(x / z)))
	tmp = 0.0
	if (z <= -4.1e+197)
		tmp = t_2;
	elseif (z <= -2.5e+123)
		tmp = t_1;
	elseif (z <= -1.6e+67)
		tmp = t_2;
	elseif (z <= -1.6e-184)
		tmp = t_1;
	elseif (z <= 8e-175)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 1.25e+113)
		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 - z) / ((a - z) / t));
	t_2 = t + ((y - a) * (x / z));
	tmp = 0.0;
	if (z <= -4.1e+197)
		tmp = t_2;
	elseif (z <= -2.5e+123)
		tmp = t_1;
	elseif (z <= -1.6e+67)
		tmp = t_2;
	elseif (z <= -1.6e-184)
		tmp = t_1;
	elseif (z <= 8e-175)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 1.25e+113)
		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[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+197], t$95$2, If[LessEqual[z, -2.5e+123], t$95$1, If[LessEqual[z, -1.6e+67], t$95$2, If[LessEqual[z, -1.6e-184], t$95$1, If[LessEqual[z, 8e-175], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+113], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1000000000000003e197 or -2.49999999999999987e123 < z < -1.59999999999999991e67 or 1.25e113 < z

   1. Initial program 37.3%

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

      1. +-commutative 37.3%

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

      2. associate-*l/ 66.4%

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

      3. fma-def 66.6%

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

   3. Simplified 66.6%

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

   4. Taylor expanded in z around inf 66.0%

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

      1. +-commutative 66.0%

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

      2. associate-/l* 84.2%

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

      3. distribute-lft-out-- 84.2%

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

      4. mul-1-neg 84.2%

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

      5. distribute-neg-frac 84.2%

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

      6. associate-/l* 66.0%

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

      7. *-commutative 66.0%

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

      8. distribute-rgt-out-- 64.4%

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

      9. unsub-neg 64.4%

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

      10. distribute-rgt-out-- 66.0%

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

      11. *-commutative 66.0%

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

      12. associate-/l* 84.2%

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

   6. Simplified 84.2%

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

   7. Taylor expanded in t around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. neg-mul-1 80.5%

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

   9. Simplified 80.5%

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

   10. Taylor expanded in z around 0 72.2%

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

       1. associate-/l* 80.5%

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

       2. associate-*r/ 80.5%

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

       3. associate-*l/ 80.5%

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

       4. metadata-eval 80.5%

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

       5. distribute-neg-frac 80.5%

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

       6. *-commutative 80.5%

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

       7. associate-/r/ 82.1%

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

       8. associate-*l/ 82.2%

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

       9. *-lft-identity 82.2%

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

   12. Simplified 82.2%

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

   if -4.1000000000000003e197 < z < -2.49999999999999987e123 or -1.59999999999999991e67 < z < -1.6e-184 or 8e-175 < z < 1.25e113

   1. Initial program 75.8%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in t around inf 78.1%

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

   if -1.6e-184 < z < 8e-175

   1. Initial program 91.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around 0 88.0%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+197}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+123}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+67}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-184}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-175}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+113}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 5: 53.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t - x \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-274}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (- t (* x (/ a z)))))
   (if (<= z -1.4e+74)
     t_2
     (if (<= z -3.8e-257)
       t_1
       (if (<= z 2.6e-274)
         (+ x (/ (* t y) a))
         (if (<= z 1.65e-185)
           t_1
           (if (<= z 2.3e-153)
             (* t (/ y (- a z)))
             (if (<= z 7.6e+84) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = t - (x * (a / z));
	double tmp;
	if (z <= -1.4e+74) {
		tmp = t_2;
	} else if (z <= -3.8e-257) {
		tmp = t_1;
	} else if (z <= 2.6e-274) {
		tmp = x + ((t * y) / a);
	} else if (z <= 1.65e-185) {
		tmp = t_1;
	} else if (z <= 2.3e-153) {
		tmp = t * (y / (a - z));
	} else if (z <= 7.6e+84) {
		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 - (x * (y / a))
    t_2 = t - (x * (a / z))
    if (z <= (-1.4d+74)) then
        tmp = t_2
    else if (z <= (-3.8d-257)) then
        tmp = t_1
    else if (z <= 2.6d-274) then
        tmp = x + ((t * y) / a)
    else if (z <= 1.65d-185) then
        tmp = t_1
    else if (z <= 2.3d-153) then
        tmp = t * (y / (a - z))
    else if (z <= 7.6d+84) 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 - (x * (y / a));
	double t_2 = t - (x * (a / z));
	double tmp;
	if (z <= -1.4e+74) {
		tmp = t_2;
	} else if (z <= -3.8e-257) {
		tmp = t_1;
	} else if (z <= 2.6e-274) {
		tmp = x + ((t * y) / a);
	} else if (z <= 1.65e-185) {
		tmp = t_1;
	} else if (z <= 2.3e-153) {
		tmp = t * (y / (a - z));
	} else if (z <= 7.6e+84) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = t - (x * (a / z))
	tmp = 0
	if z <= -1.4e+74:
		tmp = t_2
	elif z <= -3.8e-257:
		tmp = t_1
	elif z <= 2.6e-274:
		tmp = x + ((t * y) / a)
	elif z <= 1.65e-185:
		tmp = t_1
	elif z <= 2.3e-153:
		tmp = t * (y / (a - z))
	elif z <= 7.6e+84:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(t - Float64(x * Float64(a / z)))
	tmp = 0.0
	if (z <= -1.4e+74)
		tmp = t_2;
	elseif (z <= -3.8e-257)
		tmp = t_1;
	elseif (z <= 2.6e-274)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (z <= 1.65e-185)
		tmp = t_1;
	elseif (z <= 2.3e-153)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 7.6e+84)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = t - (x * (a / z));
	tmp = 0.0;
	if (z <= -1.4e+74)
		tmp = t_2;
	elseif (z <= -3.8e-257)
		tmp = t_1;
	elseif (z <= 2.6e-274)
		tmp = x + ((t * y) / a);
	elseif (z <= 1.65e-185)
		tmp = t_1;
	elseif (z <= 2.3e-153)
		tmp = t * (y / (a - z));
	elseif (z <= 7.6e+84)
		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[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+74], t$95$2, If[LessEqual[z, -3.8e-257], t$95$1, If[LessEqual[z, 2.6e-274], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-185], t$95$1, If[LessEqual[z, 2.3e-153], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e+84], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.40000000000000001e74 or 7.6000000000000002e84 < z

   1. Initial program 37.9%

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

      1. +-commutative 37.9%

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

      2. associate-*l/ 70.7%

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

      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 59.6%

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

      1. +-commutative 59.6%

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

      2. associate-/l* 77.3%

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

      3. distribute-lft-out-- 77.3%

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

      4. mul-1-neg 77.3%

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

      5. distribute-neg-frac 77.3%

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

      6. associate-/l* 59.6%

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

      7. *-commutative 59.6%

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

      8. distribute-rgt-out-- 58.4%

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

      9. unsub-neg 58.4%

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

      10. distribute-rgt-out-- 59.6%

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

      11. *-commutative 59.6%

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

      12. associate-/l* 77.3%

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

   6. Simplified 77.3%

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

   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. associate-*r/ 72.8%

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

      2. neg-mul-1 72.8%

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

   9. Simplified 72.8%

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

   10. Taylor expanded in y around 0 54.6%

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

       1. associate-*l/ 56.1%

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

       2. *-commutative 56.1%

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

   12. Simplified 56.1%

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

   if -1.40000000000000001e74 < z < -3.8000000000000004e-257 or 2.6e-274 < z < 1.6499999999999999e-185 or 2.29999999999999997e-153 < z < 7.6000000000000002e84

   1. Initial program 87.0%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in z around 0 68.3%

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

   5. Taylor expanded in t around 0 53.0%

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

      1. associate-*r/ 53.0%

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

      2. mul-1-neg 53.0%

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

      3. distribute-rgt-neg-out 53.0%

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

      4. associate-*l/ 57.5%

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

   7. Simplified 57.5%

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

   if -3.8000000000000004e-257 < z < 2.6e-274

   1. Initial program 94.3%

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

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around 0 94.4%

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

   5. Taylor expanded in t around inf 88.4%

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

   if 1.6499999999999999e-185 < z < 2.29999999999999997e-153

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. associate-*l/ 99.6%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 99.6%

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

      1. div-sub 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in y around inf 99.6%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+74}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-257}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-274}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-185}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+84}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]

Alternative 6: 55.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-272}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (+ t (* x (/ y z)))))
   (if (<= z -2.65e+63)
     t_2
     (if (<= z -1.2e-257)
       t_1
       (if (<= z 1.25e-272)
         (+ x (/ (* t y) a))
         (if (<= z 1.08e-185)
           t_1
           (if (<= z 5e-153)
             (* t (/ y (- a z)))
             (if (<= z 2.35e+112) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = t + (x * (y / z));
	double tmp;
	if (z <= -2.65e+63) {
		tmp = t_2;
	} else if (z <= -1.2e-257) {
		tmp = t_1;
	} else if (z <= 1.25e-272) {
		tmp = x + ((t * y) / a);
	} else if (z <= 1.08e-185) {
		tmp = t_1;
	} else if (z <= 5e-153) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.35e+112) {
		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 - (x * (y / a))
    t_2 = t + (x * (y / z))
    if (z <= (-2.65d+63)) then
        tmp = t_2
    else if (z <= (-1.2d-257)) then
        tmp = t_1
    else if (z <= 1.25d-272) then
        tmp = x + ((t * y) / a)
    else if (z <= 1.08d-185) then
        tmp = t_1
    else if (z <= 5d-153) then
        tmp = t * (y / (a - z))
    else if (z <= 2.35d+112) 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 - (x * (y / a));
	double t_2 = t + (x * (y / z));
	double tmp;
	if (z <= -2.65e+63) {
		tmp = t_2;
	} else if (z <= -1.2e-257) {
		tmp = t_1;
	} else if (z <= 1.25e-272) {
		tmp = x + ((t * y) / a);
	} else if (z <= 1.08e-185) {
		tmp = t_1;
	} else if (z <= 5e-153) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.35e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = t + (x * (y / z))
	tmp = 0
	if z <= -2.65e+63:
		tmp = t_2
	elif z <= -1.2e-257:
		tmp = t_1
	elif z <= 1.25e-272:
		tmp = x + ((t * y) / a)
	elif z <= 1.08e-185:
		tmp = t_1
	elif z <= 5e-153:
		tmp = t * (y / (a - z))
	elif z <= 2.35e+112:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(t + Float64(x * Float64(y / z)))
	tmp = 0.0
	if (z <= -2.65e+63)
		tmp = t_2;
	elseif (z <= -1.2e-257)
		tmp = t_1;
	elseif (z <= 1.25e-272)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (z <= 1.08e-185)
		tmp = t_1;
	elseif (z <= 5e-153)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 2.35e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = t + (x * (y / z));
	tmp = 0.0;
	if (z <= -2.65e+63)
		tmp = t_2;
	elseif (z <= -1.2e-257)
		tmp = t_1;
	elseif (z <= 1.25e-272)
		tmp = x + ((t * y) / a);
	elseif (z <= 1.08e-185)
		tmp = t_1;
	elseif (z <= 5e-153)
		tmp = t * (y / (a - z));
	elseif (z <= 2.35e+112)
		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[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.65e+63], t$95$2, If[LessEqual[z, -1.2e-257], t$95$1, If[LessEqual[z, 1.25e-272], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e-185], t$95$1, If[LessEqual[z, 5e-153], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+112], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.65e63 or 2.34999999999999999e112 < z

   1. Initial program 36.9%

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

      1. +-commutative 36.9%

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

      2. associate-*l/ 69.9%

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

      3. fma-def 70.1%

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

   3. Simplified 70.1%

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

   4. Taylor expanded in z around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. associate-/l* 80.2%

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

      3. distribute-lft-out-- 80.2%

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

      4. mul-1-neg 80.2%

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

      5. distribute-neg-frac 80.2%

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

      6. associate-/l* 60.6%

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

      7. *-commutative 60.6%

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

      8. distribute-rgt-out-- 59.3%

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

      9. unsub-neg 59.3%

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

      10. distribute-rgt-out-- 60.6%

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

      11. *-commutative 60.6%

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

      12. associate-/l* 80.2%

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

   6. Simplified 80.2%

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

   7. Taylor expanded in t around 0 74.3%

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

      1. associate-*r/ 74.3%

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

      2. neg-mul-1 74.3%

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

   9. Simplified 74.3%

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

   10. Taylor expanded in y around inf 52.8%

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

       1. mul-1-neg 52.8%

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

       2. associate-*l/ 59.6%

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

       3. distribute-rgt-neg-in 59.6%

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

   12. Simplified 59.6%

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

   if -2.65e63 < z < -1.20000000000000008e-257 or 1.24999999999999995e-272 < z < 1.08e-185 or 5.00000000000000033e-153 < z < 2.34999999999999999e112

   1. Initial program 85.9%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around 0 67.4%

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

   5. Taylor expanded in t around 0 52.6%

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

      1. associate-*r/ 52.6%

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

      2. mul-1-neg 52.6%

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

      3. distribute-rgt-neg-out 52.6%

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

      4. associate-*l/ 57.0%

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

   7. Simplified 57.0%

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

   if -1.20000000000000008e-257 < z < 1.24999999999999995e-272

   1. Initial program 94.3%

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

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around 0 94.4%

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

   5. Taylor expanded in t around inf 88.4%

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

   if 1.08e-185 < z < 5.00000000000000033e-153

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. associate-*l/ 99.6%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 99.6%

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

      1. div-sub 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in y around inf 99.6%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+63}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-257}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-272}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-185}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+112}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 7: 59.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5000:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-19}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+154}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+201}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))))
   (if (<= x -2.15e+93)
     t_1
     (if (<= x -5000.0)
       (* y (/ (- t x) (- a z)))
       (if (<= x -1.45e-19)
         (+ t (* x (/ y z)))
         (if (<= x 8.6e+86)
           (* t (/ (- y z) (- a z)))
           (if (<= x 1.08e+154)
             (+ x (/ (* t y) a))
             (if (<= x 2.25e+201) (- t (* x (/ a z))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double tmp;
	if (x <= -2.15e+93) {
		tmp = t_1;
	} else if (x <= -5000.0) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= -1.45e-19) {
		tmp = t + (x * (y / z));
	} else if (x <= 8.6e+86) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 1.08e+154) {
		tmp = x + ((t * y) / a);
	} else if (x <= 2.25e+201) {
		tmp = t - (x * (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (x * (y / a))
    if (x <= (-2.15d+93)) then
        tmp = t_1
    else if (x <= (-5000.0d0)) then
        tmp = y * ((t - x) / (a - z))
    else if (x <= (-1.45d-19)) then
        tmp = t + (x * (y / z))
    else if (x <= 8.6d+86) then
        tmp = t * ((y - z) / (a - z))
    else if (x <= 1.08d+154) then
        tmp = x + ((t * y) / a)
    else if (x <= 2.25d+201) then
        tmp = t - (x * (a / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double tmp;
	if (x <= -2.15e+93) {
		tmp = t_1;
	} else if (x <= -5000.0) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= -1.45e-19) {
		tmp = t + (x * (y / z));
	} else if (x <= 8.6e+86) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 1.08e+154) {
		tmp = x + ((t * y) / a);
	} else if (x <= 2.25e+201) {
		tmp = t - (x * (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	tmp = 0
	if x <= -2.15e+93:
		tmp = t_1
	elif x <= -5000.0:
		tmp = y * ((t - x) / (a - z))
	elif x <= -1.45e-19:
		tmp = t + (x * (y / z))
	elif x <= 8.6e+86:
		tmp = t * ((y - z) / (a - z))
	elif x <= 1.08e+154:
		tmp = x + ((t * y) / a)
	elif x <= 2.25e+201:
		tmp = t - (x * (a / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	tmp = 0.0
	if (x <= -2.15e+93)
		tmp = t_1;
	elseif (x <= -5000.0)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (x <= -1.45e-19)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (x <= 8.6e+86)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (x <= 1.08e+154)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (x <= 2.25e+201)
		tmp = Float64(t - Float64(x * Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	tmp = 0.0;
	if (x <= -2.15e+93)
		tmp = t_1;
	elseif (x <= -5000.0)
		tmp = y * ((t - x) / (a - z));
	elseif (x <= -1.45e-19)
		tmp = t + (x * (y / z));
	elseif (x <= 8.6e+86)
		tmp = t * ((y - z) / (a - z));
	elseif (x <= 1.08e+154)
		tmp = x + ((t * y) / a);
	elseif (x <= 2.25e+201)
		tmp = t - (x * (a / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.15e+93], t$95$1, If[LessEqual[x, -5000.0], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.45e-19], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.6e+86], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.08e+154], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.25e+201], N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.15e93 or 2.25000000000000005e201 < x

   1. Initial program 49.5%

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

      1. associate-*l/ 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in z around 0 60.6%

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

   5. Taylor expanded in t around 0 48.8%

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

      1. associate-*r/ 48.8%

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

      2. mul-1-neg 48.8%

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

      3. distribute-rgt-neg-out 48.8%

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

      4. associate-*l/ 58.4%

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

   7. Simplified 58.4%

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

   if -2.15e93 < x < -5e3

   1. Initial program 66.5%

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

      1. +-commutative 66.5%

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

      2. associate-*l/ 79.4%

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

      3. fma-def 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in y around inf 67.5%

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

      1. div-sub 67.5%

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

      2. *-commutative 67.5%

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

   6. Simplified 67.5%

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

   if -5e3 < x < -1.45e-19

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l/ 99.7%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 60.7%

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

      1. +-commutative 60.7%

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

      2. associate-/l* 41.2%

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

      3. distribute-lft-out-- 41.2%

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

      4. mul-1-neg 41.2%

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

      5. distribute-neg-frac 41.2%

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

      6. associate-/l* 60.7%

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

      7. *-commutative 60.7%

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

      8. distribute-rgt-out-- 60.7%

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

      9. unsub-neg 60.7%

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

      10. distribute-rgt-out-- 60.7%

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

      11. *-commutative 60.7%

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

      12. associate-/l* 41.2%

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

   6. Simplified 41.2%

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

   7. Taylor expanded in t around 0 41.2%

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

      1. associate-*r/ 41.2%

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

      2. neg-mul-1 41.2%

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

   9. Simplified 41.2%

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

   10. Taylor expanded in y around inf 60.9%

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

       1. mul-1-neg 60.9%

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

       2. associate-*l/ 60.9%

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

       3. distribute-rgt-neg-in 60.9%

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

   12. Simplified 60.9%

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

   if -1.45e-19 < x < 8.6000000000000004e86

   1. Initial program 78.3%

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

      1. +-commutative 78.3%

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

      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 t around inf 71.1%

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

      1. div-sub 71.1%

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

   6. Simplified 71.1%

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

   if 8.6000000000000004e86 < x < 1.08e154

   1. Initial program 67.5%

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

      1. associate-*l/ 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in z around 0 76.0%

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

   5. Taylor expanded in t around inf 76.5%

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

   if 1.08e154 < x < 2.25000000000000005e201

   1. Initial program 36.6%

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

      1. +-commutative 36.6%

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

      2. associate-*l/ 67.6%

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

      3. fma-def 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in z around inf 52.0%

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

      1. +-commutative 52.0%

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

      2. associate-/l* 76.1%

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

      3. distribute-lft-out-- 76.1%

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

      4. mul-1-neg 76.1%

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

      5. distribute-neg-frac 76.1%

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

      6. associate-/l* 52.0%

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

      7. *-commutative 52.0%

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

      8. distribute-rgt-out-- 52.0%

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

      9. unsub-neg 52.0%

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

      10. distribute-rgt-out-- 52.0%

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

      11. *-commutative 52.0%

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

      12. associate-/l* 76.1%

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

   6. Simplified 76.1%

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

   7. Taylor expanded in t around 0 76.1%

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

      1. associate-*r/ 76.1%

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

      2. neg-mul-1 76.1%

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

   9. Simplified 76.1%

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

   10. Taylor expanded in y around 0 44.5%

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

       1. associate-*l/ 60.1%

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

       2. *-commutative 60.1%

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

   12. Simplified 60.1%

       \[\leadsto t - \color{blue}{x \cdot \frac{a}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+93}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -5000:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-19}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+154}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+201}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 66.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -2.55e+69)
     t_2
     (if (<= z -2.05e-129)
       t_1
       (if (<= z -7.7e-205)
         (* y (/ (- t x) (- a z)))
         (if (<= z 1.15e+30)
           t_1
           (if (<= z 2.9e+115) t_2 (+ t (* x (/ y z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.55e+69) {
		tmp = t_2;
	} else if (z <= -2.05e-129) {
		tmp = t_1;
	} else if (z <= -7.7e-205) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.15e+30) {
		tmp = t_1;
	} else if (z <= 2.9e+115) {
		tmp = t_2;
	} else {
		tmp = t + (x * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-2.55d+69)) then
        tmp = t_2
    else if (z <= (-2.05d-129)) then
        tmp = t_1
    else if (z <= (-7.7d-205)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.15d+30) then
        tmp = t_1
    else if (z <= 2.9d+115) then
        tmp = t_2
    else
        tmp = t + (x * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.55e+69) {
		tmp = t_2;
	} else if (z <= -2.05e-129) {
		tmp = t_1;
	} else if (z <= -7.7e-205) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.15e+30) {
		tmp = t_1;
	} else if (z <= 2.9e+115) {
		tmp = t_2;
	} else {
		tmp = t + (x * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -2.55e+69:
		tmp = t_2
	elif z <= -2.05e-129:
		tmp = t_1
	elif z <= -7.7e-205:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.15e+30:
		tmp = t_1
	elif z <= 2.9e+115:
		tmp = t_2
	else:
		tmp = t + (x * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.55e+69)
		tmp = t_2;
	elseif (z <= -2.05e-129)
		tmp = t_1;
	elseif (z <= -7.7e-205)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.15e+30)
		tmp = t_1;
	elseif (z <= 2.9e+115)
		tmp = t_2;
	else
		tmp = Float64(t + Float64(x * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -2.55e+69)
		tmp = t_2;
	elseif (z <= -2.05e-129)
		tmp = t_1;
	elseif (z <= -7.7e-205)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.15e+30)
		tmp = t_1;
	elseif (z <= 2.9e+115)
		tmp = t_2;
	else
		tmp = t + (x * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e+69], t$95$2, If[LessEqual[z, -2.05e-129], t$95$1, If[LessEqual[z, -7.7e-205], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+30], t$95$1, If[LessEqual[z, 2.9e+115], t$95$2, N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.54999999999999999e69 or 1.15e30 < z < 2.90000000000000005e115

   1. Initial program 43.7%

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

      1. +-commutative 43.7%

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

      2. associate-*l/ 78.9%

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

      3. fma-def 78.9%

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

   3. Simplified 78.9%

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

   4. Taylor expanded in t around inf 60.3%

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

      1. div-sub 60.3%

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

   6. Simplified 60.3%

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

   if -2.54999999999999999e69 < z < -2.05e-129 or -7.7000000000000001e-205 < z < 1.15e30

   1. Initial program 90.5%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in z around 0 77.7%

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

   if -2.05e-129 < z < -7.7000000000000001e-205

   1. Initial program 83.1%

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

      1. +-commutative 83.1%

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

      2. associate-*l/ 87.4%

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

      3. fma-def 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in y around inf 81.0%

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

      1. div-sub 81.0%

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

      2. *-commutative 81.0%

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

   6. Simplified 81.0%

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

   if 2.90000000000000005e115 < z

   1. Initial program 37.2%

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

      1. +-commutative 37.2%

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

      2. associate-*l/ 64.2%

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

      3. fma-def 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in z around inf 64.6%

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

      1. +-commutative 64.6%

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

      2. associate-/l* 80.6%

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

      3. distribute-lft-out-- 80.6%

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

      4. mul-1-neg 80.6%

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

      5. distribute-neg-frac 80.6%

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

      6. associate-/l* 64.6%

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

      7. *-commutative 64.6%

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

      8. distribute-rgt-out-- 64.4%

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

      9. unsub-neg 64.4%

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

      10. distribute-rgt-out-- 64.6%

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

      11. *-commutative 64.6%

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

      12. associate-/l* 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in t around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. neg-mul-1 78.6%

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

   9. Simplified 78.6%

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

   10. Taylor expanded in y around inf 55.4%

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

       1. mul-1-neg 55.4%

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

       2. associate-*l/ 64.1%

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

       3. distribute-rgt-neg-in 64.1%

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

   12. Simplified 64.1%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-129}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+30}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 9: 78.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ t_2 := t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-174}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) t))))
        (t_2 (+ t (* (/ (- y a) z) (- x t)))))
   (if (<= z -4.6e+65)
     t_2
     (if (<= z -1.7e-184)
       t_1
       (if (<= z 1e-174)
         (+ x (* (- t x) (/ y a)))
         (if (<= z 1.4e+111) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / t));
	double t_2 = t + (((y - a) / z) * (x - t));
	double tmp;
	if (z <= -4.6e+65) {
		tmp = t_2;
	} else if (z <= -1.7e-184) {
		tmp = t_1;
	} else if (z <= 1e-174) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 1.4e+111) {
		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 - z) / ((a - z) / t))
    t_2 = t + (((y - a) / z) * (x - t))
    if (z <= (-4.6d+65)) then
        tmp = t_2
    else if (z <= (-1.7d-184)) then
        tmp = t_1
    else if (z <= 1d-174) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 1.4d+111) 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 - z) / ((a - z) / t));
	double t_2 = t + (((y - a) / z) * (x - t));
	double tmp;
	if (z <= -4.6e+65) {
		tmp = t_2;
	} else if (z <= -1.7e-184) {
		tmp = t_1;
	} else if (z <= 1e-174) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 1.4e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / t))
	t_2 = t + (((y - a) / z) * (x - t))
	tmp = 0
	if z <= -4.6e+65:
		tmp = t_2
	elif z <= -1.7e-184:
		tmp = t_1
	elif z <= 1e-174:
		tmp = x + ((t - x) * (y / a))
	elif z <= 1.4e+111:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)))
	t_2 = Float64(t + Float64(Float64(Float64(y - a) / z) * Float64(x - t)))
	tmp = 0.0
	if (z <= -4.6e+65)
		tmp = t_2;
	elseif (z <= -1.7e-184)
		tmp = t_1;
	elseif (z <= 1e-174)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 1.4e+111)
		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 - z) / ((a - z) / t));
	t_2 = t + (((y - a) / z) * (x - t));
	tmp = 0.0;
	if (z <= -4.6e+65)
		tmp = t_2;
	elseif (z <= -1.7e-184)
		tmp = t_1;
	elseif (z <= 1e-174)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 1.4e+111)
		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[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+65], t$95$2, If[LessEqual[z, -1.7e-184], t$95$1, If[LessEqual[z, 1e-174], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+111], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e65 or 1.4e111 < z

   1. Initial program 36.9%

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

      1. +-commutative 36.9%

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

      2. associate-*l/ 69.9%

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

      3. fma-def 70.1%

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

   3. Simplified 70.1%

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

   4. Taylor expanded in z around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. associate-/l* 80.2%

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

      3. distribute-lft-out-- 80.2%

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

      4. mul-1-neg 80.2%

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

      5. distribute-neg-frac 80.2%

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

      6. associate-/l* 60.6%

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

      7. *-commutative 60.6%

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

      8. distribute-rgt-out-- 59.3%

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

      9. unsub-neg 59.3%

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

      10. distribute-rgt-out-- 60.6%

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

      11. *-commutative 60.6%

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

      12. associate-/l* 80.2%

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

   6. Simplified 80.2%

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

      1. associate-/r/ 79.7%

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

   8. Applied egg-rr 79.7%

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

   if -4.6e65 < z < -1.70000000000000002e-184 or 1e-174 < z < 1.4e111

   1. Initial program 83.4%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in t around inf 77.3%

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

   if -1.70000000000000002e-184 < z < 1e-174

   1. Initial program 91.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around 0 88.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+65}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-184}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 10^{-174}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+111}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 10: 77.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+66}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-174}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) t)))))
   (if (<= z -2.2e+66)
     (+ t (/ (- a y) (/ z (- t x))))
     (if (<= z -1.7e-184)
       t_1
       (if (<= z 1e-174)
         (+ x (* (- t x) (/ y a)))
         (if (<= z 2.9e+111) t_1 (+ t (* (/ (- y a) z) (- x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (z <= -2.2e+66) {
		tmp = t + ((a - y) / (z / (t - x)));
	} else if (z <= -1.7e-184) {
		tmp = t_1;
	} else if (z <= 1e-174) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 2.9e+111) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) / ((a - z) / t))
    if (z <= (-2.2d+66)) then
        tmp = t + ((a - y) / (z / (t - x)))
    else if (z <= (-1.7d-184)) then
        tmp = t_1
    else if (z <= 1d-174) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 2.9d+111) then
        tmp = t_1
    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 t_1 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (z <= -2.2e+66) {
		tmp = t + ((a - y) / (z / (t - x)));
	} else if (z <= -1.7e-184) {
		tmp = t_1;
	} else if (z <= 1e-174) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 2.9e+111) {
		tmp = t_1;
	} else {
		tmp = t + (((y - a) / z) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / t))
	tmp = 0
	if z <= -2.2e+66:
		tmp = t + ((a - y) / (z / (t - x)))
	elif z <= -1.7e-184:
		tmp = t_1
	elif z <= 1e-174:
		tmp = x + ((t - x) * (y / a))
	elif z <= 2.9e+111:
		tmp = t_1
	else:
		tmp = t + (((y - a) / z) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (z <= -2.2e+66)
		tmp = Float64(t + Float64(Float64(a - y) / Float64(z / Float64(t - x))));
	elseif (z <= -1.7e-184)
		tmp = t_1;
	elseif (z <= 1e-174)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 2.9e+111)
		tmp = t_1;
	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)
	t_1 = x + ((y - z) / ((a - z) / t));
	tmp = 0.0;
	if (z <= -2.2e+66)
		tmp = t + ((a - y) / (z / (t - x)));
	elseif (z <= -1.7e-184)
		tmp = t_1;
	elseif (z <= 1e-174)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 2.9e+111)
		tmp = t_1;
	else
		tmp = t + (((y - a) / z) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+66], N[(t + N[(N[(a - y), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e-184], t$95$1, If[LessEqual[z, 1e-174], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+111], t$95$1, N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1999999999999998e66

   1. Initial program 37.1%

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

      1. +-commutative 37.1%

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

      2. associate-*l/ 75.2%

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

      3. fma-def 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in z around inf 58.3%

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

      1. +-commutative 58.3%

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

      2. associate-/l* 79.7%

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

      3. distribute-lft-out-- 79.7%

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

      4. mul-1-neg 79.7%

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

      5. distribute-neg-frac 79.7%

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

      6. associate-/l* 58.3%

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

      7. *-commutative 58.3%

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

      8. distribute-rgt-out-- 56.2%

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

      9. unsub-neg 56.2%

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

      10. distribute-rgt-out-- 58.3%

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

      11. *-commutative 58.3%

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

      12. associate-/l* 79.7%

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

   6. Simplified 79.7%

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

   if -2.1999999999999998e66 < z < -1.70000000000000002e-184 or 1e-174 < z < 2.9e111

   1. Initial program 83.4%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in t around inf 77.3%

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

   if -1.70000000000000002e-184 < z < 1e-174

   1. Initial program 91.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around 0 88.0%

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

   if 2.9e111 < z

   1. Initial program 36.6%

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

      1. +-commutative 36.6%

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

      2. associate-*l/ 63.5%

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

      3. fma-def 63.8%

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

   3. Simplified 63.8%

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

   4. Taylor expanded in z around inf 63.4%

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

      1. +-commutative 63.4%

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

      2. associate-/l* 80.7%

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

      3. distribute-lft-out-- 80.7%

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

      4. mul-1-neg 80.7%

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

      5. distribute-neg-frac 80.7%

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

      6. associate-/l* 63.4%

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

      7. *-commutative 63.4%

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

      8. distribute-rgt-out-- 63.1%

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

      9. unsub-neg 63.1%

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

      10. distribute-rgt-out-- 63.4%

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

      11. *-commutative 63.4%

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

      12. associate-/l* 80.7%

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

   6. Simplified 80.7%

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

      1. associate-/r/ 81.1%

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

   8. Applied egg-rr 81.1%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+66}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-184}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 10^{-174}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+111}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 11: 39.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -4.7 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-144}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+41}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= y -4.7e+184)
     t_1
     (if (<= y -1.08e-144)
       (+ t x)
       (if (<= y -1.8e-223)
         (* t (/ (- y z) a))
         (if (<= y 7.2e+41)
           (+ t x)
           (if (<= y 2.05e+217) t_1 (* x (/ y z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -4.7e+184) {
		tmp = t_1;
	} else if (y <= -1.08e-144) {
		tmp = t + x;
	} else if (y <= -1.8e-223) {
		tmp = t * ((y - z) / a);
	} else if (y <= 7.2e+41) {
		tmp = t + x;
	} else if (y <= 2.05e+217) {
		tmp = t_1;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (y <= (-4.7d+184)) then
        tmp = t_1
    else if (y <= (-1.08d-144)) then
        tmp = t + x
    else if (y <= (-1.8d-223)) then
        tmp = t * ((y - z) / a)
    else if (y <= 7.2d+41) then
        tmp = t + x
    else if (y <= 2.05d+217) then
        tmp = t_1
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -4.7e+184) {
		tmp = t_1;
	} else if (y <= -1.08e-144) {
		tmp = t + x;
	} else if (y <= -1.8e-223) {
		tmp = t * ((y - z) / a);
	} else if (y <= 7.2e+41) {
		tmp = t + x;
	} else if (y <= 2.05e+217) {
		tmp = t_1;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if y <= -4.7e+184:
		tmp = t_1
	elif y <= -1.08e-144:
		tmp = t + x
	elif y <= -1.8e-223:
		tmp = t * ((y - z) / a)
	elif y <= 7.2e+41:
		tmp = t + x
	elif y <= 2.05e+217:
		tmp = t_1
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -4.7e+184)
		tmp = t_1;
	elseif (y <= -1.08e-144)
		tmp = Float64(t + x);
	elseif (y <= -1.8e-223)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (y <= 7.2e+41)
		tmp = Float64(t + x);
	elseif (y <= 2.05e+217)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (y <= -4.7e+184)
		tmp = t_1;
	elseif (y <= -1.08e-144)
		tmp = t + x;
	elseif (y <= -1.8e-223)
		tmp = t * ((y - z) / a);
	elseif (y <= 7.2e+41)
		tmp = t + x;
	elseif (y <= 2.05e+217)
		tmp = t_1;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.7e+184], t$95$1, If[LessEqual[y, -1.08e-144], N[(t + x), $MachinePrecision], If[LessEqual[y, -1.8e-223], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+41], N[(t + x), $MachinePrecision], If[LessEqual[y, 2.05e+217], t$95$1, N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.7000000000000003e184 or 7.20000000000000051e41 < y < 2.0500000000000001e217

   1. Initial program 73.6%

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

      1. +-commutative 73.6%

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

      2. associate-*l/ 92.8%

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

      3. fma-def 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around inf 55.4%

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

      1. div-sub 55.4%

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

   6. Simplified 55.4%

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

   7. Taylor expanded in y around inf 50.1%

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

   if -4.7000000000000003e184 < y < -1.08e-144 or -1.8000000000000002e-223 < y < 7.20000000000000051e41

   1. Initial program 64.3%

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

      1. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in t around inf 68.0%

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

   5. Taylor expanded in z around inf 48.1%

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

   if -1.08e-144 < y < -1.8000000000000002e-223

   1. Initial program 71.5%

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

      1. +-commutative 71.5%

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

      2. associate-*l/ 83.1%

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

      3. fma-def 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in t around inf 49.0%

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

      1. div-sub 49.0%

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

   6. Simplified 49.0%

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

   7. Taylor expanded in a around inf 47.3%

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

   if 2.0500000000000001e217 < y

   1. Initial program 72.0%

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

      1. +-commutative 72.0%

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

      2. associate-*l/ 95.8%

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

      3. fma-def 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. associate-/l* 71.2%

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

      3. distribute-lft-out-- 71.2%

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

      4. mul-1-neg 71.2%

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

      5. distribute-neg-frac 71.2%

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

      6. associate-/l* 61.0%

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

      7. *-commutative 61.0%

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

      8. distribute-rgt-out-- 61.0%

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

      9. unsub-neg 61.0%

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

      10. distribute-rgt-out-- 61.0%

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

      11. *-commutative 61.0%

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

      12. associate-/l* 71.2%

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

   6. Simplified 71.2%

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

   7. Taylor expanded in t around 0 42.7%

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

      1. associate-*r/ 42.7%

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

      2. neg-mul-1 42.7%

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

   9. Simplified 42.7%

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

   10. Taylor expanded in y around inf 37.9%

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

       1. associate-*l/ 65.3%

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

   12. Simplified 65.3%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+184}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-144}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+41}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+217}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 12: 39.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-144}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+42}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+219}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= y -1.5e+185)
     t_1
     (if (<= y -1.08e-144)
       (+ t x)
       (if (<= y -1.8e-223)
         (* t (/ (- y z) a))
         (if (<= y 1.65e+42)
           (+ t x)
           (if (<= y 3.6e+219) t_1 (* x (/ (- y a) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -1.5e+185) {
		tmp = t_1;
	} else if (y <= -1.08e-144) {
		tmp = t + x;
	} else if (y <= -1.8e-223) {
		tmp = t * ((y - z) / a);
	} else if (y <= 1.65e+42) {
		tmp = t + x;
	} else if (y <= 3.6e+219) {
		tmp = t_1;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (y <= (-1.5d+185)) then
        tmp = t_1
    else if (y <= (-1.08d-144)) then
        tmp = t + x
    else if (y <= (-1.8d-223)) then
        tmp = t * ((y - z) / a)
    else if (y <= 1.65d+42) then
        tmp = t + x
    else if (y <= 3.6d+219) then
        tmp = t_1
    else
        tmp = x * ((y - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -1.5e+185) {
		tmp = t_1;
	} else if (y <= -1.08e-144) {
		tmp = t + x;
	} else if (y <= -1.8e-223) {
		tmp = t * ((y - z) / a);
	} else if (y <= 1.65e+42) {
		tmp = t + x;
	} else if (y <= 3.6e+219) {
		tmp = t_1;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if y <= -1.5e+185:
		tmp = t_1
	elif y <= -1.08e-144:
		tmp = t + x
	elif y <= -1.8e-223:
		tmp = t * ((y - z) / a)
	elif y <= 1.65e+42:
		tmp = t + x
	elif y <= 3.6e+219:
		tmp = t_1
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -1.5e+185)
		tmp = t_1;
	elseif (y <= -1.08e-144)
		tmp = Float64(t + x);
	elseif (y <= -1.8e-223)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (y <= 1.65e+42)
		tmp = Float64(t + x);
	elseif (y <= 3.6e+219)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (y <= -1.5e+185)
		tmp = t_1;
	elseif (y <= -1.08e-144)
		tmp = t + x;
	elseif (y <= -1.8e-223)
		tmp = t * ((y - z) / a);
	elseif (y <= 1.65e+42)
		tmp = t + x;
	elseif (y <= 3.6e+219)
		tmp = t_1;
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+185], t$95$1, If[LessEqual[y, -1.08e-144], N[(t + x), $MachinePrecision], If[LessEqual[y, -1.8e-223], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+42], N[(t + x), $MachinePrecision], If[LessEqual[y, 3.6e+219], t$95$1, N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.49999999999999997e185 or 1.6499999999999999e42 < y < 3.60000000000000006e219

   1. Initial program 73.6%

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

      1. +-commutative 73.6%

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

      2. associate-*l/ 92.8%

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

      3. fma-def 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around inf 55.4%

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

      1. div-sub 55.4%

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

   6. Simplified 55.4%

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

   7. Taylor expanded in y around inf 50.1%

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

   if -1.49999999999999997e185 < y < -1.08e-144 or -1.8000000000000002e-223 < y < 1.6499999999999999e42

   1. Initial program 64.3%

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

      1. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in t around inf 68.0%

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

   5. Taylor expanded in z around inf 48.1%

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

   if -1.08e-144 < y < -1.8000000000000002e-223

   1. Initial program 71.5%

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

      1. +-commutative 71.5%

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

      2. associate-*l/ 83.1%

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

      3. fma-def 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in t around inf 49.0%

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

      1. div-sub 49.0%

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

   6. Simplified 49.0%

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

   7. Taylor expanded in a around inf 47.3%

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

   if 3.60000000000000006e219 < y

   1. Initial program 72.0%

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

      1. +-commutative 72.0%

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

      2. associate-*l/ 95.8%

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

      3. fma-def 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. associate-/l* 71.2%

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

      3. distribute-lft-out-- 71.2%

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

      4. mul-1-neg 71.2%

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

      5. distribute-neg-frac 71.2%

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

      6. associate-/l* 61.0%

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

      7. *-commutative 61.0%

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

      8. distribute-rgt-out-- 61.0%

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

      9. unsub-neg 61.0%

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

      10. distribute-rgt-out-- 61.0%

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

      11. *-commutative 61.0%

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

      12. associate-/l* 71.2%

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

   6. Simplified 71.2%

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

   7. Taylor expanded in t around 0 42.7%

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

      1. associate-*r/ 42.7%

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

      2. neg-mul-1 42.7%

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

   9. Simplified 42.7%

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

   10. Taylor expanded in t around 0 37.9%

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

       1. associate-*l/ 65.3%

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

       2. *-commutative 65.3%

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

   12. Simplified 65.3%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+185}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-144}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+42}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+219}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]

Alternative 13: 38.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;y \leq -4.7 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-144}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t (- a z)))))
   (if (<= y -4.7e+184)
     t_1
     (if (<= y -1.08e-144)
       (+ t x)
       (if (<= y -1.8e-223)
         (* t (/ (- y z) a))
         (if (<= y 5.2e+43)
           (+ t x)
           (if (<= y 2.2e+217) t_1 (* x (/ (- y a) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (a - z));
	double tmp;
	if (y <= -4.7e+184) {
		tmp = t_1;
	} else if (y <= -1.08e-144) {
		tmp = t + x;
	} else if (y <= -1.8e-223) {
		tmp = t * ((y - z) / a);
	} else if (y <= 5.2e+43) {
		tmp = t + x;
	} else if (y <= 2.2e+217) {
		tmp = t_1;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / (a - z))
    if (y <= (-4.7d+184)) then
        tmp = t_1
    else if (y <= (-1.08d-144)) then
        tmp = t + x
    else if (y <= (-1.8d-223)) then
        tmp = t * ((y - z) / a)
    else if (y <= 5.2d+43) then
        tmp = t + x
    else if (y <= 2.2d+217) then
        tmp = t_1
    else
        tmp = x * ((y - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (a - z));
	double tmp;
	if (y <= -4.7e+184) {
		tmp = t_1;
	} else if (y <= -1.08e-144) {
		tmp = t + x;
	} else if (y <= -1.8e-223) {
		tmp = t * ((y - z) / a);
	} else if (y <= 5.2e+43) {
		tmp = t + x;
	} else if (y <= 2.2e+217) {
		tmp = t_1;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / (a - z))
	tmp = 0
	if y <= -4.7e+184:
		tmp = t_1
	elif y <= -1.08e-144:
		tmp = t + x
	elif y <= -1.8e-223:
		tmp = t * ((y - z) / a)
	elif y <= 5.2e+43:
		tmp = t + x
	elif y <= 2.2e+217:
		tmp = t_1
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (y <= -4.7e+184)
		tmp = t_1;
	elseif (y <= -1.08e-144)
		tmp = Float64(t + x);
	elseif (y <= -1.8e-223)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (y <= 5.2e+43)
		tmp = Float64(t + x);
	elseif (y <= 2.2e+217)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / (a - z));
	tmp = 0.0;
	if (y <= -4.7e+184)
		tmp = t_1;
	elseif (y <= -1.08e-144)
		tmp = t + x;
	elseif (y <= -1.8e-223)
		tmp = t * ((y - z) / a);
	elseif (y <= 5.2e+43)
		tmp = t + x;
	elseif (y <= 2.2e+217)
		tmp = t_1;
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.7e+184], t$95$1, If[LessEqual[y, -1.08e-144], N[(t + x), $MachinePrecision], If[LessEqual[y, -1.8e-223], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+43], N[(t + x), $MachinePrecision], If[LessEqual[y, 2.2e+217], t$95$1, N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.7000000000000003e184 or 5.20000000000000042e43 < y < 2.2e217

   1. Initial program 73.6%

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

      1. +-commutative 73.6%

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

      2. associate-*l/ 92.8%

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

      3. fma-def 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in y around inf 83.6%

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

      1. div-sub 83.7%

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

      2. *-commutative 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in t around inf 51.7%

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

   if -4.7000000000000003e184 < y < -1.08e-144 or -1.8000000000000002e-223 < y < 5.20000000000000042e43

   1. Initial program 64.3%

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

      1. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in t around inf 68.0%

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

   5. Taylor expanded in z around inf 48.1%

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

   if -1.08e-144 < y < -1.8000000000000002e-223

   1. Initial program 71.5%

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

      1. +-commutative 71.5%

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

      2. associate-*l/ 83.1%

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

      3. fma-def 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in t around inf 49.0%

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

      1. div-sub 49.0%

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

   6. Simplified 49.0%

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

   7. Taylor expanded in a around inf 47.3%

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

   if 2.2e217 < y

   1. Initial program 72.0%

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

      1. +-commutative 72.0%

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

      2. associate-*l/ 95.8%

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

      3. fma-def 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. associate-/l* 71.2%

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

      3. distribute-lft-out-- 71.2%

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

      4. mul-1-neg 71.2%

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

      5. distribute-neg-frac 71.2%

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

      6. associate-/l* 61.0%

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

      7. *-commutative 61.0%

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

      8. distribute-rgt-out-- 61.0%

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

      9. unsub-neg 61.0%

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

      10. distribute-rgt-out-- 61.0%

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

      11. *-commutative 61.0%

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

      12. associate-/l* 71.2%

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

   6. Simplified 71.2%

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

   7. Taylor expanded in t around 0 42.7%

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

      1. associate-*r/ 42.7%

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

      2. neg-mul-1 42.7%

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

   9. Simplified 42.7%

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

   10. Taylor expanded in t around 0 37.9%

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

       1. associate-*l/ 65.3%

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

       2. *-commutative 65.3%

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

   12. Simplified 65.3%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-144}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]

Alternative 14: 40.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-144}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;y \leq 2.12 \cdot 10^{+43}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.8e+80)
   (* y (/ (- t x) a))
   (if (<= y -1.08e-144)
     (+ t x)
     (if (<= y -1.8e-223)
       (* t (/ (- y z) a))
       (if (<= y 2.12e+43)
         (+ t x)
         (if (<= y 7e+217) (* y (/ t (- a z))) (* x (/ (- y a) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.8e+80) {
		tmp = y * ((t - x) / a);
	} else if (y <= -1.08e-144) {
		tmp = t + x;
	} else if (y <= -1.8e-223) {
		tmp = t * ((y - z) / a);
	} else if (y <= 2.12e+43) {
		tmp = t + x;
	} else if (y <= 7e+217) {
		tmp = y * (t / (a - z));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-6.8d+80)) then
        tmp = y * ((t - x) / a)
    else if (y <= (-1.08d-144)) then
        tmp = t + x
    else if (y <= (-1.8d-223)) then
        tmp = t * ((y - z) / a)
    else if (y <= 2.12d+43) then
        tmp = t + x
    else if (y <= 7d+217) then
        tmp = y * (t / (a - z))
    else
        tmp = x * ((y - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.8e+80) {
		tmp = y * ((t - x) / a);
	} else if (y <= -1.08e-144) {
		tmp = t + x;
	} else if (y <= -1.8e-223) {
		tmp = t * ((y - z) / a);
	} else if (y <= 2.12e+43) {
		tmp = t + x;
	} else if (y <= 7e+217) {
		tmp = y * (t / (a - z));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6.8e+80:
		tmp = y * ((t - x) / a)
	elif y <= -1.08e-144:
		tmp = t + x
	elif y <= -1.8e-223:
		tmp = t * ((y - z) / a)
	elif y <= 2.12e+43:
		tmp = t + x
	elif y <= 7e+217:
		tmp = y * (t / (a - z))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6.8e+80)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (y <= -1.08e-144)
		tmp = Float64(t + x);
	elseif (y <= -1.8e-223)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (y <= 2.12e+43)
		tmp = Float64(t + x);
	elseif (y <= 7e+217)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6.8e+80)
		tmp = y * ((t - x) / a);
	elseif (y <= -1.08e-144)
		tmp = t + x;
	elseif (y <= -1.8e-223)
		tmp = t * ((y - z) / a);
	elseif (y <= 2.12e+43)
		tmp = t + x;
	elseif (y <= 7e+217)
		tmp = y * (t / (a - z));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6.8e+80], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.08e-144], N[(t + x), $MachinePrecision], If[LessEqual[y, -1.8e-223], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.12e+43], N[(t + x), $MachinePrecision], If[LessEqual[y, 7e+217], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.79999999999999984e80

   1. Initial program 62.3%

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

      1. +-commutative 62.3%

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

      2. associate-*l/ 91.8%

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

      3. fma-def 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around inf 71.5%

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

      1. div-sub 71.5%

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

      2. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in a around inf 50.0%

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

   if -6.79999999999999984e80 < y < -1.08e-144 or -1.8000000000000002e-223 < y < 2.12000000000000011e43

   1. Initial program 66.2%

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

      1. associate-/l* 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in t around inf 68.4%

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

   5. Taylor expanded in z around inf 49.5%

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

   if -1.08e-144 < y < -1.8000000000000002e-223

   1. Initial program 71.5%

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

      1. +-commutative 71.5%

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

      2. associate-*l/ 83.1%

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

      3. fma-def 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in t around inf 49.0%

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

      1. div-sub 49.0%

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

   6. Simplified 49.0%

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

   7. Taylor expanded in a around inf 47.3%

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

   if 2.12000000000000011e43 < y < 6.9999999999999996e217

   1. Initial program 77.0%

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

      1. +-commutative 77.0%

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

      2. associate-*l/ 95.4%

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

      3. fma-def 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around inf 79.6%

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

      1. div-sub 79.6%

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

      2. *-commutative 79.6%

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

   6. Simplified 79.6%

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

   7. Taylor expanded in t around inf 55.8%

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

   if 6.9999999999999996e217 < y

   1. Initial program 72.0%

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

      1. +-commutative 72.0%

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

      2. associate-*l/ 95.8%

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

      3. fma-def 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. associate-/l* 71.2%

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

      3. distribute-lft-out-- 71.2%

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

      4. mul-1-neg 71.2%

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

      5. distribute-neg-frac 71.2%

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

      6. associate-/l* 61.0%

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

      7. *-commutative 61.0%

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

      8. distribute-rgt-out-- 61.0%

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

      9. unsub-neg 61.0%

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

      10. distribute-rgt-out-- 61.0%

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

      11. *-commutative 61.0%

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

      12. associate-/l* 71.2%

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

   6. Simplified 71.2%

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

   7. Taylor expanded in t around 0 42.7%

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

      1. associate-*r/ 42.7%

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

      2. neg-mul-1 42.7%

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

   9. Simplified 42.7%

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

   10. Taylor expanded in t around 0 37.9%

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

       1. associate-*l/ 65.3%

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

       2. *-commutative 65.3%

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

   12. Simplified 65.3%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-144}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;y \leq 2.12 \cdot 10^{+43}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]

Alternative 15: 67.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x - t}{z}\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1550000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ (- x t) z)))))
   (if (<= a -1.1e+73)
     (+ x (/ (- y z) (/ a t)))
     (if (<= a 2.65e-191)
       t_1
       (if (<= a 1.2e-53)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1550000000.0) t_1 (+ x (/ y (/ a (- t x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * ((x - t) / z));
	double tmp;
	if (a <= -1.1e+73) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= 2.65e-191) {
		tmp = t_1;
	} else if (a <= 1.2e-53) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1550000000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t + (y * ((x - t) / z))
    if (a <= (-1.1d+73)) then
        tmp = x + ((y - z) / (a / t))
    else if (a <= 2.65d-191) then
        tmp = t_1
    else if (a <= 1.2d-53) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1550000000.0d0) then
        tmp = t_1
    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 t_1 = t + (y * ((x - t) / z));
	double tmp;
	if (a <= -1.1e+73) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= 2.65e-191) {
		tmp = t_1;
	} else if (a <= 1.2e-53) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1550000000.0) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * ((x - t) / z))
	tmp = 0
	if a <= -1.1e+73:
		tmp = x + ((y - z) / (a / t))
	elif a <= 2.65e-191:
		tmp = t_1
	elif a <= 1.2e-53:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1550000000.0:
		tmp = t_1
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(Float64(x - t) / z)))
	tmp = 0.0
	if (a <= -1.1e+73)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / t)));
	elseif (a <= 2.65e-191)
		tmp = t_1;
	elseif (a <= 1.2e-53)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1550000000.0)
		tmp = t_1;
	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)
	t_1 = t + (y * ((x - t) / z));
	tmp = 0.0;
	if (a <= -1.1e+73)
		tmp = x + ((y - z) / (a / t));
	elseif (a <= 2.65e-191)
		tmp = t_1;
	elseif (a <= 1.2e-53)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1550000000.0)
		tmp = t_1;
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e+73], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.65e-191], t$95$1, If[LessEqual[a, 1.2e-53], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1550000000.0], t$95$1, N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.1e73

   1. Initial program 64.9%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in t around inf 80.4%

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

   5. Taylor expanded in a around inf 61.5%

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

      1. *-commutative 61.5%

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

      2. associate-/l* 65.7%

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

   7. Simplified 65.7%

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

   if -1.1e73 < a < 2.64999999999999993e-191 or 1.20000000000000004e-53 < a < 1.55e9

   1. Initial program 68.7%

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

      1. +-commutative 68.7%

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

      2. associate-*l/ 78.5%

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

      3. fma-def 78.7%

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

   3. Simplified 78.7%

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

   4. Taylor expanded in z around inf 74.2%

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

      1. +-commutative 74.2%

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

      2. associate-/l* 79.5%

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

      3. distribute-lft-out-- 79.5%

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

      4. mul-1-neg 79.5%

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

      5. distribute-neg-frac 79.5%

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

      6. associate-/l* 74.2%

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

      7. *-commutative 74.2%

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

      8. distribute-rgt-out-- 74.3%

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

      9. unsub-neg 74.3%

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

      10. distribute-rgt-out-- 74.2%

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

      11. *-commutative 74.2%

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

      12. associate-/l* 79.5%

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

   6. Simplified 79.5%

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

   7. Taylor expanded in y around inf 64.9%

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

      1. associate-*r/ 70.9%

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

   9. Simplified 70.9%

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

   if 2.64999999999999993e-191 < a < 1.20000000000000004e-53

   1. Initial program 74.4%

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

      1. +-commutative 74.4%

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

      2. associate-*l/ 80.6%

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

      3. fma-def 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in y around inf 66.2%

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

      1. div-sub 66.2%

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

      2. *-commutative 66.2%

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

   6. Simplified 66.2%

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

   if 1.55e9 < a

   1. Initial program 65.1%

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

      1. +-commutative 65.1%

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

      2. associate-*l/ 92.7%

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

      3. fma-def 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in z around 0 63.3%

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

      1. +-commutative 63.3%

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

      2. associate-/l* 80.1%

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

   6. Simplified 80.1%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-191}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1550000000:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 16: 66.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x - t}{z}\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-54}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 2400000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ (- x t) z)))))
   (if (<= a -1.25e+77)
     (+ x (/ (- y z) (/ a t)))
     (if (<= a 4.6e-188)
       t_1
       (if (<= a 1.7e-54)
         (/ (* y (- t x)) (- a z))
         (if (<= a 2400000000.0) t_1 (+ x (/ y (/ a (- t x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * ((x - t) / z));
	double tmp;
	if (a <= -1.25e+77) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= 4.6e-188) {
		tmp = t_1;
	} else if (a <= 1.7e-54) {
		tmp = (y * (t - x)) / (a - z);
	} else if (a <= 2400000000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t + (y * ((x - t) / z))
    if (a <= (-1.25d+77)) then
        tmp = x + ((y - z) / (a / t))
    else if (a <= 4.6d-188) then
        tmp = t_1
    else if (a <= 1.7d-54) then
        tmp = (y * (t - x)) / (a - z)
    else if (a <= 2400000000.0d0) then
        tmp = t_1
    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 t_1 = t + (y * ((x - t) / z));
	double tmp;
	if (a <= -1.25e+77) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= 4.6e-188) {
		tmp = t_1;
	} else if (a <= 1.7e-54) {
		tmp = (y * (t - x)) / (a - z);
	} else if (a <= 2400000000.0) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * ((x - t) / z))
	tmp = 0
	if a <= -1.25e+77:
		tmp = x + ((y - z) / (a / t))
	elif a <= 4.6e-188:
		tmp = t_1
	elif a <= 1.7e-54:
		tmp = (y * (t - x)) / (a - z)
	elif a <= 2400000000.0:
		tmp = t_1
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(Float64(x - t) / z)))
	tmp = 0.0
	if (a <= -1.25e+77)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / t)));
	elseif (a <= 4.6e-188)
		tmp = t_1;
	elseif (a <= 1.7e-54)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (a <= 2400000000.0)
		tmp = t_1;
	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)
	t_1 = t + (y * ((x - t) / z));
	tmp = 0.0;
	if (a <= -1.25e+77)
		tmp = x + ((y - z) / (a / t));
	elseif (a <= 4.6e-188)
		tmp = t_1;
	elseif (a <= 1.7e-54)
		tmp = (y * (t - x)) / (a - z);
	elseif (a <= 2400000000.0)
		tmp = t_1;
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.25e+77], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e-188], t$95$1, If[LessEqual[a, 1.7e-54], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2400000000.0], t$95$1, N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.25000000000000001e77

   1. Initial program 64.9%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in t around inf 80.4%

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

   5. Taylor expanded in a around inf 61.5%

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

      1. *-commutative 61.5%

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

      2. associate-/l* 65.7%

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

   7. Simplified 65.7%

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

   if -1.25000000000000001e77 < a < 4.6e-188 or 1.69999999999999994e-54 < a < 2.4e9

   1. Initial program 68.7%

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

      1. +-commutative 68.7%

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

      2. associate-*l/ 78.5%

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

      3. fma-def 78.7%

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

   3. Simplified 78.7%

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

   4. Taylor expanded in z around inf 74.2%

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

      1. +-commutative 74.2%

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

      2. associate-/l* 79.5%

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

      3. distribute-lft-out-- 79.5%

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

      4. mul-1-neg 79.5%

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

      5. distribute-neg-frac 79.5%

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

      6. associate-/l* 74.2%

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

      7. *-commutative 74.2%

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

      8. distribute-rgt-out-- 74.3%

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

      9. unsub-neg 74.3%

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

      10. distribute-rgt-out-- 74.2%

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

      11. *-commutative 74.2%

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

      12. associate-/l* 79.5%

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

   6. Simplified 79.5%

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

   7. Taylor expanded in y around inf 64.9%

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

      1. associate-*r/ 70.9%

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

   9. Simplified 70.9%

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

   if 4.6e-188 < a < 1.69999999999999994e-54

   1. Initial program 74.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 74.4%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 80.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 80.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in y around -inf 69.4%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

   if 2.4e9 < a

   1. Initial program 65.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 65.1%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 92.7%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 92.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 92.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around 0 63.3%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 63.3%

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

      2. associate-/l* 80.1%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 80.1%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-188}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-54}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 2400000000:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 17: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+202} \lor \neg \left(z \leq 1.95 \cdot 10^{+171}\right):\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e+202) (not (<= z 1.95e+171)))
   (+ t (* (- y a) (/ x z)))
   (+ x (* (/ (- y z) (- a z)) (- t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+202) || !(z <= 1.95e+171)) {
		tmp = t + ((y - a) * (x / z));
	} else {
		tmp = x + (((y - z) / (a - z)) * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.6d+202)) .or. (.not. (z <= 1.95d+171))) then
        tmp = t + ((y - a) * (x / z))
    else
        tmp = x + (((y - z) / (a - z)) * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+202) || !(z <= 1.95e+171)) {
		tmp = t + ((y - a) * (x / z));
	} else {
		tmp = x + (((y - z) / (a - z)) * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.6e+202) or not (z <= 1.95e+171):
		tmp = t + ((y - a) * (x / z))
	else:
		tmp = x + (((y - z) / (a - z)) * (t - x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.6e+202) || !(z <= 1.95e+171))
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.6e+202) || ~((z <= 1.95e+171)))
		tmp = t + ((y - a) * (x / z));
	else
		tmp = x + (((y - z) / (a - z)) * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.6e+202], N[Not[LessEqual[z, 1.95e+171]], $MachinePrecision]], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000006e202 or 1.95e171 < z

   1. Initial program 27.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 27.8%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 60.7%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 61.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 61.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 63.2%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 63.2%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 87.3%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 87.3%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 87.3%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 87.3%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 63.2%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 63.2%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 60.7%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 60.7%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 63.2%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 63.2%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 87.3%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 87.3%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in t around 0 87.6%

      \[\leadsto t - \frac{y - a}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 87.6%

         \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-1 \cdot z}{x}}} \]

      2. neg-mul-1 87.6%

         \[\leadsto t - \frac{y - a}{\frac{\color{blue}{-z}}{x}} \]

   9. Simplified 87.6%

      \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-z}{x}}} \]

   10. Taylor expanded in z around 0 78.9%

       \[\leadsto t - \color{blue}{-1 \cdot \frac{\left(y - a\right) \cdot x}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 87.6%

          \[\leadsto t - -1 \cdot \color{blue}{\frac{y - a}{\frac{z}{x}}} \]

       2. associate-*r/ 87.6%

          \[\leadsto t - \color{blue}{\frac{-1 \cdot \left(y - a\right)}{\frac{z}{x}}} \]

       3. associate-*l/ 87.6%

          \[\leadsto t - \color{blue}{\frac{-1}{\frac{z}{x}} \cdot \left(y - a\right)} \]

       4. metadata-eval 87.6%

          \[\leadsto t - \frac{\color{blue}{-1}}{\frac{z}{x}} \cdot \left(y - a\right) \]

       5. distribute-neg-frac 87.6%

          \[\leadsto t - \color{blue}{\left(-\frac{1}{\frac{z}{x}}\right)} \cdot \left(y - a\right) \]

       6. *-commutative 87.6%

          \[\leadsto t - \color{blue}{\left(y - a\right) \cdot \left(-\frac{1}{\frac{z}{x}}\right)} \]

       7. associate-/r/ 90.5%

          \[\leadsto t - \left(y - a\right) \cdot \left(-\color{blue}{\frac{1}{z} \cdot x}\right) \]

       8. associate-*l/ 90.6%

          \[\leadsto t - \left(y - a\right) \cdot \left(-\color{blue}{\frac{1 \cdot x}{z}}\right) \]

       9. *-lft-identity 90.6%

          \[\leadsto t - \left(y - a\right) \cdot \left(-\frac{\color{blue}{x}}{z}\right) \]

   12. Simplified 90.6%

       \[\leadsto t - \color{blue}{\left(y - a\right) \cdot \left(-\frac{x}{z}\right)} \]

   if -1.60000000000000006e202 < z < 1.95e171

   1. Initial program 75.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.8%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 90.8%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+202} \lor \neg \left(z \leq 1.95 \cdot 10^{+171}\right):\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \end{array} \]

Alternative 18: 53.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t \cdot y}{a}\\ t_2 := t - x \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-218}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* t y) a))) (t_2 (- t (* x (/ a z)))))
   (if (<= z -5.8e+100)
     t_2
     (if (<= z -1.4e-151)
       t_1
       (if (<= z -1.85e-218)
         (* (- t x) (/ y a))
         (if (<= z 1.9e+83) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t * y) / a);
	double t_2 = t - (x * (a / z));
	double tmp;
	if (z <= -5.8e+100) {
		tmp = t_2;
	} else if (z <= -1.4e-151) {
		tmp = t_1;
	} else if (z <= -1.85e-218) {
		tmp = (t - x) * (y / a);
	} else if (z <= 1.9e+83) {
		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 + ((t * y) / a)
    t_2 = t - (x * (a / z))
    if (z <= (-5.8d+100)) then
        tmp = t_2
    else if (z <= (-1.4d-151)) then
        tmp = t_1
    else if (z <= (-1.85d-218)) then
        tmp = (t - x) * (y / a)
    else if (z <= 1.9d+83) 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 + ((t * y) / a);
	double t_2 = t - (x * (a / z));
	double tmp;
	if (z <= -5.8e+100) {
		tmp = t_2;
	} else if (z <= -1.4e-151) {
		tmp = t_1;
	} else if (z <= -1.85e-218) {
		tmp = (t - x) * (y / a);
	} else if (z <= 1.9e+83) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t * y) / a)
	t_2 = t - (x * (a / z))
	tmp = 0
	if z <= -5.8e+100:
		tmp = t_2
	elif z <= -1.4e-151:
		tmp = t_1
	elif z <= -1.85e-218:
		tmp = (t - x) * (y / a)
	elif z <= 1.9e+83:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t * y) / a))
	t_2 = Float64(t - Float64(x * Float64(a / z)))
	tmp = 0.0
	if (z <= -5.8e+100)
		tmp = t_2;
	elseif (z <= -1.4e-151)
		tmp = t_1;
	elseif (z <= -1.85e-218)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 1.9e+83)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t * y) / a);
	t_2 = t - (x * (a / z));
	tmp = 0.0;
	if (z <= -5.8e+100)
		tmp = t_2;
	elseif (z <= -1.4e-151)
		tmp = t_1;
	elseif (z <= -1.85e-218)
		tmp = (t - x) * (y / a);
	elseif (z <= 1.9e+83)
		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[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+100], t$95$2, If[LessEqual[z, -1.4e-151], t$95$1, If[LessEqual[z, -1.85e-218], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+83], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8000000000000001e100 or 1.9000000000000001e83 < z

   1. Initial program 37.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 37.2%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 69.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 69.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 58.6%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 58.6%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 77.7%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 77.7%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 77.7%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 77.7%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 58.6%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 58.6%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 57.3%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 57.3%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 58.6%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 58.6%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 77.7%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 77.7%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   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. associate-*r/ 72.8%

         \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-1 \cdot z}{x}}} \]

      2. neg-mul-1 72.8%

         \[\leadsto t - \frac{y - a}{\frac{\color{blue}{-z}}{x}} \]

   9. Simplified 72.8%

      \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-z}{x}}} \]

   10. Taylor expanded in y around 0 56.5%

       \[\leadsto t - \color{blue}{\frac{a \cdot x}{z}} \]
   11. Step-by-step derivation

       1. associate-*l/ 58.0%

          \[\leadsto t - \color{blue}{\frac{a}{z} \cdot x} \]

       2. *-commutative 58.0%

          \[\leadsto t - \color{blue}{x \cdot \frac{a}{z}} \]

   12. Simplified 58.0%

       \[\leadsto t - \color{blue}{x \cdot \frac{a}{z}} \]

   if -5.8000000000000001e100 < z < -1.4e-151 or -1.8500000000000001e-218 < z < 1.9000000000000001e83

   1. Initial program 85.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 95.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around 0 69.7%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]

   5. Taylor expanded in t around inf 55.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot t}{a}} \]

   if -1.4e-151 < z < -1.8500000000000001e-218

   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/ 92.3%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 92.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in y around inf 85.7%

      \[\leadsto \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 85.7%

         \[\leadsto \color{blue}{\frac{t - x}{a - z}} \cdot y \]

      2. *-commutative 85.7%

         \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Simplified 85.7%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   7. Taylor expanded in a around inf 55.8%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 65.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

      2. associate-/r/ 69.3%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(t - x\right)} \]

   9. Simplified 69.3%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(t - x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+100}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-151}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-218}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]

Alternative 19: 60.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+202}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))))
   (if (<= x -1.15e+96)
     t_1
     (if (<= x 6.8e+85)
       (* t (/ (- y z) (- a z)))
       (if (<= x 1.12e+153)
         (+ x (/ (* t y) a))
         (if (<= x 4e+202) (- t (* x (/ a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double tmp;
	if (x <= -1.15e+96) {
		tmp = t_1;
	} else if (x <= 6.8e+85) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 1.12e+153) {
		tmp = x + ((t * y) / a);
	} else if (x <= 4e+202) {
		tmp = t - (x * (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (x * (y / a))
    if (x <= (-1.15d+96)) then
        tmp = t_1
    else if (x <= 6.8d+85) then
        tmp = t * ((y - z) / (a - z))
    else if (x <= 1.12d+153) then
        tmp = x + ((t * y) / a)
    else if (x <= 4d+202) then
        tmp = t - (x * (a / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double tmp;
	if (x <= -1.15e+96) {
		tmp = t_1;
	} else if (x <= 6.8e+85) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 1.12e+153) {
		tmp = x + ((t * y) / a);
	} else if (x <= 4e+202) {
		tmp = t - (x * (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	tmp = 0
	if x <= -1.15e+96:
		tmp = t_1
	elif x <= 6.8e+85:
		tmp = t * ((y - z) / (a - z))
	elif x <= 1.12e+153:
		tmp = x + ((t * y) / a)
	elif x <= 4e+202:
		tmp = t - (x * (a / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	tmp = 0.0
	if (x <= -1.15e+96)
		tmp = t_1;
	elseif (x <= 6.8e+85)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (x <= 1.12e+153)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (x <= 4e+202)
		tmp = Float64(t - Float64(x * Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	tmp = 0.0;
	if (x <= -1.15e+96)
		tmp = t_1;
	elseif (x <= 6.8e+85)
		tmp = t * ((y - z) / (a - z));
	elseif (x <= 1.12e+153)
		tmp = x + ((t * y) / a);
	elseif (x <= 4e+202)
		tmp = t - (x * (a / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+96], t$95$1, If[LessEqual[x, 6.8e+85], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.12e+153], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+202], N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.15000000000000008e96 or 3.9999999999999996e202 < x

   1. Initial program 49.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 74.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around 0 60.6%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]

   5. Taylor expanded in t around 0 48.8%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{y \cdot x}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 48.8%

         \[\leadsto x + \color{blue}{\frac{-1 \cdot \left(y \cdot x\right)}{a}} \]

      2. mul-1-neg 48.8%

         \[\leadsto x + \frac{\color{blue}{-y \cdot x}}{a} \]

      3. distribute-rgt-neg-out 48.8%

         \[\leadsto x + \frac{\color{blue}{y \cdot \left(-x\right)}}{a} \]

      4. associate-*l/ 58.4%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(-x\right)} \]

   7. Simplified 58.4%

      \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(-x\right)} \]

   if -1.15000000000000008e96 < x < 6.8000000000000007e85

   1. Initial program 77.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 77.9%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 92.5%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 92.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 92.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in t around inf 67.5%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 67.5%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

   6. Simplified 67.5%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if 6.8000000000000007e85 < x < 1.1200000000000001e153

   1. Initial program 67.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 75.8%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around 0 76.0%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]

   5. Taylor expanded in t around inf 76.5%

      \[\leadsto x + \color{blue}{\frac{y \cdot t}{a}} \]

   if 1.1200000000000001e153 < x < 3.9999999999999996e202

   1. Initial program 36.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 67.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 67.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 67.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 52.0%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 52.0%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 76.1%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 76.1%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 76.1%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 76.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 52.0%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 52.0%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 52.0%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 52.0%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 52.0%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 52.0%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 76.1%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 76.1%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in t around 0 76.1%

      \[\leadsto t - \frac{y - a}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 76.1%

         \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-1 \cdot z}{x}}} \]

      2. neg-mul-1 76.1%

         \[\leadsto t - \frac{y - a}{\frac{\color{blue}{-z}}{x}} \]

   9. Simplified 76.1%

      \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-z}{x}}} \]

   10. Taylor expanded in y around 0 44.5%

       \[\leadsto t - \color{blue}{\frac{a \cdot x}{z}} \]
   11. Step-by-step derivation

       1. associate-*l/ 60.1%

          \[\leadsto t - \color{blue}{\frac{a}{z} \cdot x} \]

       2. *-commutative 60.1%

          \[\leadsto t - \color{blue}{x \cdot \frac{a}{z}} \]

   12. Simplified 60.1%

       \[\leadsto t - \color{blue}{x \cdot \frac{a}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+96}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+202}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 20: 41.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -4.7 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+37}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= y -4.7e+184)
     t_1
     (if (<= y 5.8e+37) (+ t x) (if (<= y 6.5e+217) t_1 (* x (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -4.7e+184) {
		tmp = t_1;
	} else if (y <= 5.8e+37) {
		tmp = t + x;
	} else if (y <= 6.5e+217) {
		tmp = t_1;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (y <= (-4.7d+184)) then
        tmp = t_1
    else if (y <= 5.8d+37) then
        tmp = t + x
    else if (y <= 6.5d+217) then
        tmp = t_1
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -4.7e+184) {
		tmp = t_1;
	} else if (y <= 5.8e+37) {
		tmp = t + x;
	} else if (y <= 6.5e+217) {
		tmp = t_1;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if y <= -4.7e+184:
		tmp = t_1
	elif y <= 5.8e+37:
		tmp = t + x
	elif y <= 6.5e+217:
		tmp = t_1
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -4.7e+184)
		tmp = t_1;
	elseif (y <= 5.8e+37)
		tmp = Float64(t + x);
	elseif (y <= 6.5e+217)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (y <= -4.7e+184)
		tmp = t_1;
	elseif (y <= 5.8e+37)
		tmp = t + x;
	elseif (y <= 6.5e+217)
		tmp = t_1;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.7e+184], t$95$1, If[LessEqual[y, 5.8e+37], N[(t + x), $MachinePrecision], If[LessEqual[y, 6.5e+217], t$95$1, N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7000000000000003e184 or 5.79999999999999957e37 < y < 6.50000000000000005e217

   1. Initial program 73.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 73.6%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 92.8%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 92.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in t around inf 55.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 55.4%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

   6. Simplified 55.4%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Taylor expanded in y around inf 50.1%

      \[\leadsto t \cdot \color{blue}{\frac{y}{a - z}} \]

   if -4.7000000000000003e184 < y < 5.79999999999999957e37

   1. Initial program 65.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 76.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Taylor expanded in t around inf 68.0%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   5. Taylor expanded in z around inf 45.6%

      \[\leadsto x + \color{blue}{t} \]

   if 6.50000000000000005e217 < y

   1. Initial program 72.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 72.0%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 95.8%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 96.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 61.0%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 61.0%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 71.2%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 71.2%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 71.2%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 71.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 61.0%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 61.0%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 61.0%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 61.0%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 61.0%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 61.0%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 71.2%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 71.2%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in t around 0 42.7%

      \[\leadsto t - \frac{y - a}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 42.7%

         \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-1 \cdot z}{x}}} \]

      2. neg-mul-1 42.7%

         \[\leadsto t - \frac{y - a}{\frac{\color{blue}{-z}}{x}} \]

   9. Simplified 42.7%

      \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-z}{x}}} \]

   10. Taylor expanded in y around inf 37.9%

       \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
   11. Step-by-step derivation

       1. associate-*l/ 65.3%

          \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]

   12. Simplified 65.3%

       \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+184}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+37}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+217}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 21: 43.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+79}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+37}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+221}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.7e+79)
   (* (- t x) (/ y a))
   (if (<= y 2.7e+37)
     (+ t x)
     (if (<= y 5.2e+221) (* y (/ t (- a z))) (* x (/ (- y a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.7e+79) {
		tmp = (t - x) * (y / a);
	} else if (y <= 2.7e+37) {
		tmp = t + x;
	} else if (y <= 5.2e+221) {
		tmp = y * (t / (a - z));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-4.7d+79)) then
        tmp = (t - x) * (y / a)
    else if (y <= 2.7d+37) then
        tmp = t + x
    else if (y <= 5.2d+221) then
        tmp = y * (t / (a - z))
    else
        tmp = x * ((y - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.7e+79) {
		tmp = (t - x) * (y / a);
	} else if (y <= 2.7e+37) {
		tmp = t + x;
	} else if (y <= 5.2e+221) {
		tmp = y * (t / (a - z));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.7e+79:
		tmp = (t - x) * (y / a)
	elif y <= 2.7e+37:
		tmp = t + x
	elif y <= 5.2e+221:
		tmp = y * (t / (a - z))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.7e+79)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (y <= 2.7e+37)
		tmp = Float64(t + x);
	elseif (y <= 5.2e+221)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.7e+79)
		tmp = (t - x) * (y / a);
	elseif (y <= 2.7e+37)
		tmp = t + x;
	elseif (y <= 5.2e+221)
		tmp = y * (t / (a - z));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.7e+79], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+37], N[(t + x), $MachinePrecision], If[LessEqual[y, 5.2e+221], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.70000000000000023e79

   1. Initial program 62.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 62.3%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 91.8%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 91.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 91.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in y around inf 71.5%

      \[\leadsto \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 71.5%

         \[\leadsto \color{blue}{\frac{t - x}{a - z}} \cdot y \]

      2. *-commutative 71.5%

         \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Simplified 71.5%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   7. Taylor expanded in a around inf 34.8%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 50.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

      2. associate-/r/ 50.1%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(t - x\right)} \]

   9. Simplified 50.1%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(t - x\right)} \]

   if -4.70000000000000023e79 < y < 2.69999999999999986e37

   1. Initial program 66.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 75.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Taylor expanded in t around inf 68.2%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   5. Taylor expanded in z around inf 46.5%

      \[\leadsto x + \color{blue}{t} \]

   if 2.69999999999999986e37 < y < 5.20000000000000008e221

   1. Initial program 77.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 77.0%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 95.4%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 95.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in y around inf 79.6%

      \[\leadsto \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 79.6%

         \[\leadsto \color{blue}{\frac{t - x}{a - z}} \cdot y \]

      2. *-commutative 79.6%

         \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Simplified 79.6%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   7. Taylor expanded in t around inf 55.8%

      \[\leadsto y \cdot \color{blue}{\frac{t}{a - z}} \]

   if 5.20000000000000008e221 < y

   1. Initial program 72.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 72.0%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 95.8%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 96.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 61.0%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 61.0%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 71.2%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 71.2%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 71.2%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 71.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 61.0%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 61.0%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 61.0%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 61.0%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 61.0%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 61.0%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 71.2%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 71.2%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in t around 0 42.7%

      \[\leadsto t - \frac{y - a}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 42.7%

         \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-1 \cdot z}{x}}} \]

      2. neg-mul-1 42.7%

         \[\leadsto t - \frac{y - a}{\frac{\color{blue}{-z}}{x}} \]

   9. Simplified 42.7%

      \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-z}{x}}} \]

   10. Taylor expanded in t around 0 37.9%

       \[\leadsto \color{blue}{\frac{\left(y - a\right) \cdot x}{z}} \]
   11. Step-by-step derivation

       1. associate-*l/ 65.3%

          \[\leadsto \color{blue}{\frac{y - a}{z} \cdot x} \]

       2. *-commutative 65.3%

          \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]

   12. Simplified 65.3%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+79}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+37}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+221}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]

Alternative 22: 38.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+214}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.7e+184)
   (* y (/ t a))
   (if (<= y 5.2e+43)
     (+ t x)
     (if (<= y 1.9e+214) (* y (- (/ t z))) (* x (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.7e+184) {
		tmp = y * (t / a);
	} else if (y <= 5.2e+43) {
		tmp = t + x;
	} else if (y <= 1.9e+214) {
		tmp = y * -(t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-4.7d+184)) then
        tmp = y * (t / a)
    else if (y <= 5.2d+43) then
        tmp = t + x
    else if (y <= 1.9d+214) then
        tmp = y * -(t / z)
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.7e+184) {
		tmp = y * (t / a);
	} else if (y <= 5.2e+43) {
		tmp = t + x;
	} else if (y <= 1.9e+214) {
		tmp = y * -(t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.7e+184:
		tmp = y * (t / a)
	elif y <= 5.2e+43:
		tmp = t + x
	elif y <= 1.9e+214:
		tmp = y * -(t / z)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.7e+184)
		tmp = Float64(y * Float64(t / a));
	elseif (y <= 5.2e+43)
		tmp = Float64(t + x);
	elseif (y <= 1.9e+214)
		tmp = Float64(y * Float64(-Float64(t / z)));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.7e+184)
		tmp = y * (t / a);
	elseif (y <= 5.2e+43)
		tmp = t + x;
	elseif (y <= 1.9e+214)
		tmp = y * -(t / z);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.7e+184], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+43], N[(t + x), $MachinePrecision], If[LessEqual[y, 1.9e+214], N[(y * (-N[(t / z), $MachinePrecision])), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.7000000000000003e184

   1. Initial program 69.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 69.6%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 89.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 89.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in y around inf 88.4%

      \[\leadsto \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 88.4%

         \[\leadsto \color{blue}{\frac{t - x}{a - z}} \cdot y \]

      2. *-commutative 88.4%

         \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Simplified 88.4%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   7. Taylor expanded in t around inf 46.8%

      \[\leadsto y \cdot \color{blue}{\frac{t}{a - z}} \]

   8. Taylor expanded in a around inf 33.9%

      \[\leadsto y \cdot \color{blue}{\frac{t}{a}} \]

   if -4.7000000000000003e184 < y < 5.20000000000000042e43

   1. Initial program 65.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 76.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Taylor expanded in t around inf 68.0%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   5. Taylor expanded in z around inf 45.6%

      \[\leadsto x + \color{blue}{t} \]

   if 5.20000000000000042e43 < y < 1.89999999999999999e214

   1. Initial program 77.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 77.0%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 95.4%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 95.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in y around inf 79.6%

      \[\leadsto \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 79.6%

         \[\leadsto \color{blue}{\frac{t - x}{a - z}} \cdot y \]

      2. *-commutative 79.6%

         \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Simplified 79.6%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   7. Taylor expanded in t around inf 55.8%

      \[\leadsto y \cdot \color{blue}{\frac{t}{a - z}} \]

   8. Taylor expanded in a around 0 35.1%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{t}{z}\right)} \]
   9. Step-by-step derivation

      1. associate-*r/ 35.1%

         \[\leadsto y \cdot \color{blue}{\frac{-1 \cdot t}{z}} \]

      2. neg-mul-1 35.1%

         \[\leadsto y \cdot \frac{\color{blue}{-t}}{z} \]

   10. Simplified 35.1%

       \[\leadsto y \cdot \color{blue}{\frac{-t}{z}} \]

   if 1.89999999999999999e214 < y

   1. Initial program 72.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 72.0%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 95.8%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 96.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 61.0%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 61.0%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 71.2%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 71.2%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 71.2%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 71.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 61.0%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 61.0%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 61.0%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 61.0%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 61.0%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 61.0%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 71.2%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 71.2%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in t around 0 42.7%

      \[\leadsto t - \frac{y - a}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 42.7%

         \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-1 \cdot z}{x}}} \]

      2. neg-mul-1 42.7%

         \[\leadsto t - \frac{y - a}{\frac{\color{blue}{-z}}{x}} \]

   9. Simplified 42.7%

      \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-z}{x}}} \]

   10. Taylor expanded in y around inf 37.9%

       \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
   11. Step-by-step derivation

       1. associate-*l/ 65.3%

          \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]

   12. Simplified 65.3%

       \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+214}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 23: 38.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+222}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t a))))
   (if (<= y -8e+184)
     t_1
     (if (<= y 5.2e+43) (+ t x) (if (<= y 1.2e+222) t_1 (* y (/ x z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (y <= -8e+184) {
		tmp = t_1;
	} else if (y <= 5.2e+43) {
		tmp = t + x;
	} else if (y <= 1.2e+222) {
		tmp = t_1;
	} else {
		tmp = y * (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 * (t / a)
    if (y <= (-8d+184)) then
        tmp = t_1
    else if (y <= 5.2d+43) then
        tmp = t + x
    else if (y <= 1.2d+222) then
        tmp = t_1
    else
        tmp = y * (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 * (t / a);
	double tmp;
	if (y <= -8e+184) {
		tmp = t_1;
	} else if (y <= 5.2e+43) {
		tmp = t + x;
	} else if (y <= 1.2e+222) {
		tmp = t_1;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / a)
	tmp = 0
	if y <= -8e+184:
		tmp = t_1
	elif y <= 5.2e+43:
		tmp = t + x
	elif y <= 1.2e+222:
		tmp = t_1
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / a))
	tmp = 0.0
	if (y <= -8e+184)
		tmp = t_1;
	elseif (y <= 5.2e+43)
		tmp = Float64(t + x);
	elseif (y <= 1.2e+222)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / a);
	tmp = 0.0;
	if (y <= -8e+184)
		tmp = t_1;
	elseif (y <= 5.2e+43)
		tmp = t + x;
	elseif (y <= 1.2e+222)
		tmp = t_1;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+184], t$95$1, If[LessEqual[y, 5.2e+43], N[(t + x), $MachinePrecision], If[LessEqual[y, 1.2e+222], t$95$1, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.00000000000000014e184 or 5.20000000000000042e43 < y < 1.2000000000000001e222

   1. Initial program 73.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 73.6%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 92.8%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 92.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in y around inf 83.6%

      \[\leadsto \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 83.7%

         \[\leadsto \color{blue}{\frac{t - x}{a - z}} \cdot y \]

      2. *-commutative 83.7%

         \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Simplified 83.7%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   7. Taylor expanded in t around inf 51.7%

      \[\leadsto y \cdot \color{blue}{\frac{t}{a - z}} \]

   8. Taylor expanded in a around inf 33.5%

      \[\leadsto y \cdot \color{blue}{\frac{t}{a}} \]

   if -8.00000000000000014e184 < y < 5.20000000000000042e43

   1. Initial program 65.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 76.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Taylor expanded in t around inf 68.0%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   5. Taylor expanded in z around inf 45.6%

      \[\leadsto x + \color{blue}{t} \]

   if 1.2000000000000001e222 < y

   1. Initial program 72.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 72.0%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 95.8%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 96.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 61.0%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 61.0%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 71.2%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 71.2%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 71.2%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 71.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 61.0%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 61.0%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 61.0%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 61.0%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 61.0%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 61.0%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 71.2%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 71.2%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in t around 0 42.7%

      \[\leadsto t - \frac{y - a}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 42.7%

         \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-1 \cdot z}{x}}} \]

      2. neg-mul-1 42.7%

         \[\leadsto t - \frac{y - a}{\frac{\color{blue}{-z}}{x}} \]

   9. Simplified 42.7%

      \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-z}{x}}} \]

   10. Taylor expanded in t around 0 37.9%

       \[\leadsto \color{blue}{\frac{\left(y - a\right) \cdot x}{z}} \]

   11. Taylor expanded in y around inf 37.9%

       \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
   12. Step-by-step derivation

       1. associate-*r/ 50.1%

          \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   13. Simplified 50.1%

       \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+222}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 24: 39.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+186} \lor \neg \left(y \leq 4.8 \cdot 10^{+43}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.4e+186) (not (<= y 4.8e+43))) (* t (/ y a)) (+ t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.4e+186) || !(y <= 4.8e+43)) {
		tmp = t * (y / a);
	} else {
		tmp = 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 ((y <= (-2.4d+186)) .or. (.not. (y <= 4.8d+43))) then
        tmp = t * (y / a)
    else
        tmp = 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 ((y <= -2.4e+186) || !(y <= 4.8e+43)) {
		tmp = t * (y / a);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.4e+186) or not (y <= 4.8e+43):
		tmp = t * (y / a)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.4e+186) || !(y <= 4.8e+43))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.4e+186) || ~((y <= 4.8e+43)))
		tmp = t * (y / a);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.4e+186], N[Not[LessEqual[y, 4.8e+43]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999995e186 or 4.80000000000000046e43 < y

   1. Initial program 73.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 73.3%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 93.4%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      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 t around inf 50.3%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 50.3%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

   6. Simplified 50.3%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Taylor expanded in z around 0 26.8%

      \[\leadsto t \cdot \color{blue}{\frac{y}{a}} \]

   if -2.39999999999999995e186 < y < 4.80000000000000046e43

   1. Initial program 65.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 76.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Taylor expanded in t around inf 68.0%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   5. Taylor expanded in z around inf 45.6%

      \[\leadsto x + \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+186} \lor \neg \left(y \leq 4.8 \cdot 10^{+43}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 25: 39.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+184} \lor \neg \left(y \leq 4.8 \cdot 10^{+43}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -8e+184) (not (<= y 4.8e+43))) (* y (/ t a)) (+ t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8e+184) || !(y <= 4.8e+43)) {
		tmp = y * (t / a);
	} else {
		tmp = 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 ((y <= (-8d+184)) .or. (.not. (y <= 4.8d+43))) then
        tmp = y * (t / a)
    else
        tmp = 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 ((y <= -8e+184) || !(y <= 4.8e+43)) {
		tmp = y * (t / a);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -8e+184) or not (y <= 4.8e+43):
		tmp = y * (t / a)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -8e+184) || !(y <= 4.8e+43))
		tmp = Float64(y * Float64(t / a));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -8e+184) || ~((y <= 4.8e+43)))
		tmp = y * (t / a);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -8e+184], N[Not[LessEqual[y, 4.8e+43]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.00000000000000014e184 or 4.80000000000000046e43 < y

   1. Initial program 73.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 73.3%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 93.4%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      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 y around inf 85.7%

      \[\leadsto \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 85.7%

         \[\leadsto \color{blue}{\frac{t - x}{a - z}} \cdot y \]

      2. *-commutative 85.7%

         \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Simplified 85.7%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   7. Taylor expanded in t around inf 47.5%

      \[\leadsto y \cdot \color{blue}{\frac{t}{a - z}} \]

   8. Taylor expanded in a around inf 26.9%

      \[\leadsto y \cdot \color{blue}{\frac{t}{a}} \]

   if -8.00000000000000014e184 < y < 4.80000000000000046e43

   1. Initial program 65.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 76.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Taylor expanded in t around inf 68.0%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   5. Taylor expanded in z around inf 45.6%

      \[\leadsto x + \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+184} \lor \neg \left(y \leq 4.8 \cdot 10^{+43}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 26: 39.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.7e+184) (* y (/ t a)) (if (<= y 5.2e+43) (+ t x) (* x (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.7e+184) {
		tmp = y * (t / a);
	} else if (y <= 5.2e+43) {
		tmp = t + x;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-4.7d+184)) then
        tmp = y * (t / a)
    else if (y <= 5.2d+43) then
        tmp = t + x
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.7e+184) {
		tmp = y * (t / a);
	} else if (y <= 5.2e+43) {
		tmp = t + x;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.7e+184:
		tmp = y * (t / a)
	elif y <= 5.2e+43:
		tmp = t + x
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.7e+184)
		tmp = Float64(y * Float64(t / a));
	elseif (y <= 5.2e+43)
		tmp = Float64(t + x);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.7e+184)
		tmp = y * (t / a);
	elseif (y <= 5.2e+43)
		tmp = t + x;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.7e+184], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+43], N[(t + x), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7000000000000003e184

   1. Initial program 69.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 69.6%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 89.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 89.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in y around inf 88.4%

      \[\leadsto \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 88.4%

         \[\leadsto \color{blue}{\frac{t - x}{a - z}} \cdot y \]

      2. *-commutative 88.4%

         \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   6. Simplified 88.4%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   7. Taylor expanded in t around inf 46.8%

      \[\leadsto y \cdot \color{blue}{\frac{t}{a - z}} \]

   8. Taylor expanded in a around inf 33.9%

      \[\leadsto y \cdot \color{blue}{\frac{t}{a}} \]

   if -4.7000000000000003e184 < y < 5.20000000000000042e43

   1. Initial program 65.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 76.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a - z}{t - x}}} \]

   4. Taylor expanded in t around inf 68.0%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   5. Taylor expanded in z around inf 45.6%

      \[\leadsto x + \color{blue}{t} \]

   if 5.20000000000000042e43 < y

   1. Initial program 75.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 75.3%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 95.5%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 95.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 95.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 51.7%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 51.7%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 61.1%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 61.1%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 61.1%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 61.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 51.7%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 51.7%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 51.5%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 51.5%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 51.7%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 51.7%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 61.1%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 61.1%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in t around 0 31.6%

      \[\leadsto t - \frac{y - a}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 31.6%

         \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-1 \cdot z}{x}}} \]

      2. neg-mul-1 31.6%

         \[\leadsto t - \frac{y - a}{\frac{\color{blue}{-z}}{x}} \]

   9. Simplified 31.6%

      \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-z}{x}}} \]

   10. Taylor expanded in y around inf 24.3%

       \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
   11. Step-by-step derivation

       1. associate-*l/ 37.3%

          \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]

   12. Simplified 37.3%

       \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 27: 39.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+65}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.85e+65) t (if (<= z 1.52e+112) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.85e+65) {
		tmp = t;
	} else if (z <= 1.52e+112) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.85d+65)) then
        tmp = t
    else if (z <= 1.52d+112) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.85e+65) {
		tmp = t;
	} else if (z <= 1.52e+112) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.85e+65:
		tmp = t
	elif z <= 1.52e+112:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.85e+65)
		tmp = t;
	elseif (z <= 1.52e+112)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.85e+65)
		tmp = t;
	elseif (z <= 1.52e+112)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.85e+65], t, If[LessEqual[z, 1.52e+112], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999997e65 or 1.5199999999999999e112 < z

   1. Initial program 36.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 36.9%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 69.9%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 70.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 70.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 42.3%

      \[\leadsto \color{blue}{t} \]

   if -1.84999999999999997e65 < z < 1.5199999999999999e112

   1. Initial program 86.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 86.3%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      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 a around inf 35.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+65}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 28: 34.6% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ t + x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ t x))

C

double code(double x, double y, double z, double t, double a) {
	return t + x;
}

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 + x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return t + x;
}

Python

def code(x, y, z, t, a):
	return t + x

Julia

function code(x, y, z, t, a)
	return Float64(t + x)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t + x;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(t + x), $MachinePrecision]

Derivation

1. Initial program 67.6%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. associate-/l* 81.9%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

3. Simplified 81.9%

   \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a - z}{t - x}}} \]

4. Taylor expanded in t around inf 65.4%

   \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

5. Taylor expanded in z around inf 35.9%

   \[\leadsto x + \color{blue}{t} \]

6. Final simplification 35.9%

   \[\leadsto t + x \]

Alternative 29: 25.4% 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 67.6%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. +-commutative 67.6%

      \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

   2. associate-*l/ 85.6%

      \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

   3. fma-def 85.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

3. Simplified 85.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

4. Taylor expanded in z around inf 21.8%

   \[\leadsto \color{blue}{t} \]

5. Final simplification 21.8%

   \[\leadsto t \]

Developer target: 84.2% 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 2023171 
(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))))