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

Percentage Accurate: 67.4% → 88.9%

Time: 23.5s

Alternatives: 31

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.4% 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: 88.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+177}:\\ \;\;\;\;\left(t + \frac{a}{\frac{z}{t - x}} \cdot \frac{a - y}{z}\right) + t_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+243}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x t) (/ z (- y a)))))
   (if (<= z -7.2e+177)
     (+ (+ t (* (/ a (/ z (- t x))) (/ (- a y) z))) t_1)
     (if (<= z 7.4e+243) (fma (/ (- y z) (- a z)) (- t x) x) (+ t t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - t) / (z / (y - a));
	double tmp;
	if (z <= -7.2e+177) {
		tmp = (t + ((a / (z / (t - x))) * ((a - y) / z))) + t_1;
	} else if (z <= 7.4e+243) {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	} else {
		tmp = t + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - t) / Float64(z / Float64(y - a)))
	tmp = 0.0
	if (z <= -7.2e+177)
		tmp = Float64(Float64(t + Float64(Float64(a / Float64(z / Float64(t - x))) * Float64(Float64(a - y) / z))) + t_1);
	elseif (z <= 7.4e+243)
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	else
		tmp = Float64(t + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+177], N[(N[(t + N[(N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 7.4e+243], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(t + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.20000000000000005e177

   1. Initial program 21.6%

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

      1. associate-*l/ 57.9%

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

   3. Simplified 57.9%

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

   4. Taylor expanded in z around -inf 55.6%

      \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{a \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}{{z}^{2}} + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 55.6%

         \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{a \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}{{z}^{2}}\right) + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      2. mul-1-neg 55.6%

         \[\leadsto \left(t + -1 \cdot \frac{a \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}{{z}^{2}}\right) + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      3. distribute-rgt-out-- 55.5%

         \[\leadsto \left(t + -1 \cdot \frac{a \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}{{z}^{2}}\right) + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      4. unsub-neg 55.5%

         \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{a \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}{{z}^{2}}\right) - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   6. Simplified 96.4%

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

   if -7.20000000000000005e177 < z < 7.4000000000000004e243

   1. Initial program 72.6%

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

      1. +-commutative 72.6%

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

      2. associate-*l/ 87.8%

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

      3. fma-def 87.8%

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

   3. Simplified 87.8%

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

   if 7.4000000000000004e243 < z

   1. Initial program 32.2%

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

      1. associate-*l/ 55.8%

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

   3. Simplified 55.8%

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

   4. Taylor expanded in z around inf 76.1%

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

      1. associate--l+ 76.1%

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

      2. associate-*r/ 76.1%

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

      3. associate-*r/ 76.1%

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

      4. div-sub 76.1%

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

      5. distribute-lft-out-- 76.1%

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

      6. mul-1-neg 76.1%

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

      7. distribute-neg-frac 76.1%

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

      8. distribute-rgt-out-- 76.1%

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

      9. unsub-neg 76.1%

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

      10. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+177}:\\ \;\;\;\;\left(t + \frac{a}{\frac{z}{t - x}} \cdot \frac{a - y}{z}\right) + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+243}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 2: 89.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+177}:\\ \;\;\;\;\left(t + \frac{a}{\frac{z}{t - x}} \cdot \frac{a - y}{z}\right) + t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+235}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x t) (/ z (- y a)))))
   (if (<= z -8e+177)
     (+ (+ t (* (/ a (/ z (- t x))) (/ (- a y) z))) t_1)
     (if (<= z 8.5e+235) (+ x (/ (- t x) (/ (- a z) (- y z)))) (+ t t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - t) / (z / (y - a));
	double tmp;
	if (z <= -8e+177) {
		tmp = (t + ((a / (z / (t - x))) * ((a - y) / z))) + t_1;
	} else if (z <= 8.5e+235) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + 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 - t) / (z / (y - a))
    if (z <= (-8d+177)) then
        tmp = (t + ((a / (z / (t - x))) * ((a - y) / z))) + t_1
    else if (z <= 8.5d+235) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + 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 - t) / (z / (y - a));
	double tmp;
	if (z <= -8e+177) {
		tmp = (t + ((a / (z / (t - x))) * ((a - y) / z))) + t_1;
	} else if (z <= 8.5e+235) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - t) / (z / (y - a))
	tmp = 0
	if z <= -8e+177:
		tmp = (t + ((a / (z / (t - x))) * ((a - y) / z))) + t_1
	elif z <= 8.5e+235:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - t) / Float64(z / Float64(y - a)))
	tmp = 0.0
	if (z <= -8e+177)
		tmp = Float64(Float64(t + Float64(Float64(a / Float64(z / Float64(t - x))) * Float64(Float64(a - y) / z))) + t_1);
	elseif (z <= 8.5e+235)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - t) / (z / (y - a));
	tmp = 0.0;
	if (z <= -8e+177)
		tmp = (t + ((a / (z / (t - x))) * ((a - y) / z))) + t_1;
	elseif (z <= 8.5e+235)
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+177], N[(N[(t + N[(N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 8.5e+235], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.0000000000000001e177

   1. Initial program 21.6%

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

      1. associate-*l/ 57.9%

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

   3. Simplified 57.9%

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

   4. Taylor expanded in z around -inf 55.6%

      \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{a \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}{{z}^{2}} + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 55.6%

         \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{a \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}{{z}^{2}}\right) + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      2. mul-1-neg 55.6%

         \[\leadsto \left(t + -1 \cdot \frac{a \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}{{z}^{2}}\right) + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      3. distribute-rgt-out-- 55.5%

         \[\leadsto \left(t + -1 \cdot \frac{a \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}{{z}^{2}}\right) + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      4. unsub-neg 55.5%

         \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{a \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}{{z}^{2}}\right) - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   6. Simplified 96.4%

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

   if -8.0000000000000001e177 < z < 8.50000000000000017e235

   1. Initial program 72.4%

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

      1. +-commutative 72.4%

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

      2. associate-*l/ 87.6%

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

      3. fma-def 87.7%

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

   3. Simplified 87.7%

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

      1. fma-udef 87.6%

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

      2. *-commutative 87.6%

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

      3. clear-num 87.6%

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

      4. un-div-inv 87.6%

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

   5. Applied egg-rr 87.6%

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

   if 8.50000000000000017e235 < z

   1. Initial program 41.9%

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

      1. associate-*l/ 62.1%

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

   3. Simplified 62.1%

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

   4. Taylor expanded in z around inf 79.5%

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

      1. associate--l+ 79.5%

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

      2. associate-*r/ 79.5%

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

      3. associate-*r/ 79.5%

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

      4. div-sub 79.5%

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

      5. distribute-lft-out-- 79.5%

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

      6. mul-1-neg 79.5%

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

      7. distribute-neg-frac 79.5%

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

      8. distribute-rgt-out-- 79.5%

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

      9. unsub-neg 79.5%

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

      10. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+177}:\\ \;\;\;\;\left(t + \frac{a}{\frac{z}{t - x}} \cdot \frac{a - y}{z}\right) + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+235}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 3: 53.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ t_3 := y \cdot \frac{-x}{a - z}\\ \mathbf{if}\;a \leq -6800000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-155}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ z (- y z))))
        (t_2 (+ x (/ t (/ a y))))
        (t_3 (* y (/ (- x) (- a z)))))
   (if (<= a -6800000.0)
     t_2
     (if (<= a -2.4e-46)
       t_1
       (if (<= a -1.65e-155)
         t_3
         (if (<= a 5.8e-219)
           t_1
           (if (<= a 5.5e-148) t_3 (if (<= a 1.05e-41) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double t_2 = x + (t / (a / y));
	double t_3 = y * (-x / (a - z));
	double tmp;
	if (a <= -6800000.0) {
		tmp = t_2;
	} else if (a <= -2.4e-46) {
		tmp = t_1;
	} else if (a <= -1.65e-155) {
		tmp = t_3;
	} else if (a <= 5.8e-219) {
		tmp = t_1;
	} else if (a <= 5.5e-148) {
		tmp = t_3;
	} else if (a <= 1.05e-41) {
		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) :: t_3
    real(8) :: tmp
    t_1 = -t / (z / (y - z))
    t_2 = x + (t / (a / y))
    t_3 = y * (-x / (a - z))
    if (a <= (-6800000.0d0)) then
        tmp = t_2
    else if (a <= (-2.4d-46)) then
        tmp = t_1
    else if (a <= (-1.65d-155)) then
        tmp = t_3
    else if (a <= 5.8d-219) then
        tmp = t_1
    else if (a <= 5.5d-148) then
        tmp = t_3
    else if (a <= 1.05d-41) 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 = -t / (z / (y - z));
	double t_2 = x + (t / (a / y));
	double t_3 = y * (-x / (a - z));
	double tmp;
	if (a <= -6800000.0) {
		tmp = t_2;
	} else if (a <= -2.4e-46) {
		tmp = t_1;
	} else if (a <= -1.65e-155) {
		tmp = t_3;
	} else if (a <= 5.8e-219) {
		tmp = t_1;
	} else if (a <= 5.5e-148) {
		tmp = t_3;
	} else if (a <= 1.05e-41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (z / (y - z))
	t_2 = x + (t / (a / y))
	t_3 = y * (-x / (a - z))
	tmp = 0
	if a <= -6800000.0:
		tmp = t_2
	elif a <= -2.4e-46:
		tmp = t_1
	elif a <= -1.65e-155:
		tmp = t_3
	elif a <= 5.8e-219:
		tmp = t_1
	elif a <= 5.5e-148:
		tmp = t_3
	elif a <= 1.05e-41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	t_3 = Float64(y * Float64(Float64(-x) / Float64(a - z)))
	tmp = 0.0
	if (a <= -6800000.0)
		tmp = t_2;
	elseif (a <= -2.4e-46)
		tmp = t_1;
	elseif (a <= -1.65e-155)
		tmp = t_3;
	elseif (a <= 5.8e-219)
		tmp = t_1;
	elseif (a <= 5.5e-148)
		tmp = t_3;
	elseif (a <= 1.05e-41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (z / (y - z));
	t_2 = x + (t / (a / y));
	t_3 = y * (-x / (a - z));
	tmp = 0.0;
	if (a <= -6800000.0)
		tmp = t_2;
	elseif (a <= -2.4e-46)
		tmp = t_1;
	elseif (a <= -1.65e-155)
		tmp = t_3;
	elseif (a <= 5.8e-219)
		tmp = t_1;
	elseif (a <= 5.5e-148)
		tmp = t_3;
	elseif (a <= 1.05e-41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[((-x) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6800000.0], t$95$2, If[LessEqual[a, -2.4e-46], t$95$1, If[LessEqual[a, -1.65e-155], t$95$3, If[LessEqual[a, 5.8e-219], t$95$1, If[LessEqual[a, 5.5e-148], t$95$3, If[LessEqual[a, 1.05e-41], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.8e6 or 1.05000000000000006e-41 < a

   1. Initial program 64.5%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 54.6%

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

      1. associate-/l* 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in t around inf 53.0%

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

      1. associate-/l* 59.9%

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

   9. Simplified 59.9%

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

   if -6.8e6 < a < -2.40000000000000013e-46 or -1.64999999999999993e-155 < a < 5.79999999999999968e-219 or 5.5000000000000003e-148 < a < 1.05000000000000006e-41

   1. Initial program 64.5%

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

      1. +-commutative 64.5%

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

      2. associate-*l/ 75.8%

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

      3. fma-def 75.8%

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

   3. Simplified 75.8%

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

      1. fma-udef 75.8%

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

      2. *-commutative 75.8%

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

      3. clear-num 75.8%

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

      4. un-div-inv 75.8%

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

   5. Applied egg-rr 75.8%

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

   6. Taylor expanded in t around -inf 57.5%

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

      1. associate-/l* 72.9%

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

   8. Simplified 72.9%

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

   9. Taylor expanded in a around 0 52.2%

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

       1. mul-1-neg 52.2%

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

       2. associate-/l* 67.6%

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

       3. distribute-neg-frac 67.6%

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

   11. Simplified 67.6%

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

   if -2.40000000000000013e-46 < a < -1.64999999999999993e-155 or 5.79999999999999968e-219 < a < 5.5000000000000003e-148

   1. Initial program 69.7%

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

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in y around inf 67.2%

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

      1. div-sub 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in t around 0 56.2%

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

      1. associate-*r/ 56.2%

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

      2. neg-mul-1 56.2%

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

   9. Simplified 56.2%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6800000:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-155}:\\ \;\;\;\;y \cdot \frac{-x}{a - z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-219}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-148}:\\ \;\;\;\;y \cdot \frac{-x}{a - z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-41}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 4: 53.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ t_3 := \frac{-x}{\frac{a - z}{y}}\\ \mathbf{if}\;a \leq -2500000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-156}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ z (- y z))))
        (t_2 (+ x (/ t (/ a y))))
        (t_3 (/ (- x) (/ (- a z) y))))
   (if (<= a -2500000000.0)
     t_2
     (if (<= a -1.4e-45)
       t_1
       (if (<= a -2.3e-156)
         t_3
         (if (<= a 5.6e-219)
           t_1
           (if (<= a 5.5e-148) t_3 (if (<= a 9.2e-42) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double t_2 = x + (t / (a / y));
	double t_3 = -x / ((a - z) / y);
	double tmp;
	if (a <= -2500000000.0) {
		tmp = t_2;
	} else if (a <= -1.4e-45) {
		tmp = t_1;
	} else if (a <= -2.3e-156) {
		tmp = t_3;
	} else if (a <= 5.6e-219) {
		tmp = t_1;
	} else if (a <= 5.5e-148) {
		tmp = t_3;
	} else if (a <= 9.2e-42) {
		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) :: t_3
    real(8) :: tmp
    t_1 = -t / (z / (y - z))
    t_2 = x + (t / (a / y))
    t_3 = -x / ((a - z) / y)
    if (a <= (-2500000000.0d0)) then
        tmp = t_2
    else if (a <= (-1.4d-45)) then
        tmp = t_1
    else if (a <= (-2.3d-156)) then
        tmp = t_3
    else if (a <= 5.6d-219) then
        tmp = t_1
    else if (a <= 5.5d-148) then
        tmp = t_3
    else if (a <= 9.2d-42) 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 = -t / (z / (y - z));
	double t_2 = x + (t / (a / y));
	double t_3 = -x / ((a - z) / y);
	double tmp;
	if (a <= -2500000000.0) {
		tmp = t_2;
	} else if (a <= -1.4e-45) {
		tmp = t_1;
	} else if (a <= -2.3e-156) {
		tmp = t_3;
	} else if (a <= 5.6e-219) {
		tmp = t_1;
	} else if (a <= 5.5e-148) {
		tmp = t_3;
	} else if (a <= 9.2e-42) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (z / (y - z))
	t_2 = x + (t / (a / y))
	t_3 = -x / ((a - z) / y)
	tmp = 0
	if a <= -2500000000.0:
		tmp = t_2
	elif a <= -1.4e-45:
		tmp = t_1
	elif a <= -2.3e-156:
		tmp = t_3
	elif a <= 5.6e-219:
		tmp = t_1
	elif a <= 5.5e-148:
		tmp = t_3
	elif a <= 9.2e-42:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	t_3 = Float64(Float64(-x) / Float64(Float64(a - z) / y))
	tmp = 0.0
	if (a <= -2500000000.0)
		tmp = t_2;
	elseif (a <= -1.4e-45)
		tmp = t_1;
	elseif (a <= -2.3e-156)
		tmp = t_3;
	elseif (a <= 5.6e-219)
		tmp = t_1;
	elseif (a <= 5.5e-148)
		tmp = t_3;
	elseif (a <= 9.2e-42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (z / (y - z));
	t_2 = x + (t / (a / y));
	t_3 = -x / ((a - z) / y);
	tmp = 0.0;
	if (a <= -2500000000.0)
		tmp = t_2;
	elseif (a <= -1.4e-45)
		tmp = t_1;
	elseif (a <= -2.3e-156)
		tmp = t_3;
	elseif (a <= 5.6e-219)
		tmp = t_1;
	elseif (a <= 5.5e-148)
		tmp = t_3;
	elseif (a <= 9.2e-42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[((-x) / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2500000000.0], t$95$2, If[LessEqual[a, -1.4e-45], t$95$1, If[LessEqual[a, -2.3e-156], t$95$3, If[LessEqual[a, 5.6e-219], t$95$1, If[LessEqual[a, 5.5e-148], t$95$3, If[LessEqual[a, 9.2e-42], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.5e9 or 9.20000000000000015e-42 < a

   1. Initial program 64.5%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 54.6%

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

      1. associate-/l* 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in t around inf 53.0%

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

      1. associate-/l* 59.9%

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

   9. Simplified 59.9%

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

   if -2.5e9 < a < -1.4000000000000001e-45 or -2.3e-156 < a < 5.5999999999999998e-219 or 5.5000000000000003e-148 < a < 9.20000000000000015e-42

   1. Initial program 64.5%

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

      1. +-commutative 64.5%

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

      2. associate-*l/ 75.8%

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

      3. fma-def 75.8%

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

   3. Simplified 75.8%

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

      1. fma-udef 75.8%

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

      2. *-commutative 75.8%

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

      3. clear-num 75.8%

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

      4. un-div-inv 75.8%

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

   5. Applied egg-rr 75.8%

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

   6. Taylor expanded in t around -inf 57.5%

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

      1. associate-/l* 72.9%

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

   8. Simplified 72.9%

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

   9. Taylor expanded in a around 0 52.2%

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

       1. mul-1-neg 52.2%

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

       2. associate-/l* 67.6%

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

       3. distribute-neg-frac 67.6%

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

   11. Simplified 67.6%

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

   if -1.4000000000000001e-45 < a < -2.3e-156 or 5.5999999999999998e-219 < a < 5.5000000000000003e-148

   1. Initial program 69.7%

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

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in y around inf 67.2%

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

      1. div-sub 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in t around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. associate-/l* 57.7%

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

      3. distribute-neg-frac 57.7%

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

   9. Simplified 57.7%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2500000000:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-45}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-156}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-219}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 68.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -52000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-220}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a (- y z))))))
   (if (<= a -52000000.0)
     t_1
     (if (<= a 1.7e-220)
       (* t (/ (- y z) (- a z)))
       (if (<= a 1.3e-147)
         (* y (/ (- t x) (- a z)))
         (if (<= a 7.5e-49) (/ t (/ (- a z) (- y z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -52000000.0) {
		tmp = t_1;
	} else if (a <= 1.7e-220) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.3e-147) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 7.5e-49) {
		tmp = t / ((a - z) / (y - 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 + ((t - x) / (a / (y - z)))
    if (a <= (-52000000.0d0)) then
        tmp = t_1
    else if (a <= 1.7d-220) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 1.3d-147) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 7.5d-49) then
        tmp = t / ((a - z) / (y - 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 + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -52000000.0) {
		tmp = t_1;
	} else if (a <= 1.7e-220) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.3e-147) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 7.5e-49) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / (y - z)))
	tmp = 0
	if a <= -52000000.0:
		tmp = t_1
	elif a <= 1.7e-220:
		tmp = t * ((y - z) / (a - z))
	elif a <= 1.3e-147:
		tmp = y * ((t - x) / (a - z))
	elif a <= 7.5e-49:
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -52000000.0)
		tmp = t_1;
	elseif (a <= 1.7e-220)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 1.3e-147)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 7.5e-49)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / (y - z)));
	tmp = 0.0;
	if (a <= -52000000.0)
		tmp = t_1;
	elseif (a <= 1.7e-220)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 1.3e-147)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 7.5e-49)
		tmp = t / ((a - z) / (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -52000000.0], t$95$1, If[LessEqual[a, 1.7e-220], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e-147], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-49], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.2e7 or 7.4999999999999998e-49 < a

   1. Initial program 65.0%

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

      1. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in a around inf 58.8%

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

      1. associate-/l* 78.3%

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

   6. Simplified 78.3%

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

   if -5.2e7 < a < 1.69999999999999997e-220

   1. Initial program 63.6%

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

      1. associate-*l/ 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in x around 0 51.4%

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

      1. associate-*r/ 64.0%

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

   6. Simplified 64.0%

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

   if 1.69999999999999997e-220 < a < 1.2999999999999999e-147

   1. Initial program 75.2%

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

      1. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in y around inf 77.1%

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

      1. div-sub 77.1%

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

   6. Simplified 77.1%

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

   if 1.2999999999999999e-147 < a < 7.4999999999999998e-49

   1. Initial program 66.2%

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

      1. +-commutative 66.2%

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

      2. associate-*l/ 78.0%

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

      3. fma-def 78.0%

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

   3. Simplified 78.0%

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

      1. fma-udef 78.0%

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

      2. *-commutative 78.0%

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

      3. clear-num 78.0%

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

      4. un-div-inv 78.0%

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

   5. Applied egg-rr 78.0%

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

   6. Taylor expanded in t around -inf 58.4%

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

      1. associate-/l* 73.6%

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

   8. Simplified 73.6%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -52000000:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-220}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]

Alternative 6: 31.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-163}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-165}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+215}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.8e+115)
   (/ x (/ z y))
   (if (<= y -1.95e-94)
     t
     (if (<= y -4.8e-163)
       x
       (if (<= y 1.7e-165)
         t
         (if (<= y 1.9e+215) (* x (/ (- y a) z)) (/ t (/ a y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.8e+115) {
		tmp = x / (z / y);
	} else if (y <= -1.95e-94) {
		tmp = t;
	} else if (y <= -4.8e-163) {
		tmp = x;
	} else if (y <= 1.7e-165) {
		tmp = t;
	} else if (y <= 1.9e+215) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-6.8d+115)) then
        tmp = x / (z / y)
    else if (y <= (-1.95d-94)) then
        tmp = t
    else if (y <= (-4.8d-163)) then
        tmp = x
    else if (y <= 1.7d-165) then
        tmp = t
    else if (y <= 1.9d+215) then
        tmp = x * ((y - a) / z)
    else
        tmp = t / (a / y)
    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+115) {
		tmp = x / (z / y);
	} else if (y <= -1.95e-94) {
		tmp = t;
	} else if (y <= -4.8e-163) {
		tmp = x;
	} else if (y <= 1.7e-165) {
		tmp = t;
	} else if (y <= 1.9e+215) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6.8e+115:
		tmp = x / (z / y)
	elif y <= -1.95e-94:
		tmp = t
	elif y <= -4.8e-163:
		tmp = x
	elif y <= 1.7e-165:
		tmp = t
	elif y <= 1.9e+215:
		tmp = x * ((y - a) / z)
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6.8e+115)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= -1.95e-94)
		tmp = t;
	elseif (y <= -4.8e-163)
		tmp = x;
	elseif (y <= 1.7e-165)
		tmp = t;
	elseif (y <= 1.9e+215)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6.8e+115)
		tmp = x / (z / y);
	elseif (y <= -1.95e-94)
		tmp = t;
	elseif (y <= -4.8e-163)
		tmp = x;
	elseif (y <= 1.7e-165)
		tmp = t;
	elseif (y <= 1.9e+215)
		tmp = x * ((y - a) / z);
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6.8e+115], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.95e-94], t, If[LessEqual[y, -4.8e-163], x, If[LessEqual[y, 1.7e-165], t, If[LessEqual[y, 1.9e+215], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.8000000000000001e115

   1. Initial program 61.0%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around inf 44.3%

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

      1. associate--l+ 44.3%

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

      2. associate-*r/ 44.3%

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

      3. associate-*r/ 44.3%

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

      4. div-sub 44.3%

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

      5. distribute-lft-out-- 44.3%

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

      6. mul-1-neg 44.3%

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

      7. distribute-neg-frac 44.3%

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

      8. distribute-rgt-out-- 44.7%

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

      9. unsub-neg 44.7%

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

      10. associate-/l* 62.8%

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

   6. Simplified 62.8%

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

   7. Taylor expanded in t around 0 28.4%

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

      1. associate-/l* 41.9%

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

      2. associate-/r/ 41.9%

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

   9. Simplified 41.9%

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

   10. Taylor expanded in y around inf 28.5%

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

       1. associate-/l* 42.0%

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

   12. Simplified 42.0%

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

   if -6.8000000000000001e115 < y < -1.9500000000000001e-94 or -4.8000000000000001e-163 < y < 1.7e-165

   1. Initial program 60.5%

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

      1. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in z around inf 44.5%

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

   if -1.9500000000000001e-94 < y < -4.8000000000000001e-163

   1. Initial program 87.1%

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

      1. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in a around inf 80.5%

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

   if 1.7e-165 < y < 1.89999999999999984e215

   1. Initial program 69.4%

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

      1. associate-*l/ 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in z around inf 44.8%

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

      1. associate--l+ 44.8%

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

      2. associate-*r/ 44.8%

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

      3. associate-*r/ 44.8%

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

      4. div-sub 44.9%

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

      5. distribute-lft-out-- 44.9%

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

      6. mul-1-neg 44.9%

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

      7. distribute-neg-frac 44.9%

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

      8. distribute-rgt-out-- 46.4%

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

      9. unsub-neg 46.4%

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

      10. associate-/l* 56.0%

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

   6. Simplified 56.0%

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

   7. Taylor expanded in t around 0 29.4%

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

      1. associate-/l* 34.6%

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

      2. associate-/r/ 34.6%

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

   9. Simplified 34.6%

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

   10. Taylor expanded in x around 0 29.4%

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

       1. associate-*r/ 34.6%

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

   12. Simplified 34.6%

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

   if 1.89999999999999984e215 < y

   1. Initial program 67.3%

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

      1. +-commutative 67.3%

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

      2. associate-*l/ 87.6%

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

      3. fma-def 87.6%

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

   3. Simplified 87.6%

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

      1. fma-udef 87.6%

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

      2. *-commutative 87.6%

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

      3. clear-num 87.3%

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

      4. un-div-inv 87.4%

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

   5. Applied egg-rr 87.4%

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

   6. Taylor expanded in t around -inf 46.0%

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

      1. associate-/l* 58.0%

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

   8. Simplified 58.0%

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

   9. Taylor expanded in z around 0 49.7%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-163}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-165}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+215}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 36.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;z \leq -3.05 \cdot 10^{-15}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00019:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= z -3.05e-15)
     (* (- y a) (/ x z))
     (if (<= z -6.5e-173)
       t_1
       (if (<= z -2.75e-288)
         x
         (if (<= z 0.00019) t_1 (if (<= z 7e+75) x (+ t (/ a (/ z t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -3.05e-15) {
		tmp = (y - a) * (x / z);
	} else if (z <= -6.5e-173) {
		tmp = t_1;
	} else if (z <= -2.75e-288) {
		tmp = x;
	} else if (z <= 0.00019) {
		tmp = t_1;
	} else if (z <= 7e+75) {
		tmp = x;
	} else {
		tmp = t + (a / (z / 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 = y * ((t - x) / a)
    if (z <= (-3.05d-15)) then
        tmp = (y - a) * (x / z)
    else if (z <= (-6.5d-173)) then
        tmp = t_1
    else if (z <= (-2.75d-288)) then
        tmp = x
    else if (z <= 0.00019d0) then
        tmp = t_1
    else if (z <= 7d+75) then
        tmp = x
    else
        tmp = t + (a / (z / 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 = y * ((t - x) / a);
	double tmp;
	if (z <= -3.05e-15) {
		tmp = (y - a) * (x / z);
	} else if (z <= -6.5e-173) {
		tmp = t_1;
	} else if (z <= -2.75e-288) {
		tmp = x;
	} else if (z <= 0.00019) {
		tmp = t_1;
	} else if (z <= 7e+75) {
		tmp = x;
	} else {
		tmp = t + (a / (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if z <= -3.05e-15:
		tmp = (y - a) * (x / z)
	elif z <= -6.5e-173:
		tmp = t_1
	elif z <= -2.75e-288:
		tmp = x
	elif z <= 0.00019:
		tmp = t_1
	elif z <= 7e+75:
		tmp = x
	else:
		tmp = t + (a / (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (z <= -3.05e-15)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (z <= -6.5e-173)
		tmp = t_1;
	elseif (z <= -2.75e-288)
		tmp = x;
	elseif (z <= 0.00019)
		tmp = t_1;
	elseif (z <= 7e+75)
		tmp = x;
	else
		tmp = Float64(t + Float64(a / Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (z <= -3.05e-15)
		tmp = (y - a) * (x / z);
	elseif (z <= -6.5e-173)
		tmp = t_1;
	elseif (z <= -2.75e-288)
		tmp = x;
	elseif (z <= 0.00019)
		tmp = t_1;
	elseif (z <= 7e+75)
		tmp = x;
	else
		tmp = t + (a / (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.05e-15], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e-173], t$95$1, If[LessEqual[z, -2.75e-288], x, If[LessEqual[z, 0.00019], t$95$1, If[LessEqual[z, 7e+75], x, N[(t + N[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.04999999999999986e-15

   1. Initial program 42.3%

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

      1. associate-*l/ 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in z around inf 57.5%

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

      1. associate--l+ 57.5%

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

      2. associate-*r/ 57.5%

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

      3. associate-*r/ 57.5%

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

      4. div-sub 57.5%

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

      5. distribute-lft-out-- 57.5%

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

      6. mul-1-neg 57.5%

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

      7. distribute-neg-frac 57.5%

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

      8. distribute-rgt-out-- 57.6%

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

      9. unsub-neg 57.6%

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

      10. associate-/l* 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in t around 0 27.0%

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

      1. associate-/l* 37.2%

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

      2. associate-/r/ 38.4%

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

   9. Simplified 38.4%

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

   if -3.04999999999999986e-15 < z < -6.4999999999999995e-173 or -2.75e-288 < z < 1.9000000000000001e-4

   1. Initial program 84.8%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in y around inf 66.4%

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

      1. div-sub 66.4%

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

   6. Simplified 66.4%

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

   7. Taylor expanded in a around inf 52.4%

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

   if -6.4999999999999995e-173 < z < -2.75e-288 or 1.9000000000000001e-4 < z < 6.9999999999999997e75

   1. Initial program 78.0%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in a around inf 45.5%

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

   if 6.9999999999999997e75 < z

   1. Initial program 53.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 inf 65.2%

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

      1. associate--l+ 65.2%

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

      2. associate-*r/ 65.2%

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

      3. associate-*r/ 65.2%

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

      4. div-sub 65.2%

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

      5. distribute-lft-out-- 65.2%

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

      6. mul-1-neg 65.2%

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

      7. distribute-neg-frac 65.2%

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

      8. distribute-rgt-out-- 65.2%

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

      9. unsub-neg 65.2%

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

      10. associate-/l* 80.4%

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

   6. Simplified 80.4%

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

   7. Taylor expanded in y around 0 57.2%

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

      1. associate-*r/ 57.2%

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

      2. neg-mul-1 57.2%

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

   9. Simplified 57.2%

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

   10. Taylor expanded in x around 0 51.5%

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

       1. sub-neg 51.5%

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

       2. mul-1-neg 51.5%

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

       3. remove-double-neg 51.5%

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

       4. associate-/l* 53.5%

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

   12. Simplified 53.5%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{-15}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-173}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00019:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \end{array} \]

Alternative 8: 54.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{a}{\frac{z}{x}}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -33000000000000:\\ \;\;\;\;\frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+60}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ a (/ z x)))) (t_2 (+ x (/ t (/ a y)))))
   (if (<= z -4e+151)
     t_1
     (if (<= z -33000000000000.0)
       (* (/ x z) (- y a))
       (if (<= z 6.5e-89)
         t_2
         (if (<= z 2.5e+60)
           (- x (* y (/ x a)))
           (if (<= z 4.6e+76) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a / (z / x));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (z <= -4e+151) {
		tmp = t_1;
	} else if (z <= -33000000000000.0) {
		tmp = (x / z) * (y - a);
	} else if (z <= 6.5e-89) {
		tmp = t_2;
	} else if (z <= 2.5e+60) {
		tmp = x - (y * (x / a));
	} else if (z <= 4.6e+76) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = t - (a / (z / x))
    t_2 = x + (t / (a / y))
    if (z <= (-4d+151)) then
        tmp = t_1
    else if (z <= (-33000000000000.0d0)) then
        tmp = (x / z) * (y - a)
    else if (z <= 6.5d-89) then
        tmp = t_2
    else if (z <= 2.5d+60) then
        tmp = x - (y * (x / a))
    else if (z <= 4.6d+76) then
        tmp = t_2
    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 - (a / (z / x));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (z <= -4e+151) {
		tmp = t_1;
	} else if (z <= -33000000000000.0) {
		tmp = (x / z) * (y - a);
	} else if (z <= 6.5e-89) {
		tmp = t_2;
	} else if (z <= 2.5e+60) {
		tmp = x - (y * (x / a));
	} else if (z <= 4.6e+76) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a / (z / x))
	t_2 = x + (t / (a / y))
	tmp = 0
	if z <= -4e+151:
		tmp = t_1
	elif z <= -33000000000000.0:
		tmp = (x / z) * (y - a)
	elif z <= 6.5e-89:
		tmp = t_2
	elif z <= 2.5e+60:
		tmp = x - (y * (x / a))
	elif z <= 4.6e+76:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a / Float64(z / x)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (z <= -4e+151)
		tmp = t_1;
	elseif (z <= -33000000000000.0)
		tmp = Float64(Float64(x / z) * Float64(y - a));
	elseif (z <= 6.5e-89)
		tmp = t_2;
	elseif (z <= 2.5e+60)
		tmp = Float64(x - Float64(y * Float64(x / a)));
	elseif (z <= 4.6e+76)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a / (z / x));
	t_2 = x + (t / (a / y));
	tmp = 0.0;
	if (z <= -4e+151)
		tmp = t_1;
	elseif (z <= -33000000000000.0)
		tmp = (x / z) * (y - a);
	elseif (z <= 6.5e-89)
		tmp = t_2;
	elseif (z <= 2.5e+60)
		tmp = x - (y * (x / a));
	elseif (z <= 4.6e+76)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+151], t$95$1, If[LessEqual[z, -33000000000000.0], N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-89], t$95$2, If[LessEqual[z, 2.5e+60], N[(x - N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+76], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.00000000000000007e151 or 4.60000000000000002e76 < z

   1. Initial program 42.0%

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

      1. associate-*l/ 69.6%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in z around inf 65.6%

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

      1. associate--l+ 65.6%

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

      2. associate-*r/ 65.6%

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

      3. associate-*r/ 65.6%

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

      4. div-sub 65.6%

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

      5. distribute-lft-out-- 65.6%

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

      6. mul-1-neg 65.6%

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

      7. distribute-neg-frac 65.6%

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

      8. distribute-rgt-out-- 65.6%

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

      9. unsub-neg 65.6%

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

      10. associate-/l* 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in y around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. neg-mul-1 59.2%

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

   9. Simplified 59.2%

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

   10. Taylor expanded in t around 0 57.3%

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

       1. associate-/l* 59.1%

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

   12. Simplified 59.1%

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

   if -4.00000000000000007e151 < z < -3.3e13

   1. Initial program 49.4%

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

      1. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in z around inf 53.1%

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

      1. associate--l+ 53.1%

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

      2. associate-*r/ 53.1%

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

      3. associate-*r/ 53.1%

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

      4. div-sub 53.1%

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

      5. distribute-lft-out-- 53.1%

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

      6. mul-1-neg 53.1%

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

      7. distribute-neg-frac 53.1%

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

      8. distribute-rgt-out-- 53.1%

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

      9. unsub-neg 53.1%

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

      10. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in t around 0 36.8%

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

      1. associate-/l* 40.4%

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

      2. associate-/r/ 40.4%

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

   9. Simplified 40.4%

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

   if -3.3e13 < z < 6.50000000000000034e-89 or 2.49999999999999987e60 < z < 4.60000000000000002e76

   1. Initial program 86.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 67.1%

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

      1. associate-/l* 75.6%

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

   6. Simplified 75.6%

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

   7. Taylor expanded in t around inf 55.2%

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

      1. associate-/l* 62.7%

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

   9. Simplified 62.7%

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

   if 6.50000000000000034e-89 < z < 2.49999999999999987e60

   1. Initial program 68.3%

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

      1. associate-*l/ 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in z around 0 39.1%

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

      1. associate-/l* 50.3%

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

   6. Simplified 50.3%

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

   7. Taylor expanded in t around 0 39.0%

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

      1. mul-1-neg 39.0%

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

      2. associate-/l* 49.7%

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

      3. distribute-neg-frac 49.7%

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

   9. Simplified 49.7%

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

       1. add-sqr-sqrt 28.1%

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

       2. fma-def 28.1%

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

       3. distribute-frac-neg 28.1%

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

       4. add-sqr-sqrt 28.1%

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

       5. sqrt-unprod 19.4%

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

       6. sqr-neg 19.4%

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

       7. sqrt-unprod 0.0%

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

       8. add-sqr-sqrt 15.8%

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

       9. fma-neg 15.8%

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

       10. add-sqr-sqrt 34.6%

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

       11. associate-/r/ 32.1%

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

       12. add-sqr-sqrt 16.2%

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

       13. sqrt-unprod 32.7%

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

       14. sqr-neg 32.7%

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

       15. sqrt-unprod 28.0%

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

       16. add-sqr-sqrt 49.7%

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

   11. Applied egg-rr 49.7%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+151}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -33000000000000:\\ \;\;\;\;\frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+60}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+76}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \]

Alternative 9: 54.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -60000000000000:\\ \;\;\;\;\frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-92}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+47}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+73}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ a (/ z x)))))
   (if (<= z -1e+151)
     t_1
     (if (<= z -60000000000000.0)
       (* (/ x z) (- y a))
       (if (<= z 8e-92)
         (+ x (/ t (/ a y)))
         (if (<= z 9.6e+47)
           (- x (* y (/ x a)))
           (if (<= z 2.2e+73) (/ t (/ (- a z) y)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a / (z / x));
	double tmp;
	if (z <= -1e+151) {
		tmp = t_1;
	} else if (z <= -60000000000000.0) {
		tmp = (x / z) * (y - a);
	} else if (z <= 8e-92) {
		tmp = x + (t / (a / y));
	} else if (z <= 9.6e+47) {
		tmp = x - (y * (x / a));
	} else if (z <= 2.2e+73) {
		tmp = t / ((a - z) / y);
	} 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 - (a / (z / x))
    if (z <= (-1d+151)) then
        tmp = t_1
    else if (z <= (-60000000000000.0d0)) then
        tmp = (x / z) * (y - a)
    else if (z <= 8d-92) then
        tmp = x + (t / (a / y))
    else if (z <= 9.6d+47) then
        tmp = x - (y * (x / a))
    else if (z <= 2.2d+73) then
        tmp = t / ((a - z) / y)
    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 - (a / (z / x));
	double tmp;
	if (z <= -1e+151) {
		tmp = t_1;
	} else if (z <= -60000000000000.0) {
		tmp = (x / z) * (y - a);
	} else if (z <= 8e-92) {
		tmp = x + (t / (a / y));
	} else if (z <= 9.6e+47) {
		tmp = x - (y * (x / a));
	} else if (z <= 2.2e+73) {
		tmp = t / ((a - z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a / (z / x))
	tmp = 0
	if z <= -1e+151:
		tmp = t_1
	elif z <= -60000000000000.0:
		tmp = (x / z) * (y - a)
	elif z <= 8e-92:
		tmp = x + (t / (a / y))
	elif z <= 9.6e+47:
		tmp = x - (y * (x / a))
	elif z <= 2.2e+73:
		tmp = t / ((a - z) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a / Float64(z / x)))
	tmp = 0.0
	if (z <= -1e+151)
		tmp = t_1;
	elseif (z <= -60000000000000.0)
		tmp = Float64(Float64(x / z) * Float64(y - a));
	elseif (z <= 8e-92)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 9.6e+47)
		tmp = Float64(x - Float64(y * Float64(x / a)));
	elseif (z <= 2.2e+73)
		tmp = Float64(t / Float64(Float64(a - z) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a / (z / x));
	tmp = 0.0;
	if (z <= -1e+151)
		tmp = t_1;
	elseif (z <= -60000000000000.0)
		tmp = (x / z) * (y - a);
	elseif (z <= 8e-92)
		tmp = x + (t / (a / y));
	elseif (z <= 9.6e+47)
		tmp = x - (y * (x / a));
	elseif (z <= 2.2e+73)
		tmp = t / ((a - z) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+151], t$95$1, If[LessEqual[z, -60000000000000.0], N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-92], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e+47], N[(x - N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+73], N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.00000000000000002e151 or 2.2e73 < z

   1. Initial program 42.0%

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

      1. associate-*l/ 69.6%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in z around inf 65.6%

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

      1. associate--l+ 65.6%

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

      2. associate-*r/ 65.6%

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

      3. associate-*r/ 65.6%

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

      4. div-sub 65.6%

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

      5. distribute-lft-out-- 65.6%

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

      6. mul-1-neg 65.6%

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

      7. distribute-neg-frac 65.6%

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

      8. distribute-rgt-out-- 65.6%

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

      9. unsub-neg 65.6%

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

      10. associate-/l* 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in y around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. neg-mul-1 59.2%

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

   9. Simplified 59.2%

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

   10. Taylor expanded in t around 0 57.3%

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

       1. associate-/l* 59.1%

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

   12. Simplified 59.1%

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

   if -1.00000000000000002e151 < z < -6e13

   1. Initial program 49.4%

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

      1. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in z around inf 53.1%

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

      1. associate--l+ 53.1%

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

      2. associate-*r/ 53.1%

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

      3. associate-*r/ 53.1%

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

      4. div-sub 53.1%

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

      5. distribute-lft-out-- 53.1%

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

      6. mul-1-neg 53.1%

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

      7. distribute-neg-frac 53.1%

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

      8. distribute-rgt-out-- 53.1%

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

      9. unsub-neg 53.1%

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

      10. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in t around 0 36.8%

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

      1. associate-/l* 40.4%

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

      2. associate-/r/ 40.4%

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

   9. Simplified 40.4%

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

   if -6e13 < z < 7.9999999999999999e-92

   1. Initial program 86.6%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around 0 66.5%

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

      1. associate-/l* 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in t around inf 54.0%

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

      1. associate-/l* 61.9%

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

   9. Simplified 61.9%

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

   if 7.9999999999999999e-92 < z < 9.60000000000000075e47

   1. Initial program 71.3%

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

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in z around 0 42.9%

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

      1. associate-/l* 55.3%

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

   6. Simplified 55.3%

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

   7. Taylor expanded in t around 0 42.5%

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

      1. mul-1-neg 42.5%

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

      2. associate-/l* 54.3%

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

      3. distribute-neg-frac 54.3%

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

   9. Simplified 54.3%

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

       1. add-sqr-sqrt 30.9%

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

       2. fma-def 30.9%

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

       3. distribute-frac-neg 30.9%

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

       4. add-sqr-sqrt 30.9%

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

       5. sqrt-unprod 21.4%

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

       6. sqr-neg 21.4%

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

       7. sqrt-unprod 0.0%

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

       8. add-sqr-sqrt 17.4%

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

       9. fma-neg 17.4%

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

       10. add-sqr-sqrt 34.7%

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

       11. associate-/r/ 34.6%

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

       12. add-sqr-sqrt 17.2%

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

       13. sqrt-unprod 35.3%

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

       14. sqr-neg 35.3%

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

       15. sqrt-unprod 30.8%

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

       16. add-sqr-sqrt 54.3%

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

   11. Applied egg-rr 54.3%

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

   if 9.60000000000000075e47 < z < 2.2e73

   1. Initial program 65.3%

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

      1. associate-*l/ 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in y around inf 52.4%

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

      1. div-sub 52.4%

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

   6. Simplified 52.4%

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

   7. Taylor expanded in t around inf 40.4%

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

      1. associate-/l* 51.8%

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

   9. Simplified 51.8%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+151}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -60000000000000:\\ \;\;\;\;\frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-92}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+47}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+73}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \]

Alternative 10: 54.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -58000000000000:\\ \;\;\;\;\frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ a (/ z x)))))
   (if (<= z -1.8e+150)
     t_1
     (if (<= z -58000000000000.0)
       (* (/ x z) (- y a))
       (if (<= z 8.2e-88)
         (+ x (/ t (/ a y)))
         (if (<= z 3.2e+49)
           (* x (- 1.0 (/ y a)))
           (if (<= z 4.8e+72) (/ t (/ (- a z) y)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a / (z / x));
	double tmp;
	if (z <= -1.8e+150) {
		tmp = t_1;
	} else if (z <= -58000000000000.0) {
		tmp = (x / z) * (y - a);
	} else if (z <= 8.2e-88) {
		tmp = x + (t / (a / y));
	} else if (z <= 3.2e+49) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.8e+72) {
		tmp = t / ((a - z) / y);
	} 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 - (a / (z / x))
    if (z <= (-1.8d+150)) then
        tmp = t_1
    else if (z <= (-58000000000000.0d0)) then
        tmp = (x / z) * (y - a)
    else if (z <= 8.2d-88) then
        tmp = x + (t / (a / y))
    else if (z <= 3.2d+49) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 4.8d+72) then
        tmp = t / ((a - z) / y)
    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 - (a / (z / x));
	double tmp;
	if (z <= -1.8e+150) {
		tmp = t_1;
	} else if (z <= -58000000000000.0) {
		tmp = (x / z) * (y - a);
	} else if (z <= 8.2e-88) {
		tmp = x + (t / (a / y));
	} else if (z <= 3.2e+49) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.8e+72) {
		tmp = t / ((a - z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a / (z / x))
	tmp = 0
	if z <= -1.8e+150:
		tmp = t_1
	elif z <= -58000000000000.0:
		tmp = (x / z) * (y - a)
	elif z <= 8.2e-88:
		tmp = x + (t / (a / y))
	elif z <= 3.2e+49:
		tmp = x * (1.0 - (y / a))
	elif z <= 4.8e+72:
		tmp = t / ((a - z) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a / Float64(z / x)))
	tmp = 0.0
	if (z <= -1.8e+150)
		tmp = t_1;
	elseif (z <= -58000000000000.0)
		tmp = Float64(Float64(x / z) * Float64(y - a));
	elseif (z <= 8.2e-88)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 3.2e+49)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 4.8e+72)
		tmp = Float64(t / Float64(Float64(a - z) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a / (z / x));
	tmp = 0.0;
	if (z <= -1.8e+150)
		tmp = t_1;
	elseif (z <= -58000000000000.0)
		tmp = (x / z) * (y - a);
	elseif (z <= 8.2e-88)
		tmp = x + (t / (a / y));
	elseif (z <= 3.2e+49)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 4.8e+72)
		tmp = t / ((a - z) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+150], t$95$1, If[LessEqual[z, -58000000000000.0], N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-88], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+49], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+72], N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.79999999999999993e150 or 4.8000000000000002e72 < z

   1. Initial program 42.0%

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

      1. associate-*l/ 69.6%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in z around inf 65.6%

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

      1. associate--l+ 65.6%

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

      2. associate-*r/ 65.6%

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

      3. associate-*r/ 65.6%

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

      4. div-sub 65.6%

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

      5. distribute-lft-out-- 65.6%

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

      6. mul-1-neg 65.6%

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

      7. distribute-neg-frac 65.6%

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

      8. distribute-rgt-out-- 65.6%

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

      9. unsub-neg 65.6%

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

      10. associate-/l* 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in y around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. neg-mul-1 59.2%

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

   9. Simplified 59.2%

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

   10. Taylor expanded in t around 0 57.3%

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

       1. associate-/l* 59.1%

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

   12. Simplified 59.1%

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

   if -1.79999999999999993e150 < z < -5.8e13

   1. Initial program 49.4%

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

      1. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in z around inf 53.1%

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

      1. associate--l+ 53.1%

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

      2. associate-*r/ 53.1%

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

      3. associate-*r/ 53.1%

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

      4. div-sub 53.1%

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

      5. distribute-lft-out-- 53.1%

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

      6. mul-1-neg 53.1%

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

      7. distribute-neg-frac 53.1%

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

      8. distribute-rgt-out-- 53.1%

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

      9. unsub-neg 53.1%

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

      10. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in t around 0 36.8%

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

      1. associate-/l* 40.4%

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

      2. associate-/r/ 40.4%

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

   9. Simplified 40.4%

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

   if -5.8e13 < z < 8.2000000000000002e-88

   1. Initial program 86.6%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around 0 66.5%

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

      1. associate-/l* 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in t around inf 54.0%

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

      1. associate-/l* 61.9%

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

   9. Simplified 61.9%

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

   if 8.2000000000000002e-88 < z < 3.20000000000000014e49

   1. Initial program 71.3%

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

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in z around 0 42.9%

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

      1. associate-/l* 55.3%

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

   6. Simplified 55.3%

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

   7. Taylor expanded in t around 0 42.5%

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

      1. mul-1-neg 42.5%

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

      2. associate-/l* 54.3%

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

      3. distribute-neg-frac 54.3%

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

   9. Simplified 54.3%

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

   10. Taylor expanded in x around 0 54.3%

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

       1. associate-*r/ 54.3%

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

       2. neg-mul-1 54.3%

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

   12. Simplified 54.3%

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

   if 3.20000000000000014e49 < z < 4.8000000000000002e72

   1. Initial program 65.3%

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

      1. associate-*l/ 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in y around inf 52.4%

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

      1. div-sub 52.4%

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

   6. Simplified 52.4%

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

   7. Taylor expanded in t around inf 40.4%

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

      1. associate-/l* 51.8%

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

   9. Simplified 51.8%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+150}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -58000000000000:\\ \;\;\;\;\frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \]

Alternative 11: 54.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -13000000000000:\\ \;\;\;\;y \cdot \frac{-x}{a - z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ a (/ z x)))))
   (if (<= z -5.5e+123)
     t_1
     (if (<= z -13000000000000.0)
       (* y (/ (- x) (- a z)))
       (if (<= z 1.7e-88)
         (+ x (/ t (/ a y)))
         (if (<= z 1.95e+48)
           (* x (- 1.0 (/ y a)))
           (if (<= z 6.4e+72) (/ t (/ (- a z) y)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a / (z / x));
	double tmp;
	if (z <= -5.5e+123) {
		tmp = t_1;
	} else if (z <= -13000000000000.0) {
		tmp = y * (-x / (a - z));
	} else if (z <= 1.7e-88) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.95e+48) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 6.4e+72) {
		tmp = t / ((a - z) / y);
	} 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 - (a / (z / x))
    if (z <= (-5.5d+123)) then
        tmp = t_1
    else if (z <= (-13000000000000.0d0)) then
        tmp = y * (-x / (a - z))
    else if (z <= 1.7d-88) then
        tmp = x + (t / (a / y))
    else if (z <= 1.95d+48) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 6.4d+72) then
        tmp = t / ((a - z) / y)
    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 - (a / (z / x));
	double tmp;
	if (z <= -5.5e+123) {
		tmp = t_1;
	} else if (z <= -13000000000000.0) {
		tmp = y * (-x / (a - z));
	} else if (z <= 1.7e-88) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.95e+48) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 6.4e+72) {
		tmp = t / ((a - z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a / (z / x))
	tmp = 0
	if z <= -5.5e+123:
		tmp = t_1
	elif z <= -13000000000000.0:
		tmp = y * (-x / (a - z))
	elif z <= 1.7e-88:
		tmp = x + (t / (a / y))
	elif z <= 1.95e+48:
		tmp = x * (1.0 - (y / a))
	elif z <= 6.4e+72:
		tmp = t / ((a - z) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a / Float64(z / x)))
	tmp = 0.0
	if (z <= -5.5e+123)
		tmp = t_1;
	elseif (z <= -13000000000000.0)
		tmp = Float64(y * Float64(Float64(-x) / Float64(a - z)));
	elseif (z <= 1.7e-88)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 1.95e+48)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 6.4e+72)
		tmp = Float64(t / Float64(Float64(a - z) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a / (z / x));
	tmp = 0.0;
	if (z <= -5.5e+123)
		tmp = t_1;
	elseif (z <= -13000000000000.0)
		tmp = y * (-x / (a - z));
	elseif (z <= 1.7e-88)
		tmp = x + (t / (a / y));
	elseif (z <= 1.95e+48)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 6.4e+72)
		tmp = t / ((a - z) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+123], t$95$1, If[LessEqual[z, -13000000000000.0], N[(y * N[((-x) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-88], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+48], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+72], N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.5000000000000002e123 or 6.4000000000000003e72 < z

   1. Initial program 41.9%

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

      1. associate-*l/ 70.1%

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

   3. Simplified 70.1%

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

   4. Taylor expanded in z around inf 64.4%

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

      1. associate--l+ 64.4%

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

      2. associate-*r/ 64.4%

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

      3. associate-*r/ 64.4%

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

      4. div-sub 64.4%

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

      5. distribute-lft-out-- 64.4%

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

      6. mul-1-neg 64.4%

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

      7. distribute-neg-frac 64.4%

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

      8. distribute-rgt-out-- 64.4%

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

      9. unsub-neg 64.4%

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

      10. associate-/l* 81.6%

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

   6. Simplified 81.6%

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

   7. Taylor expanded in y around 0 56.5%

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

      1. associate-*r/ 56.5%

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

      2. neg-mul-1 56.5%

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

   9. Simplified 56.5%

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

   10. Taylor expanded in t around 0 54.9%

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

       1. associate-/l* 56.5%

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

   12. Simplified 56.5%

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

   if -5.5000000000000002e123 < z < -1.3e13

   1. Initial program 52.9%

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

      1. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in y around inf 58.5%

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

      1. div-sub 58.5%

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

   6. Simplified 58.5%

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

   7. Taylor expanded in t around 0 44.7%

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

      1. associate-*r/ 44.7%

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

      2. neg-mul-1 44.7%

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

   9. Simplified 44.7%

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

   if -1.3e13 < z < 1.69999999999999987e-88

   1. Initial program 86.6%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around 0 66.5%

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

      1. associate-/l* 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in t around inf 54.0%

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

      1. associate-/l* 61.9%

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

   9. Simplified 61.9%

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

   if 1.69999999999999987e-88 < z < 1.95e48

   1. Initial program 71.3%

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

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in z around 0 42.9%

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

      1. associate-/l* 55.3%

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

   6. Simplified 55.3%

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

   7. Taylor expanded in t around 0 42.5%

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

      1. mul-1-neg 42.5%

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

      2. associate-/l* 54.3%

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

      3. distribute-neg-frac 54.3%

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

   9. Simplified 54.3%

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

   10. Taylor expanded in x around 0 54.3%

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

       1. associate-*r/ 54.3%

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

       2. neg-mul-1 54.3%

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

   12. Simplified 54.3%

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

   if 1.95e48 < z < 6.4000000000000003e72

   1. Initial program 65.3%

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

      1. associate-*l/ 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in y around inf 52.4%

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

      1. div-sub 52.4%

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

   6. Simplified 52.4%

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

   7. Taylor expanded in t around inf 40.4%

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

      1. associate-/l* 51.8%

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

   9. Simplified 51.8%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+123}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -13000000000000:\\ \;\;\;\;y \cdot \frac{-x}{a - z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \]

Alternative 12: 51.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -0.076:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-102}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-41}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a y)))))
   (if (<= a -0.076)
     t_1
     (if (<= a -6.8e-102)
       (- t (/ a (/ z x)))
       (if (<= a -2.6e-122)
         t_1
         (if (<= a 4.4e-167)
           (* y (/ (- x t) z))
           (if (<= a 1.12e-41) (+ t (/ a (/ z t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double tmp;
	if (a <= -0.076) {
		tmp = t_1;
	} else if (a <= -6.8e-102) {
		tmp = t - (a / (z / x));
	} else if (a <= -2.6e-122) {
		tmp = t_1;
	} else if (a <= 4.4e-167) {
		tmp = y * ((x - t) / z);
	} else if (a <= 1.12e-41) {
		tmp = t + (a / (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t / (a / y))
    if (a <= (-0.076d0)) then
        tmp = t_1
    else if (a <= (-6.8d-102)) then
        tmp = t - (a / (z / x))
    else if (a <= (-2.6d-122)) then
        tmp = t_1
    else if (a <= 4.4d-167) then
        tmp = y * ((x - t) / z)
    else if (a <= 1.12d-41) then
        tmp = t + (a / (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double tmp;
	if (a <= -0.076) {
		tmp = t_1;
	} else if (a <= -6.8e-102) {
		tmp = t - (a / (z / x));
	} else if (a <= -2.6e-122) {
		tmp = t_1;
	} else if (a <= 4.4e-167) {
		tmp = y * ((x - t) / z);
	} else if (a <= 1.12e-41) {
		tmp = t + (a / (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / y))
	tmp = 0
	if a <= -0.076:
		tmp = t_1
	elif a <= -6.8e-102:
		tmp = t - (a / (z / x))
	elif a <= -2.6e-122:
		tmp = t_1
	elif a <= 4.4e-167:
		tmp = y * ((x - t) / z)
	elif a <= 1.12e-41:
		tmp = t + (a / (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (a <= -0.076)
		tmp = t_1;
	elseif (a <= -6.8e-102)
		tmp = Float64(t - Float64(a / Float64(z / x)));
	elseif (a <= -2.6e-122)
		tmp = t_1;
	elseif (a <= 4.4e-167)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 1.12e-41)
		tmp = Float64(t + Float64(a / Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / y));
	tmp = 0.0;
	if (a <= -0.076)
		tmp = t_1;
	elseif (a <= -6.8e-102)
		tmp = t - (a / (z / x));
	elseif (a <= -2.6e-122)
		tmp = t_1;
	elseif (a <= 4.4e-167)
		tmp = y * ((x - t) / z);
	elseif (a <= 1.12e-41)
		tmp = t + (a / (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.076], t$95$1, If[LessEqual[a, -6.8e-102], N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e-122], t$95$1, If[LessEqual[a, 4.4e-167], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.12e-41], N[(t + N[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -0.0759999999999999981 or -6.80000000000000026e-102 < a < -2.59999999999999975e-122 or 1.11999999999999999e-41 < a

   1. Initial program 65.6%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in z around 0 54.7%

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

      1. associate-/l* 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in t around inf 53.4%

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

      1. associate-/l* 60.6%

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

   9. Simplified 60.6%

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

   if -0.0759999999999999981 < a < -6.80000000000000026e-102

   1. Initial program 73.6%

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

      1. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 78.9%

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

      1. associate--l+ 78.9%

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

      2. associate-*r/ 78.9%

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

      3. associate-*r/ 78.9%

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

      4. div-sub 78.9%

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

      5. distribute-lft-out-- 78.9%

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

      6. mul-1-neg 78.9%

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

      7. distribute-neg-frac 78.9%

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

      8. distribute-rgt-out-- 78.9%

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

      9. unsub-neg 78.9%

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

      10. associate-/l* 78.8%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in y around 0 52.6%

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

      1. associate-*r/ 52.6%

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

      2. neg-mul-1 52.6%

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

   9. Simplified 52.6%

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

   10. Taylor expanded in t around 0 47.1%

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

       1. associate-/l* 47.1%

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

   12. Simplified 47.1%

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

   if -2.59999999999999975e-122 < a < 4.3999999999999999e-167

   1. Initial program 62.4%

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

      1. associate-*l/ 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in y around inf 62.2%

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

      1. div-sub 62.2%

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

   6. Simplified 62.2%

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

   7. Taylor expanded in a around 0 56.8%

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

      1. mul-1-neg 56.8%

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

      2. distribute-neg-frac 56.8%

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

   9. Simplified 56.8%

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

   if 4.3999999999999999e-167 < a < 1.11999999999999999e-41

   1. Initial program 66.7%

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

      1. associate-*l/ 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in z around inf 64.8%

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

      1. associate--l+ 64.8%

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

      2. associate-*r/ 64.8%

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

      3. associate-*r/ 64.8%

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

      4. div-sub 64.8%

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

      5. distribute-lft-out-- 64.8%

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

      6. mul-1-neg 64.8%

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

      7. distribute-neg-frac 64.8%

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

      8. distribute-rgt-out-- 64.8%

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

      9. unsub-neg 64.8%

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

      10. associate-/l* 73.8%

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

   6. Simplified 73.8%

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

   7. Taylor expanded in y around 0 53.1%

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

      1. associate-*r/ 53.1%

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

      2. neg-mul-1 53.1%

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

   9. Simplified 53.1%

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

   10. Taylor expanded in x around 0 49.9%

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

       1. sub-neg 49.9%

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

       2. mul-1-neg 49.9%

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

       3. remove-double-neg 49.9%

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

       4. associate-/l* 50.0%

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

   12. Simplified 50.0%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.076:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-102}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-122}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-41}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 13: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-148}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+230}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ t (/ a y)))))
   (if (<= a -1.25e+184)
     t_2
     (if (<= a 2e-219)
       t_1
       (if (<= a 8.4e-148)
         (/ (- x) (/ (- a z) y))
         (if (<= a 2.9e+103)
           t_1
           (if (<= a 9e+230) (- x (/ x (/ a y))) 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 = x + (t / (a / y));
	double tmp;
	if (a <= -1.25e+184) {
		tmp = t_2;
	} else if (a <= 2e-219) {
		tmp = t_1;
	} else if (a <= 8.4e-148) {
		tmp = -x / ((a - z) / y);
	} else if (a <= 2.9e+103) {
		tmp = t_1;
	} else if (a <= 9e+230) {
		tmp = x - (x / (a / y));
	} 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 = t * ((y - z) / (a - z))
    t_2 = x + (t / (a / y))
    if (a <= (-1.25d+184)) then
        tmp = t_2
    else if (a <= 2d-219) then
        tmp = t_1
    else if (a <= 8.4d-148) then
        tmp = -x / ((a - z) / y)
    else if (a <= 2.9d+103) then
        tmp = t_1
    else if (a <= 9d+230) then
        tmp = x - (x / (a / y))
    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 = x + (t / (a / y));
	double tmp;
	if (a <= -1.25e+184) {
		tmp = t_2;
	} else if (a <= 2e-219) {
		tmp = t_1;
	} else if (a <= 8.4e-148) {
		tmp = -x / ((a - z) / y);
	} else if (a <= 2.9e+103) {
		tmp = t_1;
	} else if (a <= 9e+230) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (t / (a / y))
	tmp = 0
	if a <= -1.25e+184:
		tmp = t_2
	elif a <= 2e-219:
		tmp = t_1
	elif a <= 8.4e-148:
		tmp = -x / ((a - z) / y)
	elif a <= 2.9e+103:
		tmp = t_1
	elif a <= 9e+230:
		tmp = x - (x / (a / y))
	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(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (a <= -1.25e+184)
		tmp = t_2;
	elseif (a <= 2e-219)
		tmp = t_1;
	elseif (a <= 8.4e-148)
		tmp = Float64(Float64(-x) / Float64(Float64(a - z) / y));
	elseif (a <= 2.9e+103)
		tmp = t_1;
	elseif (a <= 9e+230)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	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 = x + (t / (a / y));
	tmp = 0.0;
	if (a <= -1.25e+184)
		tmp = t_2;
	elseif (a <= 2e-219)
		tmp = t_1;
	elseif (a <= 8.4e-148)
		tmp = -x / ((a - z) / y);
	elseif (a <= 2.9e+103)
		tmp = t_1;
	elseif (a <= 9e+230)
		tmp = x - (x / (a / y));
	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[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.25e+184], t$95$2, If[LessEqual[a, 2e-219], t$95$1, If[LessEqual[a, 8.4e-148], N[((-x) / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e+103], t$95$1, If[LessEqual[a, 9e+230], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.25e184 or 8.9999999999999998e230 < a

   1. Initial program 66.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 60.8%

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

      1. associate-/l* 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in t around inf 69.5%

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

      1. associate-/l* 83.9%

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

   9. Simplified 83.9%

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

   if -1.25e184 < a < 2.0000000000000001e-219 or 8.4000000000000001e-148 < a < 2.8999999999999998e103

   1. Initial program 64.7%

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

      1. associate-*l/ 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in x around 0 47.7%

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

      1. associate-*r/ 60.9%

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

   6. Simplified 60.9%

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

   if 2.0000000000000001e-219 < a < 8.4000000000000001e-148

   1. Initial program 75.2%

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

      1. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in y around inf 77.1%

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

      1. div-sub 77.1%

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

   6. Simplified 77.1%

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

   7. Taylor expanded in t around 0 60.7%

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

      1. mul-1-neg 60.7%

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

      2. associate-/l* 66.5%

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

      3. distribute-neg-frac 66.5%

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

   9. Simplified 66.5%

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

   if 2.8999999999999998e103 < a < 8.9999999999999998e230

   1. Initial program 60.3%

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

      1. associate-*l/ 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in z around 0 56.6%

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

      1. associate-/l* 64.2%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in t around 0 56.6%

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

      1. mul-1-neg 56.6%

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

      2. associate-/l* 63.9%

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

      3. distribute-neg-frac 63.9%

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

   9. Simplified 63.9%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+184}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-148}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+230}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 14: 58.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-168}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* y (/ (- t x) (- a z)))))
   (if (<= y -3.6e+118)
     t_2
     (if (<= y -1.06e-94)
       t_1
       (if (<= y -3e-168) (- x (* y (/ x a))) (if (<= y 1e+117) t_1 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 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -3.6e+118) {
		tmp = t_2;
	} else if (y <= -1.06e-94) {
		tmp = t_1;
	} else if (y <= -3e-168) {
		tmp = x - (y * (x / a));
	} else if (y <= 1e+117) {
		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 = t * ((y - z) / (a - z))
    t_2 = y * ((t - x) / (a - z))
    if (y <= (-3.6d+118)) then
        tmp = t_2
    else if (y <= (-1.06d-94)) then
        tmp = t_1
    else if (y <= (-3d-168)) then
        tmp = x - (y * (x / a))
    else if (y <= 1d+117) 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 = t * ((y - z) / (a - z));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -3.6e+118) {
		tmp = t_2;
	} else if (y <= -1.06e-94) {
		tmp = t_1;
	} else if (y <= -3e-168) {
		tmp = x - (y * (x / a));
	} else if (y <= 1e+117) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -3.6e+118:
		tmp = t_2
	elif y <= -1.06e-94:
		tmp = t_1
	elif y <= -3e-168:
		tmp = x - (y * (x / a))
	elif y <= 1e+117:
		tmp = t_1
	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(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -3.6e+118)
		tmp = t_2;
	elseif (y <= -1.06e-94)
		tmp = t_1;
	elseif (y <= -3e-168)
		tmp = Float64(x - Float64(y * Float64(x / a)));
	elseif (y <= 1e+117)
		tmp = t_1;
	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 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -3.6e+118)
		tmp = t_2;
	elseif (y <= -1.06e-94)
		tmp = t_1;
	elseif (y <= -3e-168)
		tmp = x - (y * (x / a));
	elseif (y <= 1e+117)
		tmp = t_1;
	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[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+118], t$95$2, If[LessEqual[y, -1.06e-94], t$95$1, If[LessEqual[y, -3e-168], N[(x - N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+117], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e118 or 1.00000000000000005e117 < y

   1. Initial program 65.7%

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

      1. associate-*l/ 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around inf 86.1%

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

      1. div-sub 86.1%

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

   6. Simplified 86.1%

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

   if -3.6e118 < y < -1.06e-94 or -2.99999999999999991e-168 < y < 1.00000000000000005e117

   1. Initial program 63.0%

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

      1. associate-*l/ 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in x around 0 45.0%

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

      1. associate-*r/ 57.9%

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

   6. Simplified 57.9%

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

   if -1.06e-94 < y < -2.99999999999999991e-168

   1. Initial program 87.1%

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

      1. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in z around 0 80.8%

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

      1. associate-/l* 80.8%

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

   6. Simplified 80.8%

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

   7. Taylor expanded in t around 0 80.8%

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

      1. mul-1-neg 80.8%

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

      2. associate-/l* 80.8%

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

      3. distribute-neg-frac 80.8%

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

   9. Simplified 80.8%

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

       1. add-sqr-sqrt 39.8%

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

       2. fma-def 39.8%

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

       3. distribute-frac-neg 39.8%

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

       4. add-sqr-sqrt 39.8%

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

       5. sqrt-unprod 39.8%

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

       6. sqr-neg 39.8%

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

       7. sqrt-unprod 0.0%

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

       8. add-sqr-sqrt 39.8%

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

       9. fma-neg 39.8%

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

       10. add-sqr-sqrt 80.5%

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

       11. associate-/r/ 80.5%

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

       12. add-sqr-sqrt 40.5%

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

       13. sqrt-unprod 80.5%

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

       14. sqr-neg 80.5%

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

       15. sqrt-unprod 40.0%

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

       16. add-sqr-sqrt 80.8%

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

   11. Applied egg-rr 80.8%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-168}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 10^{+117}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternative 15: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{-129} \lor \neg \left(a \leq 5 \cdot 10^{-195}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.1e-129) (not (<= a 5e-195)))
   (+ x (* (- t x) (/ (- y z) (- a z))))
   (+ t (/ (- x t) (/ z (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.1e-129) || !(a <= 5e-195)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.1d-129)) .or. (.not. (a <= 5d-195))) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.1e-129) || !(a <= 5e-195)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.1e-129) or not (a <= 5e-195):
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.1e-129) || !(a <= 5e-195))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.1e-129) || ~((a <= 5e-195)))
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.1e-129], N[Not[LessEqual[a, 5e-195]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.0999999999999999e-129 or 5.00000000000000009e-195 < a

   1. Initial program 67.8%

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

      1. associate-*l/ 88.4%

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

   3. Simplified 88.4%

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

   if -5.0999999999999999e-129 < a < 5.00000000000000009e-195

   1. Initial program 58.7%

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

      1. associate-*l/ 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in z around inf 84.4%

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

      1. associate--l+ 84.4%

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

      2. associate-*r/ 84.4%

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

      3. associate-*r/ 84.4%

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

      4. div-sub 84.4%

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

      5. distribute-lft-out-- 84.4%

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

      6. mul-1-neg 84.4%

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

      7. distribute-neg-frac 84.4%

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

      8. distribute-rgt-out-- 84.4%

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

      9. unsub-neg 84.4%

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

      10. associate-/l* 91.2%

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

   6. Simplified 91.2%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{-129} \lor \neg \left(a \leq 5 \cdot 10^{-195}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 16: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-123} \lor \neg \left(a \leq 5 \cdot 10^{-195}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{z \cdot \frac{1}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.2e-123) (not (<= a 5e-195)))
   (+ x (* (- t x) (/ (- y z) (- a z))))
   (+ t (/ (- x t) (* z (/ 1.0 (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.2e-123) || !(a <= 5e-195)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + ((x - t) / (z * (1.0 / (y - a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.2d-123)) .or. (.not. (a <= 5d-195))) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t + ((x - t) / (z * (1.0d0 / (y - a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.2e-123) || !(a <= 5e-195)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + ((x - t) / (z * (1.0 / (y - a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.2e-123) or not (a <= 5e-195):
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + ((x - t) / (z * (1.0 / (y - a))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.2e-123) || !(a <= 5e-195))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z * Float64(1.0 / Float64(y - a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.2e-123) || ~((a <= 5e-195)))
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t + ((x - t) / (z * (1.0 / (y - a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.2e-123], N[Not[LessEqual[a, 5e-195]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z * N[(1.0 / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.19999999999999979e-123 or 5.00000000000000009e-195 < a

   1. Initial program 67.8%

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

      1. associate-*l/ 88.4%

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

   3. Simplified 88.4%

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

   if -3.19999999999999979e-123 < a < 5.00000000000000009e-195

   1. Initial program 58.7%

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

      1. associate-*l/ 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in z around inf 84.4%

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

      1. associate--l+ 84.4%

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

      2. associate-*r/ 84.4%

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

      3. associate-*r/ 84.4%

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

      4. div-sub 84.4%

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

      5. distribute-lft-out-- 84.4%

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

      6. mul-1-neg 84.4%

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

      7. distribute-neg-frac 84.4%

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

      8. distribute-rgt-out-- 84.4%

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

      9. unsub-neg 84.4%

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

      10. associate-/l* 91.2%

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

   6. Simplified 91.2%

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

      1. div-inv 91.3%

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

   8. Applied egg-rr 91.3%

      \[\leadsto t - \frac{t - x}{\color{blue}{z \cdot \frac{1}{y - a}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-123} \lor \neg \left(a \leq 5 \cdot 10^{-195}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{z \cdot \frac{1}{y - a}}\\ \end{array} \]

Alternative 17: 29.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-95}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-172}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+216}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -9.5e+114)
   (* y (/ x z))
   (if (<= y -6.6e-95)
     t
     (if (<= y -6e-172)
       x
       (if (<= y 1.45e-168)
         t
         (if (<= y 1.8e+216) (* x (/ y z)) (/ t (/ a y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9.5e+114) {
		tmp = y * (x / z);
	} else if (y <= -6.6e-95) {
		tmp = t;
	} else if (y <= -6e-172) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t;
	} else if (y <= 1.8e+216) {
		tmp = x * (y / z);
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-9.5d+114)) then
        tmp = y * (x / z)
    else if (y <= (-6.6d-95)) then
        tmp = t
    else if (y <= (-6d-172)) then
        tmp = x
    else if (y <= 1.45d-168) then
        tmp = t
    else if (y <= 1.8d+216) then
        tmp = x * (y / z)
    else
        tmp = t / (a / y)
    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 <= -9.5e+114) {
		tmp = y * (x / z);
	} else if (y <= -6.6e-95) {
		tmp = t;
	} else if (y <= -6e-172) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t;
	} else if (y <= 1.8e+216) {
		tmp = x * (y / z);
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -9.5e+114:
		tmp = y * (x / z)
	elif y <= -6.6e-95:
		tmp = t
	elif y <= -6e-172:
		tmp = x
	elif y <= 1.45e-168:
		tmp = t
	elif y <= 1.8e+216:
		tmp = x * (y / z)
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -9.5e+114)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= -6.6e-95)
		tmp = t;
	elseif (y <= -6e-172)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t;
	elseif (y <= 1.8e+216)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -9.5e+114)
		tmp = y * (x / z);
	elseif (y <= -6.6e-95)
		tmp = t;
	elseif (y <= -6e-172)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t;
	elseif (y <= 1.8e+216)
		tmp = x * (y / z);
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -9.5e+114], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.6e-95], t, If[LessEqual[y, -6e-172], x, If[LessEqual[y, 1.45e-168], t, If[LessEqual[y, 1.8e+216], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.5000000000000001e114

   1. Initial program 61.0%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around inf 44.3%

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

      1. associate--l+ 44.3%

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

      2. associate-*r/ 44.3%

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

      3. associate-*r/ 44.3%

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

      4. div-sub 44.3%

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

      5. distribute-lft-out-- 44.3%

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

      6. mul-1-neg 44.3%

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

      7. distribute-neg-frac 44.3%

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

      8. distribute-rgt-out-- 44.7%

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

      9. unsub-neg 44.7%

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

      10. associate-/l* 62.8%

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

   6. Simplified 62.8%

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

   7. Taylor expanded in t around 0 28.4%

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

      1. associate-/l* 41.9%

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

      2. associate-/r/ 41.9%

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

   9. Simplified 41.9%

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

   10. Taylor expanded in y around inf 28.5%

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

       1. associate-/l* 42.0%

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

   12. Simplified 42.0%

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

       1. associate-/r/ 42.0%

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

   14. Applied egg-rr 42.0%

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

   if -9.5000000000000001e114 < y < -6.6e-95 or -5.99999999999999967e-172 < y < 1.4499999999999999e-168

   1. Initial program 60.1%

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

      1. associate-*l/ 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in z around inf 44.9%

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

   if -6.6e-95 < y < -5.99999999999999967e-172

   1. Initial program 87.1%

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

      1. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in a around inf 80.5%

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

   if 1.4499999999999999e-168 < y < 1.8000000000000001e216

   1. Initial program 69.8%

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

      1. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in z around inf 44.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 44.2%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 44.2%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 44.2%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 44.4%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 44.4%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 44.4%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 44.4%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 45.8%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 45.8%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 55.3%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 55.3%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in t around 0 29.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 34.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. associate-/r/ 34.2%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   9. Simplified 34.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   10. Taylor expanded in y around inf 29.0%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 32.7%

          \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   12. Simplified 32.7%

       \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   13. Taylor expanded in x around 0 29.0%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   14. Step-by-step derivation

       1. associate-/l* 32.7%

          \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

       2. *-rgt-identity 32.7%

          \[\leadsto \frac{\color{blue}{x \cdot 1}}{\frac{z}{y}} \]

       3. associate-*r/ 32.7%

          \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{z}{y}}} \]

       4. associate-/r/ 32.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{z} \cdot y\right)} \]

       5. associate-*l/ 32.7%

          \[\leadsto x \cdot \color{blue}{\frac{1 \cdot y}{z}} \]

       6. *-lft-identity 32.7%

          \[\leadsto x \cdot \frac{\color{blue}{y}}{z} \]

   15. Simplified 32.7%

       \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   if 1.8000000000000001e216 < y

   1. Initial program 67.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 67.3%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 87.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 87.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 87.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right) + x} \]

      2. *-commutative 87.6%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      3. clear-num 87.3%

         \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} + x \]

      4. un-div-inv 87.4%

         \[\leadsto \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} + x \]

   5. Applied egg-rr 87.4%

      \[\leadsto \color{blue}{\frac{t - x}{\frac{a - z}{y - z}} + x} \]

   6. Taylor expanded in t around -inf 46.0%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   7. Step-by-step derivation

      1. associate-/l* 58.0%

         \[\leadsto \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

   8. Simplified 58.0%

      \[\leadsto \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

   9. Taylor expanded in z around 0 49.7%

      \[\leadsto \frac{t}{\color{blue}{\frac{a}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-95}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-172}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+216}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 18: 30.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-95}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.1 \cdot 10^{-168}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.15e+114)
   (/ x (/ z y))
   (if (<= y -5e-95)
     t
     (if (<= y -8.1e-168)
       x
       (if (<= y 1.45e-168)
         t
         (if (<= y 2e+217) (* x (/ y z)) (/ t (/ a y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.15e+114) {
		tmp = x / (z / y);
	} else if (y <= -5e-95) {
		tmp = t;
	} else if (y <= -8.1e-168) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t;
	} else if (y <= 2e+217) {
		tmp = x * (y / z);
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.15d+114)) then
        tmp = x / (z / y)
    else if (y <= (-5d-95)) then
        tmp = t
    else if (y <= (-8.1d-168)) then
        tmp = x
    else if (y <= 1.45d-168) then
        tmp = t
    else if (y <= 2d+217) then
        tmp = x * (y / z)
    else
        tmp = t / (a / y)
    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 <= -2.15e+114) {
		tmp = x / (z / y);
	} else if (y <= -5e-95) {
		tmp = t;
	} else if (y <= -8.1e-168) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t;
	} else if (y <= 2e+217) {
		tmp = x * (y / z);
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.15e+114:
		tmp = x / (z / y)
	elif y <= -5e-95:
		tmp = t
	elif y <= -8.1e-168:
		tmp = x
	elif y <= 1.45e-168:
		tmp = t
	elif y <= 2e+217:
		tmp = x * (y / z)
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.15e+114)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= -5e-95)
		tmp = t;
	elseif (y <= -8.1e-168)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t;
	elseif (y <= 2e+217)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.15e+114)
		tmp = x / (z / y);
	elseif (y <= -5e-95)
		tmp = t;
	elseif (y <= -8.1e-168)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t;
	elseif (y <= 2e+217)
		tmp = x * (y / z);
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.15e+114], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-95], t, If[LessEqual[y, -8.1e-168], x, If[LessEqual[y, 1.45e-168], t, If[LessEqual[y, 2e+217], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.15e114

   1. Initial program 61.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 44.3%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 44.3%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 44.3%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 44.3%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 44.3%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 44.3%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 44.3%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 44.3%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 44.7%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 44.7%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 62.8%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 62.8%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in t around 0 28.4%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 41.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. associate-/r/ 41.9%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   9. Simplified 41.9%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   10. Taylor expanded in y around inf 28.5%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 42.0%

          \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   12. Simplified 42.0%

       \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   if -2.15e114 < y < -4.9999999999999998e-95 or -8.1e-168 < y < 1.4499999999999999e-168

   1. Initial program 60.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 78.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 44.9%

      \[\leadsto \color{blue}{t} \]

   if -4.9999999999999998e-95 < y < -8.1e-168

   1. Initial program 87.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.1%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in a around inf 80.5%

      \[\leadsto \color{blue}{x} \]

   if 1.4499999999999999e-168 < y < 1.99999999999999992e217

   1. Initial program 69.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 82.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 44.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 44.2%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 44.2%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 44.2%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 44.4%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 44.4%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 44.4%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 44.4%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 45.8%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 45.8%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 55.3%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 55.3%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in t around 0 29.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 34.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. associate-/r/ 34.2%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   9. Simplified 34.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   10. Taylor expanded in y around inf 29.0%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 32.7%

          \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   12. Simplified 32.7%

       \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   13. Taylor expanded in x around 0 29.0%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   14. Step-by-step derivation

       1. associate-/l* 32.7%

          \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

       2. *-rgt-identity 32.7%

          \[\leadsto \frac{\color{blue}{x \cdot 1}}{\frac{z}{y}} \]

       3. associate-*r/ 32.7%

          \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{z}{y}}} \]

       4. associate-/r/ 32.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{z} \cdot y\right)} \]

       5. associate-*l/ 32.7%

          \[\leadsto x \cdot \color{blue}{\frac{1 \cdot y}{z}} \]

       6. *-lft-identity 32.7%

          \[\leadsto x \cdot \frac{\color{blue}{y}}{z} \]

   15. Simplified 32.7%

       \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   if 1.99999999999999992e217 < y

   1. Initial program 67.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 67.3%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 87.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 87.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 87.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right) + x} \]

      2. *-commutative 87.6%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      3. clear-num 87.3%

         \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} + x \]

      4. un-div-inv 87.4%

         \[\leadsto \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} + x \]

   5. Applied egg-rr 87.4%

      \[\leadsto \color{blue}{\frac{t - x}{\frac{a - z}{y - z}} + x} \]

   6. Taylor expanded in t around -inf 46.0%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   7. Step-by-step derivation

      1. associate-/l* 58.0%

         \[\leadsto \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

   8. Simplified 58.0%

      \[\leadsto \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

   9. Taylor expanded in z around 0 49.7%

      \[\leadsto \frac{t}{\color{blue}{\frac{a}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-95}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.1 \cdot 10^{-168}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 19: 36.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= z -3.2e-14)
     (* x (/ (- y a) z))
     (if (<= z -2.7e-173)
       t_1
       (if (<= z -2.9e-288) x (if (<= z 1.9e-8) t_1 (if (<= z 7e+74) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -3.2e-14) {
		tmp = x * ((y - a) / z);
	} else if (z <= -2.7e-173) {
		tmp = t_1;
	} else if (z <= -2.9e-288) {
		tmp = x;
	} else if (z <= 1.9e-8) {
		tmp = t_1;
	} else if (z <= 7e+74) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    if (z <= (-3.2d-14)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-2.7d-173)) then
        tmp = t_1
    else if (z <= (-2.9d-288)) then
        tmp = x
    else if (z <= 1.9d-8) then
        tmp = t_1
    else if (z <= 7d+74) 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 t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -3.2e-14) {
		tmp = x * ((y - a) / z);
	} else if (z <= -2.7e-173) {
		tmp = t_1;
	} else if (z <= -2.9e-288) {
		tmp = x;
	} else if (z <= 1.9e-8) {
		tmp = t_1;
	} else if (z <= 7e+74) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if z <= -3.2e-14:
		tmp = x * ((y - a) / z)
	elif z <= -2.7e-173:
		tmp = t_1
	elif z <= -2.9e-288:
		tmp = x
	elif z <= 1.9e-8:
		tmp = t_1
	elif z <= 7e+74:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (z <= -3.2e-14)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -2.7e-173)
		tmp = t_1;
	elseif (z <= -2.9e-288)
		tmp = x;
	elseif (z <= 1.9e-8)
		tmp = t_1;
	elseif (z <= 7e+74)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (z <= -3.2e-14)
		tmp = x * ((y - a) / z);
	elseif (z <= -2.7e-173)
		tmp = t_1;
	elseif (z <= -2.9e-288)
		tmp = x;
	elseif (z <= 1.9e-8)
		tmp = t_1;
	elseif (z <= 7e+74)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-14], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-173], t$95$1, If[LessEqual[z, -2.9e-288], x, If[LessEqual[z, 1.9e-8], t$95$1, If[LessEqual[z, 7e+74], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.2000000000000002e-14

   1. Initial program 42.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 72.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 72.3%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 57.5%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 57.5%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 57.5%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 57.5%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 57.5%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 57.5%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 57.5%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 57.5%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 57.6%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 57.6%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 71.5%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 71.5%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in t around 0 27.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 37.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. associate-/r/ 38.4%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   9. Simplified 38.4%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   10. Taylor expanded in x around 0 27.0%

       \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   11. Step-by-step derivation

       1. associate-*r/ 37.1%

          \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]

   12. Simplified 37.1%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]

   if -3.2000000000000002e-14 < z < -2.7e-173 or -2.90000000000000015e-288 < z < 1.90000000000000014e-8

   1. Initial program 84.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in y around inf 66.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 66.4%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   6. Simplified 66.4%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   7. Taylor expanded in a around inf 52.4%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]

   if -2.7e-173 < z < -2.90000000000000015e-288 or 1.90000000000000014e-8 < z < 7.00000000000000029e74

   1. Initial program 78.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in a around inf 45.5%

      \[\leadsto \color{blue}{x} \]

   if 7.00000000000000029e74 < z

   1. Initial program 53.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 inf 53.4%

      \[\leadsto \color{blue}{t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-173}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20: 36.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-13}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= z -1.4e-13)
     (* (- y a) (/ x z))
     (if (<= z -2.7e-173)
       t_1
       (if (<= z -3e-288) x (if (<= z 5.5e-7) t_1 (if (<= z 5.6e+73) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -1.4e-13) {
		tmp = (y - a) * (x / z);
	} else if (z <= -2.7e-173) {
		tmp = t_1;
	} else if (z <= -3e-288) {
		tmp = x;
	} else if (z <= 5.5e-7) {
		tmp = t_1;
	} else if (z <= 5.6e+73) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    if (z <= (-1.4d-13)) then
        tmp = (y - a) * (x / z)
    else if (z <= (-2.7d-173)) then
        tmp = t_1
    else if (z <= (-3d-288)) then
        tmp = x
    else if (z <= 5.5d-7) then
        tmp = t_1
    else if (z <= 5.6d+73) 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 t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -1.4e-13) {
		tmp = (y - a) * (x / z);
	} else if (z <= -2.7e-173) {
		tmp = t_1;
	} else if (z <= -3e-288) {
		tmp = x;
	} else if (z <= 5.5e-7) {
		tmp = t_1;
	} else if (z <= 5.6e+73) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if z <= -1.4e-13:
		tmp = (y - a) * (x / z)
	elif z <= -2.7e-173:
		tmp = t_1
	elif z <= -3e-288:
		tmp = x
	elif z <= 5.5e-7:
		tmp = t_1
	elif z <= 5.6e+73:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (z <= -1.4e-13)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (z <= -2.7e-173)
		tmp = t_1;
	elseif (z <= -3e-288)
		tmp = x;
	elseif (z <= 5.5e-7)
		tmp = t_1;
	elseif (z <= 5.6e+73)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (z <= -1.4e-13)
		tmp = (y - a) * (x / z);
	elseif (z <= -2.7e-173)
		tmp = t_1;
	elseif (z <= -3e-288)
		tmp = x;
	elseif (z <= 5.5e-7)
		tmp = t_1;
	elseif (z <= 5.6e+73)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e-13], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-173], t$95$1, If[LessEqual[z, -3e-288], x, If[LessEqual[z, 5.5e-7], t$95$1, If[LessEqual[z, 5.6e+73], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4000000000000001e-13

   1. Initial program 42.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 72.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 72.3%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 57.5%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 57.5%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 57.5%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 57.5%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 57.5%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 57.5%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 57.5%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 57.5%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 57.6%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 57.6%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 71.5%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 71.5%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in t around 0 27.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 37.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. associate-/r/ 38.4%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   9. Simplified 38.4%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   if -1.4000000000000001e-13 < z < -2.7e-173 or -2.99999999999999999e-288 < z < 5.5000000000000003e-7

   1. Initial program 84.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in y around inf 66.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 66.4%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   6. Simplified 66.4%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   7. Taylor expanded in a around inf 52.4%

      \[\leadsto y \cdot \color{blue}{\frac{t - x}{a}} \]

   if -2.7e-173 < z < -2.99999999999999999e-288 or 5.5000000000000003e-7 < z < 5.60000000000000016e73

   1. Initial program 78.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in a around inf 45.5%

      \[\leadsto \color{blue}{x} \]

   if 5.60000000000000016e73 < z

   1. Initial program 53.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 inf 53.4%

      \[\leadsto \color{blue}{t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-13}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-173}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21: 64.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+152}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+47}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e+152)
   (- t (/ a (/ z x)))
   (if (<= z -1.55e-100)
     (* y (/ (- t x) (- a z)))
     (if (<= z 6.5e+47) (+ x (* (- t x) (/ y a))) (* t (/ (- y z) (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+152) {
		tmp = t - (a / (z / x));
	} else if (z <= -1.55e-100) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 6.5e+47) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.95d+152)) then
        tmp = t - (a / (z / x))
    else if (z <= (-1.55d-100)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 6.5d+47) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+152) {
		tmp = t - (a / (z / x));
	} else if (z <= -1.55e-100) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 6.5e+47) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e+152:
		tmp = t - (a / (z / x))
	elif z <= -1.55e-100:
		tmp = y * ((t - x) / (a - z))
	elif z <= 6.5e+47:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e+152)
		tmp = Float64(t - Float64(a / Float64(z / x)));
	elseif (z <= -1.55e-100)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 6.5e+47)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.95e+152)
		tmp = t - (a / (z / x));
	elseif (z <= -1.55e-100)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 6.5e+47)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e+152], N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-100], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+47], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.95000000000000006e152

   1. Initial program 25.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 60.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 68.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 68.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 68.1%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 68.1%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 68.1%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 68.1%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 68.1%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 68.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 68.2%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 68.2%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 90.2%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 90.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in y around 0 63.8%

      \[\leadsto t - \frac{t - x}{\color{blue}{-1 \cdot \frac{z}{a}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 63.8%

         \[\leadsto t - \frac{t - x}{\color{blue}{\frac{-1 \cdot z}{a}}} \]

      2. neg-mul-1 63.8%

         \[\leadsto t - \frac{t - x}{\frac{\color{blue}{-z}}{a}} \]

   9. Simplified 63.8%

      \[\leadsto t - \frac{t - x}{\color{blue}{\frac{-z}{a}}} \]

   10. Taylor expanded in t around 0 61.7%

       \[\leadsto t - \color{blue}{\frac{a \cdot x}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 63.6%

          \[\leadsto t - \color{blue}{\frac{a}{\frac{z}{x}}} \]

   12. Simplified 63.6%

       \[\leadsto t - \color{blue}{\frac{a}{\frac{z}{x}}} \]

   if -1.95000000000000006e152 < z < -1.5499999999999999e-100

   1. Initial program 59.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 83.1%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in y around inf 57.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 57.4%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   6. Simplified 57.4%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -1.5499999999999999e-100 < z < 6.49999999999999988e47

   1. Initial program 86.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around 0 75.9%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]

   if 6.49999999999999988e47 < z

   1. Initial program 55.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 76.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 76.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in x around 0 49.0%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 66.9%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   6. Simplified 66.9%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+152}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+47}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 22: 63.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+152}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 7.3 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+152)
   (- t (/ a (/ z x)))
   (if (<= z -3.8e-112)
     (* y (/ (- t x) (- a z)))
     (if (<= z 7.3e+46) (+ x (/ y (/ a (- t x)))) (* t (/ (- y z) (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+152) {
		tmp = t - (a / (z / x));
	} else if (z <= -3.8e-112) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 7.3e+46) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.3d+152)) then
        tmp = t - (a / (z / x))
    else if (z <= (-3.8d-112)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 7.3d+46) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+152) {
		tmp = t - (a / (z / x));
	} else if (z <= -3.8e-112) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 7.3e+46) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+152:
		tmp = t - (a / (z / x))
	elif z <= -3.8e-112:
		tmp = y * ((t - x) / (a - z))
	elif z <= 7.3e+46:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+152)
		tmp = Float64(t - Float64(a / Float64(z / x)));
	elseif (z <= -3.8e-112)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 7.3e+46)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.3e+152)
		tmp = t - (a / (z / x));
	elseif (z <= -3.8e-112)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 7.3e+46)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+152], N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-112], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.3e+46], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.29999999999999985e152

   1. Initial program 25.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 60.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 68.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 68.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 68.1%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 68.1%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 68.1%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 68.1%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 68.1%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 68.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 68.2%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 68.2%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 90.2%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 90.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in y around 0 63.8%

      \[\leadsto t - \frac{t - x}{\color{blue}{-1 \cdot \frac{z}{a}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 63.8%

         \[\leadsto t - \frac{t - x}{\color{blue}{\frac{-1 \cdot z}{a}}} \]

      2. neg-mul-1 63.8%

         \[\leadsto t - \frac{t - x}{\frac{\color{blue}{-z}}{a}} \]

   9. Simplified 63.8%

      \[\leadsto t - \frac{t - x}{\color{blue}{\frac{-z}{a}}} \]

   10. Taylor expanded in t around 0 61.7%

       \[\leadsto t - \color{blue}{\frac{a \cdot x}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 63.6%

          \[\leadsto t - \color{blue}{\frac{a}{\frac{z}{x}}} \]

   12. Simplified 63.6%

       \[\leadsto t - \color{blue}{\frac{a}{\frac{z}{x}}} \]

   if -2.29999999999999985e152 < z < -3.79999999999999995e-112

   1. Initial program 59.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 83.1%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in y around inf 57.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 57.4%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   6. Simplified 57.4%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -3.79999999999999995e-112 < z < 7.30000000000000028e46

   1. Initial program 86.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around 0 68.0%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 75.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 75.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   if 7.30000000000000028e46 < z

   1. Initial program 55.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 76.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 76.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in x around 0 49.0%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 66.9%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   6. Simplified 66.9%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+152}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 7.3 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 23: 63.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+152}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e+152)
   (- t (/ a (/ z x)))
   (if (<= z -1.1e-115)
     (* y (/ (- t x) (- a z)))
     (if (<= z 8.8e+48) (+ x (/ y (/ a (- t x)))) (/ t (/ (- a z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+152) {
		tmp = t - (a / (z / x));
	} else if (z <= -1.1e-115) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 8.8e+48) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.2d+152)) then
        tmp = t - (a / (z / x))
    else if (z <= (-1.1d-115)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 8.8d+48) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t / ((a - z) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+152) {
		tmp = t - (a / (z / x));
	} else if (z <= -1.1e-115) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 8.8e+48) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e+152:
		tmp = t - (a / (z / x))
	elif z <= -1.1e-115:
		tmp = y * ((t - x) / (a - z))
	elif z <= 8.8e+48:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e+152)
		tmp = Float64(t - Float64(a / Float64(z / x)));
	elseif (z <= -1.1e-115)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 8.8e+48)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e+152)
		tmp = t - (a / (z / x));
	elseif (z <= -1.1e-115)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 8.8e+48)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e+152], N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-115], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+48], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1999999999999998e152

   1. Initial program 25.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 60.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 68.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 68.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 68.1%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 68.1%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 68.1%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 68.1%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 68.1%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 68.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 68.2%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 68.2%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 90.2%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 90.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in y around 0 63.8%

      \[\leadsto t - \frac{t - x}{\color{blue}{-1 \cdot \frac{z}{a}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 63.8%

         \[\leadsto t - \frac{t - x}{\color{blue}{\frac{-1 \cdot z}{a}}} \]

      2. neg-mul-1 63.8%

         \[\leadsto t - \frac{t - x}{\frac{\color{blue}{-z}}{a}} \]

   9. Simplified 63.8%

      \[\leadsto t - \frac{t - x}{\color{blue}{\frac{-z}{a}}} \]

   10. Taylor expanded in t around 0 61.7%

       \[\leadsto t - \color{blue}{\frac{a \cdot x}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 63.6%

          \[\leadsto t - \color{blue}{\frac{a}{\frac{z}{x}}} \]

   12. Simplified 63.6%

       \[\leadsto t - \color{blue}{\frac{a}{\frac{z}{x}}} \]

   if -2.1999999999999998e152 < z < -1.1e-115

   1. Initial program 59.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 83.1%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in y around inf 57.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 57.4%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   6. Simplified 57.4%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -1.1e-115 < z < 8.7999999999999997e48

   1. Initial program 86.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around 0 68.0%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 75.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 75.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   if 8.7999999999999997e48 < z

   1. Initial program 55.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 55.2%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 76.5%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 76.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 76.5%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right) + x} \]

      2. *-commutative 76.5%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      3. clear-num 76.4%

         \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} + x \]

      4. un-div-inv 76.5%

         \[\leadsto \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} + x \]

   5. Applied egg-rr 76.5%

      \[\leadsto \color{blue}{\frac{t - x}{\frac{a - z}{y - z}} + x} \]

   6. Taylor expanded in t around -inf 49.0%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   7. Step-by-step derivation

      1. associate-/l* 66.9%

         \[\leadsto \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

   8. Simplified 66.9%

      \[\leadsto \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+152}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 24: 63.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+152}:\\ \;\;\;\;t + \frac{x - t}{\frac{-z}{a}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-104}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.4e+152)
   (+ t (/ (- x t) (/ (- z) a)))
   (if (<= z -4.8e-104)
     (* y (/ (- t x) (- a z)))
     (if (<= z 1.75e+47)
       (+ x (/ y (/ a (- t x))))
       (/ t (/ (- a z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+152) {
		tmp = t + ((x - t) / (-z / a));
	} else if (z <= -4.8e-104) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.75e+47) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.4d+152)) then
        tmp = t + ((x - t) / (-z / a))
    else if (z <= (-4.8d-104)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.75d+47) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t / ((a - z) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+152) {
		tmp = t + ((x - t) / (-z / a));
	} else if (z <= -4.8e-104) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.75e+47) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.4e+152:
		tmp = t + ((x - t) / (-z / a))
	elif z <= -4.8e-104:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.75e+47:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.4e+152)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(Float64(-z) / a)));
	elseif (z <= -4.8e-104)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.75e+47)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.4e+152)
		tmp = t + ((x - t) / (-z / a));
	elseif (z <= -4.8e-104)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.75e+47)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.4e+152], N[(t + N[(N[(x - t), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-104], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+47], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4000000000000001e152

   1. Initial program 25.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 60.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 68.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 68.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 68.1%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 68.1%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 68.1%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 68.1%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 68.1%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 68.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 68.2%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 68.2%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 90.2%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 90.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in y around 0 63.8%

      \[\leadsto t - \frac{t - x}{\color{blue}{-1 \cdot \frac{z}{a}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 63.8%

         \[\leadsto t - \frac{t - x}{\color{blue}{\frac{-1 \cdot z}{a}}} \]

      2. neg-mul-1 63.8%

         \[\leadsto t - \frac{t - x}{\frac{\color{blue}{-z}}{a}} \]

   9. Simplified 63.8%

      \[\leadsto t - \frac{t - x}{\color{blue}{\frac{-z}{a}}} \]

   if -1.4000000000000001e152 < z < -4.8000000000000001e-104

   1. Initial program 59.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 83.1%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in y around inf 57.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 57.4%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   6. Simplified 57.4%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -4.8000000000000001e-104 < z < 1.75000000000000008e47

   1. Initial program 86.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around 0 68.0%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 75.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 75.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   if 1.75000000000000008e47 < z

   1. Initial program 55.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 55.2%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 76.5%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 76.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 76.5%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right) + x} \]

      2. *-commutative 76.5%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      3. clear-num 76.4%

         \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} + x \]

      4. un-div-inv 76.5%

         \[\leadsto \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} + x \]

   5. Applied egg-rr 76.5%

      \[\leadsto \color{blue}{\frac{t - x}{\frac{a - z}{y - z}} + x} \]

   6. Taylor expanded in t around -inf 49.0%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   7. Step-by-step derivation

      1. associate-/l* 66.9%

         \[\leadsto \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

   8. Simplified 66.9%

      \[\leadsto \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+152}:\\ \;\;\;\;t + \frac{x - t}{\frac{-z}{a}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-104}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 25: 77.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+32} \lor \neg \left(a \leq 8.2 \cdot 10^{-44}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.15e+32) (not (<= a 8.2e-44)))
   (+ x (/ (- t x) (/ a (- y z))))
   (+ t (/ (- x t) (/ z (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.15e+32) || !(a <= 8.2e-44)) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.15d+32)) .or. (.not. (a <= 8.2d-44))) then
        tmp = x + ((t - x) / (a / (y - z)))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.15e+32) || !(a <= 8.2e-44)) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.15e+32) or not (a <= 8.2e-44):
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.15e+32) || !(a <= 8.2e-44))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.15e+32) || ~((a <= 8.2e-44)))
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.15e+32], N[Not[LessEqual[a, 8.2e-44]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.15e32 or 8.19999999999999984e-44 < a

   1. Initial program 64.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in a around inf 59.1%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 79.1%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a}{y - z}}} \]

   6. Simplified 79.1%

      \[\leadsto \color{blue}{x + \frac{t - x}{\frac{a}{y - z}}} \]

   if -1.15e32 < a < 8.19999999999999984e-44

   1. Initial program 65.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 74.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 74.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 74.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 74.0%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 74.0%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 74.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 74.0%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 74.0%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 74.0%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 74.0%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 74.0%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 74.0%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 81.0%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 81.0%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+32} \lor \neg \left(a \leq 8.2 \cdot 10^{-44}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 26: 30.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-95}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= y -6.6e+122)
     t_1
     (if (<= y -5.8e-95)
       t
       (if (<= y -5.8e-170) x (if (<= y 1.45e-168) t t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (y <= -6.6e+122) {
		tmp = t_1;
	} else if (y <= -5.8e-95) {
		tmp = t;
	} else if (y <= -5.8e-170) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (y <= (-6.6d+122)) then
        tmp = t_1
    else if (y <= (-5.8d-95)) then
        tmp = t
    else if (y <= (-5.8d-170)) then
        tmp = x
    else if (y <= 1.45d-168) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (y <= -6.6e+122) {
		tmp = t_1;
	} else if (y <= -5.8e-95) {
		tmp = t;
	} else if (y <= -5.8e-170) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if y <= -6.6e+122:
		tmp = t_1
	elif y <= -5.8e-95:
		tmp = t
	elif y <= -5.8e-170:
		tmp = x
	elif y <= 1.45e-168:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (y <= -6.6e+122)
		tmp = t_1;
	elseif (y <= -5.8e-95)
		tmp = t;
	elseif (y <= -5.8e-170)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (y <= -6.6e+122)
		tmp = t_1;
	elseif (y <= -5.8e-95)
		tmp = t;
	elseif (y <= -5.8e-170)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.6e+122], t$95$1, If[LessEqual[y, -5.8e-95], t, If[LessEqual[y, -5.8e-170], x, If[LessEqual[y, 1.45e-168], t, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5999999999999998e122 or 1.4499999999999999e-168 < y

   1. Initial program 66.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 86.1%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 42.9%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 42.9%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 42.9%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 42.9%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 43.0%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 43.0%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 43.0%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 43.0%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 44.6%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 44.6%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 55.3%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 55.3%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in t around 0 28.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 36.1%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. associate-/r/ 35.6%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   9. Simplified 35.6%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   10. Taylor expanded in y around inf 28.1%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 35.2%

          \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   12. Simplified 35.2%

       \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   13. Taylor expanded in x around 0 28.1%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   14. Step-by-step derivation

       1. associate-/l* 35.2%

          \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

       2. *-rgt-identity 35.2%

          \[\leadsto \frac{\color{blue}{x \cdot 1}}{\frac{z}{y}} \]

       3. associate-*r/ 35.2%

          \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{z}{y}}} \]

       4. associate-/r/ 35.2%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{z} \cdot y\right)} \]

       5. associate-*l/ 35.2%

          \[\leadsto x \cdot \color{blue}{\frac{1 \cdot y}{z}} \]

       6. *-lft-identity 35.2%

          \[\leadsto x \cdot \frac{\color{blue}{y}}{z} \]

   15. Simplified 35.2%

       \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   if -6.5999999999999998e122 < y < -5.80000000000000004e-95 or -5.8000000000000001e-170 < y < 1.4499999999999999e-168

   1. Initial program 60.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 78.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 44.1%

      \[\leadsto \color{blue}{t} \]

   if -5.80000000000000004e-95 < y < -5.8000000000000001e-170

   1. Initial program 87.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.1%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in a around inf 80.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-95}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 27: 30.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-95}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-172}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.2e+114)
   (* y (/ x z))
   (if (<= y -5.1e-95)
     t
     (if (<= y -1.06e-172) x (if (<= y 1.45e-168) t (* x (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.2e+114) {
		tmp = y * (x / z);
	} else if (y <= -5.1e-95) {
		tmp = t;
	} else if (y <= -1.06e-172) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.2d+114)) then
        tmp = y * (x / z)
    else if (y <= (-5.1d-95)) then
        tmp = t
    else if (y <= (-1.06d-172)) then
        tmp = x
    else if (y <= 1.45d-168) then
        tmp = t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.2e+114) {
		tmp = y * (x / z);
	} else if (y <= -5.1e-95) {
		tmp = t;
	} else if (y <= -1.06e-172) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.2e+114:
		tmp = y * (x / z)
	elif y <= -5.1e-95:
		tmp = t
	elif y <= -1.06e-172:
		tmp = x
	elif y <= 1.45e-168:
		tmp = t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.2e+114)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= -5.1e-95)
		tmp = t;
	elseif (y <= -1.06e-172)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t;
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.2e+114)
		tmp = y * (x / z);
	elseif (y <= -5.1e-95)
		tmp = t;
	elseif (y <= -1.06e-172)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.2e+114], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.1e-95], t, If[LessEqual[y, -1.06e-172], x, If[LessEqual[y, 1.45e-168], t, N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.2e114

   1. Initial program 61.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 44.3%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 44.3%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 44.3%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 44.3%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 44.3%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 44.3%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 44.3%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 44.3%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 44.7%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 44.7%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 62.8%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 62.8%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in t around 0 28.4%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 41.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. associate-/r/ 41.9%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   9. Simplified 41.9%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   10. Taylor expanded in y around inf 28.5%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 42.0%

          \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   12. Simplified 42.0%

       \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]
   13. Step-by-step derivation

       1. associate-/r/ 42.0%

          \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]

   14. Applied egg-rr 42.0%

       \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]

   if -3.2e114 < y < -5.1e-95 or -1.05999999999999993e-172 < y < 1.4499999999999999e-168

   1. Initial program 60.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 78.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 44.9%

      \[\leadsto \color{blue}{t} \]

   if -5.1e-95 < y < -1.05999999999999993e-172

   1. Initial program 87.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.1%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in a around inf 80.5%

      \[\leadsto \color{blue}{x} \]

   if 1.4499999999999999e-168 < y

   1. Initial program 69.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 83.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 41.5%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 41.5%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 41.5%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 41.5%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 41.6%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 41.6%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 41.6%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 41.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 43.7%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 43.7%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 51.0%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 51.0%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in t around 0 27.5%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 32.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. associate-/r/ 32.3%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   9. Simplified 32.3%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   10. Taylor expanded in y around inf 27.4%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 31.7%

          \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   12. Simplified 31.7%

       \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   13. Taylor expanded in x around 0 27.4%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   14. Step-by-step derivation

       1. associate-/l* 31.7%

          \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

       2. *-rgt-identity 31.7%

          \[\leadsto \frac{\color{blue}{x \cdot 1}}{\frac{z}{y}} \]

       3. associate-*r/ 31.7%

          \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{z}{y}}} \]

       4. associate-/r/ 31.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{z} \cdot y\right)} \]

       5. associate-*l/ 31.7%

          \[\leadsto x \cdot \color{blue}{\frac{1 \cdot y}{z}} \]

       6. *-lft-identity 31.7%

          \[\leadsto x \cdot \frac{\color{blue}{y}}{z} \]

   15. Simplified 31.7%

       \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-95}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-172}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 28: 54.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -52000000000000:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ a (/ z x)))))
   (if (<= z -6.4e+150)
     t_1
     (if (<= z -52000000000000.0)
       (* (- y a) (/ x z))
       (if (<= z 7.2e+72) (+ x (/ t (/ a y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a / (z / x));
	double tmp;
	if (z <= -6.4e+150) {
		tmp = t_1;
	} else if (z <= -52000000000000.0) {
		tmp = (y - a) * (x / z);
	} else if (z <= 7.2e+72) {
		tmp = x + (t / (a / y));
	} 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 - (a / (z / x))
    if (z <= (-6.4d+150)) then
        tmp = t_1
    else if (z <= (-52000000000000.0d0)) then
        tmp = (y - a) * (x / z)
    else if (z <= 7.2d+72) then
        tmp = x + (t / (a / y))
    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 - (a / (z / x));
	double tmp;
	if (z <= -6.4e+150) {
		tmp = t_1;
	} else if (z <= -52000000000000.0) {
		tmp = (y - a) * (x / z);
	} else if (z <= 7.2e+72) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a / (z / x))
	tmp = 0
	if z <= -6.4e+150:
		tmp = t_1
	elif z <= -52000000000000.0:
		tmp = (y - a) * (x / z)
	elif z <= 7.2e+72:
		tmp = x + (t / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a / Float64(z / x)))
	tmp = 0.0
	if (z <= -6.4e+150)
		tmp = t_1;
	elseif (z <= -52000000000000.0)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (z <= 7.2e+72)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a / (z / x));
	tmp = 0.0;
	if (z <= -6.4e+150)
		tmp = t_1;
	elseif (z <= -52000000000000.0)
		tmp = (y - a) * (x / z);
	elseif (z <= 7.2e+72)
		tmp = x + (t / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.4e+150], t$95$1, If[LessEqual[z, -52000000000000.0], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+72], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.40000000000000031e150 or 7.20000000000000069e72 < z

   1. Initial program 42.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 69.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 69.6%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 65.6%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 65.6%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 65.6%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 65.6%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 65.6%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 65.6%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 65.6%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 65.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 65.6%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 65.6%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 83.3%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 83.3%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in y around 0 59.2%

      \[\leadsto t - \frac{t - x}{\color{blue}{-1 \cdot \frac{z}{a}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 59.2%

         \[\leadsto t - \frac{t - x}{\color{blue}{\frac{-1 \cdot z}{a}}} \]

      2. neg-mul-1 59.2%

         \[\leadsto t - \frac{t - x}{\frac{\color{blue}{-z}}{a}} \]

   9. Simplified 59.2%

      \[\leadsto t - \frac{t - x}{\color{blue}{\frac{-z}{a}}} \]

   10. Taylor expanded in t around 0 57.3%

       \[\leadsto t - \color{blue}{\frac{a \cdot x}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 59.1%

          \[\leadsto t - \color{blue}{\frac{a}{\frac{z}{x}}} \]

   12. Simplified 59.1%

       \[\leadsto t - \color{blue}{\frac{a}{\frac{z}{x}}} \]

   if -6.40000000000000031e150 < z < -5.2e13

   1. Initial program 49.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 78.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 53.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 53.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 53.1%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 53.1%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 53.1%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 53.1%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 53.1%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 53.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 53.1%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 53.1%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 63.0%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 63.0%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in t around 0 36.8%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 40.4%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. associate-/r/ 40.4%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   9. Simplified 40.4%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   if -5.2e13 < z < 7.20000000000000069e72

   1. Initial program 82.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around 0 60.6%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 69.8%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 69.8%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   7. Taylor expanded in t around inf 50.7%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 56.4%

         \[\leadsto x + \color{blue}{\frac{t}{\frac{a}{y}}} \]

   9. Simplified 56.4%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{a}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+150}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -52000000000000:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \]

Alternative 29: 48.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -34000000000000:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -34000000000000.0)
   (* (- y a) (/ x z))
   (if (<= z 3.2e+73) (+ x (/ t (/ a y))) (+ t (/ a (/ z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -34000000000000.0) {
		tmp = (y - a) * (x / z);
	} else if (z <= 3.2e+73) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t + (a / (z / 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 <= (-34000000000000.0d0)) then
        tmp = (y - a) * (x / z)
    else if (z <= 3.2d+73) then
        tmp = x + (t / (a / y))
    else
        tmp = t + (a / (z / 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 <= -34000000000000.0) {
		tmp = (y - a) * (x / z);
	} else if (z <= 3.2e+73) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t + (a / (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -34000000000000.0:
		tmp = (y - a) * (x / z)
	elif z <= 3.2e+73:
		tmp = x + (t / (a / y))
	else:
		tmp = t + (a / (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -34000000000000.0)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (z <= 3.2e+73)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(t + Float64(a / Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -34000000000000.0)
		tmp = (y - a) * (x / z);
	elseif (z <= 3.2e+73)
		tmp = x + (t / (a / y));
	else
		tmp = t + (a / (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -34000000000000.0], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+73], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4e13

   1. Initial program 36.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 69.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 69.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 60.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 60.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 60.1%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 60.1%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 60.1%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 60.1%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 60.1%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 60.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 60.2%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 60.2%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 76.2%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 76.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in t around 0 29.3%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 41.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. associate-/r/ 42.4%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   9. Simplified 42.4%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]

   if -3.4e13 < z < 3.19999999999999982e73

   1. Initial program 82.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around 0 60.6%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 69.8%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 69.8%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   7. Taylor expanded in t around inf 50.7%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 56.4%

         \[\leadsto x + \color{blue}{\frac{t}{\frac{a}{y}}} \]

   9. Simplified 56.4%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{a}{y}}} \]

   if 3.19999999999999982e73 < z

   1. Initial program 53.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 inf 65.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. Step-by-step derivation

      1. associate--l+ 65.2%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 65.2%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 65.2%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 65.2%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 65.2%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. mul-1-neg 65.2%

         \[\leadsto t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-neg-frac 65.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 65.2%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 65.2%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 80.4%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Simplified 80.4%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   7. Taylor expanded in y around 0 57.2%

      \[\leadsto t - \frac{t - x}{\color{blue}{-1 \cdot \frac{z}{a}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 57.2%

         \[\leadsto t - \frac{t - x}{\color{blue}{\frac{-1 \cdot z}{a}}} \]

      2. neg-mul-1 57.2%

         \[\leadsto t - \frac{t - x}{\frac{\color{blue}{-z}}{a}} \]

   9. Simplified 57.2%

      \[\leadsto t - \frac{t - x}{\color{blue}{\frac{-z}{a}}} \]

   10. Taylor expanded in x around 0 51.5%

       \[\leadsto \color{blue}{t - -1 \cdot \frac{a \cdot t}{z}} \]
   11. Step-by-step derivation

       1. sub-neg 51.5%

          \[\leadsto \color{blue}{t + \left(--1 \cdot \frac{a \cdot t}{z}\right)} \]

       2. mul-1-neg 51.5%

          \[\leadsto t + \left(-\color{blue}{\left(-\frac{a \cdot t}{z}\right)}\right) \]

       3. remove-double-neg 51.5%

          \[\leadsto t + \color{blue}{\frac{a \cdot t}{z}} \]

       4. associate-/l* 53.5%

          \[\leadsto t + \color{blue}{\frac{a}{\frac{z}{t}}} \]

   12. Simplified 53.5%

       \[\leadsto \color{blue}{t + \frac{a}{\frac{z}{t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -34000000000000:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \end{array} \]

Alternative 30: 37.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1e+184)
   x
   (if (<= a -4.8e+95) t (if (<= a -7.8e+37) x (if (<= a 1.2e-41) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+184) {
		tmp = x;
	} else if (a <= -4.8e+95) {
		tmp = t;
	} else if (a <= -7.8e+37) {
		tmp = x;
	} else if (a <= 1.2e-41) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1d+184)) then
        tmp = x
    else if (a <= (-4.8d+95)) then
        tmp = t
    else if (a <= (-7.8d+37)) then
        tmp = x
    else if (a <= 1.2d-41) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+184) {
		tmp = x;
	} else if (a <= -4.8e+95) {
		tmp = t;
	} else if (a <= -7.8e+37) {
		tmp = x;
	} else if (a <= 1.2e-41) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1e+184:
		tmp = x
	elif a <= -4.8e+95:
		tmp = t
	elif a <= -7.8e+37:
		tmp = x
	elif a <= 1.2e-41:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1e+184)
		tmp = x;
	elseif (a <= -4.8e+95)
		tmp = t;
	elseif (a <= -7.8e+37)
		tmp = x;
	elseif (a <= 1.2e-41)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1e+184)
		tmp = x;
	elseif (a <= -4.8e+95)
		tmp = t;
	elseif (a <= -7.8e+37)
		tmp = x;
	elseif (a <= 1.2e-41)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1e+184], x, If[LessEqual[a, -4.8e+95], t, If[LessEqual[a, -7.8e+37], x, If[LessEqual[a, 1.2e-41], t, x]]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.00000000000000002e184 or -4.8000000000000001e95 < a < -7.7999999999999997e37 or 1.20000000000000011e-41 < a

   1. Initial program 69.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 92.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in a around inf 48.4%

      \[\leadsto \color{blue}{x} \]

   if -1.00000000000000002e184 < a < -4.8000000000000001e95 or -7.7999999999999997e37 < a < 1.20000000000000011e-41

   1. Initial program 62.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 76.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around inf 36.6%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 31: 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 65.3%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. associate-*l/ 83.1%

      \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

3. Simplified 83.1%

   \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

4. Taylor expanded in z around inf 24.5%

   \[\leadsto \color{blue}{t} \]

5. Final simplification 24.5%

   \[\leadsto t \]

Developer target: 84.1% 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 2023271 
(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))))