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

Percentage Accurate: 68.3% → 90.4%

Time: 29.2s

Alternatives: 23

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.3% 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: 90.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1 - \frac{x}{\frac{z}{a - y}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x \cdot \left(\frac{z}{a - z} + \left(1 - \frac{y}{a - z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ (- a z) (- y z)))))
   (if (<= z -1.5e+80)
     (- t_1 (/ x (/ z (- a y))))
     (if (<= z 1.4e-116)
       (fma (/ (- y z) (- a z)) (- t x) x)
       (+ t_1 (* x (+ (/ z (- a z)) (- 1.0 (/ y (- a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -1.5e+80) {
		tmp = t_1 - (x / (z / (a - y)));
	} else if (z <= 1.4e-116) {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	} else {
		tmp = t_1 + (x * ((z / (a - z)) + (1.0 - (y / (a - z)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(Float64(a - z) / Float64(y - z)))
	tmp = 0.0
	if (z <= -1.5e+80)
		tmp = Float64(t_1 - Float64(x / Float64(z / Float64(a - y))));
	elseif (z <= 1.4e-116)
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	else
		tmp = Float64(t_1 + Float64(x * Float64(Float64(z / Float64(a - z)) + Float64(1.0 - Float64(y / Float64(a - z))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+80], N[(t$95$1 - N[(x / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-116], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(t$95$1 + N[(x * N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(1.0 - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.49999999999999993e80

   1. Initial program 34.6%

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

   3. Taylor expanded in x around -inf 48.1%

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

      1. +-commutative 48.1%

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

      2. mul-1-neg 48.1%

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

      3. unsub-neg 48.1%

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

      4. associate-/l* 87.4%

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

      5. associate--r+ 81.6%

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

      6. sub-neg 81.6%

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

      7. metadata-eval 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in z around inf 79.3%

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

      1. associate-/l* 94.8%

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

      2. mul-1-neg 94.8%

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

      3. unsub-neg 94.8%

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

   8. Simplified 94.8%

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

   if -1.49999999999999993e80 < z < 1.3999999999999999e-116

   1. Initial program 89.0%

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

      1. +-commutative 89.0%

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

      2. associate-*l/ 94.2%

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

      3. fma-define 94.2%

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

   3. Simplified 94.2%

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

   if 1.3999999999999999e-116 < z

   1. Initial program 56.3%

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

   3. Taylor expanded in x around -inf 75.1%

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

      1. +-commutative 75.1%

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

      2. mul-1-neg 75.1%

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

      3. unsub-neg 75.1%

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

      4. associate-/l* 92.5%

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

      5. associate--r+ 88.2%

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

      6. sub-neg 88.2%

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

      7. metadata-eval 88.2%

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

   5. Simplified 88.2%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+80}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} - \frac{x}{\frac{z}{a - y}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} + x \cdot \left(\frac{z}{a - z} + \left(1 - \frac{y}{a - z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-295}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) (- t x)))))
        (t_2 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-295)
       t_2
       (if (<= t_2 0.0)
         (+ t (/ (* (- y a) (- x t)) z))
         (if (<= t_2 2e+305) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-295) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else if (t_2 <= 2e+305) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-295) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else if (t_2 <= 2e+305) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / (t - x)))
	t_2 = x - (((y - z) * (x - t)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-295:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + (((y - a) * (x - t)) / z)
	elif t_2 <= 2e+305:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))))
	t_2 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-295)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	elseif (t_2 <= 2e+305)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / ((a - z) / (t - x)));
	t_2 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-295)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + (((y - a) * (x - t)) / z);
	elseif (t_2 <= 2e+305)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-295], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+305], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 1.9999999999999999e305 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 34.3%

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

      1. associate-/l* 83.6%

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

   3. Simplified 83.6%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2.00000000000000012e-295 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1.9999999999999999e305

   1. Initial program 95.3%

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

   if -2.00000000000000012e-295 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. mul-1-neg 99.8%

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

      8. unsub-neg 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -2 \cdot 10^{-295}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 2 \cdot 10^{+305}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+160}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-174}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -2.4e+160)
     x
     (if (<= a -3.2e+138)
       t_1
       (if (<= a -4.7e+99)
         x
         (if (<= a -4.8e-94)
           t_1
           (if (<= a -3.4e-174) (/ x (/ z y)) (if (<= a 3.2e+48) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -2.4e+160) {
		tmp = x;
	} else if (a <= -3.2e+138) {
		tmp = t_1;
	} else if (a <= -4.7e+99) {
		tmp = x;
	} else if (a <= -4.8e-94) {
		tmp = t_1;
	} else if (a <= -3.4e-174) {
		tmp = x / (z / y);
	} else if (a <= 3.2e+48) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-2.4d+160)) then
        tmp = x
    else if (a <= (-3.2d+138)) then
        tmp = t_1
    else if (a <= (-4.7d+99)) then
        tmp = x
    else if (a <= (-4.8d-94)) then
        tmp = t_1
    else if (a <= (-3.4d-174)) then
        tmp = x / (z / y)
    else if (a <= 3.2d+48) then
        tmp = t_1
    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 t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -2.4e+160) {
		tmp = x;
	} else if (a <= -3.2e+138) {
		tmp = t_1;
	} else if (a <= -4.7e+99) {
		tmp = x;
	} else if (a <= -4.8e-94) {
		tmp = t_1;
	} else if (a <= -3.4e-174) {
		tmp = x / (z / y);
	} else if (a <= 3.2e+48) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -2.4e+160:
		tmp = x
	elif a <= -3.2e+138:
		tmp = t_1
	elif a <= -4.7e+99:
		tmp = x
	elif a <= -4.8e-94:
		tmp = t_1
	elif a <= -3.4e-174:
		tmp = x / (z / y)
	elif a <= 3.2e+48:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -2.4e+160)
		tmp = x;
	elseif (a <= -3.2e+138)
		tmp = t_1;
	elseif (a <= -4.7e+99)
		tmp = x;
	elseif (a <= -4.8e-94)
		tmp = t_1;
	elseif (a <= -3.4e-174)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 3.2e+48)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -2.4e+160)
		tmp = x;
	elseif (a <= -3.2e+138)
		tmp = t_1;
	elseif (a <= -4.7e+99)
		tmp = x;
	elseif (a <= -4.8e-94)
		tmp = t_1;
	elseif (a <= -3.4e-174)
		tmp = x / (z / y);
	elseif (a <= 3.2e+48)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e+160], x, If[LessEqual[a, -3.2e+138], t$95$1, If[LessEqual[a, -4.7e+99], x, If[LessEqual[a, -4.8e-94], t$95$1, If[LessEqual[a, -3.4e-174], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+48], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4000000000000001e160 or -3.2000000000000001e138 < a < -4.69999999999999982e99 or 3.2000000000000001e48 < a

   1. Initial program 72.8%

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

   3. Taylor expanded in a around inf 57.2%

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

   if -2.4000000000000001e160 < a < -3.2000000000000001e138 or -4.69999999999999982e99 < a < -4.8e-94 or -3.4000000000000002e-174 < a < 3.2000000000000001e48

   1. Initial program 63.2%

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

   3. Taylor expanded in t around inf 42.1%

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

   4. Taylor expanded in a around 0 31.7%

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

      1. mul-1-neg 31.7%

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

      2. unsub-neg 31.7%

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

      3. associate-/l* 44.8%

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

   6. Simplified 44.8%

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

   7. Taylor expanded in t around inf 50.8%

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

   if -4.8e-94 < a < -3.4000000000000002e-174

   1. Initial program 55.7%

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

   3. Taylor expanded in x around inf 38.5%

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

      1. mul-1-neg 38.5%

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

      2. unsub-neg 38.5%

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

   5. Simplified 38.5%

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

   6. Taylor expanded in a around 0 65.0%

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

      1. associate-/l* 65.0%

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

   8. Simplified 65.0%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+160}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-174}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.15 \cdot 10^{-75} \lor \neg \left(a \leq 3.95 \cdot 10^{-168}\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} + x \cdot \left(\frac{z}{a - z} + \left(1 - \frac{y}{a - z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.15e-75) (not (<= a 3.95e-168)))
   (+ (/ t (/ (- a z) (- y z))) (* x (+ (/ z (- a z)) (- 1.0 (/ y (- a z))))))
   (+ t (/ (* (- y a) (- x t)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.15e-75) || !(a <= 3.95e-168)) {
		tmp = (t / ((a - z) / (y - z))) + (x * ((z / (a - z)) + (1.0 - (y / (a - z)))));
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.15d-75)) .or. (.not. (a <= 3.95d-168))) then
        tmp = (t / ((a - z) / (y - z))) + (x * ((z / (a - z)) + (1.0d0 - (y / (a - z)))))
    else
        tmp = t + (((y - a) * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.15e-75) || !(a <= 3.95e-168)) {
		tmp = (t / ((a - z) / (y - z))) + (x * ((z / (a - z)) + (1.0 - (y / (a - z)))));
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.15e-75) or not (a <= 3.95e-168):
		tmp = (t / ((a - z) / (y - z))) + (x * ((z / (a - z)) + (1.0 - (y / (a - z)))))
	else:
		tmp = t + (((y - a) * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.15e-75) || !(a <= 3.95e-168))
		tmp = Float64(Float64(t / Float64(Float64(a - z) / Float64(y - z))) + Float64(x * Float64(Float64(z / Float64(a - z)) + Float64(1.0 - Float64(y / Float64(a - z))))));
	else
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.15e-75) || ~((a <= 3.95e-168)))
		tmp = (t / ((a - z) / (y - z))) + (x * ((z / (a - z)) + (1.0 - (y / (a - z)))));
	else
		tmp = t + (((y - a) * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.15e-75], N[Not[LessEqual[a, 3.95e-168]], $MachinePrecision]], N[(N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(1.0 - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.14999999999999987e-75 or 3.9499999999999999e-168 < a

   1. Initial program 65.2%

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

   3. Taylor expanded in x around -inf 76.9%

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

      1. +-commutative 76.9%

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

      2. mul-1-neg 76.9%

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

      3. unsub-neg 76.9%

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

      4. associate-/l* 92.8%

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

      5. associate--r+ 92.0%

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

      6. sub-neg 92.0%

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

      7. metadata-eval 92.0%

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

   5. Simplified 92.0%

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

   if -4.14999999999999987e-75 < a < 3.9499999999999999e-168

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 90.4%

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

      1. associate--l+ 90.4%

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

      2. associate-*r/ 90.4%

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

      3. associate-*r/ 90.4%

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

      4. div-sub 90.4%

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

      5. distribute-lft-out-- 90.4%

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

      6. associate-*r/ 90.4%

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

      7. mul-1-neg 90.4%

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

      8. unsub-neg 90.4%

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

      9. distribute-rgt-out-- 90.4%

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

   5. Simplified 90.4%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.15 \cdot 10^{-75} \lor \neg \left(a \leq 3.95 \cdot 10^{-168}\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} + x \cdot \left(\frac{z}{a - z} + \left(1 - \frac{y}{a - z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-68} \lor \neg \left(t \leq 4.5 \cdot 10^{-135} \lor \neg \left(t \leq 3.5 \cdot 10^{-79}\right) \land t \leq 135000\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.5e-68)
         (not (or (<= t 4.5e-135) (and (not (<= t 3.5e-79)) (<= t 135000.0)))))
   (/ t (/ (- a z) (- y z)))
   (* x (- 1.0 (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e-68) || !((t <= 4.5e-135) || (!(t <= 3.5e-79) && (t <= 135000.0)))) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8.5d-68)) .or. (.not. (t <= 4.5d-135) .or. (.not. (t <= 3.5d-79)) .and. (t <= 135000.0d0))) then
        tmp = t / ((a - z) / (y - z))
    else
        tmp = x * (1.0d0 - ((y - z) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e-68) || !((t <= 4.5e-135) || (!(t <= 3.5e-79) && (t <= 135000.0)))) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.5e-68) or not ((t <= 4.5e-135) or (not (t <= 3.5e-79) and (t <= 135000.0))):
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = x * (1.0 - ((y - z) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.5e-68) || !((t <= 4.5e-135) || (!(t <= 3.5e-79) && (t <= 135000.0))))
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(Float64(y - z) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.5e-68) || ~(((t <= 4.5e-135) || (~((t <= 3.5e-79)) && (t <= 135000.0)))))
		tmp = t / ((a - z) / (y - z));
	else
		tmp = x * (1.0 - ((y - z) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.5e-68], N[Not[Or[LessEqual[t, 4.5e-135], And[N[Not[LessEqual[t, 3.5e-79]], $MachinePrecision], LessEqual[t, 135000.0]]]], $MachinePrecision]], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.50000000000000026e-68 or 4.49999999999999987e-135 < t < 3.5000000000000003e-79 or 135000 < t

   1. Initial program 61.5%

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

   3. Taylor expanded in t around inf 58.9%

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

      1. associate-/l* 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in x around 0 52.1%

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

      1. associate-/l* 73.2%

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

   8. Simplified 73.2%

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

   if -8.50000000000000026e-68 < t < 4.49999999999999987e-135 or 3.5000000000000003e-79 < t < 135000

   1. Initial program 74.5%

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

   3. Taylor expanded in x around inf 72.8%

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

      1. mul-1-neg 72.8%

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

      2. unsub-neg 72.8%

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

   5. Simplified 72.8%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-68} \lor \neg \left(t \leq 4.5 \cdot 10^{-135} \lor \neg \left(t \leq 3.5 \cdot 10^{-79}\right) \land t \leq 135000\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}} + x\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-138}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ t (/ (- a z) (- y z))) x)))
   (if (<= a -2.9e+26)
     t_1
     (if (<= a 4.1e-138)
       (+ t (/ (* (- y a) (- x t)) z))
       (if (<= a 3.9e-15) (- x (/ (* (- y z) (- x t)) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / ((a - z) / (y - z))) + x;
	double tmp;
	if (a <= -2.9e+26) {
		tmp = t_1;
	} else if (a <= 4.1e-138) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else if (a <= 3.9e-15) {
		tmp = x - (((y - z) * (x - t)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t / ((a - z) / (y - z))) + x
    if (a <= (-2.9d+26)) then
        tmp = t_1
    else if (a <= 4.1d-138) then
        tmp = t + (((y - a) * (x - t)) / z)
    else if (a <= 3.9d-15) then
        tmp = x - (((y - z) * (x - t)) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / ((a - z) / (y - z))) + x;
	double tmp;
	if (a <= -2.9e+26) {
		tmp = t_1;
	} else if (a <= 4.1e-138) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else if (a <= 3.9e-15) {
		tmp = x - (((y - z) * (x - t)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t / ((a - z) / (y - z))) + x
	tmp = 0
	if a <= -2.9e+26:
		tmp = t_1
	elif a <= 4.1e-138:
		tmp = t + (((y - a) * (x - t)) / z)
	elif a <= 3.9e-15:
		tmp = x - (((y - z) * (x - t)) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / Float64(Float64(a - z) / Float64(y - z))) + x)
	tmp = 0.0
	if (a <= -2.9e+26)
		tmp = t_1;
	elseif (a <= 4.1e-138)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	elseif (a <= 3.9e-15)
		tmp = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t / ((a - z) / (y - z))) + x;
	tmp = 0.0;
	if (a <= -2.9e+26)
		tmp = t_1;
	elseif (a <= 4.1e-138)
		tmp = t + (((y - a) * (x - t)) / z);
	elseif (a <= 3.9e-15)
		tmp = x - (((y - z) * (x - t)) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.9e+26], t$95$1, If[LessEqual[a, 4.1e-138], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e-15], N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.9e26 or 3.90000000000000026e-15 < a

   1. Initial program 64.2%

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

   3. Taylor expanded in t around inf 66.0%

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

      1. associate-/l* 80.1%

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

   5. Simplified 80.1%

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

   if -2.9e26 < a < 4.09999999999999999e-138

   1. Initial program 66.4%

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

   3. Taylor expanded in z around inf 87.2%

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

      1. associate--l+ 87.2%

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

      2. associate-*r/ 87.2%

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

      3. associate-*r/ 87.2%

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

      4. div-sub 87.2%

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

      5. distribute-lft-out-- 87.2%

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

      6. associate-*r/ 87.2%

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

      7. mul-1-neg 87.2%

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

      8. unsub-neg 87.2%

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

      9. distribute-rgt-out-- 87.2%

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

   5. Simplified 87.2%

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

   if 4.09999999999999999e-138 < a < 3.90000000000000026e-15

   1. Initial program 93.5%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} + x\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-138}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+78} \lor \neg \left(z \leq 3.3 \cdot 10^{+139}\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} - \frac{x}{\frac{z}{a - y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e+78) (not (<= z 3.3e+139)))
   (- (/ t (/ (- a z) (- y z))) (/ x (/ z (- a y))))
   (+ x (/ (- y z) (/ (- a z) (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+78) || !(z <= 3.3e+139)) {
		tmp = (t / ((a - z) / (y - z))) - (x / (z / (a - y)));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.2d+78)) .or. (.not. (z <= 3.3d+139))) then
        tmp = (t / ((a - z) / (y - z))) - (x / (z / (a - y)))
    else
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+78) || !(z <= 3.3e+139)) {
		tmp = (t / ((a - z) / (y - z))) - (x / (z / (a - y)));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e+78) or not (z <= 3.3e+139):
		tmp = (t / ((a - z) / (y - z))) - (x / (z / (a - y)))
	else:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e+78) || !(z <= 3.3e+139))
		tmp = Float64(Float64(t / Float64(Float64(a - z) / Float64(y - z))) - Float64(x / Float64(z / Float64(a - y))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.2e+78) || ~((z <= 3.3e+139)))
		tmp = (t / ((a - z) / (y - z))) - (x / (z / (a - y)));
	else
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.2e+78], N[Not[LessEqual[z, 3.3e+139]], $MachinePrecision]], N[(N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e78 or 3.3000000000000002e139 < z

   1. Initial program 29.7%

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

   3. Taylor expanded in x around -inf 47.1%

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

      1. +-commutative 47.1%

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

      2. mul-1-neg 47.1%

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

      3. unsub-neg 47.1%

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

      4. associate-/l* 85.8%

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

      5. associate--r+ 79.5%

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

      6. sub-neg 79.5%

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

      7. metadata-eval 79.5%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in z around inf 75.2%

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

      1. associate-/l* 89.7%

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

      2. mul-1-neg 89.7%

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

      3. unsub-neg 89.7%

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

   8. Simplified 89.7%

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

   if -5.2e78 < z < 3.3000000000000002e139

   1. Initial program 84.3%

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

      1. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+78} \lor \neg \left(z \leq 3.3 \cdot 10^{+139}\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} - \frac{x}{\frac{z}{a - y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-24}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+198}:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{z} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ (- a z) (- y z)))))
   (if (<= z -2.25e+104)
     t_1
     (if (<= z 2e-24)
       (+ x (* y (/ (- t x) (- a z))))
       (if (<= z 3.8e+198) (+ t_1 x) (- t (* (/ a z) (- x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -2.25e+104) {
		tmp = t_1;
	} else if (z <= 2e-24) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else if (z <= 3.8e+198) {
		tmp = t_1 + x;
	} else {
		tmp = t - ((a / z) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / ((a - z) / (y - z))
    if (z <= (-2.25d+104)) then
        tmp = t_1
    else if (z <= 2d-24) then
        tmp = x + (y * ((t - x) / (a - z)))
    else if (z <= 3.8d+198) then
        tmp = t_1 + x
    else
        tmp = t - ((a / z) * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -2.25e+104) {
		tmp = t_1;
	} else if (z <= 2e-24) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else if (z <= 3.8e+198) {
		tmp = t_1 + x;
	} else {
		tmp = t - ((a / z) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / ((a - z) / (y - z))
	tmp = 0
	if z <= -2.25e+104:
		tmp = t_1
	elif z <= 2e-24:
		tmp = x + (y * ((t - x) / (a - z)))
	elif z <= 3.8e+198:
		tmp = t_1 + x
	else:
		tmp = t - ((a / z) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(Float64(a - z) / Float64(y - z)))
	tmp = 0.0
	if (z <= -2.25e+104)
		tmp = t_1;
	elseif (z <= 2e-24)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	elseif (z <= 3.8e+198)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(t - Float64(Float64(a / z) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / ((a - z) / (y - z));
	tmp = 0.0;
	if (z <= -2.25e+104)
		tmp = t_1;
	elseif (z <= 2e-24)
		tmp = x + (y * ((t - x) / (a - z)));
	elseif (z <= 3.8e+198)
		tmp = t_1 + x;
	else
		tmp = t - ((a / z) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+104], t$95$1, If[LessEqual[z, 2e-24], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+198], N[(t$95$1 + x), $MachinePrecision], N[(t - N[(N[(a / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2499999999999999e104

   1. Initial program 34.5%

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

   3. Taylor expanded in t around inf 27.7%

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

      1. associate-/l* 68.0%

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

   5. Simplified 68.0%

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

   6. Taylor expanded in x around 0 34.2%

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

      1. associate-/l* 77.1%

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

   8. Simplified 77.1%

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

   if -2.2499999999999999e104 < z < 1.99999999999999985e-24

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 80.6%

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

      1. associate-*r/ 84.6%

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

   5. Simplified 84.6%

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

   if 1.99999999999999985e-24 < z < 3.79999999999999988e198

   1. Initial program 55.9%

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

   3. Taylor expanded in t around inf 59.9%

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

      1. associate-/l* 72.3%

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

   5. Simplified 72.3%

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

   if 3.79999999999999988e198 < z

   1. Initial program 27.5%

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

   3. Taylor expanded in y around 0 22.9%

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

      1. +-commutative 22.9%

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

      2. mul-1-neg 22.9%

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

      3. associate-*r/ 41.1%

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

      4. distribute-lft-neg-in 41.1%

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

      5. fma-define 41.5%

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

   5. Simplified 41.5%

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

   6. Taylor expanded in a around 0 74.6%

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

      1. mul-1-neg 74.6%

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

      2. unsub-neg 74.6%

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

   8. Simplified 74.6%

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

   9. Taylor expanded in z around 0 70.5%

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

       1. *-rgt-identity 70.5%

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

       2. times-frac 79.0%

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

       3. /-rgt-identity 79.0%

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

   11. Simplified 79.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+104}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-24}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+198}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} + x\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{z} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}} + x\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-128}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{-15}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ t (/ (- a z) (- y z))) x)))
   (if (<= a -1.75e+26)
     t_1
     (if (<= a 3.6e-128)
       (+ t (/ (* (- y a) (- x t)) z))
       (if (<= a 1.48e-15) (+ x (* y (/ (- t x) (- a z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / ((a - z) / (y - z))) + x;
	double tmp;
	if (a <= -1.75e+26) {
		tmp = t_1;
	} else if (a <= 3.6e-128) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else if (a <= 1.48e-15) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t / ((a - z) / (y - z))) + x
    if (a <= (-1.75d+26)) then
        tmp = t_1
    else if (a <= 3.6d-128) then
        tmp = t + (((y - a) * (x - t)) / z)
    else if (a <= 1.48d-15) then
        tmp = x + (y * ((t - x) / (a - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / ((a - z) / (y - z))) + x;
	double tmp;
	if (a <= -1.75e+26) {
		tmp = t_1;
	} else if (a <= 3.6e-128) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else if (a <= 1.48e-15) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t / ((a - z) / (y - z))) + x
	tmp = 0
	if a <= -1.75e+26:
		tmp = t_1
	elif a <= 3.6e-128:
		tmp = t + (((y - a) * (x - t)) / z)
	elif a <= 1.48e-15:
		tmp = x + (y * ((t - x) / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / Float64(Float64(a - z) / Float64(y - z))) + x)
	tmp = 0.0
	if (a <= -1.75e+26)
		tmp = t_1;
	elseif (a <= 3.6e-128)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	elseif (a <= 1.48e-15)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t / ((a - z) / (y - z))) + x;
	tmp = 0.0;
	if (a <= -1.75e+26)
		tmp = t_1;
	elseif (a <= 3.6e-128)
		tmp = t + (((y - a) * (x - t)) / z);
	elseif (a <= 1.48e-15)
		tmp = x + (y * ((t - x) / (a - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.75e+26], t$95$1, If[LessEqual[a, 3.6e-128], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.48e-15], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.75e26 or 1.48e-15 < a

   1. Initial program 64.2%

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

   3. Taylor expanded in t around inf 66.0%

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

      1. associate-/l* 80.1%

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

   5. Simplified 80.1%

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

   if -1.75e26 < a < 3.60000000000000025e-128

   1. Initial program 66.4%

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

   3. Taylor expanded in z around inf 87.2%

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

      1. associate--l+ 87.2%

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

      2. associate-*r/ 87.2%

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

      3. associate-*r/ 87.2%

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

      4. div-sub 87.2%

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

      5. distribute-lft-out-- 87.2%

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

      6. associate-*r/ 87.2%

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

      7. mul-1-neg 87.2%

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

      8. unsub-neg 87.2%

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

      9. distribute-rgt-out-- 87.2%

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

   5. Simplified 87.2%

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

   if 3.60000000000000025e-128 < a < 1.48e-15

   1. Initial program 93.5%

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

   3. Taylor expanded in y around inf 81.4%

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

      1. associate-*r/ 81.6%

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

   5. Simplified 81.6%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} + x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-128}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{-15}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+139}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ a (/ z (- t x))))))
   (if (<= z -1.6e+79)
     t_1
     (if (<= z 6.8e-91)
       (+ x (/ y (/ a (- t x))))
       (if (<= z 9e+139) (+ x (/ t (/ a (- y z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (a / (z / (t - x)));
	double tmp;
	if (z <= -1.6e+79) {
		tmp = t_1;
	} else if (z <= 6.8e-91) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 9e+139) {
		tmp = x + (t / (a / (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 = t + (a / (z / (t - x)))
    if (z <= (-1.6d+79)) then
        tmp = t_1
    else if (z <= 6.8d-91) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 9d+139) then
        tmp = x + (t / (a / (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 = t + (a / (z / (t - x)));
	double tmp;
	if (z <= -1.6e+79) {
		tmp = t_1;
	} else if (z <= 6.8e-91) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 9e+139) {
		tmp = x + (t / (a / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (a / (z / (t - x)))
	tmp = 0
	if z <= -1.6e+79:
		tmp = t_1
	elif z <= 6.8e-91:
		tmp = x + (y / (a / (t - x)))
	elif z <= 9e+139:
		tmp = x + (t / (a / (y - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(a / Float64(z / Float64(t - x))))
	tmp = 0.0
	if (z <= -1.6e+79)
		tmp = t_1;
	elseif (z <= 6.8e-91)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 9e+139)
		tmp = Float64(x + Float64(t / Float64(a / Float64(y - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (a / (z / (t - x)));
	tmp = 0.0;
	if (z <= -1.6e+79)
		tmp = t_1;
	elseif (z <= 6.8e-91)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 9e+139)
		tmp = x + (t / (a / (y - z)));
	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 / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+79], t$95$1, If[LessEqual[z, 6.8e-91], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+139], N[(x + N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000001e79 or 8.9999999999999999e139 < z

   1. Initial program 29.7%

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

   3. Taylor expanded in y around 0 22.3%

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

      1. +-commutative 22.3%

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

      2. mul-1-neg 22.3%

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

      3. associate-*r/ 44.9%

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

      4. distribute-lft-neg-in 44.9%

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

      5. fma-define 45.5%

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

   5. Simplified 45.5%

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

   6. Taylor expanded in z around inf 53.1%

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

      1. associate-/l* 64.4%

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

   8. Simplified 64.4%

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

   if -1.60000000000000001e79 < z < 6.80000000000000053e-91

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 66.6%

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

      1. associate-/l* 71.6%

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

   5. Simplified 71.6%

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

   if 6.80000000000000053e-91 < z < 8.9999999999999999e139

   1. Initial program 76.8%

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

   3. Taylor expanded in t around inf 75.0%

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

   4. Taylor expanded in a around inf 62.0%

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

      1. +-commutative 62.0%

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

      2. associate-/l* 62.0%

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

   6. Simplified 62.0%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+79}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+139}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+139}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{z} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+79)
   (+ t (/ a (/ z (- t x))))
   (if (<= z 1.35e-90)
     (+ x (/ y (/ a (- t x))))
     (if (<= z 9e+139) (+ x (/ t (/ a (- y z)))) (- t (* (/ a z) (- x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+79) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= 1.35e-90) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 9e+139) {
		tmp = x + (t / (a / (y - z)));
	} else {
		tmp = t - ((a / z) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.7d+79)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= 1.35d-90) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 9d+139) then
        tmp = x + (t / (a / (y - z)))
    else
        tmp = t - ((a / z) * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+79) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= 1.35e-90) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 9e+139) {
		tmp = x + (t / (a / (y - z)));
	} else {
		tmp = t - ((a / z) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+79:
		tmp = t + (a / (z / (t - x)))
	elif z <= 1.35e-90:
		tmp = x + (y / (a / (t - x)))
	elif z <= 9e+139:
		tmp = x + (t / (a / (y - z)))
	else:
		tmp = t - ((a / z) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e+79)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= 1.35e-90)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 9e+139)
		tmp = Float64(x + Float64(t / Float64(a / Float64(y - z))));
	else
		tmp = Float64(t - Float64(Float64(a / z) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.7e+79)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= 1.35e-90)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 9e+139)
		tmp = x + (t / (a / (y - z)));
	else
		tmp = t - ((a / z) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e+79], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-90], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+139], N[(x + N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(a / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7e79

   1. Initial program 34.6%

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

   3. Taylor expanded in y around 0 22.8%

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

      1. +-commutative 22.8%

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

      2. mul-1-neg 22.8%

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

      3. associate-*r/ 42.5%

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

      4. distribute-lft-neg-in 42.5%

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

      5. fma-define 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in z around inf 51.7%

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

      1. associate-/l* 62.9%

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

   8. Simplified 62.9%

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

   if -2.7e79 < z < 1.34999999999999998e-90

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 66.6%

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

      1. associate-/l* 71.6%

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

   5. Simplified 71.6%

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

   if 1.34999999999999998e-90 < z < 8.9999999999999999e139

   1. Initial program 76.8%

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

   3. Taylor expanded in t around inf 75.0%

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

   4. Taylor expanded in a around inf 62.0%

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

      1. +-commutative 62.0%

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

      2. associate-/l* 62.0%

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

   6. Simplified 62.0%

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

   if 8.9999999999999999e139 < z

   1. Initial program 24.3%

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

   3. Taylor expanded in y around 0 21.7%

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

      1. +-commutative 21.7%

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

      2. mul-1-neg 21.7%

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

      3. associate-*r/ 47.5%

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

      4. distribute-lft-neg-in 47.5%

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

      5. fma-define 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in a around 0 66.5%

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

      1. mul-1-neg 66.5%

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

      2. unsub-neg 66.5%

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

   8. Simplified 66.5%

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

   9. Taylor expanded in z around 0 54.6%

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

       1. *-rgt-identity 54.6%

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

       2. times-frac 69.0%

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

       3. /-rgt-identity 69.0%

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

   11. Simplified 69.0%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+139}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{z} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -34000000000000:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+137}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{z} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -34000000000000.0)
   (/ t (/ (- a z) (- y z)))
   (if (<= z 5.5e-91)
     (+ x (/ y (/ a (- t x))))
     (if (<= z 1.4e+137)
       (+ x (/ t (/ a (- y z))))
       (- t (* (/ a z) (- x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -34000000000000.0) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 5.5e-91) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 1.4e+137) {
		tmp = x + (t / (a / (y - z)));
	} else {
		tmp = t - ((a / z) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-34000000000000.0d0)) then
        tmp = t / ((a - z) / (y - z))
    else if (z <= 5.5d-91) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 1.4d+137) then
        tmp = x + (t / (a / (y - z)))
    else
        tmp = t - ((a / z) * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -34000000000000.0) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 5.5e-91) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 1.4e+137) {
		tmp = x + (t / (a / (y - z)));
	} else {
		tmp = t - ((a / z) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -34000000000000.0:
		tmp = t / ((a - z) / (y - z))
	elif z <= 5.5e-91:
		tmp = x + (y / (a / (t - x)))
	elif z <= 1.4e+137:
		tmp = x + (t / (a / (y - z)))
	else:
		tmp = t - ((a / z) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -34000000000000.0)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (z <= 5.5e-91)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 1.4e+137)
		tmp = Float64(x + Float64(t / Float64(a / Float64(y - z))));
	else
		tmp = Float64(t - Float64(Float64(a / z) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -34000000000000.0)
		tmp = t / ((a - z) / (y - z));
	elseif (z <= 5.5e-91)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 1.4e+137)
		tmp = x + (t / (a / (y - z)));
	else
		tmp = t - ((a / z) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -34000000000000.0], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-91], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+137], N[(x + N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(a / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4e13

   1. Initial program 44.4%

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

   3. Taylor expanded in t around inf 36.2%

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

      1. associate-/l* 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in x around 0 37.0%

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

      1. associate-/l* 68.1%

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

   8. Simplified 68.1%

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

   if -3.4e13 < z < 5.49999999999999965e-91

   1. Initial program 88.4%

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

   3. Taylor expanded in z around 0 68.7%

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

      1. associate-/l* 74.2%

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

   5. Simplified 74.2%

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

   if 5.49999999999999965e-91 < z < 1.4e137

   1. Initial program 76.8%

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

   3. Taylor expanded in t around inf 75.0%

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

   4. Taylor expanded in a around inf 62.0%

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

      1. +-commutative 62.0%

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

      2. associate-/l* 62.0%

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

   6. Simplified 62.0%

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

   if 1.4e137 < z

   1. Initial program 24.3%

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

   3. Taylor expanded in y around 0 21.7%

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

      1. +-commutative 21.7%

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

      2. mul-1-neg 21.7%

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

      3. associate-*r/ 47.5%

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

      4. distribute-lft-neg-in 47.5%

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

      5. fma-define 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in a around 0 66.5%

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

      1. mul-1-neg 66.5%

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

      2. unsub-neg 66.5%

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

   8. Simplified 66.5%

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

   9. Taylor expanded in z around 0 54.6%

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

       1. *-rgt-identity 54.6%

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

       2. times-frac 69.0%

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

       3. /-rgt-identity 69.0%

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

   11. Simplified 69.0%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -34000000000000:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+137}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{z} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+96}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+140}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{z} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+96)
   (/ t (/ (- a z) (- y z)))
   (if (<= z 3.3e+140)
     (+ x (* y (/ (- t x) (- a z))))
     (- t (* (/ a z) (- x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+96) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 3.3e+140) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else {
		tmp = t - ((a / z) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.3d+96)) then
        tmp = t / ((a - z) / (y - z))
    else if (z <= 3.3d+140) then
        tmp = x + (y * ((t - x) / (a - z)))
    else
        tmp = t - ((a / z) * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+96) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 3.3e+140) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else {
		tmp = t - ((a / z) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+96:
		tmp = t / ((a - z) / (y - z))
	elif z <= 3.3e+140:
		tmp = x + (y * ((t - x) / (a - z)))
	else:
		tmp = t - ((a / z) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+96)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (z <= 3.3e+140)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(t - Float64(Float64(a / z) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+96)
		tmp = t / ((a - z) / (y - z));
	elseif (z <= 3.3e+140)
		tmp = x + (y * ((t - x) / (a - z)));
	else
		tmp = t - ((a / z) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+96], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+140], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(a / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e96

   1. Initial program 34.5%

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

   3. Taylor expanded in t around inf 27.7%

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

      1. associate-/l* 68.0%

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

   5. Simplified 68.0%

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

   6. Taylor expanded in x around 0 34.2%

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

      1. associate-/l* 77.1%

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

   8. Simplified 77.1%

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

   if -1.3e96 < z < 3.3000000000000002e140

   1. Initial program 82.7%

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

   3. Taylor expanded in y around inf 77.2%

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

      1. associate-*r/ 79.8%

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

   5. Simplified 79.8%

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

   if 3.3000000000000002e140 < z

   1. Initial program 24.3%

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

   3. Taylor expanded in y around 0 21.7%

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

      1. +-commutative 21.7%

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

      2. mul-1-neg 21.7%

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

      3. associate-*r/ 47.5%

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

      4. distribute-lft-neg-in 47.5%

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

      5. fma-define 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in a around 0 66.5%

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

      1. mul-1-neg 66.5%

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

      2. unsub-neg 66.5%

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

   8. Simplified 66.5%

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

   9. Taylor expanded in z around 0 54.6%

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

       1. *-rgt-identity 54.6%

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

       2. times-frac 69.0%

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

       3. /-rgt-identity 69.0%

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

   11. Simplified 69.0%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+96}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+140}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{z} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+16} \lor \neg \left(z \leq 2.9 \cdot 10^{+139}\right):\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+16) (not (<= z 2.9e+139)))
   (+ t (/ a (/ z (- t x))))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+16) || !(z <= 2.9e+139)) {
		tmp = t + (a / (z / (t - x)));
	} else {
		tmp = x + (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 ((z <= (-1.35d+16)) .or. (.not. (z <= 2.9d+139))) then
        tmp = t + (a / (z / (t - x)))
    else
        tmp = x + (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 ((z <= -1.35e+16) || !(z <= 2.9e+139)) {
		tmp = t + (a / (z / (t - x)));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e+16) or not (z <= 2.9e+139):
		tmp = t + (a / (z / (t - x)))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+16) || !(z <= 2.9e+139))
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.35e+16) || ~((z <= 2.9e+139)))
		tmp = t + (a / (z / (t - x)));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+16], N[Not[LessEqual[z, 2.9e+139]], $MachinePrecision]], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e16 or 2.8999999999999999e139 < z

   1. Initial program 36.0%

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

   3. Taylor expanded in y around 0 26.3%

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

      1. +-commutative 26.3%

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

      2. mul-1-neg 26.3%

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

      3. associate-*r/ 46.2%

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

      4. distribute-lft-neg-in 46.2%

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

      5. fma-define 46.9%

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

   5. Simplified 46.9%

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

   6. Taylor expanded in z around inf 51.3%

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

      1. associate-/l* 61.3%

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

   8. Simplified 61.3%

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

   if -1.35e16 < z < 2.8999999999999999e139

   1. Initial program 84.4%

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

   3. Taylor expanded in t around inf 70.0%

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

      1. associate-/l* 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in z around 0 55.5%

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

      1. associate-/l* 57.4%

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

   8. Simplified 57.4%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+16} \lor \neg \left(z \leq 2.9 \cdot 10^{+139}\right):\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+79} \lor \neg \left(z \leq 3.1 \cdot 10^{+137}\right):\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+79) (not (<= z 3.1e+137)))
   (+ t (/ a (/ z (- t x))))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+79) || !(z <= 3.1e+137)) {
		tmp = t + (a / (z / (t - x)));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.5d+79)) .or. (.not. (z <= 3.1d+137))) then
        tmp = t + (a / (z / (t - x)))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+79) || !(z <= 3.1e+137)) {
		tmp = t + (a / (z / (t - x)));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e+79) or not (z <= 3.1e+137):
		tmp = t + (a / (z / (t - x)))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+79) || !(z <= 3.1e+137))
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.5e+79) || ~((z <= 3.1e+137)))
		tmp = t + (a / (z / (t - x)));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+79], N[Not[LessEqual[z, 3.1e+137]], $MachinePrecision]], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.49999999999999994e79 or 3.0999999999999999e137 < z

   1. Initial program 29.7%

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

   3. Taylor expanded in y around 0 22.3%

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

      1. +-commutative 22.3%

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

      2. mul-1-neg 22.3%

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

      3. associate-*r/ 44.9%

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

      4. distribute-lft-neg-in 44.9%

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

      5. fma-define 45.5%

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

   5. Simplified 45.5%

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

   6. Taylor expanded in z around inf 53.1%

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

      1. associate-/l* 64.4%

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

   8. Simplified 64.4%

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

   if -9.49999999999999994e79 < z < 3.0999999999999999e137

   1. Initial program 84.3%

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

   3. Taylor expanded in z around 0 62.9%

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

      1. associate-/l* 65.2%

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

   5. Simplified 65.2%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+79} \lor \neg \left(z \leq 3.1 \cdot 10^{+137}\right):\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+82} \lor \neg \left(z \leq 1.05 \cdot 10^{+137}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.4e+82) (not (<= z 1.05e+137)))
   (* t (- 1.0 (/ y z)))
   (* x (- 1.0 (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+82) || !(z <= 1.05e+137)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.4d+82)) .or. (.not. (z <= 1.05d+137))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+82) || !(z <= 1.05e+137)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.4e+82) or not (z <= 1.05e+137):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.4e+82) || !(z <= 1.05e+137))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.4e+82) || ~((z <= 1.05e+137)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.4e+82], N[Not[LessEqual[z, 1.05e+137]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e82 or 1.05e137 < z

   1. Initial program 30.4%

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

   3. Taylor expanded in t around inf 26.2%

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

   4. Taylor expanded in a around 0 20.7%

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

      1. mul-1-neg 20.7%

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

      2. unsub-neg 20.7%

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

      3. associate-/l* 52.2%

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

   6. Simplified 52.2%

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

   7. Taylor expanded in t around inf 59.6%

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

   if -1.4e82 < z < 1.05e137

   1. Initial program 83.3%

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

   3. Taylor expanded in z around 0 62.3%

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

   4. Taylor expanded in x around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. unsub-neg 50.1%

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

   6. Simplified 50.1%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+82} \lor \neg \left(z \leq 1.05 \cdot 10^{+137}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 55.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+82} \lor \neg \left(z \leq 1.15 \cdot 10^{+139}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5e+82) (not (<= z 1.15e+139)))
   (* t (- 1.0 (/ y z)))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5e+82) || !(z <= 1.15e+139)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (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 ((z <= (-5d+82)) .or. (.not. (z <= 1.15d+139))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + (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 ((z <= -5e+82) || !(z <= 1.15e+139)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5e+82) or not (z <= 1.15e+139):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5e+82) || !(z <= 1.15e+139))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5e+82) || ~((z <= 1.15e+139)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5e+82], N[Not[LessEqual[z, 1.15e+139]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000015e82 or 1.15e139 < z

   1. Initial program 30.4%

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

   3. Taylor expanded in t around inf 26.2%

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

   4. Taylor expanded in a around 0 20.7%

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

      1. mul-1-neg 20.7%

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

      2. unsub-neg 20.7%

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

      3. associate-/l* 52.2%

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

   6. Simplified 52.2%

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

   7. Taylor expanded in t around inf 59.6%

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

   if -5.00000000000000015e82 < z < 1.15e139

   1. Initial program 83.3%

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

   3. Taylor expanded in t around inf 69.6%

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

      1. associate-/l* 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in z around 0 53.9%

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

      1. associate-/l* 55.6%

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

   8. Simplified 55.6%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+82} \lor \neg \left(z \leq 1.15 \cdot 10^{+139}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 56.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+78} \lor \neg \left(z \leq 9.5 \cdot 10^{+136}\right):\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e+78) (not (<= z 9.5e+136)))
   (- t (* a (/ x z)))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+78) || !(z <= 9.5e+136)) {
		tmp = t - (a * (x / z));
	} else {
		tmp = x + (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 ((z <= (-1.85d+78)) .or. (.not. (z <= 9.5d+136))) then
        tmp = t - (a * (x / z))
    else
        tmp = x + (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 ((z <= -1.85e+78) || !(z <= 9.5e+136)) {
		tmp = t - (a * (x / z));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.85e+78) or not (z <= 9.5e+136):
		tmp = t - (a * (x / z))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e+78) || !(z <= 9.5e+136))
		tmp = Float64(t - Float64(a * Float64(x / z)));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.85e+78) || ~((z <= 9.5e+136)))
		tmp = t - (a * (x / z));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.85e+78], N[Not[LessEqual[z, 9.5e+136]], $MachinePrecision]], N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999992e78 or 9.49999999999999907e136 < z

   1. Initial program 29.7%

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

   3. Taylor expanded in y around 0 22.3%

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

      1. +-commutative 22.3%

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

      2. mul-1-neg 22.3%

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

      3. associate-*r/ 44.9%

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

      4. distribute-lft-neg-in 44.9%

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

      5. fma-define 45.5%

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

   5. Simplified 45.5%

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

   6. Taylor expanded in a around 0 64.6%

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

      1. mul-1-neg 64.6%

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

      2. unsub-neg 64.6%

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

   8. Simplified 64.6%

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

   9. Taylor expanded in x around inf 64.2%

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

   if -1.84999999999999992e78 < z < 9.49999999999999907e136

   1. Initial program 84.3%

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

   3. Taylor expanded in t around inf 70.3%

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

      1. associate-/l* 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in z around 0 54.4%

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

      1. associate-/l* 56.1%

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

   8. Simplified 56.1%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+78} \lor \neg \left(z \leq 9.5 \cdot 10^{+136}\right):\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 36.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 10^{-215}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.08e-7)
   t
   (if (<= z 1e-215) (* y (/ t a)) (if (<= z 1.12e+138) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.08e-7) {
		tmp = t;
	} else if (z <= 1e-215) {
		tmp = y * (t / a);
	} else if (z <= 1.12e+138) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.08d-7)) then
        tmp = t
    else if (z <= 1d-215) then
        tmp = y * (t / a)
    else if (z <= 1.12d+138) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.08e-7) {
		tmp = t;
	} else if (z <= 1e-215) {
		tmp = y * (t / a);
	} else if (z <= 1.12e+138) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.08e-7:
		tmp = t
	elif z <= 1e-215:
		tmp = y * (t / a)
	elif z <= 1.12e+138:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.08e-7)
		tmp = t;
	elseif (z <= 1e-215)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 1.12e+138)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.08e-7)
		tmp = t;
	elseif (z <= 1e-215)
		tmp = y * (t / a);
	elseif (z <= 1.12e+138)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.08e-7], t, If[LessEqual[z, 1e-215], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+138], x, t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.08000000000000001e-7 or 1.12e138 < z

   1. Initial program 36.7%

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

   3. Taylor expanded in z around inf 47.6%

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

   if -1.08000000000000001e-7 < z < 1.00000000000000004e-215

   1. Initial program 88.7%

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

   3. Taylor expanded in z around 0 69.9%

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

   4. Taylor expanded in y around inf 51.6%

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

      1. div-sub 51.6%

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

   6. Simplified 51.6%

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

   7. Taylor expanded in t around inf 35.6%

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

   if 1.00000000000000004e-215 < z < 1.12e138

   1. Initial program 80.4%

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

   3. Taylor expanded in a around inf 44.4%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 10^{-215}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 36.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.003:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-304}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.003)
   t
   (if (<= z -2.3e-304) (/ t (/ a y)) (if (<= z 9.5e+138) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.003) {
		tmp = t;
	} else if (z <= -2.3e-304) {
		tmp = t / (a / y);
	} else if (z <= 9.5e+138) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-0.003d0)) then
        tmp = t
    else if (z <= (-2.3d-304)) then
        tmp = t / (a / y)
    else if (z <= 9.5d+138) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.003) {
		tmp = t;
	} else if (z <= -2.3e-304) {
		tmp = t / (a / y);
	} else if (z <= 9.5e+138) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.003:
		tmp = t
	elif z <= -2.3e-304:
		tmp = t / (a / y)
	elif z <= 9.5e+138:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.003)
		tmp = t;
	elseif (z <= -2.3e-304)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 9.5e+138)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.003)
		tmp = t;
	elseif (z <= -2.3e-304)
		tmp = t / (a / y);
	elseif (z <= 9.5e+138)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.003], t, If[LessEqual[z, -2.3e-304], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+138], x, t]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0030000000000000001 or 9.49999999999999998e138 < z

   1. Initial program 36.7%

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

   3. Taylor expanded in z around inf 47.6%

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

   if -0.0030000000000000001 < z < -2.3e-304

   1. Initial program 89.2%

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

   3. Taylor expanded in z around 0 67.3%

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

   4. Taylor expanded in y around inf 51.7%

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

      1. div-sub 51.7%

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

   6. Simplified 51.7%

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

   7. Taylor expanded in t around inf 34.6%

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

      1. associate-/l* 36.0%

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

   9. Simplified 36.0%

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

   if -2.3e-304 < z < 9.49999999999999998e138

   1. Initial program 81.4%

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

   3. Taylor expanded in a around inf 43.4%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.003:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-304}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 38.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+109}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+147}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.7e+109)
   (/ t (/ a y))
   (if (<= y 2.3e+147) (+ t x) (* y (- (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.7e+109) {
		tmp = t / (a / y);
	} else if (y <= 2.3e+147) {
		tmp = t + x;
	} else {
		tmp = y * -(t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.7d+109)) then
        tmp = t / (a / y)
    else if (y <= 2.3d+147) then
        tmp = t + x
    else
        tmp = y * -(t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.7e+109) {
		tmp = t / (a / y);
	} else if (y <= 2.3e+147) {
		tmp = t + x;
	} else {
		tmp = y * -(t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.7e+109:
		tmp = t / (a / y)
	elif y <= 2.3e+147:
		tmp = t + x
	else:
		tmp = y * -(t / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.7e+109)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 2.3e+147)
		tmp = Float64(t + x);
	else
		tmp = Float64(y * Float64(-Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.7e+109)
		tmp = t / (a / y);
	elseif (y <= 2.3e+147)
		tmp = t + x;
	else
		tmp = y * -(t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.7e+109], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+147], N[(t + x), $MachinePrecision], N[(y * (-N[(t / z), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7000000000000002e109

   1. Initial program 73.2%

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

   3. Taylor expanded in z around 0 49.0%

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

   4. Taylor expanded in y around inf 53.1%

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

      1. div-sub 53.1%

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

   6. Simplified 53.1%

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

   7. Taylor expanded in t around inf 30.0%

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

      1. associate-/l* 40.6%

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

   9. Simplified 40.6%

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

   if -3.7000000000000002e109 < y < 2.2999999999999999e147

   1. Initial program 64.1%

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

   3. Taylor expanded in t around inf 57.7%

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

   4. Taylor expanded in z around inf 42.6%

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

   if 2.2999999999999999e147 < y

   1. Initial program 78.3%

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

   3. Taylor expanded in t around inf 59.5%

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

   4. Taylor expanded in a around 0 37.3%

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

      1. mul-1-neg 37.3%

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

      2. unsub-neg 37.3%

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

      3. associate-/l* 44.0%

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

   6. Simplified 44.0%

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

   7. Taylor expanded in z around 0 33.3%

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

      1. mul-1-neg 33.3%

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

      2. associate-*l/ 36.4%

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

      3. *-commutative 36.4%

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

      4. distribute-rgt-neg-in 36.4%

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

   9. Simplified 36.4%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+109}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+147}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 38.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e+22) t (if (<= z 8.2e+136) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+22) {
		tmp = t;
	} else if (z <= 8.2e+136) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3d+22)) then
        tmp = t
    else if (z <= 8.2d+136) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+22) {
		tmp = t;
	} else if (z <= 8.2e+136) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e+22:
		tmp = t
	elif z <= 8.2e+136:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e+22)
		tmp = t;
	elseif (z <= 8.2e+136)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e+22)
		tmp = t;
	elseif (z <= 8.2e+136)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e+22], t, If[LessEqual[z, 8.2e+136], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -3e22 or 8.1999999999999995e136 < z

   1. Initial program 34.6%

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

   3. Taylor expanded in z around inf 49.1%

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

   if -3e22 < z < 8.1999999999999995e136

   1. Initial program 84.6%

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

   3. Taylor expanded in a around inf 35.9%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 25.0% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.8%

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

3. Taylor expanded in z around inf 22.8%

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

4. Final simplification 22.8%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 84.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024034 
(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))))