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

Percentage Accurate: 68.3% → 88.9%

Time: 14.4s

Alternatives: 21

Speedup: 0.7×

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: 88.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+73}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t \cdot \left(\frac{1}{a - z} + \frac{\frac{x}{t}}{z - a}\right), x\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \mathsf{fma}\left(-1, \frac{t}{x} \cdot \frac{y - z}{a - z}, \frac{y}{a - z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.35e+73)
   (fma (- y z) (* t (+ (/ 1.0 (- a z)) (/ (/ x t) (- z a)))) x)
   (if (<= t 1.6e+25)
     (*
      x
      (-
       (+ 1.0 (/ z (- a z)))
       (fma -1.0 (* (/ t x) (/ (- y z) (- a z))) (/ y (- a z)))))
     (+ x (/ (- t x) (/ (- a z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.35e+73) {
		tmp = fma((y - z), (t * ((1.0 / (a - z)) + ((x / t) / (z - a)))), x);
	} else if (t <= 1.6e+25) {
		tmp = x * ((1.0 + (z / (a - z))) - fma(-1.0, ((t / x) * ((y - z) / (a - z))), (y / (a - z))));
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.35e+73)
		tmp = fma(Float64(y - z), Float64(t * Float64(Float64(1.0 / Float64(a - z)) + Float64(Float64(x / t) / Float64(z - a)))), x);
	elseif (t <= 1.6e+25)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(z / Float64(a - z))) - fma(-1.0, Float64(Float64(t / x) * Float64(Float64(y - z) / Float64(a - z))), Float64(y / Float64(a - z)))));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.35e+73], N[(N[(y - z), $MachinePrecision] * N[(t * N[(N[(1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(N[(x / t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.6e+25], N[(x * N[(N[(1.0 + N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-1.0 * N[(N[(t / x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3500000000000001e73

   1. Initial program 57.2%

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

      1. +-commutative 57.2%

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

      2. associate-/l* 90.4%

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

      3. fma-define 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in t around -inf 88.4%

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

      1. mul-1-neg 88.4%

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

      2. associate-/r* 90.7%

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

   7. Simplified 90.7%

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

   if -2.3500000000000001e73 < t < 1.6e25

   1. Initial program 69.2%

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

      1. +-commutative 69.2%

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

      2. associate-/l* 65.2%

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

      3. fma-define 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in x around -inf 84.0%

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

      1. associate-*r* 84.0%

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

      2. neg-mul-1 84.0%

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

      3. fma-define 84.0%

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

      4. times-frac 89.2%

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

      5. +-commutative 89.2%

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

   7. Simplified 89.2%

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

   if 1.6e25 < t

   1. Initial program 61.2%

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

      1. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

      1. *-commutative 89.2%

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

      2. associate-*l/ 61.2%

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

      3. associate-*r/ 96.2%

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

      4. clear-num 96.1%

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

      5. un-div-inv 96.2%

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

   6. Applied egg-rr 96.2%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+73}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t \cdot \left(\frac{1}{a - z} + \frac{\frac{x}{t}}{z - a}\right), x\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \mathsf{fma}\left(-1, \frac{t}{x} \cdot \frac{y - z}{a - z}, \frac{y}{a - z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-289} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- x t)) (- z a)))))
   (if (or (<= t_1 -1e-289) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (- t (* x (/ (- a y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (x - t)) / (z - a));
	double tmp;
	if ((t_1 <= -1e-289) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t - (x * ((a - y) / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(z - a)))
	tmp = 0.0
	if ((t_1 <= -1e-289) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-289], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1e-289 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 70.8%

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

      1. +-commutative 70.8%

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

      2. *-commutative 70.8%

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

      3. associate-/l* 88.8%

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

      4. fma-define 88.8%

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

   3. Simplified 88.8%

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

   if -1e-289 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.8%

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

      1. +-commutative 3.8%

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

      2. associate-/l* 3.4%

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

      3. fma-define 3.7%

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

   3. Simplified 3.7%

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

   5. Taylor expanded in x around -inf 84.2%

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

      1. mul-1-neg 84.2%

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

      2. distribute-rgt-neg-in 84.2%

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

      3. +-commutative 84.2%

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

      4. mul-1-neg 84.2%

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

      5. unsub-neg 84.2%

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

      6. associate-/r* 84.0%

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

      7. +-commutative 84.0%

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

   7. Simplified 84.0%

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

   8. Taylor expanded in z around inf 84.3%

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

   9. Taylor expanded in z around inf 99.7%

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

       1. mul-1-neg 99.7%

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

       2. unsub-neg 99.7%

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

       3. associate-/l* 99.8%

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

       4. neg-mul-1 99.8%

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

       5. sub-neg 99.8%

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

   11. Simplified 99.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq -1 \cdot 10^{-289} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-289}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+287}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- x t) (- z a)))))
        (t_2 (+ x (/ (* (- y z) (- x t)) (- z a)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-289)
       t_2
       (if (<= t_2 0.0)
         (- t (* x (/ (- a y) z)))
         (if (<= t_2 5e+287) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((x - t) / (z - a)));
	double t_2 = x + (((y - z) * (x - t)) / (z - a));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-289) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t - (x * ((a - y) / z));
	} else if (t_2 <= 5e+287) {
		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) * ((x - t) / (z - a)));
	double t_2 = x + (((y - z) * (x - t)) / (z - a));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-289) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t - (x * ((a - y) / z));
	} else if (t_2 <= 5e+287) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((x - t) / (z - a)))
	t_2 = x + (((y - z) * (x - t)) / (z - a))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-289:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t - (x * ((a - y) / z))
	elif t_2 <= 5e+287:
		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(x - t) / Float64(z - a))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(z - a)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-289)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	elseif (t_2 <= 5e+287)
		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) * ((x - t) / (z - a)));
	t_2 = x + (((y - z) * (x - t)) / (z - a));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-289)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t - (x * ((a - y) / z));
	elseif (t_2 <= 5e+287)
		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[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-289], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+287], 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 5e287 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 38.7%

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

      1. associate-/l* 78.4%

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

   3. Simplified 78.4%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1e-289 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5e287

   1. Initial program 96.0%

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

   if -1e-289 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.8%

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

      1. +-commutative 3.8%

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

      2. associate-/l* 3.4%

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

      3. fma-define 3.7%

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

   3. Simplified 3.7%

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

   5. Taylor expanded in x around -inf 84.2%

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

      1. mul-1-neg 84.2%

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

      2. distribute-rgt-neg-in 84.2%

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

      3. +-commutative 84.2%

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

      4. mul-1-neg 84.2%

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

      5. unsub-neg 84.2%

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

      6. associate-/r* 84.0%

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

      7. +-commutative 84.0%

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

   7. Simplified 84.0%

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

   8. Taylor expanded in z around inf 84.3%

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

   9. Taylor expanded in z around inf 99.7%

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

       1. mul-1-neg 99.7%

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

       2. unsub-neg 99.7%

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

       3. associate-/l* 99.8%

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

       4. neg-mul-1 99.8%

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

       5. sub-neg 99.8%

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

   11. Simplified 99.8%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq -1 \cdot 10^{-289}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq 0:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq 5 \cdot 10^{+287}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-289} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- x t)) (- z a)))))
   (if (or (<= t_1 -1e-289) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (- t (* x (/ (- a y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (x - t)) / (z - a));
	double tmp;
	if ((t_1 <= -1e-289) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t - (x * ((a - y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (x - t)) / (z - a))
    if ((t_1 <= (-1d-289)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t - (x * ((a - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (x - t)) / (z - a));
	double tmp;
	if ((t_1 <= -1e-289) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t - (x * ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (x - t)) / (z - a))
	tmp = 0
	if (t_1 <= -1e-289) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t - (x * ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(z - a)))
	tmp = 0.0
	if ((t_1 <= -1e-289) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (x - t)) / (z - a));
	tmp = 0.0;
	if ((t_1 <= -1e-289) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t - (x * ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-289], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1e-289 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 70.8%

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

      1. associate-/l* 80.3%

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

   3. Simplified 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-*l/ 70.8%

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

      3. associate-*r/ 88.8%

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

      4. clear-num 88.7%

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

      5. un-div-inv 88.7%

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

   6. Applied egg-rr 88.7%

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

   if -1e-289 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.8%

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

      1. +-commutative 3.8%

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

      2. associate-/l* 3.4%

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

      3. fma-define 3.7%

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

   3. Simplified 3.7%

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

   5. Taylor expanded in x around -inf 84.2%

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

      1. mul-1-neg 84.2%

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

      2. distribute-rgt-neg-in 84.2%

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

      3. +-commutative 84.2%

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

      4. mul-1-neg 84.2%

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

      5. unsub-neg 84.2%

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

      6. associate-/r* 84.0%

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

      7. +-commutative 84.0%

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

   7. Simplified 84.0%

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

   8. Taylor expanded in z around inf 84.3%

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

   9. Taylor expanded in z around inf 99.7%

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

       1. mul-1-neg 99.7%

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

       2. unsub-neg 99.7%

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

       3. associate-/l* 99.8%

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

       4. neg-mul-1 99.8%

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

       5. sub-neg 99.8%

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

   11. Simplified 99.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq -1 \cdot 10^{-289} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-107}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ z (- z a)))))
   (if (<= z -3.5e+69)
     t_1
     (if (<= z -1.05e+28)
       x
       (if (<= z -8.2e-120)
         (* x (/ y z))
         (if (<= z -1.75e-190)
           x
           (if (<= z 9e-107)
             (/ (* y (- t x)) a)
             (if (<= z 8.5e-6) x t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double tmp;
	if (z <= -3.5e+69) {
		tmp = t_1;
	} else if (z <= -1.05e+28) {
		tmp = x;
	} else if (z <= -8.2e-120) {
		tmp = x * (y / z);
	} else if (z <= -1.75e-190) {
		tmp = x;
	} else if (z <= 9e-107) {
		tmp = (y * (t - x)) / a;
	} else if (z <= 8.5e-6) {
		tmp = 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 * (z / (z - a))
    if (z <= (-3.5d+69)) then
        tmp = t_1
    else if (z <= (-1.05d+28)) then
        tmp = x
    else if (z <= (-8.2d-120)) then
        tmp = x * (y / z)
    else if (z <= (-1.75d-190)) then
        tmp = x
    else if (z <= 9d-107) then
        tmp = (y * (t - x)) / a
    else if (z <= 8.5d-6) then
        tmp = 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 * (z / (z - a));
	double tmp;
	if (z <= -3.5e+69) {
		tmp = t_1;
	} else if (z <= -1.05e+28) {
		tmp = x;
	} else if (z <= -8.2e-120) {
		tmp = x * (y / z);
	} else if (z <= -1.75e-190) {
		tmp = x;
	} else if (z <= 9e-107) {
		tmp = (y * (t - x)) / a;
	} else if (z <= 8.5e-6) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (z / (z - a))
	tmp = 0
	if z <= -3.5e+69:
		tmp = t_1
	elif z <= -1.05e+28:
		tmp = x
	elif z <= -8.2e-120:
		tmp = x * (y / z)
	elif z <= -1.75e-190:
		tmp = x
	elif z <= 9e-107:
		tmp = (y * (t - x)) / a
	elif z <= 8.5e-6:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -3.5e+69)
		tmp = t_1;
	elseif (z <= -1.05e+28)
		tmp = x;
	elseif (z <= -8.2e-120)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -1.75e-190)
		tmp = x;
	elseif (z <= 9e-107)
		tmp = Float64(Float64(y * Float64(t - x)) / a);
	elseif (z <= 8.5e-6)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -3.5e+69)
		tmp = t_1;
	elseif (z <= -1.05e+28)
		tmp = x;
	elseif (z <= -8.2e-120)
		tmp = x * (y / z);
	elseif (z <= -1.75e-190)
		tmp = x;
	elseif (z <= 9e-107)
		tmp = (y * (t - x)) / a;
	elseif (z <= 8.5e-6)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+69], t$95$1, If[LessEqual[z, -1.05e+28], x, If[LessEqual[z, -8.2e-120], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.75e-190], x, If[LessEqual[z, 9e-107], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 8.5e-6], x, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.49999999999999987e69 or 8.4999999999999999e-6 < z

   1. Initial program 40.1%

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

      1. +-commutative 40.1%

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

      2. associate-/l* 57.4%

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

      3. fma-define 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in y around 0 28.7%

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

      1. mul-1-neg 28.7%

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

      2. associate-/l* 44.5%

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

      3. distribute-lft-neg-out 44.5%

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

      4. *-commutative 44.5%

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

   7. Simplified 44.5%

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

   8. Taylor expanded in x around 0 31.8%

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

      1. mul-1-neg 31.8%

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

      2. associate-/l* 51.7%

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

      3. distribute-lft-neg-in 51.7%

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

   10. Simplified 51.7%

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

   if -3.49999999999999987e69 < z < -1.04999999999999995e28 or -8.20000000000000068e-120 < z < -1.75e-190 or 9.00000000000000032e-107 < z < 8.4999999999999999e-6

   1. Initial program 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-/l* 87.6%

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

      3. fma-define 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in a around inf 60.9%

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

   if -1.04999999999999995e28 < z < -8.20000000000000068e-120

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. associate-/l* 96.2%

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

      3. fma-define 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around -inf 81.7%

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

      1. associate-*r* 81.7%

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

      2. neg-mul-1 81.7%

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

      3. fma-define 81.7%

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

      4. times-frac 85.4%

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

      5. +-commutative 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in x around inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. *-commutative 74.7%

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

      3. distribute-rgt-neg-in 74.7%

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

   10. Simplified 74.7%

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

   11. Taylor expanded in a around 0 53.6%

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

       1. associate-*r/ 53.6%

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

       2. neg-mul-1 53.6%

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

   13. Simplified 53.6%

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

   if -1.75e-190 < z < 9.00000000000000032e-107

   1. Initial program 90.4%

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

      1. +-commutative 90.4%

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

      2. associate-/l* 87.5%

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

      3. fma-define 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around -inf 62.2%

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

   6. Taylor expanded in a around inf 56.6%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-107}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ t_2 := t - x \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+227}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+86}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- x t) (- z a)))))
        (t_2 (- t (* x (/ (- a y) z)))))
   (if (<= z -2.6e+227)
     t_2
     (if (<= z -7.2e+106)
       t_1
       (if (<= z -2.6e+86)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= z 1.9e+105) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((x - t) / (z - a)));
	double t_2 = t - (x * ((a - y) / z));
	double tmp;
	if (z <= -2.6e+227) {
		tmp = t_2;
	} else if (z <= -7.2e+106) {
		tmp = t_1;
	} else if (z <= -2.6e+86) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= 1.9e+105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) * ((x - t) / (z - a)))
    t_2 = t - (x * ((a - y) / z))
    if (z <= (-2.6d+227)) then
        tmp = t_2
    else if (z <= (-7.2d+106)) then
        tmp = t_1
    else if (z <= (-2.6d+86)) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (z <= 1.9d+105) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((x - t) / (z - a)));
	double t_2 = t - (x * ((a - y) / z));
	double tmp;
	if (z <= -2.6e+227) {
		tmp = t_2;
	} else if (z <= -7.2e+106) {
		tmp = t_1;
	} else if (z <= -2.6e+86) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= 1.9e+105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((x - t) / (z - a)))
	t_2 = t - (x * ((a - y) / z))
	tmp = 0
	if z <= -2.6e+227:
		tmp = t_2
	elif z <= -7.2e+106:
		tmp = t_1
	elif z <= -2.6e+86:
		tmp = t + (((t - x) * (a - y)) / z)
	elif z <= 1.9e+105:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(z - a))))
	t_2 = Float64(t - Float64(x * Float64(Float64(a - y) / z)))
	tmp = 0.0
	if (z <= -2.6e+227)
		tmp = t_2;
	elseif (z <= -7.2e+106)
		tmp = t_1;
	elseif (z <= -2.6e+86)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (z <= 1.9e+105)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((x - t) / (z - a)));
	t_2 = t - (x * ((a - y) / z));
	tmp = 0.0;
	if (z <= -2.6e+227)
		tmp = t_2;
	elseif (z <= -7.2e+106)
		tmp = t_1;
	elseif (z <= -2.6e+86)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (z <= 1.9e+105)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+227], t$95$2, If[LessEqual[z, -7.2e+106], t$95$1, If[LessEqual[z, -2.6e+86], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+105], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.59999999999999982e227 or 1.9e105 < z

   1. Initial program 31.9%

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

      1. +-commutative 31.9%

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

      2. associate-/l* 45.2%

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

      3. fma-define 45.3%

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

   3. Simplified 45.3%

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

   5. Taylor expanded in x around -inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. distribute-rgt-neg-in 51.4%

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

      3. +-commutative 51.4%

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

      4. mul-1-neg 51.4%

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

      5. unsub-neg 51.4%

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

      6. associate-/r* 41.6%

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

      7. +-commutative 41.6%

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

   7. Simplified 41.6%

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

   8. Taylor expanded in z around inf 76.9%

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

   9. Taylor expanded in z around inf 72.1%

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

       1. mul-1-neg 72.1%

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

       2. unsub-neg 72.1%

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

       3. associate-/l* 87.6%

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

       4. neg-mul-1 87.6%

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

       5. sub-neg 87.6%

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

   11. Simplified 87.6%

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

   if -2.59999999999999982e227 < z < -7.2000000000000002e106 or -2.5999999999999998e86 < z < 1.9e105

   1. Initial program 78.5%

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

      1. associate-/l* 85.6%

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

   3. Simplified 85.6%

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

   if -7.2000000000000002e106 < z < -2.5999999999999998e86

   1. Initial program 17.2%

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

      1. +-commutative 17.2%

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

      2. associate-/l* 31.4%

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

      3. fma-define 30.3%

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

   3. Simplified 30.3%

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

   5. Taylor expanded in z around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. associate-*r/ 99.6%

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

      4. mul-1-neg 99.6%

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

      5. div-sub 99.6%

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

      6. mul-1-neg 99.6%

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

      7. distribute-lft-out-- 99.6%

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

      8. associate-*r/ 99.6%

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

      9. mul-1-neg 99.6%

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

      10. unsub-neg 99.6%

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

      11. distribute-rgt-out-- 99.6%

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

   7. Simplified 99.6%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+227}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+106}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+86}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+105}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 40.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e+69)
   t
   (if (<= z -1.2e+28)
     x
     (if (<= z -9e-120)
       (* x (/ y z))
       (if (<= z -4e-190)
         x
         (if (<= z 8.5e-114) (/ (* y (- t x)) a) (if (<= z 2.45e-5) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+69) {
		tmp = t;
	} else if (z <= -1.2e+28) {
		tmp = x;
	} else if (z <= -9e-120) {
		tmp = x * (y / z);
	} else if (z <= -4e-190) {
		tmp = x;
	} else if (z <= 8.5e-114) {
		tmp = (y * (t - x)) / a;
	} else if (z <= 2.45e-5) {
		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+69)) then
        tmp = t
    else if (z <= (-1.2d+28)) then
        tmp = x
    else if (z <= (-9d-120)) then
        tmp = x * (y / z)
    else if (z <= (-4d-190)) then
        tmp = x
    else if (z <= 8.5d-114) then
        tmp = (y * (t - x)) / a
    else if (z <= 2.45d-5) 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+69) {
		tmp = t;
	} else if (z <= -1.2e+28) {
		tmp = x;
	} else if (z <= -9e-120) {
		tmp = x * (y / z);
	} else if (z <= -4e-190) {
		tmp = x;
	} else if (z <= 8.5e-114) {
		tmp = (y * (t - x)) / a;
	} else if (z <= 2.45e-5) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e+69:
		tmp = t
	elif z <= -1.2e+28:
		tmp = x
	elif z <= -9e-120:
		tmp = x * (y / z)
	elif z <= -4e-190:
		tmp = x
	elif z <= 8.5e-114:
		tmp = (y * (t - x)) / a
	elif z <= 2.45e-5:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e+69)
		tmp = t;
	elseif (z <= -1.2e+28)
		tmp = x;
	elseif (z <= -9e-120)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -4e-190)
		tmp = x;
	elseif (z <= 8.5e-114)
		tmp = Float64(Float64(y * Float64(t - x)) / a);
	elseif (z <= 2.45e-5)
		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+69)
		tmp = t;
	elseif (z <= -1.2e+28)
		tmp = x;
	elseif (z <= -9e-120)
		tmp = x * (y / z);
	elseif (z <= -4e-190)
		tmp = x;
	elseif (z <= 8.5e-114)
		tmp = (y * (t - x)) / a;
	elseif (z <= 2.45e-5)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e+69], t, If[LessEqual[z, -1.2e+28], x, If[LessEqual[z, -9e-120], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e-190], x, If[LessEqual[z, 8.5e-114], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 2.45e-5], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.99999999999999983e69 or 2.45e-5 < z

   1. Initial program 40.1%

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

      1. +-commutative 40.1%

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

      2. associate-/l* 57.4%

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

      3. fma-define 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in z around inf 48.1%

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

   if -2.99999999999999983e69 < z < -1.19999999999999991e28 or -9e-120 < z < -4.0000000000000001e-190 or 8.5000000000000006e-114 < z < 2.45e-5

   1. Initial program 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-/l* 87.6%

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

      3. fma-define 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in a around inf 60.9%

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

   if -1.19999999999999991e28 < z < -9e-120

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. associate-/l* 96.2%

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

      3. fma-define 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around -inf 81.7%

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

      1. associate-*r* 81.7%

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

      2. neg-mul-1 81.7%

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

      3. fma-define 81.7%

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

      4. times-frac 85.4%

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

      5. +-commutative 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in x around inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. *-commutative 74.7%

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

      3. distribute-rgt-neg-in 74.7%

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

   10. Simplified 74.7%

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

   11. Taylor expanded in a around 0 53.6%

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

       1. associate-*r/ 53.6%

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

       2. neg-mul-1 53.6%

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

   13. Simplified 53.6%

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

   if -4.0000000000000001e-190 < z < 8.5000000000000006e-114

   1. Initial program 90.4%

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

      1. +-commutative 90.4%

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

      2. associate-/l* 87.5%

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

      3. fma-define 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around -inf 62.2%

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

   6. Taylor expanded in a around inf 56.6%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-108}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.1e+69)
   t
   (if (<= z -1.8e+28)
     x
     (if (<= z -2.2e-119)
       (* x (/ y z))
       (if (<= z -1.3e-190)
         x
         (if (<= z 3.8e-108) (* y (/ (- t x) a)) (if (<= z 2.5e-5) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e+69) {
		tmp = t;
	} else if (z <= -1.8e+28) {
		tmp = x;
	} else if (z <= -2.2e-119) {
		tmp = x * (y / z);
	} else if (z <= -1.3e-190) {
		tmp = x;
	} else if (z <= 3.8e-108) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.5e-5) {
		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 <= (-5.1d+69)) then
        tmp = t
    else if (z <= (-1.8d+28)) then
        tmp = x
    else if (z <= (-2.2d-119)) then
        tmp = x * (y / z)
    else if (z <= (-1.3d-190)) then
        tmp = x
    else if (z <= 3.8d-108) then
        tmp = y * ((t - x) / a)
    else if (z <= 2.5d-5) 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 <= -5.1e+69) {
		tmp = t;
	} else if (z <= -1.8e+28) {
		tmp = x;
	} else if (z <= -2.2e-119) {
		tmp = x * (y / z);
	} else if (z <= -1.3e-190) {
		tmp = x;
	} else if (z <= 3.8e-108) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.5e-5) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.1e+69:
		tmp = t
	elif z <= -1.8e+28:
		tmp = x
	elif z <= -2.2e-119:
		tmp = x * (y / z)
	elif z <= -1.3e-190:
		tmp = x
	elif z <= 3.8e-108:
		tmp = y * ((t - x) / a)
	elif z <= 2.5e-5:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.1e+69)
		tmp = t;
	elseif (z <= -1.8e+28)
		tmp = x;
	elseif (z <= -2.2e-119)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -1.3e-190)
		tmp = x;
	elseif (z <= 3.8e-108)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 2.5e-5)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.1e+69)
		tmp = t;
	elseif (z <= -1.8e+28)
		tmp = x;
	elseif (z <= -2.2e-119)
		tmp = x * (y / z);
	elseif (z <= -1.3e-190)
		tmp = x;
	elseif (z <= 3.8e-108)
		tmp = y * ((t - x) / a);
	elseif (z <= 2.5e-5)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.1e+69], t, If[LessEqual[z, -1.8e+28], x, If[LessEqual[z, -2.2e-119], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-190], x, If[LessEqual[z, 3.8e-108], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-5], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.09999999999999999e69 or 2.50000000000000012e-5 < z

   1. Initial program 40.1%

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

      1. +-commutative 40.1%

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

      2. associate-/l* 57.4%

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

      3. fma-define 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in z around inf 48.1%

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

   if -5.09999999999999999e69 < z < -1.8e28 or -2.2000000000000001e-119 < z < -1.2999999999999999e-190 or 3.79999999999999973e-108 < z < 2.50000000000000012e-5

   1. Initial program 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-/l* 87.6%

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

      3. fma-define 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in a around inf 60.9%

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

   if -1.8e28 < z < -2.2000000000000001e-119

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. associate-/l* 96.2%

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

      3. fma-define 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around -inf 81.7%

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

      1. associate-*r* 81.7%

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

      2. neg-mul-1 81.7%

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

      3. fma-define 81.7%

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

      4. times-frac 85.4%

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

      5. +-commutative 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in x around inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. *-commutative 74.7%

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

      3. distribute-rgt-neg-in 74.7%

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

   10. Simplified 74.7%

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

   11. Taylor expanded in a around 0 53.6%

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

       1. associate-*r/ 53.6%

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

       2. neg-mul-1 53.6%

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

   13. Simplified 53.6%

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

   if -1.2999999999999999e-190 < z < 3.79999999999999973e-108

   1. Initial program 90.4%

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

      1. +-commutative 90.4%

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

      2. associate-/l* 87.5%

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

      3. fma-define 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around -inf 62.2%

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

   6. Taylor expanded in a around inf 56.6%

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

      1. associate-/l* 52.3%

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

   8. Simplified 52.3%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-108}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= z -1.6e+69)
     t
     (if (<= z -5.8e+27)
       x
       (if (<= z -6.8e-140)
         t_1
         (if (<= z -1.7e-191)
           x
           (if (<= z 1.5e-117) t_1 (if (<= z 3e-5) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -1.6e+69) {
		tmp = t;
	} else if (z <= -5.8e+27) {
		tmp = x;
	} else if (z <= -6.8e-140) {
		tmp = t_1;
	} else if (z <= -1.7e-191) {
		tmp = x;
	} else if (z <= 1.5e-117) {
		tmp = t_1;
	} else if (z <= 3e-5) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    if (z <= (-1.6d+69)) then
        tmp = t
    else if (z <= (-5.8d+27)) then
        tmp = x
    else if (z <= (-6.8d-140)) then
        tmp = t_1
    else if (z <= (-1.7d-191)) then
        tmp = x
    else if (z <= 1.5d-117) then
        tmp = t_1
    else if (z <= 3d-5) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -1.6e+69) {
		tmp = t;
	} else if (z <= -5.8e+27) {
		tmp = x;
	} else if (z <= -6.8e-140) {
		tmp = t_1;
	} else if (z <= -1.7e-191) {
		tmp = x;
	} else if (z <= 1.5e-117) {
		tmp = t_1;
	} else if (z <= 3e-5) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if z <= -1.6e+69:
		tmp = t
	elif z <= -5.8e+27:
		tmp = x
	elif z <= -6.8e-140:
		tmp = t_1
	elif z <= -1.7e-191:
		tmp = x
	elif z <= 1.5e-117:
		tmp = t_1
	elif z <= 3e-5:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (z <= -1.6e+69)
		tmp = t;
	elseif (z <= -5.8e+27)
		tmp = x;
	elseif (z <= -6.8e-140)
		tmp = t_1;
	elseif (z <= -1.7e-191)
		tmp = x;
	elseif (z <= 1.5e-117)
		tmp = t_1;
	elseif (z <= 3e-5)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (z <= -1.6e+69)
		tmp = t;
	elseif (z <= -5.8e+27)
		tmp = x;
	elseif (z <= -6.8e-140)
		tmp = t_1;
	elseif (z <= -1.7e-191)
		tmp = x;
	elseif (z <= 1.5e-117)
		tmp = t_1;
	elseif (z <= 3e-5)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+69], t, If[LessEqual[z, -5.8e+27], x, If[LessEqual[z, -6.8e-140], t$95$1, If[LessEqual[z, -1.7e-191], x, If[LessEqual[z, 1.5e-117], t$95$1, If[LessEqual[z, 3e-5], x, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.59999999999999992e69 or 3.00000000000000008e-5 < z

   1. Initial program 40.1%

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

      1. +-commutative 40.1%

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

      2. associate-/l* 57.4%

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

      3. fma-define 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in z around inf 48.1%

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

   if -1.59999999999999992e69 < z < -5.8000000000000002e27 or -6.80000000000000017e-140 < z < -1.69999999999999997e-191 or 1.49999999999999996e-117 < z < 3.00000000000000008e-5

   1. Initial program 78.2%

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

      1. +-commutative 78.2%

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

      2. associate-/l* 89.0%

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

      3. fma-define 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in a around inf 64.3%

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

   if -5.8000000000000002e27 < z < -6.80000000000000017e-140 or -1.69999999999999997e-191 < z < 1.49999999999999996e-117

   1. Initial program 91.4%

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

      1. +-commutative 91.4%

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

      2. associate-/l* 89.3%

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

      3. fma-define 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in y around -inf 64.5%

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

   6. Taylor expanded in a around inf 54.4%

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

      1. associate-/l* 51.4%

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

   8. Simplified 51.4%

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

Alternative 10: 72.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+34}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+104}:\\ \;\;\;\;x + z \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (* (- t x) (- a y)) z))))
   (if (<= z -5.1e+69)
     t_1
     (if (<= z 4.1e+34)
       (+ x (* (- t x) (/ (- y z) a)))
       (if (<= z 6.5e+96)
         t_1
         (if (<= z 3.5e+104)
           (+ x (* z (/ (- t x) (- z a))))
           (- t (* x (/ (- a y) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) * (a - y)) / z);
	double tmp;
	if (z <= -5.1e+69) {
		tmp = t_1;
	} else if (z <= 4.1e+34) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else if (z <= 6.5e+96) {
		tmp = t_1;
	} else if (z <= 3.5e+104) {
		tmp = x + (z * ((t - x) / (z - a)));
	} else {
		tmp = t - (x * ((a - y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (((t - x) * (a - y)) / z)
    if (z <= (-5.1d+69)) then
        tmp = t_1
    else if (z <= 4.1d+34) then
        tmp = x + ((t - x) * ((y - z) / a))
    else if (z <= 6.5d+96) then
        tmp = t_1
    else if (z <= 3.5d+104) then
        tmp = x + (z * ((t - x) / (z - a)))
    else
        tmp = t - (x * ((a - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) * (a - y)) / z);
	double tmp;
	if (z <= -5.1e+69) {
		tmp = t_1;
	} else if (z <= 4.1e+34) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else if (z <= 6.5e+96) {
		tmp = t_1;
	} else if (z <= 3.5e+104) {
		tmp = x + (z * ((t - x) / (z - a)));
	} else {
		tmp = t - (x * ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) * (a - y)) / z)
	tmp = 0
	if z <= -5.1e+69:
		tmp = t_1
	elif z <= 4.1e+34:
		tmp = x + ((t - x) * ((y - z) / a))
	elif z <= 6.5e+96:
		tmp = t_1
	elif z <= 3.5e+104:
		tmp = x + (z * ((t - x) / (z - a)))
	else:
		tmp = t - (x * ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z))
	tmp = 0.0
	if (z <= -5.1e+69)
		tmp = t_1;
	elseif (z <= 4.1e+34)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	elseif (z <= 6.5e+96)
		tmp = t_1;
	elseif (z <= 3.5e+104)
		tmp = Float64(x + Float64(z * Float64(Float64(t - x) / Float64(z - a))));
	else
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) * (a - y)) / z);
	tmp = 0.0;
	if (z <= -5.1e+69)
		tmp = t_1;
	elseif (z <= 4.1e+34)
		tmp = x + ((t - x) * ((y - z) / a));
	elseif (z <= 6.5e+96)
		tmp = t_1;
	elseif (z <= 3.5e+104)
		tmp = x + (z * ((t - x) / (z - a)));
	else
		tmp = t - (x * ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.1e+69], t$95$1, If[LessEqual[z, 4.1e+34], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+96], t$95$1, If[LessEqual[z, 3.5e+104], N[(x + N[(z * N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.09999999999999999e69 or 4.0999999999999998e34 < z < 6.5e96

   1. Initial program 39.4%

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

      1. +-commutative 39.4%

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

      2. associate-/l* 59.6%

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

      3. fma-define 59.5%

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

   3. Simplified 59.5%

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

   5. Taylor expanded in z around inf 67.2%

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

      1. associate--l+ 67.2%

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

      2. associate-*r/ 67.2%

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

      3. associate-*r/ 67.2%

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

      4. mul-1-neg 67.2%

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

      5. div-sub 67.2%

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

      6. mul-1-neg 67.2%

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

      7. distribute-lft-out-- 67.2%

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

      8. associate-*r/ 67.2%

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

      9. mul-1-neg 67.2%

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

      10. unsub-neg 67.2%

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

      11. distribute-rgt-out-- 68.6%

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

   7. Simplified 68.6%

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

   if -5.09999999999999999e69 < z < 4.0999999999999998e34

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. associate-/l* 89.4%

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

      3. fma-define 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around inf 76.9%

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

      1. associate-/l* 83.0%

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

   7. Simplified 83.0%

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

   if 6.5e96 < z < 3.5000000000000002e104

   1. Initial program 61.5%

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

      1. +-commutative 61.5%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 61.5%

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

      1. mul-1-neg 61.5%

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

      2. associate-/l* 100.0%

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

      3. distribute-lft-neg-out 100.0%

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

      4. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 3.5000000000000002e104 < z

   1. Initial program 36.0%

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

      1. +-commutative 36.0%

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

      2. associate-/l* 46.7%

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

      3. fma-define 46.6%

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

   3. Simplified 46.6%

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

   5. Taylor expanded in x around -inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-rgt-neg-in 53.4%

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

      3. +-commutative 53.4%

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

      4. mul-1-neg 53.4%

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

      5. unsub-neg 53.4%

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

      6. associate-/r* 38.7%

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

      7. +-commutative 38.7%

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

   7. Simplified 38.7%

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

   8. Taylor expanded in z around inf 74.8%

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

   9. Taylor expanded in z around inf 70.2%

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

       1. mul-1-neg 70.2%

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

       2. unsub-neg 70.2%

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

       3. associate-/l* 88.5%

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

       4. neg-mul-1 88.5%

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

       5. sub-neg 88.5%

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

   11. Simplified 88.5%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+69}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+34}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+96}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+104}:\\ \;\;\;\;x + z \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-x\right) \cdot \left(-1 + \frac{y}{a}\right)\\ t_2 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+128}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-222}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x) (+ -1.0 (/ y a)))) (t_2 (* t (/ z (- z a)))))
   (if (<= z -6.8e+128)
     t_2
     (if (<= z -1.7e-275)
       t_1
       (if (<= z 2.8e-222)
         (* t (/ y (- a z)))
         (if (<= z 1.55e+90) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -x * (-1.0 + (y / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -6.8e+128) {
		tmp = t_2;
	} else if (z <= -1.7e-275) {
		tmp = t_1;
	} else if (z <= 2.8e-222) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.55e+90) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -x * ((-1.0d0) + (y / a))
    t_2 = t * (z / (z - a))
    if (z <= (-6.8d+128)) then
        tmp = t_2
    else if (z <= (-1.7d-275)) then
        tmp = t_1
    else if (z <= 2.8d-222) then
        tmp = t * (y / (a - z))
    else if (z <= 1.55d+90) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -x * (-1.0 + (y / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -6.8e+128) {
		tmp = t_2;
	} else if (z <= -1.7e-275) {
		tmp = t_1;
	} else if (z <= 2.8e-222) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.55e+90) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -x * (-1.0 + (y / a))
	t_2 = t * (z / (z - a))
	tmp = 0
	if z <= -6.8e+128:
		tmp = t_2
	elif z <= -1.7e-275:
		tmp = t_1
	elif z <= 2.8e-222:
		tmp = t * (y / (a - z))
	elif z <= 1.55e+90:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-x) * Float64(-1.0 + Float64(y / a)))
	t_2 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -6.8e+128)
		tmp = t_2;
	elseif (z <= -1.7e-275)
		tmp = t_1;
	elseif (z <= 2.8e-222)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1.55e+90)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -x * (-1.0 + (y / a));
	t_2 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -6.8e+128)
		tmp = t_2;
	elseif (z <= -1.7e-275)
		tmp = t_1;
	elseif (z <= 2.8e-222)
		tmp = t * (y / (a - z));
	elseif (z <= 1.55e+90)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-x) * N[(-1.0 + N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+128], t$95$2, If[LessEqual[z, -1.7e-275], t$95$1, If[LessEqual[z, 2.8e-222], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+90], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.7999999999999997e128 or 1.54999999999999994e90 < z

   1. Initial program 34.6%

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

      1. +-commutative 34.6%

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

      2. associate-/l* 53.1%

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

      3. fma-define 53.2%

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

   3. Simplified 53.2%

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

   5. Taylor expanded in y around 0 28.2%

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

      1. mul-1-neg 28.2%

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

      2. associate-/l* 44.8%

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

      3. distribute-lft-neg-out 44.8%

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

      4. *-commutative 44.8%

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

   7. Simplified 44.8%

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

   8. Taylor expanded in x around 0 34.0%

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

      1. mul-1-neg 34.0%

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

      2. associate-/l* 58.3%

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

      3. distribute-lft-neg-in 58.3%

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

   10. Simplified 58.3%

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

   if -6.7999999999999997e128 < z < -1.69999999999999984e-275 or 2.80000000000000007e-222 < z < 1.54999999999999994e90

   1. Initial program 79.6%

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

      1. +-commutative 79.6%

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

      2. associate-/l* 86.7%

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

      3. fma-define 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in x around -inf 81.5%

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

      1. associate-*r* 81.5%

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

      2. neg-mul-1 81.5%

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

      3. fma-define 81.5%

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

      4. times-frac 86.5%

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

      5. +-commutative 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in x around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. *-commutative 62.2%

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

      3. distribute-rgt-neg-in 62.2%

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

   10. Simplified 62.2%

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

   11. Taylor expanded in z around 0 52.2%

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

   if -1.69999999999999984e-275 < z < 2.80000000000000007e-222

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. associate-/l* 83.1%

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

      3. fma-define 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in y around -inf 67.0%

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

   6. Taylor expanded in t around inf 63.6%

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

      1. associate-/l* 66.7%

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

   8. Simplified 66.7%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+128}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-275}:\\ \;\;\;\;\left(-x\right) \cdot \left(-1 + \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-222}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+90}:\\ \;\;\;\;\left(-x\right) \cdot \left(-1 + \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-102}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ z (- z a)))))
   (if (<= z -2.5e+101)
     t_1
     (if (<= z -6e-65)
       (* y (/ (- x t) z))
       (if (<= z 6.4e-102) (/ (* y (- t x)) a) (if (<= z 2.45e-5) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double tmp;
	if (z <= -2.5e+101) {
		tmp = t_1;
	} else if (z <= -6e-65) {
		tmp = y * ((x - t) / z);
	} else if (z <= 6.4e-102) {
		tmp = (y * (t - x)) / a;
	} else if (z <= 2.45e-5) {
		tmp = 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 * (z / (z - a))
    if (z <= (-2.5d+101)) then
        tmp = t_1
    else if (z <= (-6d-65)) then
        tmp = y * ((x - t) / z)
    else if (z <= 6.4d-102) then
        tmp = (y * (t - x)) / a
    else if (z <= 2.45d-5) then
        tmp = 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 * (z / (z - a));
	double tmp;
	if (z <= -2.5e+101) {
		tmp = t_1;
	} else if (z <= -6e-65) {
		tmp = y * ((x - t) / z);
	} else if (z <= 6.4e-102) {
		tmp = (y * (t - x)) / a;
	} else if (z <= 2.45e-5) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (z / (z - a))
	tmp = 0
	if z <= -2.5e+101:
		tmp = t_1
	elif z <= -6e-65:
		tmp = y * ((x - t) / z)
	elif z <= 6.4e-102:
		tmp = (y * (t - x)) / a
	elif z <= 2.45e-5:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -2.5e+101)
		tmp = t_1;
	elseif (z <= -6e-65)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (z <= 6.4e-102)
		tmp = Float64(Float64(y * Float64(t - x)) / a);
	elseif (z <= 2.45e-5)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -2.5e+101)
		tmp = t_1;
	elseif (z <= -6e-65)
		tmp = y * ((x - t) / z);
	elseif (z <= 6.4e-102)
		tmp = (y * (t - x)) / a;
	elseif (z <= 2.45e-5)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+101], t$95$1, If[LessEqual[z, -6e-65], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e-102], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 2.45e-5], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.49999999999999994e101 or 2.45e-5 < z

   1. Initial program 39.9%

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

      1. +-commutative 39.9%

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

      2. associate-/l* 57.9%

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

      3. fma-define 57.9%

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

   3. Simplified 57.9%

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

   5. Taylor expanded in y around 0 29.2%

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

      1. mul-1-neg 29.2%

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

      2. associate-/l* 46.4%

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

      3. distribute-lft-neg-out 46.4%

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

      4. *-commutative 46.4%

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

   7. Simplified 46.4%

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

   8. Taylor expanded in x around 0 32.2%

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

      1. mul-1-neg 32.2%

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

      2. associate-/l* 54.0%

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

      3. distribute-lft-neg-in 54.0%

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

   10. Simplified 54.0%

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

   if -2.49999999999999994e101 < z < -5.99999999999999996e-65

   1. Initial program 70.5%

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

      1. +-commutative 70.5%

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

      2. associate-/l* 80.3%

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

      3. fma-define 80.2%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in y around -inf 45.9%

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

   6. Taylor expanded in a around 0 39.0%

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

      1. mul-1-neg 39.0%

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

      2. associate-/l* 43.8%

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

      3. distribute-lft-neg-in 43.8%

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

   8. Simplified 43.8%

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

   if -5.99999999999999996e-65 < z < 6.39999999999999973e-102

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-/l* 89.5%

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

      3. fma-define 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in y around -inf 60.6%

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

   6. Taylor expanded in a around inf 55.0%

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

   if 6.39999999999999973e-102 < z < 2.45e-5

   1. Initial program 79.5%

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

      1. +-commutative 79.5%

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

      2. associate-/l* 86.2%

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

      3. fma-define 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in a around inf 59.0%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+101}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-102}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-105}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.95e+69)
   t
   (if (<= z -1.25e-191)
     x
     (if (<= z 5.5e-105) (* t (/ y (- a z))) (if (<= z 1.6e-5) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.95e+69) {
		tmp = t;
	} else if (z <= -1.25e-191) {
		tmp = x;
	} else if (z <= 5.5e-105) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.6e-5) {
		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 <= (-2.95d+69)) then
        tmp = t
    else if (z <= (-1.25d-191)) then
        tmp = x
    else if (z <= 5.5d-105) then
        tmp = t * (y / (a - z))
    else if (z <= 1.6d-5) 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 <= -2.95e+69) {
		tmp = t;
	} else if (z <= -1.25e-191) {
		tmp = x;
	} else if (z <= 5.5e-105) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.6e-5) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.95e+69:
		tmp = t
	elif z <= -1.25e-191:
		tmp = x
	elif z <= 5.5e-105:
		tmp = t * (y / (a - z))
	elif z <= 1.6e-5:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.95e+69)
		tmp = t;
	elseif (z <= -1.25e-191)
		tmp = x;
	elseif (z <= 5.5e-105)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1.6e-5)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.95e+69)
		tmp = t;
	elseif (z <= -1.25e-191)
		tmp = x;
	elseif (z <= 5.5e-105)
		tmp = t * (y / (a - z));
	elseif (z <= 1.6e-5)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.95e+69], t, If[LessEqual[z, -1.25e-191], x, If[LessEqual[z, 5.5e-105], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-5], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.95000000000000002e69 or 1.59999999999999993e-5 < z

   1. Initial program 40.1%

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

      1. +-commutative 40.1%

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

      2. associate-/l* 57.4%

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

      3. fma-define 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in z around inf 48.1%

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

   if -2.95000000000000002e69 < z < -1.25e-191 or 5.50000000000000029e-105 < z < 1.59999999999999993e-5

   1. Initial program 85.4%

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

      1. +-commutative 85.4%

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

      2. associate-/l* 91.1%

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

      3. fma-define 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around inf 44.6%

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

   if -1.25e-191 < z < 5.50000000000000029e-105

   1. Initial program 90.4%

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

      1. +-commutative 90.4%

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

      2. associate-/l* 87.5%

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

      3. fma-define 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around -inf 62.2%

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

   6. Taylor expanded in t around inf 48.0%

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

      1. associate-/l* 50.4%

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

   8. Simplified 50.4%

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

Alternative 14: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+69} \lor \neg \left(z \leq 5.6 \cdot 10^{+34}\right):\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.62e+69) (not (<= z 5.6e+34)))
   (- t (* x (/ (- a y) z)))
   (+ x (* (- t x) (/ (- y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.62e+69) || !(z <= 5.6e+34)) {
		tmp = t - (x * ((a - y) / z));
	} else {
		tmp = x + ((t - x) * ((y - z) / 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 <= (-1.62d+69)) .or. (.not. (z <= 5.6d+34))) then
        tmp = t - (x * ((a - y) / z))
    else
        tmp = x + ((t - x) * ((y - z) / 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 <= -1.62e+69) || !(z <= 5.6e+34)) {
		tmp = t - (x * ((a - y) / z));
	} else {
		tmp = x + ((t - x) * ((y - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.62e+69) or not (z <= 5.6e+34):
		tmp = t - (x * ((a - y) / z))
	else:
		tmp = x + ((t - x) * ((y - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.62e+69) || !(z <= 5.6e+34))
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.62e+69) || ~((z <= 5.6e+34)))
		tmp = t - (x * ((a - y) / z));
	else
		tmp = x + ((t - x) * ((y - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.62e+69], N[Not[LessEqual[z, 5.6e+34]], $MachinePrecision]], N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.62e69 or 5.60000000000000016e34 < z

   1. Initial program 39.1%

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

      1. +-commutative 39.1%

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

      2. associate-/l* 56.7%

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

      3. fma-define 56.6%

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

   3. Simplified 56.6%

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

   5. Taylor expanded in x around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

      2. distribute-rgt-neg-in 57.0%

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

      3. +-commutative 57.0%

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

      4. mul-1-neg 57.0%

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

      5. unsub-neg 57.0%

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

      6. associate-/r* 48.7%

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

      7. +-commutative 48.7%

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

   7. Simplified 48.7%

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

   8. Taylor expanded in z around inf 67.4%

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

   9. Taylor expanded in z around inf 64.7%

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

       1. mul-1-neg 64.7%

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

       2. unsub-neg 64.7%

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

       3. associate-/l* 72.9%

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

       4. neg-mul-1 72.9%

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

       5. sub-neg 72.9%

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

   11. Simplified 72.9%

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

   if -1.62e69 < z < 5.60000000000000016e34

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. associate-/l* 89.4%

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

      3. fma-define 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around inf 76.9%

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

      1. associate-/l* 83.0%

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

   7. Simplified 83.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+69} \lor \neg \left(z \leq 5.6 \cdot 10^{+34}\right):\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+69}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+35}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.65e+69)
   (+ t (/ (* (- t x) (- a y)) z))
   (if (<= z 1.6e+35)
     (+ x (* (- t x) (/ (- y z) a)))
     (- t (* x (/ (- a y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e+69) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= 1.6e+35) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else {
		tmp = t - (x * ((a - y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.65d+69)) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (z <= 1.6d+35) then
        tmp = x + ((t - x) * ((y - z) / a))
    else
        tmp = t - (x * ((a - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e+69) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= 1.6e+35) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else {
		tmp = t - (x * ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.65e+69:
		tmp = t + (((t - x) * (a - y)) / z)
	elif z <= 1.6e+35:
		tmp = x + ((t - x) * ((y - z) / a))
	else:
		tmp = t - (x * ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.65e+69)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (z <= 1.6e+35)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	else
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.65e+69)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (z <= 1.6e+35)
		tmp = x + ((t - x) * ((y - z) / a));
	else
		tmp = t - (x * ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.65e+69], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+35], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6499999999999999e69

   1. Initial program 35.7%

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

      1. +-commutative 35.7%

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

      2. associate-/l* 56.2%

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

      3. fma-define 56.1%

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

   3. Simplified 56.1%

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

   5. Taylor expanded in z around inf 65.0%

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

      1. associate--l+ 65.0%

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

      2. associate-*r/ 65.0%

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

      3. associate-*r/ 65.0%

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

      4. mul-1-neg 65.0%

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

      5. div-sub 65.0%

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

      6. mul-1-neg 65.0%

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

      7. distribute-lft-out-- 65.0%

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

      8. associate-*r/ 65.0%

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

      9. mul-1-neg 65.0%

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

      10. unsub-neg 65.0%

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

      11. distribute-rgt-out-- 66.7%

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

   7. Simplified 66.7%

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

   if -1.6499999999999999e69 < z < 1.59999999999999991e35

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. associate-/l* 89.4%

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

      3. fma-define 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around inf 76.9%

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

      1. associate-/l* 83.0%

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

   7. Simplified 83.0%

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

   if 1.59999999999999991e35 < z

   1. Initial program 42.7%

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

      1. +-commutative 42.7%

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

      2. associate-/l* 57.3%

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

      3. fma-define 57.1%

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

   3. Simplified 57.1%

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

   5. Taylor expanded in x around -inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. distribute-rgt-neg-in 52.3%

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

      3. +-commutative 52.3%

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

      4. mul-1-neg 52.3%

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

      5. unsub-neg 52.3%

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

      6. associate-/r* 40.0%

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

      7. +-commutative 40.0%

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

   7. Simplified 40.0%

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

   8. Taylor expanded in z around inf 65.0%

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

   9. Taylor expanded in z around inf 66.0%

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

       1. mul-1-neg 66.0%

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

       2. unsub-neg 66.0%

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

       3. associate-/l* 79.5%

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

       4. neg-mul-1 79.5%

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

       5. sub-neg 79.5%

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

   11. Simplified 79.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+69}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+35}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 71.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+69} \lor \neg \left(z \leq 2.4 \cdot 10^{-6}\right):\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2e+69) (not (<= z 2.4e-6)))
   (- t (* x (/ (- a y) z)))
   (+ x (/ (- t x) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e+69) || !(z <= 2.4e-6)) {
		tmp = t - (x * ((a - y) / z));
	} else {
		tmp = x + ((t - x) / (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 <= (-2d+69)) .or. (.not. (z <= 2.4d-6))) then
        tmp = t - (x * ((a - y) / z))
    else
        tmp = x + ((t - x) / (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 <= -2e+69) || !(z <= 2.4e-6)) {
		tmp = t - (x * ((a - y) / z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2e+69) or not (z <= 2.4e-6):
		tmp = t - (x * ((a - y) / z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2e+69) || !(z <= 2.4e-6))
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2e+69) || ~((z <= 2.4e-6)))
		tmp = t - (x * ((a - y) / z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2e+69], N[Not[LessEqual[z, 2.4e-6]], $MachinePrecision]], N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e69 or 2.3999999999999999e-6 < z

   1. Initial program 40.1%

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

      1. +-commutative 40.1%

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

      2. associate-/l* 57.4%

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

      3. fma-define 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in x around -inf 57.7%

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

      1. mul-1-neg 57.7%

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

      2. distribute-rgt-neg-in 57.7%

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

      3. +-commutative 57.7%

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

      4. mul-1-neg 57.7%

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

      5. unsub-neg 57.7%

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

      6. associate-/r* 49.6%

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

      7. +-commutative 49.6%

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

   7. Simplified 49.6%

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

   8. Taylor expanded in z around inf 67.9%

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

   9. Taylor expanded in z around inf 64.5%

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

       1. mul-1-neg 64.5%

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

       2. unsub-neg 64.5%

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

       3. associate-/l* 72.5%

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

       4. neg-mul-1 72.5%

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

       5. sub-neg 72.5%

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

   11. Simplified 72.5%

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

   if -2.0000000000000001e69 < z < 2.3999999999999999e-6

   1. Initial program 88.0%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

      1. *-commutative 89.3%

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

      2. associate-*l/ 88.0%

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

      3. associate-*r/ 94.9%

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

      4. clear-num 94.9%

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

      5. un-div-inv 94.9%

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

   6. Applied egg-rr 94.9%

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

   7. Taylor expanded in z around 0 80.7%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+69} \lor \neg \left(z \leq 2.4 \cdot 10^{-6}\right):\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \lor \neg \left(x \leq 2.45 \cdot 10^{+120}\right):\\ \;\;\;\;\left(-x\right) \cdot \left(-1 + \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.8) (not (<= x 2.45e+120)))
   (* (- x) (+ -1.0 (/ y a)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.8) || !(x <= 2.45e+120)) {
		tmp = -x * (-1.0 + (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-4.8d0)) .or. (.not. (x <= 2.45d+120))) then
        tmp = -x * ((-1.0d0) + (y / a))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.8) || !(x <= 2.45e+120)) {
		tmp = -x * (-1.0 + (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.8) or not (x <= 2.45e+120):
		tmp = -x * (-1.0 + (y / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.8) || !(x <= 2.45e+120))
		tmp = Float64(Float64(-x) * Float64(-1.0 + Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -4.8) || ~((x <= 2.45e+120)))
		tmp = -x * (-1.0 + (y / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.8], N[Not[LessEqual[x, 2.45e+120]], $MachinePrecision]], N[((-x) * N[(-1.0 + N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999982 or 2.45000000000000005e120 < x

   1. Initial program 53.1%

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

      1. +-commutative 53.1%

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

      2. associate-/l* 70.8%

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

      3. fma-define 70.7%

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

   3. Simplified 70.7%

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

   5. Taylor expanded in x around -inf 68.3%

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

      1. associate-*r* 68.3%

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

      2. neg-mul-1 68.3%

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

      3. fma-define 68.3%

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

      4. times-frac 86.0%

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

      5. +-commutative 86.0%

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

   7. Simplified 86.0%

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

   8. Taylor expanded in x around inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. *-commutative 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

   10. Simplified 70.5%

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

   11. Taylor expanded in z around 0 57.0%

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

   if -4.79999999999999982 < x < 2.45000000000000005e120

   1. Initial program 74.3%

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

      1. +-commutative 74.3%

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

      2. associate-/l* 76.8%

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

      3. fma-define 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in t around inf 72.1%

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

      1. div-sub 72.2%

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

   7. Simplified 72.2%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \lor \neg \left(x \leq 2.45 \cdot 10^{+120}\right):\\ \;\;\;\;\left(-x\right) \cdot \left(-1 + \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 66.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(\frac{t}{x} + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.65e+69)
   (* x (+ (/ t x) (/ y z)))
   (if (<= z 5.6e-7) (+ x (/ (- t x) (/ a y))) (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.65e+69) {
		tmp = x * ((t / x) + (y / z));
	} else if (z <= 5.6e-7) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.65d+69)) then
        tmp = x * ((t / x) + (y / z))
    else if (z <= 5.6d-7) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.65e+69) {
		tmp = x * ((t / x) + (y / z));
	} else if (z <= 5.6e-7) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.65e+69:
		tmp = x * ((t / x) + (y / z))
	elif z <= 5.6e-7:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.65e+69)
		tmp = Float64(x * Float64(Float64(t / x) + Float64(y / z)));
	elseif (z <= 5.6e-7)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.65e+69)
		tmp = x * ((t / x) + (y / z));
	elseif (z <= 5.6e-7)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.65e+69], N[(x * N[(N[(t / x), $MachinePrecision] + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-7], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.65e69

   1. Initial program 35.7%

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

      1. +-commutative 35.7%

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

      2. associate-/l* 56.2%

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

      3. fma-define 56.1%

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

   3. Simplified 56.1%

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

   5. Taylor expanded in x around -inf 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-rgt-neg-in 61.4%

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

      3. +-commutative 61.4%

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

      4. mul-1-neg 61.4%

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

      5. unsub-neg 61.4%

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

      6. associate-/r* 56.8%

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

      7. +-commutative 56.8%

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

   7. Simplified 56.8%

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

   8. Taylor expanded in z around inf 69.6%

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

   9. Taylor expanded in a around 0 55.4%

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

       1. cancel-sign-sub-inv 55.4%

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

       2. metadata-eval 55.4%

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

       3. *-lft-identity 55.4%

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

   11. Simplified 55.4%

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

   if -2.65e69 < z < 5.60000000000000038e-7

   1. Initial program 88.0%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

      1. *-commutative 89.3%

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

      2. associate-*l/ 88.0%

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

      3. associate-*r/ 94.9%

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

      4. clear-num 94.9%

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

      5. un-div-inv 94.9%

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

   6. Applied egg-rr 94.9%

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

   7. Taylor expanded in z around 0 80.7%

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

   if 5.60000000000000038e-7 < z

   1. Initial program 44.6%

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

      1. +-commutative 44.6%

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

      2. associate-/l* 58.7%

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

      3. fma-define 58.6%

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

   3. Simplified 58.6%

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

   5. Taylor expanded in t around inf 67.6%

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

      1. div-sub 67.6%

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

   7. Simplified 67.6%

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

Alternative 19: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(\frac{t}{x} + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+69)
   (* x (+ (/ t x) (/ y z)))
   (if (<= z 3.5e-6) (+ x (* y (/ (- t x) a))) (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+69) {
		tmp = x * ((t / x) + (y / z));
	} else if (z <= 3.5e-6) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.8d+69)) then
        tmp = x * ((t / x) + (y / z))
    else if (z <= 3.5d-6) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+69) {
		tmp = x * ((t / x) + (y / z));
	} else if (z <= 3.5e-6) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+69:
		tmp = x * ((t / x) + (y / z))
	elif z <= 3.5e-6:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+69)
		tmp = Float64(x * Float64(Float64(t / x) + Float64(y / z)));
	elseif (z <= 3.5e-6)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.8e+69)
		tmp = x * ((t / x) + (y / z));
	elseif (z <= 3.5e-6)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+69], N[(x * N[(N[(t / x), $MachinePrecision] + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-6], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000003e69

   1. Initial program 35.7%

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

      1. +-commutative 35.7%

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

      2. associate-/l* 56.2%

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

      3. fma-define 56.1%

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

   3. Simplified 56.1%

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

   5. Taylor expanded in x around -inf 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-rgt-neg-in 61.4%

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

      3. +-commutative 61.4%

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

      4. mul-1-neg 61.4%

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

      5. unsub-neg 61.4%

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

      6. associate-/r* 56.8%

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

      7. +-commutative 56.8%

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

   7. Simplified 56.8%

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

   8. Taylor expanded in z around inf 69.6%

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

   9. Taylor expanded in a around 0 55.4%

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

       1. cancel-sign-sub-inv 55.4%

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

       2. metadata-eval 55.4%

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

       3. *-lft-identity 55.4%

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

   11. Simplified 55.4%

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

   if -4.8000000000000003e69 < z < 3.49999999999999995e-6

   1. Initial program 88.0%

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

      1. +-commutative 88.0%

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

      2. associate-/l* 89.3%

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

      3. fma-define 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around 0 76.0%

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

      1. associate-/l* 76.4%

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

   7. Simplified 76.4%

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

   if 3.49999999999999995e-6 < z

   1. Initial program 44.6%

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

      1. +-commutative 44.6%

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

      2. associate-/l* 58.7%

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

      3. fma-define 58.6%

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

   3. Simplified 58.6%

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

   5. Taylor expanded in t around inf 67.6%

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

      1. div-sub 67.6%

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

   7. Simplified 67.6%

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

Alternative 20: 39.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+56}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.6e+74) x (if (<= a 3.8e+56) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.6e+74) {
		tmp = x;
	} else if (a <= 3.8e+56) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.6d+74)) then
        tmp = x
    else if (a <= 3.8d+56) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.6e+74) {
		tmp = x;
	} else if (a <= 3.8e+56) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.6e+74:
		tmp = x
	elif a <= 3.8e+56:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.6e+74)
		tmp = x;
	elseif (a <= 3.8e+56)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.6e+74)
		tmp = x;
	elseif (a <= 3.8e+56)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.6e+74], x, If[LessEqual[a, 3.8e+56], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -8.60000000000000001e74 or 3.79999999999999996e56 < a

   1. Initial program 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-/l* 86.1%

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

      3. fma-define 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in a around inf 56.6%

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

   if -8.60000000000000001e74 < a < 3.79999999999999996e56

   1. Initial program 63.4%

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

      1. +-commutative 63.4%

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

      2. associate-/l* 67.6%

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

      3. fma-define 67.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in z around inf 34.8%

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

Alternative 21: 26.0% 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 65.5%

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

   1. +-commutative 65.5%

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

   2. associate-/l* 74.3%

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

   3. fma-define 74.4%

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

3. Simplified 74.4%

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

5. Taylor expanded in z around inf 26.6%

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

Developer target: 84.3% 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 2024111 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (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))))