Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.7% → 94.6%

Time: 22.4s

Alternatives: 21

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.7% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - a\right) \cdot \frac{t - x}{z}\\ t_2 := \frac{t - x}{a - z}\\ t_3 := \mathsf{fma}\left(y - z, t_2, x\right)\\ t_4 := x + \left(y - z\right) \cdot t_2\\ t_5 := \frac{\left(y - z\right) \cdot t}{a - z} - x \cdot \left(\frac{y}{a - z} + \left(-1 - \frac{z}{a - z}\right)\right)\\ \mathbf{if}\;t_4 \leq -2 \cdot 10^{-39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_4 \leq -1 \cdot 10^{-297}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(y - a, \frac{x - t}{z}, t_1\right) + \left(t - t_1\right)\\ \mathbf{elif}\;t_4 \leq 0.0004:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y a) (/ (- t x) z)))
        (t_2 (/ (- t x) (- a z)))
        (t_3 (fma (- y z) t_2 x))
        (t_4 (+ x (* (- y z) t_2)))
        (t_5
         (-
          (/ (* (- y z) t) (- a z))
          (* x (+ (/ y (- a z)) (- -1.0 (/ z (- a z))))))))
   (if (<= t_4 -2e-39)
     t_3
     (if (<= t_4 -1e-297)
       t_5
       (if (<= t_4 0.0)
         (+ (fma (- y a) (/ (- x t) z) t_1) (- t t_1))
         (if (<= t_4 0.0004) t_5 t_3))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - a) * ((t - x) / z);
	double t_2 = (t - x) / (a - z);
	double t_3 = fma((y - z), t_2, x);
	double t_4 = x + ((y - z) * t_2);
	double t_5 = (((y - z) * t) / (a - z)) - (x * ((y / (a - z)) + (-1.0 - (z / (a - z)))));
	double tmp;
	if (t_4 <= -2e-39) {
		tmp = t_3;
	} else if (t_4 <= -1e-297) {
		tmp = t_5;
	} else if (t_4 <= 0.0) {
		tmp = fma((y - a), ((x - t) / z), t_1) + (t - t_1);
	} else if (t_4 <= 0.0004) {
		tmp = t_5;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - a) * Float64(Float64(t - x) / z))
	t_2 = Float64(Float64(t - x) / Float64(a - z))
	t_3 = fma(Float64(y - z), t_2, x)
	t_4 = Float64(x + Float64(Float64(y - z) * t_2))
	t_5 = Float64(Float64(Float64(Float64(y - z) * t) / Float64(a - z)) - Float64(x * Float64(Float64(y / Float64(a - z)) + Float64(-1.0 - Float64(z / Float64(a - z))))))
	tmp = 0.0
	if (t_4 <= -2e-39)
		tmp = t_3;
	elseif (t_4 <= -1e-297)
		tmp = t_5;
	elseif (t_4 <= 0.0)
		tmp = Float64(fma(Float64(y - a), Float64(Float64(x - t) / z), t_1) + Float64(t - t_1));
	elseif (t_4 <= 0.0004)
		tmp = t_5;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - a), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y - z), $MachinePrecision] * t$95$2 + x), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -2e-39], t$95$3, If[LessEqual[t$95$4, -1e-297], t$95$5, If[LessEqual[t$95$4, 0.0], N[(N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(t - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0004], t$95$5, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999986e-39 or 4.00000000000000019e-4 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      2. fma-def 95.0%

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

   3. Simplified 95.0%

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

   if -1.99999999999999986e-39 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000004e-297 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.00000000000000019e-4

   1. Initial program 72.9%

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

   2. Taylor expanded in x around -inf 99.8%

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

   if -1.00000000000000004e-297 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

   2. Taylor expanded in z around inf 94.4%

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

      1. associate--l+ 94.4%

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

      2. distribute-lft-out-- 94.4%

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

      3. div-sub 94.4%

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

      4. mul-1-neg 94.4%

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

      5. unsub-neg 94.4%

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

      6. distribute-rgt-out-- 94.4%

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

      7. associate-/l* 99.7%

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

   4. Simplified 99.7%

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

      1. *-un-lft-identity 99.7%

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

      2. add-sqr-sqrt 49.9%

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

      3. prod-diff 49.9%

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

      4. add-sqr-sqrt 49.9%

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

      5. fma-neg 49.9%

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

      6. *-un-lft-identity 49.9%

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

      7. add-sqr-sqrt 49.9%

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

   6. Applied egg-rr 49.9%

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

      1. associate-/r/ 49.9%

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

      2. *-commutative 49.9%

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

      3. fma-udef 49.9%

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

      4. distribute-lft-neg-in 49.9%

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

      5. rem-square-sqrt 99.8%

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

      6. neg-mul-1 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-297}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} - x \cdot \left(\frac{y}{a - z} + \left(-1 - \frac{z}{a - z}\right)\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\mathsf{fma}\left(y - a, \frac{x - t}{z}, \left(y - a\right) \cdot \frac{t - x}{z}\right) + \left(t - \left(y - a\right) \cdot \frac{t - x}{z}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0.0004:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} - x \cdot \left(\frac{y}{a - z} + \left(-1 - \frac{z}{a - z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]

Alternative 2: 94.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := \mathsf{fma}\left(y - z, t_1, x\right)\\ t_3 := x + \left(y - z\right) \cdot t_1\\ t_4 := \frac{\left(y - z\right) \cdot t}{a - z} - x \cdot \left(\frac{y}{a - z} + \left(-1 - \frac{z}{a - z}\right)\right)\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-297}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t - \left(y - a\right) \cdot \frac{t - x}{z}\\ \mathbf{elif}\;t_3 \leq 0.0004:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z)))
        (t_2 (fma (- y z) t_1 x))
        (t_3 (+ x (* (- y z) t_1)))
        (t_4
         (-
          (/ (* (- y z) t) (- a z))
          (* x (+ (/ y (- a z)) (- -1.0 (/ z (- a z))))))))
   (if (<= t_3 -2e-39)
     t_2
     (if (<= t_3 -1e-297)
       t_4
       (if (<= t_3 0.0)
         (- t (* (- y a) (/ (- t x) z)))
         (if (<= t_3 0.0004) t_4 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = fma((y - z), t_1, x);
	double t_3 = x + ((y - z) * t_1);
	double t_4 = (((y - z) * t) / (a - z)) - (x * ((y / (a - z)) + (-1.0 - (z / (a - z)))));
	double tmp;
	if (t_3 <= -2e-39) {
		tmp = t_2;
	} else if (t_3 <= -1e-297) {
		tmp = t_4;
	} else if (t_3 <= 0.0) {
		tmp = t - ((y - a) * ((t - x) / z));
	} else if (t_3 <= 0.0004) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = fma(Float64(y - z), t_1, x)
	t_3 = Float64(x + Float64(Float64(y - z) * t_1))
	t_4 = Float64(Float64(Float64(Float64(y - z) * t) / Float64(a - z)) - Float64(x * Float64(Float64(y / Float64(a - z)) + Float64(-1.0 - Float64(z / Float64(a - z))))))
	tmp = 0.0
	if (t_3 <= -2e-39)
		tmp = t_2;
	elseif (t_3 <= -1e-297)
		tmp = t_4;
	elseif (t_3 <= 0.0)
		tmp = Float64(t - Float64(Float64(y - a) * Float64(Float64(t - x) / z)));
	elseif (t_3 <= 0.0004)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e-39], t$95$2, If[LessEqual[t$95$3, -1e-297], t$95$4, If[LessEqual[t$95$3, 0.0], N[(t - N[(N[(y - a), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0004], t$95$4, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999986e-39 or 4.00000000000000019e-4 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      2. fma-def 95.0%

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

   3. Simplified 95.0%

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

   if -1.99999999999999986e-39 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000004e-297 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.00000000000000019e-4

   1. Initial program 72.9%

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

   2. Taylor expanded in x around -inf 99.8%

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

   if -1.00000000000000004e-297 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

   2. Taylor expanded in z around inf 94.4%

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

      1. associate--l+ 94.4%

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

      2. distribute-lft-out-- 94.4%

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

      3. div-sub 94.4%

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

      4. mul-1-neg 94.4%

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

      5. unsub-neg 94.4%

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

      6. distribute-rgt-out-- 94.4%

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

      7. associate-/l* 99.7%

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

   4. Simplified 99.7%

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

      1. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-297}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} - x \cdot \left(\frac{y}{a - z} + \left(-1 - \frac{z}{a - z}\right)\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t - \left(y - a\right) \cdot \frac{t - x}{z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0.0004:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} - x \cdot \left(\frac{y}{a - z} + \left(-1 - \frac{z}{a - z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]

Alternative 3: 94.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z} - x \cdot \left(\frac{y}{a - z} + \left(-1 - \frac{z}{a - z}\right)\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t - \left(y - a\right) \cdot \frac{t - x}{z}\\ \mathbf{elif}\;t_2 \leq 0.0004:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1
         (-
          (/ (* (- y z) t) (- a z))
          (* x (+ (/ y (- a z)) (- -1.0 (/ z (- a z)))))))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -2e-39)
     t_2
     (if (<= t_2 -1e-297)
       t_1
       (if (<= t_2 0.0)
         (- t (* (- y a) (/ (- t x) z)))
         (if (<= t_2 0.0004) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (((y - z) * t) / (a - z)) - (x * ((y / (a - z)) + (-1.0 - (z / (a - z)))));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -2e-39) {
		tmp = t_2;
	} else if (t_2 <= -1e-297) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t - ((y - a) * ((t - x) / z));
	} else if (t_2 <= 0.0004) {
		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 = (((y - z) * t) / (a - z)) - (x * ((y / (a - z)) + ((-1.0d0) - (z / (a - z)))))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-2d-39)) then
        tmp = t_2
    else if (t_2 <= (-1d-297)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t - ((y - a) * ((t - x) / z))
    else if (t_2 <= 0.0004d0) 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 = (((y - z) * t) / (a - z)) - (x * ((y / (a - z)) + (-1.0 - (z / (a - z)))));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -2e-39) {
		tmp = t_2;
	} else if (t_2 <= -1e-297) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t - ((y - a) * ((t - x) / z));
	} else if (t_2 <= 0.0004) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (((y - z) * t) / (a - z)) - (x * ((y / (a - z)) + (-1.0 - (z / (a - z)))))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -2e-39:
		tmp = t_2
	elif t_2 <= -1e-297:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t - ((y - a) * ((t - x) / z))
	elif t_2 <= 0.0004:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(Float64(y - z) * t) / Float64(a - z)) - Float64(x * Float64(Float64(y / Float64(a - z)) + Float64(-1.0 - Float64(z / Float64(a - z))))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -2e-39)
		tmp = t_2;
	elseif (t_2 <= -1e-297)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(Float64(y - a) * Float64(Float64(t - x) / z)));
	elseif (t_2 <= 0.0004)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (((y - z) * t) / (a - z)) - (x * ((y / (a - z)) + (-1.0 - (z / (a - z)))));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -2e-39)
		tmp = t_2;
	elseif (t_2 <= -1e-297)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t - ((y - a) * ((t - x) / z));
	elseif (t_2 <= 0.0004)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-39], t$95$2, If[LessEqual[t$95$2, -1e-297], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t - N[(N[(y - a), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0004], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999986e-39 or 4.00000000000000019e-4 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 95.0%

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

   if -1.99999999999999986e-39 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000004e-297 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.00000000000000019e-4

   1. Initial program 72.9%

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

   2. Taylor expanded in x around -inf 99.8%

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

   if -1.00000000000000004e-297 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

   2. Taylor expanded in z around inf 94.4%

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

      1. associate--l+ 94.4%

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

      2. distribute-lft-out-- 94.4%

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

      3. div-sub 94.4%

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

      4. mul-1-neg 94.4%

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

      5. unsub-neg 94.4%

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

      6. distribute-rgt-out-- 94.4%

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

      7. associate-/l* 99.7%

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

   4. Simplified 99.7%

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

      1. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-39}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-297}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} - x \cdot \left(\frac{y}{a - z} + \left(-1 - \frac{z}{a - z}\right)\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t - \left(y - a\right) \cdot \frac{t - x}{z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0.0004:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} - x \cdot \left(\frac{y}{a - z} + \left(-1 - \frac{z}{a - z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternative 4: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-204} \lor \neg \left(t_1 \leq 4 \cdot 10^{-281}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-204) (not (<= t_1 4e-281)))
     t_1
     (- t (/ (- t x) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-204) || !(t_1 <= 4e-281)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-204)) .or. (.not. (t_1 <= 4d-281))) then
        tmp = t_1
    else
        tmp = t - ((t - x) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-204) || !(t_1 <= 4e-281)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-204) or not (t_1 <= 4e-281):
		tmp = t_1
	else:
		tmp = t - ((t - x) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-204) || !(t_1 <= 4e-281))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-204) || ~((t_1 <= 4e-281)))
		tmp = t_1;
	else
		tmp = t - ((t - x) / (z / (y - a)));
	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[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-204], N[Not[LessEqual[t$95$1, 4e-281]], $MachinePrecision]], t$95$1, N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000002e-204 or 4.0000000000000001e-281 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.5%

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

   if -5.0000000000000002e-204 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.0000000000000001e-281

   1. Initial program 9.9%

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

   2. Taylor expanded in z around inf 86.9%

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

      1. associate--l+ 86.9%

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

      2. distribute-lft-out-- 86.9%

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

      3. div-sub 86.9%

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

      4. mul-1-neg 86.9%

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

      5. unsub-neg 86.9%

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

      6. distribute-rgt-out-- 86.9%

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

      7. associate-/l* 91.2%

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

   4. Simplified 91.2%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-204} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 4 \cdot 10^{-281}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 5: 61.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{a}{-\frac{z}{x}}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{+190}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+66}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+24}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-86}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+108}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ a (- (/ z x))))))
   (if (<= z -2.05e+226)
     t_1
     (if (<= z -8.6e+190)
       (/ (- y) (/ z (- t x)))
       (if (<= z -3.3e+66)
         (/ (- t) (/ (- a z) z))
         (if (<= z -8e+24)
           (* (- t x) (/ y (- a z)))
           (if (<= z -5.5e-86)
             (* (- y z) (/ t (- a z)))
             (if (<= z 3.7e+108) (+ x (* (- t x) (/ y a))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (a / -(z / x));
	double tmp;
	if (z <= -2.05e+226) {
		tmp = t_1;
	} else if (z <= -8.6e+190) {
		tmp = -y / (z / (t - x));
	} else if (z <= -3.3e+66) {
		tmp = -t / ((a - z) / z);
	} else if (z <= -8e+24) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= -5.5e-86) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 3.7e+108) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (a / -(z / x))
    if (z <= (-2.05d+226)) then
        tmp = t_1
    else if (z <= (-8.6d+190)) then
        tmp = -y / (z / (t - x))
    else if (z <= (-3.3d+66)) then
        tmp = -t / ((a - z) / z)
    else if (z <= (-8d+24)) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= (-5.5d-86)) then
        tmp = (y - z) * (t / (a - z))
    else if (z <= 3.7d+108) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (a / -(z / x));
	double tmp;
	if (z <= -2.05e+226) {
		tmp = t_1;
	} else if (z <= -8.6e+190) {
		tmp = -y / (z / (t - x));
	} else if (z <= -3.3e+66) {
		tmp = -t / ((a - z) / z);
	} else if (z <= -8e+24) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= -5.5e-86) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 3.7e+108) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (a / -(z / x))
	tmp = 0
	if z <= -2.05e+226:
		tmp = t_1
	elif z <= -8.6e+190:
		tmp = -y / (z / (t - x))
	elif z <= -3.3e+66:
		tmp = -t / ((a - z) / z)
	elif z <= -8e+24:
		tmp = (t - x) * (y / (a - z))
	elif z <= -5.5e-86:
		tmp = (y - z) * (t / (a - z))
	elif z <= 3.7e+108:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(a / Float64(-Float64(z / x))))
	tmp = 0.0
	if (z <= -2.05e+226)
		tmp = t_1;
	elseif (z <= -8.6e+190)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (z <= -3.3e+66)
		tmp = Float64(Float64(-t) / Float64(Float64(a - z) / z));
	elseif (z <= -8e+24)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= -5.5e-86)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (z <= 3.7e+108)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (a / -(z / x));
	tmp = 0.0;
	if (z <= -2.05e+226)
		tmp = t_1;
	elseif (z <= -8.6e+190)
		tmp = -y / (z / (t - x));
	elseif (z <= -3.3e+66)
		tmp = -t / ((a - z) / z);
	elseif (z <= -8e+24)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= -5.5e-86)
		tmp = (y - z) * (t / (a - z));
	elseif (z <= 3.7e+108)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(a / (-N[(z / x), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+226], t$95$1, If[LessEqual[z, -8.6e+190], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e+66], N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8e+24], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-86], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+108], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.04999999999999993e226 or 3.6999999999999998e108 < z

   1. Initial program 46.6%

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

   2. Taylor expanded in z around inf 74.7%

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

      1. associate--l+ 74.7%

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

      2. distribute-lft-out-- 74.7%

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

      3. div-sub 74.7%

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

      4. mul-1-neg 74.7%

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

      5. unsub-neg 74.7%

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

      6. distribute-rgt-out-- 74.9%

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

      7. associate-/l* 89.8%

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

   4. Simplified 89.8%

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

   5. Taylor expanded in y around 0 68.3%

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

      1. sub-neg 68.3%

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

      2. mul-1-neg 68.3%

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

      3. remove-double-neg 68.3%

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

      4. associate-/l* 75.3%

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

   7. Simplified 75.3%

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

   8. Taylor expanded in t around 0 75.3%

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

      1. associate-*r/ 75.3%

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

      2. mul-1-neg 75.3%

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

   10. Simplified 75.3%

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

   if -2.04999999999999993e226 < z < -8.6000000000000001e190

   1. Initial program 60.3%

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

   2. Taylor expanded in z around inf 38.9%

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

      1. associate--l+ 38.9%

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

      2. distribute-lft-out-- 38.9%

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

      3. div-sub 38.9%

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

      4. mul-1-neg 38.9%

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

      5. unsub-neg 38.9%

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

      6. distribute-rgt-out-- 38.9%

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

      7. associate-/l* 82.0%

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

   4. Simplified 82.0%

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

   5. Taylor expanded in y around -inf 24.0%

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

      1. mul-1-neg 24.0%

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

      2. associate-/l* 58.5%

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

      3. distribute-neg-frac 58.5%

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

   7. Simplified 58.5%

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

   if -8.6000000000000001e190 < z < -3.3000000000000001e66

   1. Initial program 77.9%

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

   2. Taylor expanded in x around 0 54.8%

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

   3. Taylor expanded in y around 0 50.6%

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

      1. associate-*r/ 50.6%

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

      2. mul-1-neg 50.6%

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

      3. distribute-rgt-neg-in 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in t around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. associate-/l* 74.8%

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

   8. Simplified 74.8%

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

   if -3.3000000000000001e66 < z < -7.9999999999999999e24

   1. Initial program 83.4%

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

   2. Taylor expanded in y around inf 83.5%

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

      1. div-sub 83.5%

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

      2. associate-*r/ 84.2%

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

      3. associate-/l* 84.0%

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

      4. associate-/r/ 83.8%

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

   4. Simplified 83.8%

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

   if -7.9999999999999999e24 < z < -5.5e-86

   1. Initial program 87.1%

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

   2. Taylor expanded in x around 0 53.6%

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

      1. associate-/l* 53.6%

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

      2. associate-/r/ 53.5%

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

   4. Simplified 53.5%

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

   if -5.5e-86 < z < 3.6999999999999998e108

   1. Initial program 92.2%

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

   2. Taylor expanded in z around 0 68.9%

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

      1. associate-/l* 70.2%

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

      2. associate-/r/ 70.2%

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

   4. Simplified 70.2%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+226}:\\ \;\;\;\;t + \frac{a}{-\frac{z}{x}}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{+190}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+66}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+24}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-86}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+108}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{-\frac{z}{x}}\\ \end{array} \]

Alternative 6: 48.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{\frac{a}{y}}\\ t_2 := t + \frac{a}{-\frac{z}{x}}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+188}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-37}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-307}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ x (/ a y)))) (t_2 (+ t (/ a (- (/ z x))))))
   (if (<= z -2.05e+226)
     t_2
     (if (<= z -5.5e+188)
       (/ (- y) (/ z (- t x)))
       (if (<= z -1.55e-37)
         (/ (- t) (/ (- a z) z))
         (if (<= z -4.8e-245)
           t_1
           (if (<= z -1.05e-307)
             (/ (* y t) (- a z))
             (if (<= z 1.04e+74) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double t_2 = t + (a / -(z / x));
	double tmp;
	if (z <= -2.05e+226) {
		tmp = t_2;
	} else if (z <= -5.5e+188) {
		tmp = -y / (z / (t - x));
	} else if (z <= -1.55e-37) {
		tmp = -t / ((a - z) / z);
	} else if (z <= -4.8e-245) {
		tmp = t_1;
	} else if (z <= -1.05e-307) {
		tmp = (y * t) / (a - z);
	} else if (z <= 1.04e+74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (x / (a / y))
    t_2 = t + (a / -(z / x))
    if (z <= (-2.05d+226)) then
        tmp = t_2
    else if (z <= (-5.5d+188)) then
        tmp = -y / (z / (t - x))
    else if (z <= (-1.55d-37)) then
        tmp = -t / ((a - z) / z)
    else if (z <= (-4.8d-245)) then
        tmp = t_1
    else if (z <= (-1.05d-307)) then
        tmp = (y * t) / (a - z)
    else if (z <= 1.04d+74) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double t_2 = t + (a / -(z / x));
	double tmp;
	if (z <= -2.05e+226) {
		tmp = t_2;
	} else if (z <= -5.5e+188) {
		tmp = -y / (z / (t - x));
	} else if (z <= -1.55e-37) {
		tmp = -t / ((a - z) / z);
	} else if (z <= -4.8e-245) {
		tmp = t_1;
	} else if (z <= -1.05e-307) {
		tmp = (y * t) / (a - z);
	} else if (z <= 1.04e+74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x / (a / y))
	t_2 = t + (a / -(z / x))
	tmp = 0
	if z <= -2.05e+226:
		tmp = t_2
	elif z <= -5.5e+188:
		tmp = -y / (z / (t - x))
	elif z <= -1.55e-37:
		tmp = -t / ((a - z) / z)
	elif z <= -4.8e-245:
		tmp = t_1
	elif z <= -1.05e-307:
		tmp = (y * t) / (a - z)
	elif z <= 1.04e+74:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x / Float64(a / y)))
	t_2 = Float64(t + Float64(a / Float64(-Float64(z / x))))
	tmp = 0.0
	if (z <= -2.05e+226)
		tmp = t_2;
	elseif (z <= -5.5e+188)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (z <= -1.55e-37)
		tmp = Float64(Float64(-t) / Float64(Float64(a - z) / z));
	elseif (z <= -4.8e-245)
		tmp = t_1;
	elseif (z <= -1.05e-307)
		tmp = Float64(Float64(y * t) / Float64(a - z));
	elseif (z <= 1.04e+74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x / (a / y));
	t_2 = t + (a / -(z / x));
	tmp = 0.0;
	if (z <= -2.05e+226)
		tmp = t_2;
	elseif (z <= -5.5e+188)
		tmp = -y / (z / (t - x));
	elseif (z <= -1.55e-37)
		tmp = -t / ((a - z) / z);
	elseif (z <= -4.8e-245)
		tmp = t_1;
	elseif (z <= -1.05e-307)
		tmp = (y * t) / (a - z);
	elseif (z <= 1.04e+74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(a / (-N[(z / x), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+226], t$95$2, If[LessEqual[z, -5.5e+188], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-37], N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-245], t$95$1, If[LessEqual[z, -1.05e-307], N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.04e+74], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.04999999999999993e226 or 1.04e74 < z

   1. Initial program 50.7%

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

   2. Taylor expanded in z around inf 72.5%

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

      1. associate--l+ 72.5%

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

      2. distribute-lft-out-- 72.5%

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

      3. div-sub 72.5%

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

      4. mul-1-neg 72.5%

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

      5. unsub-neg 72.5%

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

      6. distribute-rgt-out-- 72.7%

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

      7. associate-/l* 85.7%

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

   4. Simplified 85.7%

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

   5. Taylor expanded in y around 0 65.6%

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

      1. sub-neg 65.6%

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

      2. mul-1-neg 65.6%

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

      3. remove-double-neg 65.6%

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

      4. associate-/l* 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in t around 0 70.3%

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

      1. associate-*r/ 70.3%

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

      2. mul-1-neg 70.3%

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

   10. Simplified 70.3%

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

   if -2.04999999999999993e226 < z < -5.50000000000000013e188

   1. Initial program 60.3%

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

   2. Taylor expanded in z around inf 38.9%

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

      1. associate--l+ 38.9%

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

      2. distribute-lft-out-- 38.9%

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

      3. div-sub 38.9%

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

      4. mul-1-neg 38.9%

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

      5. unsub-neg 38.9%

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

      6. distribute-rgt-out-- 38.9%

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

      7. associate-/l* 82.0%

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

   4. Simplified 82.0%

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

   5. Taylor expanded in y around -inf 24.0%

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

      1. mul-1-neg 24.0%

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

      2. associate-/l* 58.5%

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

      3. distribute-neg-frac 58.5%

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

   7. Simplified 58.5%

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

   if -5.50000000000000013e188 < z < -1.54999999999999997e-37

   1. Initial program 81.9%

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

   2. Taylor expanded in x around 0 53.4%

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

   3. Taylor expanded in y around 0 44.0%

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

      1. associate-*r/ 44.0%

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

      2. mul-1-neg 44.0%

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

      3. distribute-rgt-neg-in 44.0%

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

   5. Simplified 44.0%

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

   6. Taylor expanded in t around 0 44.0%

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

      1. mul-1-neg 44.0%

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

      2. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

   if -1.54999999999999997e-37 < z < -4.8e-245 or -1.0500000000000001e-307 < z < 1.04e74

   1. Initial program 92.4%

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

   2. Taylor expanded in z around 0 66.0%

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

      1. associate-/l* 67.5%

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

      2. associate-/r/ 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in t around 0 51.9%

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

      1. mul-1-neg 51.9%

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

      2. unsub-neg 51.9%

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

      3. associate-/l* 55.7%

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

   7. Simplified 55.7%

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

   if -4.8e-245 < z < -1.0500000000000001e-307

   1. Initial program 92.2%

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

   2. Taylor expanded in x around 0 76.3%

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

   3. Taylor expanded in y around inf 76.3%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+226}:\\ \;\;\;\;t + \frac{a}{-\frac{z}{x}}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+188}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-37}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-245}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-307}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{+74}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{-\frac{z}{x}}\\ \end{array} \]

Alternative 7: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \left(y - a\right) \cdot \frac{t - x}{z}\\ t_2 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -21500000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+25}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (- y a) (/ (- t x) z)))) (t_2 (+ x (* (- t x) (/ y a)))))
   (if (<= a -21500000000000.0)
     t_2
     (if (<= a 2.5e-51)
       t_1
       (if (<= a 1.45e+25)
         (/ t (/ (- a z) (- y z)))
         (if (<= a 1.25e+59) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y - a) * ((t - x) / z));
	double t_2 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -21500000000000.0) {
		tmp = t_2;
	} else if (a <= 2.5e-51) {
		tmp = t_1;
	} else if (a <= 1.45e+25) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 1.25e+59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - ((y - a) * ((t - x) / z))
    t_2 = x + ((t - x) * (y / a))
    if (a <= (-21500000000000.0d0)) then
        tmp = t_2
    else if (a <= 2.5d-51) then
        tmp = t_1
    else if (a <= 1.45d+25) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 1.25d+59) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y - a) * ((t - x) / z));
	double t_2 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -21500000000000.0) {
		tmp = t_2;
	} else if (a <= 2.5e-51) {
		tmp = t_1;
	} else if (a <= 1.45e+25) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 1.25e+59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y - a) * ((t - x) / z))
	t_2 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -21500000000000.0:
		tmp = t_2
	elif a <= 2.5e-51:
		tmp = t_1
	elif a <= 1.45e+25:
		tmp = t / ((a - z) / (y - z))
	elif a <= 1.25e+59:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y - a) * Float64(Float64(t - x) / z)))
	t_2 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -21500000000000.0)
		tmp = t_2;
	elseif (a <= 2.5e-51)
		tmp = t_1;
	elseif (a <= 1.45e+25)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 1.25e+59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y - a) * ((t - x) / z));
	t_2 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -21500000000000.0)
		tmp = t_2;
	elseif (a <= 2.5e-51)
		tmp = t_1;
	elseif (a <= 1.45e+25)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 1.25e+59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y - a), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -21500000000000.0], t$95$2, If[LessEqual[a, 2.5e-51], t$95$1, If[LessEqual[a, 1.45e+25], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+59], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.15e13 or 1.2499999999999999e59 < a

   1. Initial program 91.0%

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

   2. Taylor expanded in z around 0 65.0%

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

      1. associate-/l* 71.4%

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

      2. associate-/r/ 70.1%

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

   4. Simplified 70.1%

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

   if -2.15e13 < a < 2.50000000000000002e-51 or 1.44999999999999995e25 < a < 1.2499999999999999e59

   1. Initial program 67.1%

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

   2. Taylor expanded in z around inf 80.0%

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

      1. associate--l+ 80.0%

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

      2. distribute-lft-out-- 80.0%

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

      3. div-sub 82.9%

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

      4. mul-1-neg 82.9%

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

      5. unsub-neg 82.9%

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

      6. distribute-rgt-out-- 82.9%

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

      7. associate-/l* 87.7%

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

   4. Simplified 87.7%

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

      1. associate-/r/ 84.4%

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

   6. Applied egg-rr 84.4%

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

   if 2.50000000000000002e-51 < a < 1.44999999999999995e25

   1. Initial program 87.5%

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

   2. Taylor expanded in x around 0 75.2%

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

      1. associate-/l* 75.4%

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

   4. Simplified 75.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -21500000000000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-51}:\\ \;\;\;\;t - \left(y - a\right) \cdot \frac{t - x}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+25}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+59}:\\ \;\;\;\;t - \left(y - a\right) \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 72.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -400000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-53}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 10^{+59}:\\ \;\;\;\;t - \left(y - a\right) \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))))
   (if (<= a -400000000000.0)
     t_1
     (if (<= a 9.6e-53)
       (- t (/ (- t x) (/ z (- y a))))
       (if (<= a 4.5e+26)
         (/ t (/ (- a z) (- y z)))
         (if (<= a 1e+59) (- t (* (- y a) (/ (- t x) z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -400000000000.0) {
		tmp = t_1;
	} else if (a <= 9.6e-53) {
		tmp = t - ((t - x) / (z / (y - a)));
	} else if (a <= 4.5e+26) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 1e+59) {
		tmp = t - ((y - a) * ((t - x) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    if (a <= (-400000000000.0d0)) then
        tmp = t_1
    else if (a <= 9.6d-53) then
        tmp = t - ((t - x) / (z / (y - a)))
    else if (a <= 4.5d+26) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 1d+59) then
        tmp = t - ((y - a) * ((t - x) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -400000000000.0) {
		tmp = t_1;
	} else if (a <= 9.6e-53) {
		tmp = t - ((t - x) / (z / (y - a)));
	} else if (a <= 4.5e+26) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 1e+59) {
		tmp = t - ((y - a) * ((t - x) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -400000000000.0:
		tmp = t_1
	elif a <= 9.6e-53:
		tmp = t - ((t - x) / (z / (y - a)))
	elif a <= 4.5e+26:
		tmp = t / ((a - z) / (y - z))
	elif a <= 1e+59:
		tmp = t - ((y - a) * ((t - x) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -400000000000.0)
		tmp = t_1;
	elseif (a <= 9.6e-53)
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	elseif (a <= 4.5e+26)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 1e+59)
		tmp = Float64(t - Float64(Float64(y - a) * Float64(Float64(t - x) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -400000000000.0)
		tmp = t_1;
	elseif (a <= 9.6e-53)
		tmp = t - ((t - x) / (z / (y - a)));
	elseif (a <= 4.5e+26)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 1e+59)
		tmp = t - ((y - a) * ((t - x) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -400000000000.0], t$95$1, If[LessEqual[a, 9.6e-53], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+26], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+59], N[(t - N[(N[(y - a), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4e11 or 9.99999999999999972e58 < a

   1. Initial program 91.0%

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

   2. Taylor expanded in z around 0 65.0%

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

      1. associate-/l* 71.4%

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

      2. associate-/r/ 70.1%

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

   4. Simplified 70.1%

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

   if -4e11 < a < 9.6000000000000003e-53

   1. Initial program 67.6%

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

   2. Taylor expanded in z around inf 80.4%

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

      1. associate--l+ 80.4%

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

      2. distribute-lft-out-- 80.4%

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

      3. div-sub 83.5%

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

      4. mul-1-neg 83.5%

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

      5. unsub-neg 83.5%

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

      6. distribute-rgt-out-- 83.5%

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

      7. associate-/l* 87.1%

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

   4. Simplified 87.1%

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

   if 9.6000000000000003e-53 < a < 4.49999999999999978e26

   1. Initial program 87.5%

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

   2. Taylor expanded in x around 0 75.2%

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

      1. associate-/l* 75.4%

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

   4. Simplified 75.4%

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

   if 4.49999999999999978e26 < a < 9.99999999999999972e58

   1. Initial program 58.4%

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

   2. Taylor expanded in z around inf 71.7%

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

      1. associate--l+ 71.7%

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

      2. distribute-lft-out-- 71.7%

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

      3. div-sub 71.7%

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

      4. mul-1-neg 71.7%

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

      5. unsub-neg 71.7%

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

      6. distribute-rgt-out-- 71.7%

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

      7. associate-/l* 99.8%

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

   4. Simplified 99.8%

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

      1. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -400000000000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-53}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 10^{+59}:\\ \;\;\;\;t - \left(y - a\right) \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9: 71.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -12000000000000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-51}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+25}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+62}:\\ \;\;\;\;t - \left(y - a\right) \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{a - z} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -12000000000000.0)
   (+ x (* (- t x) (/ y a)))
   (if (<= a 2.35e-51)
     (- t (/ (- t x) (/ z (- y a))))
     (if (<= a 2.6e+25)
       (/ t (/ (- a z) (- y z)))
       (if (<= a 7.8e+62)
         (- t (* (- y a) (/ (- t x) z)))
         (+ x (* (/ z (- a z)) (- x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -12000000000000.0) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 2.35e-51) {
		tmp = t - ((t - x) / (z / (y - a)));
	} else if (a <= 2.6e+25) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 7.8e+62) {
		tmp = t - ((y - a) * ((t - x) / z));
	} else {
		tmp = x + ((z / (a - z)) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-12000000000000.0d0)) then
        tmp = x + ((t - x) * (y / a))
    else if (a <= 2.35d-51) then
        tmp = t - ((t - x) / (z / (y - a)))
    else if (a <= 2.6d+25) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 7.8d+62) then
        tmp = t - ((y - a) * ((t - x) / z))
    else
        tmp = x + ((z / (a - z)) * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -12000000000000.0) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 2.35e-51) {
		tmp = t - ((t - x) / (z / (y - a)));
	} else if (a <= 2.6e+25) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 7.8e+62) {
		tmp = t - ((y - a) * ((t - x) / z));
	} else {
		tmp = x + ((z / (a - z)) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -12000000000000.0:
		tmp = x + ((t - x) * (y / a))
	elif a <= 2.35e-51:
		tmp = t - ((t - x) / (z / (y - a)))
	elif a <= 2.6e+25:
		tmp = t / ((a - z) / (y - z))
	elif a <= 7.8e+62:
		tmp = t - ((y - a) * ((t - x) / z))
	else:
		tmp = x + ((z / (a - z)) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -12000000000000.0)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (a <= 2.35e-51)
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	elseif (a <= 2.6e+25)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 7.8e+62)
		tmp = Float64(t - Float64(Float64(y - a) * Float64(Float64(t - x) / z)));
	else
		tmp = Float64(x + Float64(Float64(z / Float64(a - z)) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -12000000000000.0)
		tmp = x + ((t - x) * (y / a));
	elseif (a <= 2.35e-51)
		tmp = t - ((t - x) / (z / (y - a)));
	elseif (a <= 2.6e+25)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 7.8e+62)
		tmp = t - ((y - a) * ((t - x) / z));
	else
		tmp = x + ((z / (a - z)) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -12000000000000.0], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.35e-51], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+25], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.8e+62], N[(t - N[(N[(y - a), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.2e13

   1. Initial program 88.0%

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

   2. Taylor expanded in z around 0 59.9%

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

      1. associate-/l* 69.1%

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

      2. associate-/r/ 69.8%

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

   4. Simplified 69.8%

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

   if -1.2e13 < a < 2.3499999999999999e-51

   1. Initial program 67.6%

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

   2. Taylor expanded in z around inf 80.4%

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

      1. associate--l+ 80.4%

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

      2. distribute-lft-out-- 80.4%

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

      3. div-sub 83.5%

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

      4. mul-1-neg 83.5%

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

      5. unsub-neg 83.5%

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

      6. distribute-rgt-out-- 83.5%

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

      7. associate-/l* 87.1%

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

   4. Simplified 87.1%

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

   if 2.3499999999999999e-51 < a < 2.5999999999999998e25

   1. Initial program 87.5%

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

   2. Taylor expanded in x around 0 75.2%

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

      1. associate-/l* 75.4%

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

   4. Simplified 75.4%

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

   if 2.5999999999999998e25 < a < 7.8e62

   1. Initial program 63.6%

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

   2. Taylor expanded in z around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. distribute-lft-out-- 62.8%

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

      3. div-sub 62.8%

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

      4. mul-1-neg 62.8%

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

      5. unsub-neg 62.8%

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

      6. distribute-rgt-out-- 75.3%

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

      7. associate-/l* 99.8%

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

   4. Simplified 99.8%

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

      1. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   if 7.8e62 < a

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. unsub-neg 58.6%

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

      3. associate-/l* 75.7%

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

      4. associate-/r/ 77.4%

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

   4. Simplified 77.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -12000000000000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-51}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+25}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+62}:\\ \;\;\;\;t - \left(y - a\right) \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{a - z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 10: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+76}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-43} \lor \neg \left(x \leq 3.3 \cdot 10^{+102}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ x (/ a y)))))
   (if (<= x -4.5e+176)
     t_1
     (if (<= x -4.2e+76)
       (* (- y a) (/ x z))
       (if (or (<= x -2.25e-43) (not (<= x 3.3e+102)))
         t_1
         (* (- y z) (/ t (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double tmp;
	if (x <= -4.5e+176) {
		tmp = t_1;
	} else if (x <= -4.2e+76) {
		tmp = (y - a) * (x / z);
	} else if ((x <= -2.25e-43) || !(x <= 3.3e+102)) {
		tmp = t_1;
	} else {
		tmp = (y - z) * (t / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (x / (a / y))
    if (x <= (-4.5d+176)) then
        tmp = t_1
    else if (x <= (-4.2d+76)) then
        tmp = (y - a) * (x / z)
    else if ((x <= (-2.25d-43)) .or. (.not. (x <= 3.3d+102))) then
        tmp = t_1
    else
        tmp = (y - z) * (t / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double tmp;
	if (x <= -4.5e+176) {
		tmp = t_1;
	} else if (x <= -4.2e+76) {
		tmp = (y - a) * (x / z);
	} else if ((x <= -2.25e-43) || !(x <= 3.3e+102)) {
		tmp = t_1;
	} else {
		tmp = (y - z) * (t / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x / (a / y))
	tmp = 0
	if x <= -4.5e+176:
		tmp = t_1
	elif x <= -4.2e+76:
		tmp = (y - a) * (x / z)
	elif (x <= -2.25e-43) or not (x <= 3.3e+102):
		tmp = t_1
	else:
		tmp = (y - z) * (t / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x / Float64(a / y)))
	tmp = 0.0
	if (x <= -4.5e+176)
		tmp = t_1;
	elseif (x <= -4.2e+76)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif ((x <= -2.25e-43) || !(x <= 3.3e+102))
		tmp = t_1;
	else
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x / (a / y));
	tmp = 0.0;
	if (x <= -4.5e+176)
		tmp = t_1;
	elseif (x <= -4.2e+76)
		tmp = (y - a) * (x / z);
	elseif ((x <= -2.25e-43) || ~((x <= 3.3e+102)))
		tmp = t_1;
	else
		tmp = (y - z) * (t / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+176], t$95$1, If[LessEqual[x, -4.2e+76], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -2.25e-43], N[Not[LessEqual[x, 3.3e+102]], $MachinePrecision]], t$95$1, N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.50000000000000003e176 or -4.20000000000000013e76 < x < -2.25000000000000012e-43 or 3.29999999999999999e102 < x

   1. Initial program 74.1%

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

   2. Taylor expanded in z around 0 53.6%

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

      1. associate-/l* 58.2%

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

      2. associate-/r/ 59.6%

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

   4. Simplified 59.6%

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

   5. Taylor expanded in t around 0 54.5%

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

      1. mul-1-neg 54.5%

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

      2. unsub-neg 54.5%

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

      3. associate-/l* 59.5%

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

   7. Simplified 59.5%

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

   if -4.50000000000000003e176 < x < -4.20000000000000013e76

   1. Initial program 56.4%

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

   2. Taylor expanded in z around inf 66.3%

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

      1. associate--l+ 66.3%

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

      2. distribute-lft-out-- 66.3%

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

      3. div-sub 66.3%

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

      4. mul-1-neg 66.3%

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

      5. unsub-neg 66.3%

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

      6. distribute-rgt-out-- 66.6%

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

      7. associate-/l* 80.8%

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

   4. Simplified 80.8%

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

   5. Taylor expanded in t around 0 48.2%

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

      1. associate-/l* 62.4%

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

      2. associate-/r/ 62.3%

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

   7. Simplified 62.3%

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

   if -2.25000000000000012e-43 < x < 3.29999999999999999e102

   1. Initial program 83.8%

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

   2. Taylor expanded in x around 0 61.1%

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

      1. associate-/l* 72.0%

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

      2. associate-/r/ 64.6%

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

   4. Simplified 64.6%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+176}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+76}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-43} \lor \neg \left(x \leq 3.3 \cdot 10^{+102}\right):\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]

Alternative 11: 55.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{\frac{a}{y}}\\ t_2 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;x \leq -160000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+102}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ x (/ a y)))) (t_2 (* (- t x) (/ y (- a z)))))
   (if (<= x -160000000.0)
     t_2
     (if (<= x -2.3e-26)
       t_1
       (if (<= x -7.6e-48)
         t_2
         (if (<= x 5.6e+102) (* (- y z) (/ t (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double t_2 = (t - x) * (y / (a - z));
	double tmp;
	if (x <= -160000000.0) {
		tmp = t_2;
	} else if (x <= -2.3e-26) {
		tmp = t_1;
	} else if (x <= -7.6e-48) {
		tmp = t_2;
	} else if (x <= 5.6e+102) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (x / (a / y))
    t_2 = (t - x) * (y / (a - z))
    if (x <= (-160000000.0d0)) then
        tmp = t_2
    else if (x <= (-2.3d-26)) then
        tmp = t_1
    else if (x <= (-7.6d-48)) then
        tmp = t_2
    else if (x <= 5.6d+102) then
        tmp = (y - z) * (t / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double t_2 = (t - x) * (y / (a - z));
	double tmp;
	if (x <= -160000000.0) {
		tmp = t_2;
	} else if (x <= -2.3e-26) {
		tmp = t_1;
	} else if (x <= -7.6e-48) {
		tmp = t_2;
	} else if (x <= 5.6e+102) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x / (a / y))
	t_2 = (t - x) * (y / (a - z))
	tmp = 0
	if x <= -160000000.0:
		tmp = t_2
	elif x <= -2.3e-26:
		tmp = t_1
	elif x <= -7.6e-48:
		tmp = t_2
	elif x <= 5.6e+102:
		tmp = (y - z) * (t / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x / Float64(a / y)))
	t_2 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (x <= -160000000.0)
		tmp = t_2;
	elseif (x <= -2.3e-26)
		tmp = t_1;
	elseif (x <= -7.6e-48)
		tmp = t_2;
	elseif (x <= 5.6e+102)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x / (a / y));
	t_2 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (x <= -160000000.0)
		tmp = t_2;
	elseif (x <= -2.3e-26)
		tmp = t_1;
	elseif (x <= -7.6e-48)
		tmp = t_2;
	elseif (x <= 5.6e+102)
		tmp = (y - z) * (t / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -160000000.0], t$95$2, If[LessEqual[x, -2.3e-26], t$95$1, If[LessEqual[x, -7.6e-48], t$95$2, If[LessEqual[x, 5.6e+102], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6e8 or -2.30000000000000009e-26 < x < -7.60000000000000005e-48

   1. Initial program 62.5%

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

   2. Taylor expanded in y around inf 47.3%

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

      1. div-sub 47.3%

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

      2. associate-*r/ 47.2%

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

      3. associate-/l* 48.1%

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

      4. associate-/r/ 53.5%

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

   4. Simplified 53.5%

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

   if -1.6e8 < x < -2.30000000000000009e-26 or 5.60000000000000037e102 < x

   1. Initial program 79.1%

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

   2. Taylor expanded in z around 0 56.9%

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

      1. associate-/l* 63.5%

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

      2. associate-/r/ 63.5%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in t around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

      3. associate-/l* 65.2%

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

   7. Simplified 65.2%

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

   if -7.60000000000000005e-48 < x < 5.60000000000000037e102

   1. Initial program 84.3%

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

   2. Taylor expanded in x around 0 61.5%

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

      1. associate-/l* 72.5%

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

      2. associate-/r/ 65.1%

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

   4. Simplified 65.1%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -160000000:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-48}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+102}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 12: 70.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t - x}{\frac{z}{y}}\\ t_2 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -4000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+25}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (- t x) (/ z y)))) (t_2 (+ x (* (- t x) (/ y a)))))
   (if (<= a -4000000000.0)
     t_2
     (if (<= a 6.8e-56)
       t_1
       (if (<= a 2.6e+25)
         (/ t (/ (- a z) (- y z)))
         (if (<= a 6.2e+58) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((t - x) / (z / y));
	double t_2 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -4000000000.0) {
		tmp = t_2;
	} else if (a <= 6.8e-56) {
		tmp = t_1;
	} else if (a <= 2.6e+25) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 6.2e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - ((t - x) / (z / y))
    t_2 = x + ((t - x) * (y / a))
    if (a <= (-4000000000.0d0)) then
        tmp = t_2
    else if (a <= 6.8d-56) then
        tmp = t_1
    else if (a <= 2.6d+25) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 6.2d+58) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((t - x) / (z / y));
	double t_2 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -4000000000.0) {
		tmp = t_2;
	} else if (a <= 6.8e-56) {
		tmp = t_1;
	} else if (a <= 2.6e+25) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 6.2e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((t - x) / (z / y))
	t_2 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -4000000000.0:
		tmp = t_2
	elif a <= 6.8e-56:
		tmp = t_1
	elif a <= 2.6e+25:
		tmp = t / ((a - z) / (y - z))
	elif a <= 6.2e+58:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(t - x) / Float64(z / y)))
	t_2 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -4000000000.0)
		tmp = t_2;
	elseif (a <= 6.8e-56)
		tmp = t_1;
	elseif (a <= 2.6e+25)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 6.2e+58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((t - x) / (z / y));
	t_2 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -4000000000.0)
		tmp = t_2;
	elseif (a <= 6.8e-56)
		tmp = t_1;
	elseif (a <= 2.6e+25)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 6.2e+58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4000000000.0], t$95$2, If[LessEqual[a, 6.8e-56], t$95$1, If[LessEqual[a, 2.6e+25], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+58], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4e9 or 6.1999999999999998e58 < a

   1. Initial program 91.0%

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

   2. Taylor expanded in z around 0 65.0%

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

      1. associate-/l* 71.4%

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

      2. associate-/r/ 70.1%

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

   4. Simplified 70.1%

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

   if -4e9 < a < 6.79999999999999964e-56 or 2.5999999999999998e25 < a < 6.1999999999999998e58

   1. Initial program 67.1%

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

   2. Taylor expanded in z around inf 80.0%

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

      1. associate--l+ 80.0%

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

      2. distribute-lft-out-- 80.0%

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

      3. div-sub 82.9%

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

      4. mul-1-neg 82.9%

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

      5. unsub-neg 82.9%

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

      6. distribute-rgt-out-- 82.9%

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

      7. associate-/l* 87.7%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in y around inf 83.7%

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

   if 6.79999999999999964e-56 < a < 2.5999999999999998e25

   1. Initial program 87.5%

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

   2. Taylor expanded in x around 0 75.2%

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

      1. associate-/l* 75.4%

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

   4. Simplified 75.4%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4000000000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-56}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+25}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+58}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 13: 48.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{\frac{a}{y}}\\ t_2 := \frac{-t}{\frac{a - z}{z}}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{-37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-309}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ x (/ a y)))) (t_2 (/ (- t) (/ (- a z) z))))
   (if (<= z -1.45e-37)
     t_2
     (if (<= z -1.95e-249)
       t_1
       (if (<= z -7e-309) (/ (* y t) (- a z)) (if (<= z 6.5e+92) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double t_2 = -t / ((a - z) / z);
	double tmp;
	if (z <= -1.45e-37) {
		tmp = t_2;
	} else if (z <= -1.95e-249) {
		tmp = t_1;
	} else if (z <= -7e-309) {
		tmp = (y * t) / (a - z);
	} else if (z <= 6.5e+92) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (x / (a / y))
    t_2 = -t / ((a - z) / z)
    if (z <= (-1.45d-37)) then
        tmp = t_2
    else if (z <= (-1.95d-249)) then
        tmp = t_1
    else if (z <= (-7d-309)) then
        tmp = (y * t) / (a - z)
    else if (z <= 6.5d+92) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double t_2 = -t / ((a - z) / z);
	double tmp;
	if (z <= -1.45e-37) {
		tmp = t_2;
	} else if (z <= -1.95e-249) {
		tmp = t_1;
	} else if (z <= -7e-309) {
		tmp = (y * t) / (a - z);
	} else if (z <= 6.5e+92) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x / (a / y))
	t_2 = -t / ((a - z) / z)
	tmp = 0
	if z <= -1.45e-37:
		tmp = t_2
	elif z <= -1.95e-249:
		tmp = t_1
	elif z <= -7e-309:
		tmp = (y * t) / (a - z)
	elif z <= 6.5e+92:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x / Float64(a / y)))
	t_2 = Float64(Float64(-t) / Float64(Float64(a - z) / z))
	tmp = 0.0
	if (z <= -1.45e-37)
		tmp = t_2;
	elseif (z <= -1.95e-249)
		tmp = t_1;
	elseif (z <= -7e-309)
		tmp = Float64(Float64(y * t) / Float64(a - z));
	elseif (z <= 6.5e+92)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x / (a / y));
	t_2 = -t / ((a - z) / z);
	tmp = 0.0;
	if (z <= -1.45e-37)
		tmp = t_2;
	elseif (z <= -1.95e-249)
		tmp = t_1;
	elseif (z <= -7e-309)
		tmp = (y * t) / (a - z);
	elseif (z <= 6.5e+92)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e-37], t$95$2, If[LessEqual[z, -1.95e-249], t$95$1, If[LessEqual[z, -7e-309], N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+92], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45000000000000002e-37 or 6.49999999999999999e92 < z

   1. Initial program 60.7%

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

   2. Taylor expanded in x around 0 46.0%

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

   3. Taylor expanded in y around 0 41.6%

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

      1. associate-*r/ 41.6%

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

      2. mul-1-neg 41.6%

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

      3. distribute-rgt-neg-in 41.6%

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

   5. Simplified 41.6%

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

   6. Taylor expanded in t around 0 41.6%

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

      1. mul-1-neg 41.6%

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

      2. associate-/l* 60.3%

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

   8. Simplified 60.3%

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

   if -1.45000000000000002e-37 < z < -1.95e-249 or -6.9999999999999984e-309 < z < 6.49999999999999999e92

   1. Initial program 91.4%

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

   2. Taylor expanded in z around 0 63.8%

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

      1. associate-/l* 65.7%

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

      2. associate-/r/ 66.5%

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

   4. Simplified 66.5%

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

   5. Taylor expanded in t around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. unsub-neg 50.4%

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

      3. associate-/l* 53.9%

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

   7. Simplified 53.9%

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

   if -1.95e-249 < z < -6.9999999999999984e-309

   1. Initial program 92.2%

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

   2. Taylor expanded in x around 0 76.3%

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

   3. Taylor expanded in y around inf 76.3%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-37}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-249}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-309}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+92}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \end{array} \]

Alternative 14: 49.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -1 \cdot 10^{-39}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-307}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{-\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ x (/ a y)))))
   (if (<= z -1e-39)
     (/ (- t) (/ (- a z) z))
     (if (<= z -4.8e-245)
       t_1
       (if (<= z -2e-307)
         (/ (* y t) (- a z))
         (if (<= z 4.1e+74) t_1 (+ t (/ a (- (/ z x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double tmp;
	if (z <= -1e-39) {
		tmp = -t / ((a - z) / z);
	} else if (z <= -4.8e-245) {
		tmp = t_1;
	} else if (z <= -2e-307) {
		tmp = (y * t) / (a - z);
	} else if (z <= 4.1e+74) {
		tmp = t_1;
	} else {
		tmp = t + (a / -(z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (x / (a / y))
    if (z <= (-1d-39)) then
        tmp = -t / ((a - z) / z)
    else if (z <= (-4.8d-245)) then
        tmp = t_1
    else if (z <= (-2d-307)) then
        tmp = (y * t) / (a - z)
    else if (z <= 4.1d+74) then
        tmp = t_1
    else
        tmp = t + (a / -(z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double tmp;
	if (z <= -1e-39) {
		tmp = -t / ((a - z) / z);
	} else if (z <= -4.8e-245) {
		tmp = t_1;
	} else if (z <= -2e-307) {
		tmp = (y * t) / (a - z);
	} else if (z <= 4.1e+74) {
		tmp = t_1;
	} else {
		tmp = t + (a / -(z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x / (a / y))
	tmp = 0
	if z <= -1e-39:
		tmp = -t / ((a - z) / z)
	elif z <= -4.8e-245:
		tmp = t_1
	elif z <= -2e-307:
		tmp = (y * t) / (a - z)
	elif z <= 4.1e+74:
		tmp = t_1
	else:
		tmp = t + (a / -(z / x))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x / Float64(a / y)))
	tmp = 0.0
	if (z <= -1e-39)
		tmp = Float64(Float64(-t) / Float64(Float64(a - z) / z));
	elseif (z <= -4.8e-245)
		tmp = t_1;
	elseif (z <= -2e-307)
		tmp = Float64(Float64(y * t) / Float64(a - z));
	elseif (z <= 4.1e+74)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(a / Float64(-Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x / (a / y));
	tmp = 0.0;
	if (z <= -1e-39)
		tmp = -t / ((a - z) / z);
	elseif (z <= -4.8e-245)
		tmp = t_1;
	elseif (z <= -2e-307)
		tmp = (y * t) / (a - z);
	elseif (z <= 4.1e+74)
		tmp = t_1;
	else
		tmp = t + (a / -(z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e-39], N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-245], t$95$1, If[LessEqual[z, -2e-307], N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+74], t$95$1, N[(t + N[(a / (-N[(z / x), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.99999999999999929e-40

   1. Initial program 63.7%

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

   2. Taylor expanded in x around 0 46.1%

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

   3. Taylor expanded in y around 0 38.8%

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

      1. associate-*r/ 38.8%

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

      2. mul-1-neg 38.8%

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

      3. distribute-rgt-neg-in 38.8%

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

   5. Simplified 38.8%

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

   6. Taylor expanded in t around 0 38.8%

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

      1. mul-1-neg 38.8%

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

      2. associate-/l* 55.2%

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

   8. Simplified 55.2%

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

   if -9.99999999999999929e-40 < z < -4.8e-245 or -1.99999999999999982e-307 < z < 4.1e74

   1. Initial program 92.4%

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

   2. Taylor expanded in z around 0 66.0%

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

      1. associate-/l* 67.5%

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

      2. associate-/r/ 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in t around 0 51.9%

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

      1. mul-1-neg 51.9%

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

      2. unsub-neg 51.9%

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

      3. associate-/l* 55.7%

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

   7. Simplified 55.7%

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

   if -4.8e-245 < z < -1.99999999999999982e-307

   1. Initial program 92.2%

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

   2. Taylor expanded in x around 0 76.3%

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

   3. Taylor expanded in y around inf 76.3%

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

   if 4.1e74 < z

   1. Initial program 59.0%

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

   2. Taylor expanded in z around inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. distribute-lft-out-- 67.9%

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

      3. div-sub 67.9%

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

      4. mul-1-neg 67.9%

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

      5. unsub-neg 67.9%

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

      6. distribute-rgt-out-- 68.1%

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

      7. associate-/l* 82.1%

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

   4. Simplified 82.1%

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

   5. Taylor expanded in y around 0 65.8%

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

      1. sub-neg 65.8%

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

      2. mul-1-neg 65.8%

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

      3. remove-double-neg 65.8%

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

      4. associate-/l* 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in t around 0 70.5%

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

      1. associate-*r/ 70.5%

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

      2. mul-1-neg 70.5%

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

   10. Simplified 70.5%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-39}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-245}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-307}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+74}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{-\frac{z}{x}}\\ \end{array} \]

Alternative 15: 38.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -18500000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-191}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-278}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -18500000000.0)
     x
     (if (<= a -8e-191)
       t
       (if (<= a 6e-303)
         t_1
         (if (<= a 8.8e-278)
           t
           (if (<= a 4.2e-203) t_1 (if (<= a 4.3e+60) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -18500000000.0) {
		tmp = x;
	} else if (a <= -8e-191) {
		tmp = t;
	} else if (a <= 6e-303) {
		tmp = t_1;
	} else if (a <= 8.8e-278) {
		tmp = t;
	} else if (a <= 4.2e-203) {
		tmp = t_1;
	} else if (a <= 4.3e+60) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-18500000000.0d0)) then
        tmp = x
    else if (a <= (-8d-191)) then
        tmp = t
    else if (a <= 6d-303) then
        tmp = t_1
    else if (a <= 8.8d-278) then
        tmp = t
    else if (a <= 4.2d-203) then
        tmp = t_1
    else if (a <= 4.3d+60) 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 t_1 = x * (y / z);
	double tmp;
	if (a <= -18500000000.0) {
		tmp = x;
	} else if (a <= -8e-191) {
		tmp = t;
	} else if (a <= 6e-303) {
		tmp = t_1;
	} else if (a <= 8.8e-278) {
		tmp = t;
	} else if (a <= 4.2e-203) {
		tmp = t_1;
	} else if (a <= 4.3e+60) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -18500000000.0:
		tmp = x
	elif a <= -8e-191:
		tmp = t
	elif a <= 6e-303:
		tmp = t_1
	elif a <= 8.8e-278:
		tmp = t
	elif a <= 4.2e-203:
		tmp = t_1
	elif a <= 4.3e+60:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -18500000000.0)
		tmp = x;
	elseif (a <= -8e-191)
		tmp = t;
	elseif (a <= 6e-303)
		tmp = t_1;
	elseif (a <= 8.8e-278)
		tmp = t;
	elseif (a <= 4.2e-203)
		tmp = t_1;
	elseif (a <= 4.3e+60)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -18500000000.0)
		tmp = x;
	elseif (a <= -8e-191)
		tmp = t;
	elseif (a <= 6e-303)
		tmp = t_1;
	elseif (a <= 8.8e-278)
		tmp = t;
	elseif (a <= 4.2e-203)
		tmp = t_1;
	elseif (a <= 4.3e+60)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -18500000000.0], x, If[LessEqual[a, -8e-191], t, If[LessEqual[a, 6e-303], t$95$1, If[LessEqual[a, 8.8e-278], t, If[LessEqual[a, 4.2e-203], t$95$1, If[LessEqual[a, 4.3e+60], t, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.85e10 or 4.29999999999999971e60 < a

   1. Initial program 90.9%

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

   2. Taylor expanded in a around inf 54.1%

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

   if -1.85e10 < a < -8.0000000000000002e-191 or 6.00000000000000055e-303 < a < 8.8000000000000003e-278 or 4.20000000000000004e-203 < a < 4.29999999999999971e60

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf 47.5%

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

   if -8.0000000000000002e-191 < a < 6.00000000000000055e-303 or 8.8000000000000003e-278 < a < 4.20000000000000004e-203

   1. Initial program 71.9%

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

   2. Taylor expanded in x around inf 51.9%

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

      1. mul-1-neg 51.9%

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

      2. unsub-neg 51.9%

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

   4. Simplified 51.9%

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

   5. Taylor expanded in a around 0 58.2%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -18500000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-191}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-303}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-278}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 38.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ t_2 := t + \frac{t \cdot a}{z}\\ \mathbf{if}\;a \leq -6600000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))) (t_2 (+ t (/ (* t a) z))))
   (if (<= a -6600000000000.0)
     x
     (if (<= a -4.2e-192)
       t_2
       (if (<= a -8.5e-306)
         t_1
         (if (<= a 1.9e-277)
           t_2
           (if (<= a 4.2e-203) t_1 (if (<= a 5.8e+61) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double t_2 = t + ((t * a) / z);
	double tmp;
	if (a <= -6600000000000.0) {
		tmp = x;
	} else if (a <= -4.2e-192) {
		tmp = t_2;
	} else if (a <= -8.5e-306) {
		tmp = t_1;
	} else if (a <= 1.9e-277) {
		tmp = t_2;
	} else if (a <= 4.2e-203) {
		tmp = t_1;
	} else if (a <= 5.8e+61) {
		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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / z)
    t_2 = t + ((t * a) / z)
    if (a <= (-6600000000000.0d0)) then
        tmp = x
    else if (a <= (-4.2d-192)) then
        tmp = t_2
    else if (a <= (-8.5d-306)) then
        tmp = t_1
    else if (a <= 1.9d-277) then
        tmp = t_2
    else if (a <= 4.2d-203) then
        tmp = t_1
    else if (a <= 5.8d+61) 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 t_1 = x * (y / z);
	double t_2 = t + ((t * a) / z);
	double tmp;
	if (a <= -6600000000000.0) {
		tmp = x;
	} else if (a <= -4.2e-192) {
		tmp = t_2;
	} else if (a <= -8.5e-306) {
		tmp = t_1;
	} else if (a <= 1.9e-277) {
		tmp = t_2;
	} else if (a <= 4.2e-203) {
		tmp = t_1;
	} else if (a <= 5.8e+61) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	t_2 = t + ((t * a) / z)
	tmp = 0
	if a <= -6600000000000.0:
		tmp = x
	elif a <= -4.2e-192:
		tmp = t_2
	elif a <= -8.5e-306:
		tmp = t_1
	elif a <= 1.9e-277:
		tmp = t_2
	elif a <= 4.2e-203:
		tmp = t_1
	elif a <= 5.8e+61:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	t_2 = Float64(t + Float64(Float64(t * a) / z))
	tmp = 0.0
	if (a <= -6600000000000.0)
		tmp = x;
	elseif (a <= -4.2e-192)
		tmp = t_2;
	elseif (a <= -8.5e-306)
		tmp = t_1;
	elseif (a <= 1.9e-277)
		tmp = t_2;
	elseif (a <= 4.2e-203)
		tmp = t_1;
	elseif (a <= 5.8e+61)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	t_2 = t + ((t * a) / z);
	tmp = 0.0;
	if (a <= -6600000000000.0)
		tmp = x;
	elseif (a <= -4.2e-192)
		tmp = t_2;
	elseif (a <= -8.5e-306)
		tmp = t_1;
	elseif (a <= 1.9e-277)
		tmp = t_2;
	elseif (a <= 4.2e-203)
		tmp = t_1;
	elseif (a <= 5.8e+61)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6600000000000.0], x, If[LessEqual[a, -4.2e-192], t$95$2, If[LessEqual[a, -8.5e-306], t$95$1, If[LessEqual[a, 1.9e-277], t$95$2, If[LessEqual[a, 4.2e-203], t$95$1, If[LessEqual[a, 5.8e+61], t, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.6e12 or 5.8000000000000001e61 < a

   1. Initial program 90.9%

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

   2. Taylor expanded in a around inf 54.1%

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

   if -6.6e12 < a < -4.19999999999999986e-192 or -8.5000000000000002e-306 < a < 1.89999999999999993e-277

   1. Initial program 64.8%

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

   2. Taylor expanded in x around 0 58.4%

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

   3. Taylor expanded in y around 0 37.8%

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

      1. associate-*r/ 37.8%

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

      2. mul-1-neg 37.8%

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

      3. distribute-rgt-neg-in 37.8%

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

   5. Simplified 37.8%

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

   6. Taylor expanded in z around inf 53.3%

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

   if -4.19999999999999986e-192 < a < -8.5000000000000002e-306 or 1.89999999999999993e-277 < a < 4.20000000000000004e-203

   1. Initial program 71.9%

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

   2. Taylor expanded in x around inf 51.9%

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

      1. mul-1-neg 51.9%

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

      2. unsub-neg 51.9%

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

   4. Simplified 51.9%

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

   5. Taylor expanded in a around 0 58.2%

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

   if 4.20000000000000004e-203 < a < 5.8000000000000001e61

   1. Initial program 69.9%

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

   2. Taylor expanded in z around inf 43.9%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6600000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-192}:\\ \;\;\;\;t + \frac{t \cdot a}{z}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-277}:\\ \;\;\;\;t + \frac{t \cdot a}{z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 47.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-307}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ x (/ a y)))))
   (if (<= z -1.15e+81)
     t
     (if (<= z -2e-249)
       t_1
       (if (<= z -1.8e-307) (/ (* y t) (- a z)) (if (<= z 1.2e+122) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double tmp;
	if (z <= -1.15e+81) {
		tmp = t;
	} else if (z <= -2e-249) {
		tmp = t_1;
	} else if (z <= -1.8e-307) {
		tmp = (y * t) / (a - z);
	} else if (z <= 1.2e+122) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (x / (a / y))
    if (z <= (-1.15d+81)) then
        tmp = t
    else if (z <= (-2d-249)) then
        tmp = t_1
    else if (z <= (-1.8d-307)) then
        tmp = (y * t) / (a - z)
    else if (z <= 1.2d+122) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double tmp;
	if (z <= -1.15e+81) {
		tmp = t;
	} else if (z <= -2e-249) {
		tmp = t_1;
	} else if (z <= -1.8e-307) {
		tmp = (y * t) / (a - z);
	} else if (z <= 1.2e+122) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x / (a / y))
	tmp = 0
	if z <= -1.15e+81:
		tmp = t
	elif z <= -2e-249:
		tmp = t_1
	elif z <= -1.8e-307:
		tmp = (y * t) / (a - z)
	elif z <= 1.2e+122:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x / Float64(a / y)))
	tmp = 0.0
	if (z <= -1.15e+81)
		tmp = t;
	elseif (z <= -2e-249)
		tmp = t_1;
	elseif (z <= -1.8e-307)
		tmp = Float64(Float64(y * t) / Float64(a - z));
	elseif (z <= 1.2e+122)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x / (a / y));
	tmp = 0.0;
	if (z <= -1.15e+81)
		tmp = t;
	elseif (z <= -2e-249)
		tmp = t_1;
	elseif (z <= -1.8e-307)
		tmp = (y * t) / (a - z);
	elseif (z <= 1.2e+122)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+81], t, If[LessEqual[z, -2e-249], t$95$1, If[LessEqual[z, -1.8e-307], N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+122], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1499999999999999e81 or 1.2000000000000001e122 < z

   1. Initial program 54.9%

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

   2. Taylor expanded in z around inf 61.0%

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

   if -1.1499999999999999e81 < z < -2.00000000000000011e-249 or -1.80000000000000003e-307 < z < 1.2000000000000001e122

   1. Initial program 90.7%

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

   2. Taylor expanded in z around 0 59.4%

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

      1. associate-/l* 61.7%

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

      2. associate-/r/ 62.4%

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

   4. Simplified 62.4%

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

   5. Taylor expanded in t around 0 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

      3. associate-/l* 50.9%

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

   7. Simplified 50.9%

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

   if -2.00000000000000011e-249 < z < -1.80000000000000003e-307

   1. Initial program 92.2%

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

   2. Taylor expanded in x around 0 76.3%

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

   3. Taylor expanded in y around inf 76.3%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-249}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-307}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+122}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18: 70.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -52000000 \lor \neg \left(a \leq 7 \cdot 10^{+58}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -52000000.0) (not (<= a 7e+58)))
   (+ x (* (- t x) (/ y a)))
   (- t (/ (- t x) (/ z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -52000000.0) || !(a <= 7e+58)) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t - ((t - x) / (z / 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 ((a <= (-52000000.0d0)) .or. (.not. (a <= 7d+58))) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t - ((t - x) / (z / 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 ((a <= -52000000.0) || !(a <= 7e+58)) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t - ((t - x) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -52000000.0) or not (a <= 7e+58):
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t - ((t - x) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -52000000.0) || !(a <= 7e+58))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -52000000.0) || ~((a <= 7e+58)))
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t - ((t - x) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -52000000.0], N[Not[LessEqual[a, 7e+58]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.2e7 or 6.9999999999999995e58 < a

   1. Initial program 91.0%

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

   2. Taylor expanded in z around 0 65.0%

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

      1. associate-/l* 71.4%

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

      2. associate-/r/ 70.1%

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

   4. Simplified 70.1%

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

   if -5.2e7 < a < 6.9999999999999995e58

   1. Initial program 68.2%

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

   2. Taylor expanded in z around inf 76.3%

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

      1. associate--l+ 76.3%

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

      2. distribute-lft-out-- 76.3%

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

      3. div-sub 79.1%

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

      4. mul-1-neg 79.1%

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

      5. unsub-neg 79.1%

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

      6. distribute-rgt-out-- 79.1%

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

      7. associate-/l* 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in y around inf 79.9%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -52000000 \lor \neg \left(a \leq 7 \cdot 10^{+58}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \end{array} \]

Alternative 19: 48.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+123}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.8e+81) t (if (<= z 1.6e+123) (- x (/ x (/ a y))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.8e+81) {
		tmp = t;
	} else if (z <= 1.6e+123) {
		tmp = x - (x / (a / y));
	} 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 <= (-9.8d+81)) then
        tmp = t
    else if (z <= 1.6d+123) then
        tmp = x - (x / (a / y))
    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 <= -9.8e+81) {
		tmp = t;
	} else if (z <= 1.6e+123) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.8e+81:
		tmp = t
	elif z <= 1.6e+123:
		tmp = x - (x / (a / y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.8e+81)
		tmp = t;
	elseif (z <= 1.6e+123)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.8e+81)
		tmp = t;
	elseif (z <= 1.6e+123)
		tmp = x - (x / (a / y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.8e+81], t, If[LessEqual[z, 1.6e+123], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -9.80000000000000045e81 or 1.60000000000000002e123 < z

   1. Initial program 54.9%

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

   2. Taylor expanded in z around inf 61.0%

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

   if -9.80000000000000045e81 < z < 1.60000000000000002e123

   1. Initial program 90.8%

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

   2. Taylor expanded in z around 0 61.8%

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

      1. associate-/l* 63.9%

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

      2. associate-/r/ 63.9%

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

   4. Simplified 63.9%

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

   5. Taylor expanded in t around 0 46.4%

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

      1. mul-1-neg 46.4%

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

      2. unsub-neg 46.4%

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

      3. associate-/l* 50.3%

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

   7. Simplified 50.3%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+123}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20: 38.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2200000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+62}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2200000000000.0) x (if (<= a 1.25e+62) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2200000000000.0) {
		tmp = x;
	} else if (a <= 1.25e+62) {
		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 <= (-2200000000000.0d0)) then
        tmp = x
    else if (a <= 1.25d+62) 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 <= -2200000000000.0) {
		tmp = x;
	} else if (a <= 1.25e+62) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2200000000000.0:
		tmp = x
	elif a <= 1.25e+62:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2200000000000.0)
		tmp = x;
	elseif (a <= 1.25e+62)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2200000000000.0)
		tmp = x;
	elseif (a <= 1.25e+62)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2200000000000.0], x, If[LessEqual[a, 1.25e+62], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2e12 or 1.25000000000000007e62 < a

   1. Initial program 90.9%

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

   2. Taylor expanded in a around inf 54.1%

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

   if -2.2e12 < a < 1.25000000000000007e62

   1. Initial program 68.4%

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

   2. Taylor expanded in z around inf 40.0%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2200000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+62}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 25.8% 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 78.0%

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

2. Taylor expanded in z around inf 27.9%

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

3. Final simplification 27.9%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023308 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))