Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.7% → 94.1%

Time: 20.1s

Alternatives: 24

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: 94.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{a - z}\\ t_2 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ t_3 := \sqrt[3]{t - x}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-274}:\\ \;\;\;\;\mathsf{fma}\left(t - x, t_1, x\right)\\ \mathbf{elif}\;t_2 \leq 3 \cdot 10^{-279}:\\ \;\;\;\;\left(\left(t - \frac{y \cdot t}{z}\right) + \frac{y - a}{\frac{z}{x}}\right) + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+145}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+303}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a - z}, y - z, x \cdot \left(\frac{z - y}{a - z} - -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left({t_3}^{2}, t_1 \cdot t_3, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (- a z)))
        (t_2 (- x (* (- y z) (/ (- x t) (- a z)))))
        (t_3 (cbrt (- t x))))
   (if (<= t_2 -5e-274)
     (fma (- t x) t_1 x)
     (if (<= t_2 3e-279)
       (+ (+ (- t (/ (* y t) z)) (/ (- y a) (/ z x))) (/ a (/ z t)))
       (if (<= t_2 2e+145)
         (+
          (/ (* (- y z) t) (- a z))
          (* x (- (+ (/ z (- a z)) 1.0) (/ y (- a z)))))
         (if (<= t_2 5e+303)
           (fma (/ t (- a z)) (- y z) (* x (- (/ (- z y) (- a z)) -1.0)))
           (fma (pow t_3 2.0) (* t_1 t_3) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (a - z);
	double t_2 = x - ((y - z) * ((x - t) / (a - z)));
	double t_3 = cbrt((t - x));
	double tmp;
	if (t_2 <= -5e-274) {
		tmp = fma((t - x), t_1, x);
	} else if (t_2 <= 3e-279) {
		tmp = ((t - ((y * t) / z)) + ((y - a) / (z / x))) + (a / (z / t));
	} else if (t_2 <= 2e+145) {
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))));
	} else if (t_2 <= 5e+303) {
		tmp = fma((t / (a - z)), (y - z), (x * (((z - y) / (a - z)) - -1.0)));
	} else {
		tmp = fma(pow(t_3, 2.0), (t_1 * t_3), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / Float64(a - z))
	t_2 = Float64(x - Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(a - z))))
	t_3 = cbrt(Float64(t - x))
	tmp = 0.0
	if (t_2 <= -5e-274)
		tmp = fma(Float64(t - x), t_1, x);
	elseif (t_2 <= 3e-279)
		tmp = Float64(Float64(Float64(t - Float64(Float64(y * t) / z)) + Float64(Float64(y - a) / Float64(z / x))) + Float64(a / Float64(z / t)));
	elseif (t_2 <= 2e+145)
		tmp = Float64(Float64(Float64(Float64(y - z) * t) / Float64(a - z)) + Float64(x * Float64(Float64(Float64(z / Float64(a - z)) + 1.0) - Float64(y / Float64(a - z)))));
	elseif (t_2 <= 5e+303)
		tmp = fma(Float64(t / Float64(a - z)), Float64(y - z), Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) - -1.0)));
	else
		tmp = fma((t_3 ^ 2.0), Float64(t_1 * t_3), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Power[N[(t - x), $MachinePrecision], 1/3], $MachinePrecision]}, If[LessEqual[t$95$2, -5e-274], N[(N[(t - x), $MachinePrecision] * t$95$1 + x), $MachinePrecision], If[LessEqual[t$95$2, 3e-279], N[(N[(N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+145], N[(N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+303], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[t$95$3, 2.0], $MachinePrecision] * N[(t$95$1 * t$95$3), $MachinePrecision] + x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5e-274

   1. Initial program 91.0%

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

      1. +-commutative 91.0%

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

      2. associate-*r/ 76.0%

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

      3. *-commutative 76.0%

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

      4. associate-*r/ 94.1%

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

      5. fma-def 94.1%

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

   3. Simplified 94.1%

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

   if -5e-274 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 3e-279

   1. Initial program 3.2%

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

   2. Taylor expanded in x around -inf 56.6%

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

   3. Taylor expanded in z around inf 84.0%

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

      1. sub-neg 84.0%

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

      2. +-commutative 84.0%

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

      3. mul-1-neg 84.0%

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

      4. unsub-neg 84.0%

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

      5. +-commutative 84.0%

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

      6. mul-1-neg 84.0%

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

      7. unsub-neg 84.0%

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

      8. *-commutative 84.0%

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

      9. associate-/l* 96.5%

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

      10. mul-1-neg 96.5%

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

      11. unsub-neg 96.5%

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

      12. mul-1-neg 96.5%

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

      13. remove-double-neg 96.5%

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

      14. associate-/l* 96.5%

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

   5. Simplified 96.5%

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

   if 3e-279 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e145

   1. Initial program 86.0%

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

   2. Taylor expanded in x around -inf 96.8%

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

   if 2e145 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999997e303

   1. Initial program 92.2%

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

   2. Taylor expanded in x around -inf 63.2%

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

      1. *-un-lft-identity 63.2%

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

      2. fma-def 63.2%

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

      3. associate-/l* 94.6%

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

      4. mul-1-neg 94.6%

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

      5. *-commutative 94.6%

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

      6. associate--r+ 94.6%

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

      7. div-sub 94.6%

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

   4. Applied egg-rr 94.6%

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

      1. fma-udef 94.6%

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

      2. *-lft-identity 94.6%

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

      3. associate-/r/ 94.6%

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

      4. fma-def 94.6%

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

      5. *-commutative 94.6%

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

      6. distribute-rgt-neg-in 94.6%

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

      7. sub-neg 94.6%

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

      8. metadata-eval 94.6%

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

   6. Simplified 94.6%

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

   if 4.9999999999999997e303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 78.6%

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

      1. +-commutative 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*l/ 88.3%

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

      4. associate-*r/ 94.2%

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

      5. add-cube-cbrt 94.6%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}\right)} \cdot \frac{y - z}{a - z} + x \]

      6. associate-*l* 94.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \left(\sqrt[3]{t - x} \cdot \frac{y - z}{a - z}\right)} + x \]

      7. fma-def 94.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}, \sqrt[3]{t - x} \cdot \frac{y - z}{a - z}, x\right)} \]

      8. pow2 94.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{2}}, \sqrt[3]{t - x} \cdot \frac{y - z}{a - z}, x\right) \]

   3. Applied egg-rr 94.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{t - x}\right)}^{2}, \sqrt[3]{t - x} \cdot \frac{y - z}{a - z}, x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-274}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 3 \cdot 10^{-279}:\\ \;\;\;\;\left(\left(t - \frac{y \cdot t}{z}\right) + \frac{y - a}{\frac{z}{x}}\right) + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 2 \cdot 10^{+145}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 5 \cdot 10^{+303}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a - z}, y - z, x \cdot \left(\frac{z - y}{a - z} - -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left({\left(\sqrt[3]{t - x}\right)}^{2}, \frac{y - z}{a - z} \cdot \sqrt[3]{t - x}, x\right)\\ \end{array} \]

Alternative 2: 94.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ t_2 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 3 \cdot 10^{-279}:\\ \;\;\;\;\left(\left(t - \frac{y \cdot t}{z}\right) + \frac{y - a}{\frac{z}{x}}\right) + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+145}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{elif}\;t_2 \leq 10^{+281}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a - z}, y - z, x \cdot \left(\frac{z - y}{a - z} - -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) (- a z)) x))
        (t_2 (- x (* (- y z) (/ (- x t) (- a z))))))
   (if (<= t_2 -5e-274)
     t_1
     (if (<= t_2 3e-279)
       (+ (+ (- t (/ (* y t) z)) (/ (- y a) (/ z x))) (/ a (/ z t)))
       (if (<= t_2 2e+145)
         (+
          (/ (* (- y z) t) (- a z))
          (* x (- (+ (/ z (- a z)) 1.0) (/ y (- a z)))))
         (if (<= t_2 1e+281)
           (fma (/ t (- a z)) (- y z) (* x (- (/ (- z y) (- a z)) -1.0)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((y - z) / (a - z)), x);
	double t_2 = x - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if (t_2 <= -5e-274) {
		tmp = t_1;
	} else if (t_2 <= 3e-279) {
		tmp = ((t - ((y * t) / z)) + ((y - a) / (z / x))) + (a / (z / t));
	} else if (t_2 <= 2e+145) {
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))));
	} else if (t_2 <= 1e+281) {
		tmp = fma((t / (a - z)), (y - z), (x * (((z - y) / (a - z)) - -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x)
	t_2 = Float64(x - Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -5e-274)
		tmp = t_1;
	elseif (t_2 <= 3e-279)
		tmp = Float64(Float64(Float64(t - Float64(Float64(y * t) / z)) + Float64(Float64(y - a) / Float64(z / x))) + Float64(a / Float64(z / t)));
	elseif (t_2 <= 2e+145)
		tmp = Float64(Float64(Float64(Float64(y - z) * t) / Float64(a - z)) + Float64(x * Float64(Float64(Float64(z / Float64(a - z)) + 1.0) - Float64(y / Float64(a - z)))));
	elseif (t_2 <= 1e+281)
		tmp = fma(Float64(t / Float64(a - z)), Float64(y - z), Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) - -1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-274], t$95$1, If[LessEqual[t$95$2, 3e-279], N[(N[(N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+145], N[(N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+281], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5e-274 or 1e281 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.7%

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

      1. +-commutative 89.7%

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

      2. associate-*r/ 75.2%

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

      3. *-commutative 75.2%

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

      4. associate-*r/ 94.4%

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

      5. fma-def 94.4%

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

   3. Simplified 94.4%

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

   if -5e-274 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 3e-279

   1. Initial program 3.2%

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

   2. Taylor expanded in x around -inf 56.6%

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

   3. Taylor expanded in z around inf 84.0%

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

      1. sub-neg 84.0%

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

      2. +-commutative 84.0%

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

      3. mul-1-neg 84.0%

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

      4. unsub-neg 84.0%

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

      5. +-commutative 84.0%

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

      6. mul-1-neg 84.0%

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

      7. unsub-neg 84.0%

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

      8. *-commutative 84.0%

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

      9. associate-/l* 96.5%

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

      10. mul-1-neg 96.5%

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

      11. unsub-neg 96.5%

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

      12. mul-1-neg 96.5%

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

      13. remove-double-neg 96.5%

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

      14. associate-/l* 96.5%

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

   5. Simplified 96.5%

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

   if 3e-279 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e145

   1. Initial program 86.0%

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

   2. Taylor expanded in x around -inf 96.8%

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

   if 2e145 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1e281

   1. Initial program 90.7%

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

   2. Taylor expanded in x around -inf 64.6%

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

      1. *-un-lft-identity 64.6%

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

      2. fma-def 64.6%

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

      3. associate-/l* 93.6%

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

      4. mul-1-neg 93.6%

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

      5. *-commutative 93.6%

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

      6. associate--r+ 93.6%

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

      7. div-sub 93.6%

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

   4. Applied egg-rr 93.6%

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

      1. fma-udef 93.6%

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

      2. *-lft-identity 93.6%

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

      3. associate-/r/ 93.6%

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

      4. fma-def 93.6%

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

      5. *-commutative 93.6%

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

      6. distribute-rgt-neg-in 93.6%

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

      7. sub-neg 93.6%

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

      8. metadata-eval 93.6%

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

   6. Simplified 93.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{a - z}, y - z, \left(\frac{y - z}{a - z} + -1\right) \cdot \left(-x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-274}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 3 \cdot 10^{-279}:\\ \;\;\;\;\left(\left(t - \frac{y \cdot t}{z}\right) + \frac{y - a}{\frac{z}{x}}\right) + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 2 \cdot 10^{+145}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 10^{+281}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a - z}, y - z, x \cdot \left(\frac{z - y}{a - z} - -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]

Alternative 3: 94.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-274} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t - \frac{y \cdot t}{z}\right) + \frac{y - a}{\frac{z}{x}}\right) + \frac{a}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -5e-274) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ (+ (- t (/ (* y t) z)) (/ (- y a) (/ z x))) (/ a (/ z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-274) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = ((t - ((y * t) / z)) + ((y - a) / (z / x))) + (a / (z / t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-274) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(Float64(Float64(t - Float64(Float64(y * t) / z)) + Float64(Float64(y - a) / Float64(z / x))) + Float64(a / Float64(z / t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-274], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(z / t), $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)))) < -5e-274 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 88.5%

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

      1. +-commutative 88.5%

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

      2. associate-*r/ 75.7%

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

      3. *-commutative 75.7%

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

      4. associate-*r/ 93.1%

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

      5. fma-def 93.2%

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

   3. Simplified 93.2%

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

   if -5e-274 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.1%

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

   2. Taylor expanded in x around -inf 55.1%

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

   3. Taylor expanded in z around inf 83.4%

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

      1. sub-neg 83.4%

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

      2. +-commutative 83.4%

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

      3. mul-1-neg 83.4%

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

      4. unsub-neg 83.4%

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

      5. +-commutative 83.4%

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

      6. mul-1-neg 83.4%

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

      7. unsub-neg 83.4%

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

      8. *-commutative 83.4%

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

      9. associate-/l* 96.4%

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

      10. mul-1-neg 96.4%

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

      11. unsub-neg 96.4%

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

      12. mul-1-neg 96.4%

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

      13. remove-double-neg 96.4%

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

      14. associate-/l* 96.4%

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

   5. Simplified 96.4%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-274} \lor \neg \left(x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t - \frac{y \cdot t}{z}\right) + \frac{y - a}{\frac{z}{x}}\right) + \frac{a}{\frac{z}{t}}\\ \end{array} \]

Alternative 4: 90.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 3 \cdot 10^{-279}:\\ \;\;\;\;\left(\left(t - \frac{y \cdot t}{z}\right) + \frac{y - a}{\frac{z}{x}}\right) + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+169}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- x t) (- a z))))))
   (if (<= t_1 -1e-198)
     t_1
     (if (<= t_1 3e-279)
       (+ (+ (- t (/ (* y t) z)) (/ (- y a) (/ z x))) (/ a (/ z t)))
       (if (<= t_1 5e+169)
         (+
          (/ (* (- y z) t) (- a z))
          (* x (- (+ (/ z (- a z)) 1.0) (/ y (- a z)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if (t_1 <= -1e-198) {
		tmp = t_1;
	} else if (t_1 <= 3e-279) {
		tmp = ((t - ((y * t) / z)) + ((y - a) / (z / x))) + (a / (z / t));
	} else if (t_1 <= 5e+169) {
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y - z) * ((x - t) / (a - z)))
    if (t_1 <= (-1d-198)) then
        tmp = t_1
    else if (t_1 <= 3d-279) then
        tmp = ((t - ((y * t) / z)) + ((y - a) / (z / x))) + (a / (z / t))
    else if (t_1 <= 5d+169) then
        tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0d0) - (y / (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 - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if (t_1 <= -1e-198) {
		tmp = t_1;
	} else if (t_1 <= 3e-279) {
		tmp = ((t - ((y * t) / z)) + ((y - a) / (z / x))) + (a / (z / t));
	} else if (t_1 <= 5e+169) {
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) * ((x - t) / (a - z)))
	tmp = 0
	if t_1 <= -1e-198:
		tmp = t_1
	elif t_1 <= 3e-279:
		tmp = ((t - ((y * t) / z)) + ((y - a) / (z / x))) + (a / (z / t))
	elif t_1 <= 5e+169:
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-198)
		tmp = t_1;
	elseif (t_1 <= 3e-279)
		tmp = Float64(Float64(Float64(t - Float64(Float64(y * t) / z)) + Float64(Float64(y - a) / Float64(z / x))) + Float64(a / Float64(z / t)));
	elseif (t_1 <= 5e+169)
		tmp = Float64(Float64(Float64(Float64(y - z) * t) / Float64(a - z)) + Float64(x * Float64(Float64(Float64(z / Float64(a - z)) + 1.0) - Float64(y / Float64(a - z)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y - z) * ((x - t) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -1e-198)
		tmp = t_1;
	elseif (t_1 <= 3e-279)
		tmp = ((t - ((y * t) / z)) + ((y - a) / (z / x))) + (a / (z / t));
	elseif (t_1 <= 5e+169)
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (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[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-198], t$95$1, If[LessEqual[t$95$1, 3e-279], N[(N[(N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+169], N[(N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999991e-199 or 5.00000000000000017e169 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.1%

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

   if -9.9999999999999991e-199 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 3e-279

   1. Initial program 6.6%

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

   2. Taylor expanded in x around -inf 61.7%

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

   3. Taylor expanded in z around inf 83.0%

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

      1. sub-neg 83.0%

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

      2. +-commutative 83.0%

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

      3. mul-1-neg 83.0%

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

      4. unsub-neg 83.0%

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

      5. +-commutative 83.0%

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

      6. mul-1-neg 83.0%

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

      7. unsub-neg 83.0%

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

      8. *-commutative 83.0%

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

      9. associate-/l* 94.0%

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

      10. mul-1-neg 94.0%

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

      11. unsub-neg 94.0%

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

      12. mul-1-neg 94.0%

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

      13. remove-double-neg 94.0%

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

      14. associate-/l* 94.0%

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

   5. Simplified 94.0%

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

   if 3e-279 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.00000000000000017e169

   1. Initial program 87.0%

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

   2. Taylor expanded in x around -inf 97.0%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-198}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 3 \cdot 10^{-279}:\\ \;\;\;\;\left(\left(t - \frac{y \cdot t}{z}\right) + \frac{y - a}{\frac{z}{x}}\right) + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 5 \cdot 10^{+169}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \end{array} \]

Alternative 5: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-198} \lor \neg \left(t_1 \leq 5 \cdot 10^{-271}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t - \frac{y \cdot t}{z}\right) + \frac{y - a}{\frac{z}{x}}\right) + \frac{a}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -1e-198) (not (<= t_1 5e-271)))
     t_1
     (+ (+ (- t (/ (* y t) z)) (/ (- y a) (/ z x))) (/ a (/ z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-198) || !(t_1 <= 5e-271)) {
		tmp = t_1;
	} else {
		tmp = ((t - ((y * t) / z)) + ((y - a) / (z / x))) + (a / (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y - z) * ((x - t) / (a - z)))
    if ((t_1 <= (-1d-198)) .or. (.not. (t_1 <= 5d-271))) then
        tmp = t_1
    else
        tmp = ((t - ((y * t) / z)) + ((y - a) / (z / x))) + (a / (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-198) || !(t_1 <= 5e-271)) {
		tmp = t_1;
	} else {
		tmp = ((t - ((y * t) / z)) + ((y - a) / (z / x))) + (a / (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) * ((x - t) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-198) or not (t_1 <= 5e-271):
		tmp = t_1
	else:
		tmp = ((t - ((y * t) / z)) + ((y - a) / (z / x))) + (a / (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-198) || !(t_1 <= 5e-271))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(t - Float64(Float64(y * t) / z)) + Float64(Float64(y - a) / Float64(z / x))) + Float64(a / Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y - z) * ((x - t) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-198) || ~((t_1 <= 5e-271)))
		tmp = t_1;
	else
		tmp = ((t - ((y * t) / z)) + ((y - a) / (z / x))) + (a / (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-198], N[Not[LessEqual[t$95$1, 5e-271]], $MachinePrecision]], t$95$1, N[(N[(N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(z / t), $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)))) < -9.9999999999999991e-199 or 5.0000000000000002e-271 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.6%

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

   if -9.9999999999999991e-199 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.0000000000000002e-271

   1. Initial program 6.5%

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

   2. Taylor expanded in x around -inf 63.8%

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

   3. Taylor expanded in z around inf 83.9%

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

      1. sub-neg 83.9%

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

      2. +-commutative 83.9%

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

      3. mul-1-neg 83.9%

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

      4. unsub-neg 83.9%

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

      5. +-commutative 83.9%

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

      6. mul-1-neg 83.9%

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

      7. unsub-neg 83.9%

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

      8. *-commutative 83.9%

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

      9. associate-/l* 94.4%

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

      10. mul-1-neg 94.4%

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

      11. unsub-neg 94.4%

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

      12. mul-1-neg 94.4%

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

      13. remove-double-neg 94.4%

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

      14. associate-/l* 94.4%

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

   5. Simplified 94.4%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-198} \lor \neg \left(x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 5 \cdot 10^{-271}\right):\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t - \frac{y \cdot t}{z}\right) + \frac{y - a}{\frac{z}{x}}\right) + \frac{a}{\frac{z}{t}}\\ \end{array} \]

Alternative 6: 88.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-198} \lor \neg \left(t_1 \leq 5 \cdot 10^{-271}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -1e-198) (not (<= t_1 5e-271)))
     t_1
     (+ t (/ (* (- y a) (- x t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-198) || !(t_1 <= 5e-271)) {
		tmp = t_1;
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y - z) * ((x - t) / (a - z)))
    if ((t_1 <= (-1d-198)) .or. (.not. (t_1 <= 5d-271))) then
        tmp = t_1
    else
        tmp = t + (((y - a) * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-198) || !(t_1 <= 5e-271)) {
		tmp = t_1;
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) * ((x - t) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-198) or not (t_1 <= 5e-271):
		tmp = t_1
	else:
		tmp = t + (((y - a) * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-198) || !(t_1 <= 5e-271))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y - z) * ((x - t) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-198) || ~((t_1 <= 5e-271)))
		tmp = t_1;
	else
		tmp = t + (((y - a) * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-198], N[Not[LessEqual[t$95$1, 5e-271]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999991e-199 or 5.0000000000000002e-271 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.6%

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

   if -9.9999999999999991e-199 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.0000000000000002e-271

   1. Initial program 6.5%

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

   2. Taylor expanded in z around inf 84.1%

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

      1. +-commutative 84.1%

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

      2. associate--l+ 84.1%

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

      3. associate-*r/ 84.1%

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

      4. associate-*r/ 84.1%

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

      5. div-sub 84.1%

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

      6. distribute-lft-out-- 84.1%

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

      7. mul-1-neg 84.1%

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

      8. distribute-neg-frac 84.1%

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

      9. unsub-neg 84.1%

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

      10. distribute-rgt-out-- 84.1%

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

   4. Simplified 84.1%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-198} \lor \neg \left(x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 5 \cdot 10^{-271}\right):\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \]

Alternative 7: 56.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_3 := x - \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;t \leq -6500000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-12}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-186}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-287}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-19}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z))))
        (t_2 (* (- t x) (/ y (- a z))))
        (t_3 (- x (/ y (/ a x)))))
   (if (<= t -6500000000.0)
     t_1
     (if (<= t -4.5e-5)
       t_2
       (if (<= t -5e-12)
         (/ (- t) (/ z (- y z)))
         (if (<= t -2.7e-186)
           x
           (if (<= t 1.3e-287)
             t_3
             (if (<= t 8.5e-156) t_2 (if (<= t 3.2e-19) t_3 t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = (t - x) * (y / (a - z));
	double t_3 = x - (y / (a / x));
	double tmp;
	if (t <= -6500000000.0) {
		tmp = t_1;
	} else if (t <= -4.5e-5) {
		tmp = t_2;
	} else if (t <= -5e-12) {
		tmp = -t / (z / (y - z));
	} else if (t <= -2.7e-186) {
		tmp = x;
	} else if (t <= 1.3e-287) {
		tmp = t_3;
	} else if (t <= 8.5e-156) {
		tmp = t_2;
	} else if (t <= 3.2e-19) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = (t - x) * (y / (a - z))
    t_3 = x - (y / (a / x))
    if (t <= (-6500000000.0d0)) then
        tmp = t_1
    else if (t <= (-4.5d-5)) then
        tmp = t_2
    else if (t <= (-5d-12)) then
        tmp = -t / (z / (y - z))
    else if (t <= (-2.7d-186)) then
        tmp = x
    else if (t <= 1.3d-287) then
        tmp = t_3
    else if (t <= 8.5d-156) then
        tmp = t_2
    else if (t <= 3.2d-19) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = (t - x) * (y / (a - z));
	double t_3 = x - (y / (a / x));
	double tmp;
	if (t <= -6500000000.0) {
		tmp = t_1;
	} else if (t <= -4.5e-5) {
		tmp = t_2;
	} else if (t <= -5e-12) {
		tmp = -t / (z / (y - z));
	} else if (t <= -2.7e-186) {
		tmp = x;
	} else if (t <= 1.3e-287) {
		tmp = t_3;
	} else if (t <= 8.5e-156) {
		tmp = t_2;
	} else if (t <= 3.2e-19) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = (t - x) * (y / (a - z))
	t_3 = x - (y / (a / x))
	tmp = 0
	if t <= -6500000000.0:
		tmp = t_1
	elif t <= -4.5e-5:
		tmp = t_2
	elif t <= -5e-12:
		tmp = -t / (z / (y - z))
	elif t <= -2.7e-186:
		tmp = x
	elif t <= 1.3e-287:
		tmp = t_3
	elif t <= 8.5e-156:
		tmp = t_2
	elif t <= 3.2e-19:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_3 = Float64(x - Float64(y / Float64(a / x)))
	tmp = 0.0
	if (t <= -6500000000.0)
		tmp = t_1;
	elseif (t <= -4.5e-5)
		tmp = t_2;
	elseif (t <= -5e-12)
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	elseif (t <= -2.7e-186)
		tmp = x;
	elseif (t <= 1.3e-287)
		tmp = t_3;
	elseif (t <= 8.5e-156)
		tmp = t_2;
	elseif (t <= 3.2e-19)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = (t - x) * (y / (a - z));
	t_3 = x - (y / (a / x));
	tmp = 0.0;
	if (t <= -6500000000.0)
		tmp = t_1;
	elseif (t <= -4.5e-5)
		tmp = t_2;
	elseif (t <= -5e-12)
		tmp = -t / (z / (y - z));
	elseif (t <= -2.7e-186)
		tmp = x;
	elseif (t <= 1.3e-287)
		tmp = t_3;
	elseif (t <= 8.5e-156)
		tmp = t_2;
	elseif (t <= 3.2e-19)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6500000000.0], t$95$1, If[LessEqual[t, -4.5e-5], t$95$2, If[LessEqual[t, -5e-12], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.7e-186], x, If[LessEqual[t, 1.3e-287], t$95$3, If[LessEqual[t, 8.5e-156], t$95$2, If[LessEqual[t, 3.2e-19], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.5e9 or 3.19999999999999982e-19 < t

   1. Initial program 86.3%

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

   2. Taylor expanded in t around inf 77.7%

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

      1. div-sub 77.7%

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

   4. Simplified 77.7%

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

   if -6.5e9 < t < -4.50000000000000028e-5 or 1.3e-287 < t < 8.5e-156

   1. Initial program 72.6%

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

      1. add-cube-cbrt 72.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

      2. fma-def 72.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right)} \]

      3. pow2 72.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right) \]

      4. *-commutative 72.6%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)}\right) \]

      5. associate-*l/ 63.0%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}}\right) \]

      6. associate-*r/ 78.6%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}}\right) \]

   3. Applied egg-rr 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(t - x\right) \cdot \frac{y - z}{a - z}\right)} \]

   4. Taylor expanded in y around -inf 62.3%

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

      1. associate-*l/ 73.7%

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

   6. Simplified 73.7%

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

   if -4.50000000000000028e-5 < t < -4.9999999999999997e-12

   1. Initial program 99.2%

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

   2. Taylor expanded in a around 0 99.2%

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

      1. associate-*r/ 99.2%

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

      2. neg-mul-1 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in x around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. associate-/l* 77.1%

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

   7. Simplified 77.1%

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

   if -4.9999999999999997e-12 < t < -2.6999999999999999e-186

   1. Initial program 68.1%

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

   2. Taylor expanded in a around inf 44.1%

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

   if -2.6999999999999999e-186 < t < 1.3e-287 or 8.5e-156 < t < 3.19999999999999982e-19

   1. Initial program 73.6%

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

   2. Taylor expanded in z around 0 55.1%

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

   3. Taylor expanded in t around 0 53.7%

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

      1. +-commutative 53.7%

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

      2. mul-1-neg 53.7%

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

      3. unsub-neg 53.7%

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

      4. associate-/l* 56.7%

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

   5. Simplified 56.7%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6500000000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-5}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-12}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-186}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-287}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-156}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-19}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 8: 43.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x - t}{z}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-62}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-268}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- x t) z))) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= a -5.6e+119)
     x
     (if (<= a -2.5e-62)
       (* (- y z) (/ t a))
       (if (<= a -6e-122)
         t_1
         (if (<= a -4.2e-268)
           t_2
           (if (<= a 1.15e-49) t_1 (if (<= a 1.32e+38) t_2 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / z);
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -5.6e+119) {
		tmp = x;
	} else if (a <= -2.5e-62) {
		tmp = (y - z) * (t / a);
	} else if (a <= -6e-122) {
		tmp = t_1;
	} else if (a <= -4.2e-268) {
		tmp = t_2;
	} else if (a <= 1.15e-49) {
		tmp = t_1;
	} else if (a <= 1.32e+38) {
		tmp = t_2;
	} 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 = y * ((x - t) / z)
    t_2 = t * (1.0d0 - (y / z))
    if (a <= (-5.6d+119)) then
        tmp = x
    else if (a <= (-2.5d-62)) then
        tmp = (y - z) * (t / a)
    else if (a <= (-6d-122)) then
        tmp = t_1
    else if (a <= (-4.2d-268)) then
        tmp = t_2
    else if (a <= 1.15d-49) then
        tmp = t_1
    else if (a <= 1.32d+38) then
        tmp = t_2
    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 = y * ((x - t) / z);
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -5.6e+119) {
		tmp = x;
	} else if (a <= -2.5e-62) {
		tmp = (y - z) * (t / a);
	} else if (a <= -6e-122) {
		tmp = t_1;
	} else if (a <= -4.2e-268) {
		tmp = t_2;
	} else if (a <= 1.15e-49) {
		tmp = t_1;
	} else if (a <= 1.32e+38) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((x - t) / z)
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -5.6e+119:
		tmp = x
	elif a <= -2.5e-62:
		tmp = (y - z) * (t / a)
	elif a <= -6e-122:
		tmp = t_1
	elif a <= -4.2e-268:
		tmp = t_2
	elif a <= 1.15e-49:
		tmp = t_1
	elif a <= 1.32e+38:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(x - t) / z))
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -5.6e+119)
		tmp = x;
	elseif (a <= -2.5e-62)
		tmp = Float64(Float64(y - z) * Float64(t / a));
	elseif (a <= -6e-122)
		tmp = t_1;
	elseif (a <= -4.2e-268)
		tmp = t_2;
	elseif (a <= 1.15e-49)
		tmp = t_1;
	elseif (a <= 1.32e+38)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((x - t) / z);
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -5.6e+119)
		tmp = x;
	elseif (a <= -2.5e-62)
		tmp = (y - z) * (t / a);
	elseif (a <= -6e-122)
		tmp = t_1;
	elseif (a <= -4.2e-268)
		tmp = t_2;
	elseif (a <= 1.15e-49)
		tmp = t_1;
	elseif (a <= 1.32e+38)
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+119], x, If[LessEqual[a, -2.5e-62], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6e-122], t$95$1, If[LessEqual[a, -4.2e-268], t$95$2, If[LessEqual[a, 1.15e-49], t$95$1, If[LessEqual[a, 1.32e+38], t$95$2, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.60000000000000026e119 or 1.32e38 < a

   1. Initial program 89.6%

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

   2. Taylor expanded in a around inf 56.3%

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

   if -5.60000000000000026e119 < a < -2.5000000000000001e-62

   1. Initial program 85.4%

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

      1. add-cube-cbrt 85.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

      2. fma-def 85.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right)} \]

      3. pow2 85.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right) \]

      4. *-commutative 85.6%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)}\right) \]

      5. associate-*l/ 70.8%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}}\right) \]

      6. associate-*r/ 88.9%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}}\right) \]

   3. Applied egg-rr 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(t - x\right) \cdot \frac{y - z}{a - z}\right)} \]

   4. Taylor expanded in x around 0 50.8%

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

      1. associate-/l* 59.9%

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

      2. associate-/r/ 56.7%

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

   6. Simplified 56.7%

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

   7. Taylor expanded in a around inf 41.9%

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

   if -2.5000000000000001e-62 < a < -6.00000000000000009e-122 or -4.19999999999999996e-268 < a < 1.15e-49

   1. Initial program 66.8%

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

   2. Taylor expanded in a around 0 52.7%

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

      1. associate-*r/ 52.7%

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

      2. neg-mul-1 52.7%

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

   4. Simplified 52.7%

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

   5. Taylor expanded in y around inf 52.0%

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

      1. div-sub 52.1%

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

   7. Simplified 52.1%

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

   if -6.00000000000000009e-122 < a < -4.19999999999999996e-268 or 1.15e-49 < a < 1.32e38

   1. Initial program 76.2%

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

   2. Taylor expanded in a around 0 49.3%

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

      1. +-commutative 49.3%

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

      2. mul-1-neg 49.3%

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

      3. unsub-neg 49.3%

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

      4. associate-/l* 50.7%

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

   4. Simplified 50.7%

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

   5. Taylor expanded in t around inf 58.5%

      \[\leadsto \color{blue}{\left(1 - \frac{y}{z}\right) \cdot t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-62}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-268}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 64.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-77}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+30} \lor \neg \left(y \leq 4.8 \cdot 10^{+97}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))))
   (if (<= y -1.02e+155)
     t_1
     (if (<= y -1.9e-65)
       (+ x (/ y (/ a (- t x))))
       (if (<= y 3.3e-77)
         (- x (/ t (/ (- a z) z)))
         (if (or (<= y 5.6e+30) (not (<= y 4.8e+97)))
           t_1
           (* t (/ (- y z) (- a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -1.02e+155) {
		tmp = t_1;
	} else if (y <= -1.9e-65) {
		tmp = x + (y / (a / (t - x)));
	} else if (y <= 3.3e-77) {
		tmp = x - (t / ((a - z) / z));
	} else if ((y <= 5.6e+30) || !(y <= 4.8e+97)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    if (y <= (-1.02d+155)) then
        tmp = t_1
    else if (y <= (-1.9d-65)) then
        tmp = x + (y / (a / (t - x)))
    else if (y <= 3.3d-77) then
        tmp = x - (t / ((a - z) / z))
    else if ((y <= 5.6d+30) .or. (.not. (y <= 4.8d+97))) then
        tmp = t_1
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -1.02e+155) {
		tmp = t_1;
	} else if (y <= -1.9e-65) {
		tmp = x + (y / (a / (t - x)));
	} else if (y <= 3.3e-77) {
		tmp = x - (t / ((a - z) / z));
	} else if ((y <= 5.6e+30) || !(y <= 4.8e+97)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	tmp = 0
	if y <= -1.02e+155:
		tmp = t_1
	elif y <= -1.9e-65:
		tmp = x + (y / (a / (t - x)))
	elif y <= 3.3e-77:
		tmp = x - (t / ((a - z) / z))
	elif (y <= 5.6e+30) or not (y <= 4.8e+97):
		tmp = t_1
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -1.02e+155)
		tmp = t_1;
	elseif (y <= -1.9e-65)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (y <= 3.3e-77)
		tmp = Float64(x - Float64(t / Float64(Float64(a - z) / z)));
	elseif ((y <= 5.6e+30) || !(y <= 4.8e+97))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (y <= -1.02e+155)
		tmp = t_1;
	elseif (y <= -1.9e-65)
		tmp = x + (y / (a / (t - x)));
	elseif (y <= 3.3e-77)
		tmp = x - (t / ((a - z) / z));
	elseif ((y <= 5.6e+30) || ~((y <= 4.8e+97)))
		tmp = t_1;
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e+155], t$95$1, If[LessEqual[y, -1.9e-65], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-77], N[(x - N[(t / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 5.6e+30], N[Not[LessEqual[y, 4.8e+97]], $MachinePrecision]], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.02e155 or 3.29999999999999991e-77 < y < 5.59999999999999966e30 or 4.8e97 < y

   1. Initial program 82.8%

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

      1. add-cube-cbrt 82.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

      2. fma-def 82.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right)} \]

      3. pow2 82.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right) \]

      4. *-commutative 82.9%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)}\right) \]

      5. associate-*l/ 64.6%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}}\right) \]

      6. associate-*r/ 84.2%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}}\right) \]

   3. Applied egg-rr 84.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(t - x\right) \cdot \frac{y - z}{a - z}\right)} \]

   4. Taylor expanded in y around -inf 61.4%

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

      1. associate-*l/ 76.5%

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

   6. Simplified 76.5%

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

   if -1.02e155 < y < -1.9000000000000001e-65

   1. Initial program 84.6%

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

   2. Taylor expanded in z around 0 56.5%

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

      1. +-commutative 56.5%

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

      2. associate-/l* 60.2%

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

   4. Simplified 60.2%

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

   if -1.9000000000000001e-65 < y < 3.29999999999999991e-77

   1. Initial program 71.4%

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

   2. Taylor expanded in x around -inf 75.9%

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

      1. *-un-lft-identity 75.9%

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

      2. fma-def 75.9%

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

      3. associate-/l* 87.6%

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

      4. mul-1-neg 87.6%

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

      5. *-commutative 87.6%

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

      6. associate--r+ 84.7%

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

      7. div-sub 84.7%

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

   4. Applied egg-rr 84.7%

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

      1. fma-udef 84.7%

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

      2. *-lft-identity 84.7%

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

      3. associate-/r/ 80.7%

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

      4. fma-def 80.7%

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

      5. *-commutative 80.7%

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

      6. distribute-rgt-neg-in 80.7%

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

      7. sub-neg 80.7%

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

      8. metadata-eval 80.7%

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

   6. Simplified 80.7%

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

   7. Taylor expanded in z around 0 68.2%

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

      1. associate-*r* 68.2%

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

      2. sub-neg 68.2%

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

      3. metadata-eval 68.2%

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

      4. distribute-lft-in 68.2%

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

      5. metadata-eval 68.2%

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

      6. +-commutative 68.2%

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

      7. *-commutative 68.2%

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

      8. mul-1-neg 68.2%

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

      9. unsub-neg 68.2%

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

   9. Simplified 68.2%

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

   10. Taylor expanded in y around 0 59.8%

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

       1. +-commutative 59.8%

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

       2. mul-1-neg 59.8%

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

       3. unsub-neg 59.8%

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

       4. associate-/l* 70.5%

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

   12. Simplified 70.5%

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

   if 5.59999999999999966e30 < y < 4.8e97

   1. Initial program 81.7%

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

   2. Taylor expanded in t around inf 75.8%

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

      1. div-sub 75.8%

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

   4. Simplified 75.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+155}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-77}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+30} \lor \neg \left(y \leq 4.8 \cdot 10^{+97}\right):\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 10: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ t_3 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-14}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+129}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z))))
        (t_2 (* t (/ (- y z) (- a z))))
        (t_3 (+ x (/ y (/ a (- t x))))))
   (if (<= z -1.85e+93)
     t_2
     (if (<= z -7.5e-150)
       t_1
       (if (<= z 5e-14)
         t_3
         (if (<= z 2.45e+58) t_1 (if (<= z 6.5e+129) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double t_3 = x + (y / (a / (t - x)));
	double tmp;
	if (z <= -1.85e+93) {
		tmp = t_2;
	} else if (z <= -7.5e-150) {
		tmp = t_1;
	} else if (z <= 5e-14) {
		tmp = t_3;
	} else if (z <= 2.45e+58) {
		tmp = t_1;
	} else if (z <= 6.5e+129) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    t_2 = t * ((y - z) / (a - z))
    t_3 = x + (y / (a / (t - x)))
    if (z <= (-1.85d+93)) then
        tmp = t_2
    else if (z <= (-7.5d-150)) then
        tmp = t_1
    else if (z <= 5d-14) then
        tmp = t_3
    else if (z <= 2.45d+58) then
        tmp = t_1
    else if (z <= 6.5d+129) then
        tmp = t_3
    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 - x) * (y / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double t_3 = x + (y / (a / (t - x)));
	double tmp;
	if (z <= -1.85e+93) {
		tmp = t_2;
	} else if (z <= -7.5e-150) {
		tmp = t_1;
	} else if (z <= 5e-14) {
		tmp = t_3;
	} else if (z <= 2.45e+58) {
		tmp = t_1;
	} else if (z <= 6.5e+129) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	t_2 = t * ((y - z) / (a - z))
	t_3 = x + (y / (a / (t - x)))
	tmp = 0
	if z <= -1.85e+93:
		tmp = t_2
	elif z <= -7.5e-150:
		tmp = t_1
	elif z <= 5e-14:
		tmp = t_3
	elif z <= 2.45e+58:
		tmp = t_1
	elif z <= 6.5e+129:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_3 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (z <= -1.85e+93)
		tmp = t_2;
	elseif (z <= -7.5e-150)
		tmp = t_1;
	elseif (z <= 5e-14)
		tmp = t_3;
	elseif (z <= 2.45e+58)
		tmp = t_1;
	elseif (z <= 6.5e+129)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	t_2 = t * ((y - z) / (a - z));
	t_3 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (z <= -1.85e+93)
		tmp = t_2;
	elseif (z <= -7.5e-150)
		tmp = t_1;
	elseif (z <= 5e-14)
		tmp = t_3;
	elseif (z <= 2.45e+58)
		tmp = t_1;
	elseif (z <= 6.5e+129)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e+93], t$95$2, If[LessEqual[z, -7.5e-150], t$95$1, If[LessEqual[z, 5e-14], t$95$3, If[LessEqual[z, 2.45e+58], t$95$1, If[LessEqual[z, 6.5e+129], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.84999999999999994e93 or 6.4999999999999995e129 < z

   1. Initial program 56.3%

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

   2. Taylor expanded in t around inf 64.9%

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

      1. div-sub 64.9%

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

   4. Simplified 64.9%

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

   if -1.84999999999999994e93 < z < -7.5000000000000004e-150 or 5.0000000000000002e-14 < z < 2.45000000000000009e58

   1. Initial program 84.3%

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

      1. add-cube-cbrt 84.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

      2. fma-def 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right)} \]

      3. pow2 84.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right) \]

      4. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)}\right) \]

      5. associate-*l/ 79.8%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}}\right) \]

      6. associate-*r/ 86.6%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}}\right) \]

   3. Applied egg-rr 86.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(t - x\right) \cdot \frac{y - z}{a - z}\right)} \]

   4. Taylor expanded in y around -inf 57.0%

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

      1. associate-*l/ 60.9%

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

   6. Simplified 60.9%

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

   if -7.5000000000000004e-150 < z < 5.0000000000000002e-14 or 2.45000000000000009e58 < z < 6.4999999999999995e129

   1. Initial program 92.7%

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

   2. Taylor expanded in z around 0 74.2%

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

      1. +-commutative 74.2%

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

      2. associate-/l* 77.7%

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

   4. Simplified 77.7%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-150}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+58}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+129}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 11: 64.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-77}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))))
   (if (<= y -1e+155)
     t_1
     (if (<= y -4.8e-65)
       (+ x (/ y (/ a (- t x))))
       (if (<= y 3.5e-77)
         (- x (/ t (/ (- a z) z)))
         (if (<= y 8.8e+29)
           t_1
           (if (<= y 1.2e+94)
             (* t (/ (- y z) (- a z)))
             (/ y (/ (- a z) (- t x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -1e+155) {
		tmp = t_1;
	} else if (y <= -4.8e-65) {
		tmp = x + (y / (a / (t - x)));
	} else if (y <= 3.5e-77) {
		tmp = x - (t / ((a - z) / z));
	} else if (y <= 8.8e+29) {
		tmp = t_1;
	} else if (y <= 1.2e+94) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = y / ((a - z) / (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    if (y <= (-1d+155)) then
        tmp = t_1
    else if (y <= (-4.8d-65)) then
        tmp = x + (y / (a / (t - x)))
    else if (y <= 3.5d-77) then
        tmp = x - (t / ((a - z) / z))
    else if (y <= 8.8d+29) then
        tmp = t_1
    else if (y <= 1.2d+94) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = y / ((a - z) / (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -1e+155) {
		tmp = t_1;
	} else if (y <= -4.8e-65) {
		tmp = x + (y / (a / (t - x)));
	} else if (y <= 3.5e-77) {
		tmp = x - (t / ((a - z) / z));
	} else if (y <= 8.8e+29) {
		tmp = t_1;
	} else if (y <= 1.2e+94) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = y / ((a - z) / (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	tmp = 0
	if y <= -1e+155:
		tmp = t_1
	elif y <= -4.8e-65:
		tmp = x + (y / (a / (t - x)))
	elif y <= 3.5e-77:
		tmp = x - (t / ((a - z) / z))
	elif y <= 8.8e+29:
		tmp = t_1
	elif y <= 1.2e+94:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = y / ((a - z) / (t - x))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -1e+155)
		tmp = t_1;
	elseif (y <= -4.8e-65)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (y <= 3.5e-77)
		tmp = Float64(x - Float64(t / Float64(Float64(a - z) / z)));
	elseif (y <= 8.8e+29)
		tmp = t_1;
	elseif (y <= 1.2e+94)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (y <= -1e+155)
		tmp = t_1;
	elseif (y <= -4.8e-65)
		tmp = x + (y / (a / (t - x)));
	elseif (y <= 3.5e-77)
		tmp = x - (t / ((a - z) / z));
	elseif (y <= 8.8e+29)
		tmp = t_1;
	elseif (y <= 1.2e+94)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = y / ((a - z) / (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+155], t$95$1, If[LessEqual[y, -4.8e-65], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-77], N[(x - N[(t / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e+29], t$95$1, If[LessEqual[y, 1.2e+94], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.00000000000000001e155 or 3.50000000000000013e-77 < y < 8.8000000000000005e29

   1. Initial program 79.0%

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

      1. add-cube-cbrt 79.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

      2. fma-def 79.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right)} \]

      3. pow2 79.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right) \]

      4. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)}\right) \]

      5. associate-*l/ 63.1%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}}\right) \]

      6. associate-*r/ 79.7%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}}\right) \]

   3. Applied egg-rr 79.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(t - x\right) \cdot \frac{y - z}{a - z}\right)} \]

   4. Taylor expanded in y around -inf 63.0%

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

      1. associate-*l/ 78.7%

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

   6. Simplified 78.7%

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

   if -1.00000000000000001e155 < y < -4.8000000000000003e-65

   1. Initial program 84.6%

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

   2. Taylor expanded in z around 0 56.5%

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

      1. +-commutative 56.5%

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

      2. associate-/l* 60.2%

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

   4. Simplified 60.2%

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

   if -4.8000000000000003e-65 < y < 3.50000000000000013e-77

   1. Initial program 71.4%

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

   2. Taylor expanded in x around -inf 75.9%

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

      1. *-un-lft-identity 75.9%

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

      2. fma-def 75.9%

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

      3. associate-/l* 87.6%

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

      4. mul-1-neg 87.6%

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

      5. *-commutative 87.6%

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

      6. associate--r+ 84.7%

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

      7. div-sub 84.7%

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

   4. Applied egg-rr 84.7%

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

      1. fma-udef 84.7%

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

      2. *-lft-identity 84.7%

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

      3. associate-/r/ 80.7%

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

      4. fma-def 80.7%

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

      5. *-commutative 80.7%

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

      6. distribute-rgt-neg-in 80.7%

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

      7. sub-neg 80.7%

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

      8. metadata-eval 80.7%

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

   6. Simplified 80.7%

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

   7. Taylor expanded in z around 0 68.2%

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

      1. associate-*r* 68.2%

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

      2. sub-neg 68.2%

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

      3. metadata-eval 68.2%

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

      4. distribute-lft-in 68.2%

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

      5. metadata-eval 68.2%

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

      6. +-commutative 68.2%

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

      7. *-commutative 68.2%

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

      8. mul-1-neg 68.2%

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

      9. unsub-neg 68.2%

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

   9. Simplified 68.2%

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

   10. Taylor expanded in y around 0 59.8%

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

       1. +-commutative 59.8%

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

       2. mul-1-neg 59.8%

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

       3. unsub-neg 59.8%

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

       4. associate-/l* 70.5%

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

   12. Simplified 70.5%

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

   if 8.8000000000000005e29 < y < 1.19999999999999991e94

   1. Initial program 81.7%

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

   2. Taylor expanded in t around inf 75.8%

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

      1. div-sub 75.8%

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

   4. Simplified 75.8%

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

   if 1.19999999999999991e94 < y

   1. Initial program 86.0%

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

   2. Taylor expanded in y around inf 76.5%

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

      1. div-sub 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-*r/ 60.1%

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

      4. associate-/l* 76.5%

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

   4. Simplified 76.5%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+155}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-77}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+29}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \end{array} \]

Alternative 12: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-65}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-77}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))))
   (if (<= y -2.7e+155)
     t_1
     (if (<= y -2.5e-65)
       (+ x (* (- z y) (/ (- x t) a)))
       (if (<= y 5e-77)
         (- x (/ t (/ (- a z) z)))
         (if (<= y 3.4e+30)
           t_1
           (if (<= y 2.75e+94)
             (* t (/ (- y z) (- a z)))
             (/ y (/ (- a z) (- t x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -2.7e+155) {
		tmp = t_1;
	} else if (y <= -2.5e-65) {
		tmp = x + ((z - y) * ((x - t) / a));
	} else if (y <= 5e-77) {
		tmp = x - (t / ((a - z) / z));
	} else if (y <= 3.4e+30) {
		tmp = t_1;
	} else if (y <= 2.75e+94) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = y / ((a - z) / (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    if (y <= (-2.7d+155)) then
        tmp = t_1
    else if (y <= (-2.5d-65)) then
        tmp = x + ((z - y) * ((x - t) / a))
    else if (y <= 5d-77) then
        tmp = x - (t / ((a - z) / z))
    else if (y <= 3.4d+30) then
        tmp = t_1
    else if (y <= 2.75d+94) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = y / ((a - z) / (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -2.7e+155) {
		tmp = t_1;
	} else if (y <= -2.5e-65) {
		tmp = x + ((z - y) * ((x - t) / a));
	} else if (y <= 5e-77) {
		tmp = x - (t / ((a - z) / z));
	} else if (y <= 3.4e+30) {
		tmp = t_1;
	} else if (y <= 2.75e+94) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = y / ((a - z) / (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	tmp = 0
	if y <= -2.7e+155:
		tmp = t_1
	elif y <= -2.5e-65:
		tmp = x + ((z - y) * ((x - t) / a))
	elif y <= 5e-77:
		tmp = x - (t / ((a - z) / z))
	elif y <= 3.4e+30:
		tmp = t_1
	elif y <= 2.75e+94:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = y / ((a - z) / (t - x))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -2.7e+155)
		tmp = t_1;
	elseif (y <= -2.5e-65)
		tmp = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / a)));
	elseif (y <= 5e-77)
		tmp = Float64(x - Float64(t / Float64(Float64(a - z) / z)));
	elseif (y <= 3.4e+30)
		tmp = t_1;
	elseif (y <= 2.75e+94)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (y <= -2.7e+155)
		tmp = t_1;
	elseif (y <= -2.5e-65)
		tmp = x + ((z - y) * ((x - t) / a));
	elseif (y <= 5e-77)
		tmp = x - (t / ((a - z) / z));
	elseif (y <= 3.4e+30)
		tmp = t_1;
	elseif (y <= 2.75e+94)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = y / ((a - z) / (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+155], t$95$1, If[LessEqual[y, -2.5e-65], N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-77], N[(x - N[(t / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+30], t$95$1, If[LessEqual[y, 2.75e+94], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.69999999999999994e155 or 4.99999999999999963e-77 < y < 3.4000000000000002e30

   1. Initial program 79.0%

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

      1. add-cube-cbrt 79.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

      2. fma-def 79.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right)} \]

      3. pow2 79.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right) \]

      4. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)}\right) \]

      5. associate-*l/ 63.1%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}}\right) \]

      6. associate-*r/ 79.7%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}}\right) \]

   3. Applied egg-rr 79.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(t - x\right) \cdot \frac{y - z}{a - z}\right)} \]

   4. Taylor expanded in y around -inf 63.0%

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

      1. associate-*l/ 78.7%

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

   6. Simplified 78.7%

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

   if -2.69999999999999994e155 < y < -2.49999999999999991e-65

   1. Initial program 84.6%

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

   2. Taylor expanded in a around inf 61.9%

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

   if -2.49999999999999991e-65 < y < 4.99999999999999963e-77

   1. Initial program 71.4%

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

   2. Taylor expanded in x around -inf 75.9%

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

      1. *-un-lft-identity 75.9%

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

      2. fma-def 75.9%

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

      3. associate-/l* 87.6%

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

      4. mul-1-neg 87.6%

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

      5. *-commutative 87.6%

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

      6. associate--r+ 84.7%

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

      7. div-sub 84.7%

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

   4. Applied egg-rr 84.7%

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

      1. fma-udef 84.7%

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

      2. *-lft-identity 84.7%

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

      3. associate-/r/ 80.7%

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

      4. fma-def 80.7%

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

      5. *-commutative 80.7%

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

      6. distribute-rgt-neg-in 80.7%

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

      7. sub-neg 80.7%

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

      8. metadata-eval 80.7%

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

   6. Simplified 80.7%

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

   7. Taylor expanded in z around 0 68.2%

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

      1. associate-*r* 68.2%

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

      2. sub-neg 68.2%

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

      3. metadata-eval 68.2%

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

      4. distribute-lft-in 68.2%

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

      5. metadata-eval 68.2%

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

      6. +-commutative 68.2%

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

      7. *-commutative 68.2%

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

      8. mul-1-neg 68.2%

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

      9. unsub-neg 68.2%

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

   9. Simplified 68.2%

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

   10. Taylor expanded in y around 0 59.8%

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

       1. +-commutative 59.8%

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

       2. mul-1-neg 59.8%

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

       3. unsub-neg 59.8%

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

       4. associate-/l* 70.5%

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

   12. Simplified 70.5%

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

   if 3.4000000000000002e30 < y < 2.7499999999999999e94

   1. Initial program 81.7%

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

   2. Taylor expanded in t around inf 75.8%

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

      1. div-sub 75.8%

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

   4. Simplified 75.8%

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

   if 2.7499999999999999e94 < y

   1. Initial program 86.0%

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

   2. Taylor expanded in y around inf 76.5%

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

      1. div-sub 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-*r/ 60.1%

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

      4. associate-/l* 76.5%

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

   4. Simplified 76.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+155}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-65}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-77}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+30}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \end{array} \]

Alternative 13: 47.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;a \leq -4.7 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-149}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-119}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ a x)))))
   (if (<= a -4.7e+60)
     t_1
     (if (<= a -2.45e-231)
       (* t (- 1.0 (/ y z)))
       (if (<= a 1.06e-149)
         (/ (* y (- x t)) z)
         (if (<= a 1.1e-119)
           t
           (if (<= a 6.8e-63) (* y (/ (- x t) z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / x));
	double tmp;
	if (a <= -4.7e+60) {
		tmp = t_1;
	} else if (a <= -2.45e-231) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 1.06e-149) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 1.1e-119) {
		tmp = t;
	} else if (a <= 6.8e-63) {
		tmp = y * ((x - t) / 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 - (y / (a / x))
    if (a <= (-4.7d+60)) then
        tmp = t_1
    else if (a <= (-2.45d-231)) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 1.06d-149) then
        tmp = (y * (x - t)) / z
    else if (a <= 1.1d-119) then
        tmp = t
    else if (a <= 6.8d-63) then
        tmp = y * ((x - t) / 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 - (y / (a / x));
	double tmp;
	if (a <= -4.7e+60) {
		tmp = t_1;
	} else if (a <= -2.45e-231) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 1.06e-149) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 1.1e-119) {
		tmp = t;
	} else if (a <= 6.8e-63) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (a / x))
	tmp = 0
	if a <= -4.7e+60:
		tmp = t_1
	elif a <= -2.45e-231:
		tmp = t * (1.0 - (y / z))
	elif a <= 1.06e-149:
		tmp = (y * (x - t)) / z
	elif a <= 1.1e-119:
		tmp = t
	elif a <= 6.8e-63:
		tmp = y * ((x - t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(a / x)))
	tmp = 0.0
	if (a <= -4.7e+60)
		tmp = t_1;
	elseif (a <= -2.45e-231)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 1.06e-149)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 1.1e-119)
		tmp = t;
	elseif (a <= 6.8e-63)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (a / x));
	tmp = 0.0;
	if (a <= -4.7e+60)
		tmp = t_1;
	elseif (a <= -2.45e-231)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 1.06e-149)
		tmp = (y * (x - t)) / z;
	elseif (a <= 1.1e-119)
		tmp = t;
	elseif (a <= 6.8e-63)
		tmp = y * ((x - t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.7e+60], t$95$1, If[LessEqual[a, -2.45e-231], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.06e-149], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.1e-119], t, If[LessEqual[a, 6.8e-63], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.6999999999999998e60 or 6.79999999999999997e-63 < a

   1. Initial program 86.2%

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

   2. Taylor expanded in z around 0 65.1%

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

   3. Taylor expanded in t around 0 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. associate-/l* 57.6%

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

   5. Simplified 57.6%

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

   if -4.6999999999999998e60 < a < -2.45000000000000002e-231

   1. Initial program 76.0%

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

   2. Taylor expanded in a around 0 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

      4. associate-/l* 56.8%

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

   4. Simplified 56.8%

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

   5. Taylor expanded in t around inf 52.9%

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

   if -2.45000000000000002e-231 < a < 1.05999999999999998e-149

   1. Initial program 72.5%

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

   2. Taylor expanded in y around inf 61.9%

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

      1. div-sub 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*r/ 66.8%

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

      4. associate-/l* 62.3%

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

   4. Simplified 62.3%

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

   5. Taylor expanded in a around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. associate-/l* 60.2%

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

      3. associate-/r/ 58.9%

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

      4. distribute-rgt-neg-in 58.9%

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

   7. Simplified 58.9%

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

   8. Taylor expanded in y around 0 63.7%

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

   if 1.05999999999999998e-149 < a < 1.1e-119

   1. Initial program 63.9%

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

   2. Taylor expanded in z around inf 63.4%

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

   if 1.1e-119 < a < 6.79999999999999997e-63

   1. Initial program 59.4%

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

   2. Taylor expanded in a around 0 34.9%

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

      1. associate-*r/ 34.9%

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

      2. neg-mul-1 34.9%

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

   4. Simplified 34.9%

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

   5. Taylor expanded in y around inf 45.6%

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

      1. div-sub 45.6%

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

   7. Simplified 45.6%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+60}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-149}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-119}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 14: 47.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;a \leq -4.7 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-152}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-120}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ a x)))))
   (if (<= a -4.7e+60)
     t_1
     (if (<= a -6.6e-233)
       (* t (- 1.0 (/ y z)))
       (if (<= a 8.5e-152)
         (/ (* y (- x t)) z)
         (if (<= a 9.2e-120)
           t
           (if (<= a 1.22e-63) (* (/ y z) (- x t)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / x));
	double tmp;
	if (a <= -4.7e+60) {
		tmp = t_1;
	} else if (a <= -6.6e-233) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 8.5e-152) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 9.2e-120) {
		tmp = t;
	} else if (a <= 1.22e-63) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (a / x))
    if (a <= (-4.7d+60)) then
        tmp = t_1
    else if (a <= (-6.6d-233)) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 8.5d-152) then
        tmp = (y * (x - t)) / z
    else if (a <= 9.2d-120) then
        tmp = t
    else if (a <= 1.22d-63) then
        tmp = (y / z) * (x - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / x));
	double tmp;
	if (a <= -4.7e+60) {
		tmp = t_1;
	} else if (a <= -6.6e-233) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 8.5e-152) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 9.2e-120) {
		tmp = t;
	} else if (a <= 1.22e-63) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (a / x))
	tmp = 0
	if a <= -4.7e+60:
		tmp = t_1
	elif a <= -6.6e-233:
		tmp = t * (1.0 - (y / z))
	elif a <= 8.5e-152:
		tmp = (y * (x - t)) / z
	elif a <= 9.2e-120:
		tmp = t
	elif a <= 1.22e-63:
		tmp = (y / z) * (x - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(a / x)))
	tmp = 0.0
	if (a <= -4.7e+60)
		tmp = t_1;
	elseif (a <= -6.6e-233)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 8.5e-152)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 9.2e-120)
		tmp = t;
	elseif (a <= 1.22e-63)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (a / x));
	tmp = 0.0;
	if (a <= -4.7e+60)
		tmp = t_1;
	elseif (a <= -6.6e-233)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 8.5e-152)
		tmp = (y * (x - t)) / z;
	elseif (a <= 9.2e-120)
		tmp = t;
	elseif (a <= 1.22e-63)
		tmp = (y / z) * (x - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.7e+60], t$95$1, If[LessEqual[a, -6.6e-233], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-152], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 9.2e-120], t, If[LessEqual[a, 1.22e-63], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.6999999999999998e60 or 1.2199999999999999e-63 < a

   1. Initial program 86.2%

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

   2. Taylor expanded in z around 0 65.1%

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

   3. Taylor expanded in t around 0 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. associate-/l* 57.6%

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

   5. Simplified 57.6%

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

   if -4.6999999999999998e60 < a < -6.6000000000000001e-233

   1. Initial program 76.0%

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

   2. Taylor expanded in a around 0 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

      4. associate-/l* 56.8%

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

   4. Simplified 56.8%

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

   5. Taylor expanded in t around inf 52.9%

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

   if -6.6000000000000001e-233 < a < 8.5000000000000007e-152

   1. Initial program 72.5%

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

   2. Taylor expanded in y around inf 61.9%

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

      1. div-sub 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*r/ 66.8%

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

      4. associate-/l* 62.3%

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

   4. Simplified 62.3%

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

   5. Taylor expanded in a around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. associate-/l* 60.2%

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

      3. associate-/r/ 58.9%

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

      4. distribute-rgt-neg-in 58.9%

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

   7. Simplified 58.9%

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

   8. Taylor expanded in y around 0 63.7%

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

   if 8.5000000000000007e-152 < a < 9.19999999999999946e-120

   1. Initial program 63.9%

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

   2. Taylor expanded in z around inf 63.4%

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

   if 9.19999999999999946e-120 < a < 1.2199999999999999e-63

   1. Initial program 59.4%

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

   2. Taylor expanded in y around inf 58.3%

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

      1. div-sub 58.3%

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

      2. *-commutative 58.3%

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

      3. associate-*r/ 47.1%

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

      4. associate-/l* 58.3%

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

   4. Simplified 58.3%

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

   5. Taylor expanded in a around 0 34.2%

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

      1. mul-1-neg 34.2%

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

      2. associate-/l* 45.6%

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

      3. associate-/r/ 45.6%

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

      4. distribute-rgt-neg-in 45.6%

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

   7. Simplified 45.6%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+60}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-152}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-120}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 15: 47.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;a \leq -3.15 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-120}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ a x)))))
   (if (<= a -3.15e+59)
     t_1
     (if (<= a -1.8e-233)
       (* t (- 1.0 (/ y z)))
       (if (<= a 7.6e-150)
         (/ (* y (- x t)) z)
         (if (<= a 8e-120)
           (/ (- t) (/ (- a z) z))
           (if (<= a 6.5e-64) (* (/ y z) (- x t)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / x));
	double tmp;
	if (a <= -3.15e+59) {
		tmp = t_1;
	} else if (a <= -1.8e-233) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 7.6e-150) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 8e-120) {
		tmp = -t / ((a - z) / z);
	} else if (a <= 6.5e-64) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (a / x))
    if (a <= (-3.15d+59)) then
        tmp = t_1
    else if (a <= (-1.8d-233)) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 7.6d-150) then
        tmp = (y * (x - t)) / z
    else if (a <= 8d-120) then
        tmp = -t / ((a - z) / z)
    else if (a <= 6.5d-64) then
        tmp = (y / z) * (x - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / x));
	double tmp;
	if (a <= -3.15e+59) {
		tmp = t_1;
	} else if (a <= -1.8e-233) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 7.6e-150) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 8e-120) {
		tmp = -t / ((a - z) / z);
	} else if (a <= 6.5e-64) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (a / x))
	tmp = 0
	if a <= -3.15e+59:
		tmp = t_1
	elif a <= -1.8e-233:
		tmp = t * (1.0 - (y / z))
	elif a <= 7.6e-150:
		tmp = (y * (x - t)) / z
	elif a <= 8e-120:
		tmp = -t / ((a - z) / z)
	elif a <= 6.5e-64:
		tmp = (y / z) * (x - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(a / x)))
	tmp = 0.0
	if (a <= -3.15e+59)
		tmp = t_1;
	elseif (a <= -1.8e-233)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 7.6e-150)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 8e-120)
		tmp = Float64(Float64(-t) / Float64(Float64(a - z) / z));
	elseif (a <= 6.5e-64)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (a / x));
	tmp = 0.0;
	if (a <= -3.15e+59)
		tmp = t_1;
	elseif (a <= -1.8e-233)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 7.6e-150)
		tmp = (y * (x - t)) / z;
	elseif (a <= 8e-120)
		tmp = -t / ((a - z) / z);
	elseif (a <= 6.5e-64)
		tmp = (y / z) * (x - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.15e+59], t$95$1, If[LessEqual[a, -1.8e-233], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e-150], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 8e-120], N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-64], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.15e59 or 6.5000000000000004e-64 < a

   1. Initial program 86.2%

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

   2. Taylor expanded in z around 0 65.1%

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

   3. Taylor expanded in t around 0 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. associate-/l* 57.6%

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

   5. Simplified 57.6%

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

   if -3.15e59 < a < -1.80000000000000004e-233

   1. Initial program 76.0%

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

   2. Taylor expanded in a around 0 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

      4. associate-/l* 56.8%

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

   4. Simplified 56.8%

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

   5. Taylor expanded in t around inf 52.9%

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

   if -1.80000000000000004e-233 < a < 7.5999999999999997e-150

   1. Initial program 72.5%

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

   2. Taylor expanded in y around inf 61.9%

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

      1. div-sub 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*r/ 66.8%

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

      4. associate-/l* 62.3%

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

   4. Simplified 62.3%

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

   5. Taylor expanded in a around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. associate-/l* 60.2%

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

      3. associate-/r/ 58.9%

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

      4. distribute-rgt-neg-in 58.9%

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

   7. Simplified 58.9%

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

   8. Taylor expanded in y around 0 63.7%

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

   if 7.5999999999999997e-150 < a < 7.99999999999999983e-120

   1. Initial program 63.9%

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

      1. add-cube-cbrt 64.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

      2. fma-def 64.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right)} \]

      3. pow2 64.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right) \]

      4. *-commutative 64.2%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)}\right) \]

      5. associate-*l/ 51.7%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}}\right) \]

      6. associate-*r/ 76.2%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}}\right) \]

   3. Applied egg-rr 76.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(t - x\right) \cdot \frac{y - z}{a - z}\right)} \]

   4. Taylor expanded in x around 0 64.7%

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

      1. associate-/l* 88.3%

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

      2. associate-/r/ 75.9%

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

   6. Simplified 75.9%

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

   7. Taylor expanded in y around 0 40.5%

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

      1. mul-1-neg 40.5%

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

      2. associate-/l* 64.1%

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

      3. distribute-neg-frac 64.1%

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

   9. Simplified 64.1%

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

   if 7.99999999999999983e-120 < a < 6.5000000000000004e-64

   1. Initial program 59.4%

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

   2. Taylor expanded in y around inf 58.3%

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

      1. div-sub 58.3%

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

      2. *-commutative 58.3%

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

      3. associate-*r/ 47.1%

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

      4. associate-/l* 58.3%

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

   4. Simplified 58.3%

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

   5. Taylor expanded in a around 0 34.2%

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

      1. mul-1-neg 34.2%

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

      2. associate-/l* 45.6%

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

      3. associate-/r/ 45.6%

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

      4. distribute-rgt-neg-in 45.6%

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

   7. Simplified 45.6%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.15 \cdot 10^{+59}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-120}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 16: 57.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{a}{x}}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -3600:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-162}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ a x)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -3600.0)
     t_2
     (if (<= t 2.9e-260)
       t_1
       (if (<= t 4.8e-162) (* (/ y z) (- x t)) (if (<= t 2.7e-19) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / x));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -3600.0) {
		tmp = t_2;
	} else if (t <= 2.9e-260) {
		tmp = t_1;
	} else if (t <= 4.8e-162) {
		tmp = (y / z) * (x - t);
	} else if (t <= 2.7e-19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y / (a / x))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-3600.0d0)) then
        tmp = t_2
    else if (t <= 2.9d-260) then
        tmp = t_1
    else if (t <= 4.8d-162) then
        tmp = (y / z) * (x - t)
    else if (t <= 2.7d-19) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / x));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -3600.0) {
		tmp = t_2;
	} else if (t <= 2.9e-260) {
		tmp = t_1;
	} else if (t <= 4.8e-162) {
		tmp = (y / z) * (x - t);
	} else if (t <= 2.7e-19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (a / x))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -3600.0:
		tmp = t_2
	elif t <= 2.9e-260:
		tmp = t_1
	elif t <= 4.8e-162:
		tmp = (y / z) * (x - t)
	elif t <= 2.7e-19:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(a / x)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -3600.0)
		tmp = t_2;
	elseif (t <= 2.9e-260)
		tmp = t_1;
	elseif (t <= 4.8e-162)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (t <= 2.7e-19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (a / x));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -3600.0)
		tmp = t_2;
	elseif (t <= 2.9e-260)
		tmp = t_1;
	elseif (t <= 4.8e-162)
		tmp = (y / z) * (x - t);
	elseif (t <= 2.7e-19)
		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[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3600.0], t$95$2, If[LessEqual[t, 2.9e-260], t$95$1, If[LessEqual[t, 4.8e-162], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-19], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3600 or 2.7000000000000001e-19 < t

   1. Initial program 86.3%

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

   2. Taylor expanded in t around inf 77.7%

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

      1. div-sub 77.7%

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

   4. Simplified 77.7%

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

   if -3600 < t < 2.8999999999999999e-260 or 4.8000000000000004e-162 < t < 2.7000000000000001e-19

   1. Initial program 73.4%

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

   2. Taylor expanded in z around 0 51.0%

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

   3. Taylor expanded in t around 0 48.6%

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

      1. +-commutative 48.6%

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

      2. mul-1-neg 48.6%

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

      3. unsub-neg 48.6%

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

      4. associate-/l* 51.2%

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

   5. Simplified 51.2%

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

   if 2.8999999999999999e-260 < t < 4.8000000000000004e-162

   1. Initial program 68.1%

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

   2. Taylor expanded in y around inf 65.9%

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

      1. div-sub 65.9%

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

      2. *-commutative 65.9%

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

      3. associate-*r/ 68.4%

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

      4. associate-/l* 66.6%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in a around 0 56.5%

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

      1. mul-1-neg 56.5%

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

      2. associate-/l* 53.1%

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

      3. associate-/r/ 60.3%

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

      4. distribute-rgt-neg-in 60.3%

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

   7. Simplified 60.3%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3600:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-260}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-162}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-19}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 17: 71.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-30}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) a)))))
   (if (<= a -1.8e+47)
     t_1
     (if (<= a -7.2e-80)
       (/ y (/ (- a z) (- t x)))
       (if (<= a 1.55e-30) (+ t (/ (* (- y a) (- x t)) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / a));
	double tmp;
	if (a <= -1.8e+47) {
		tmp = t_1;
	} else if (a <= -7.2e-80) {
		tmp = y / ((a - z) / (t - x));
	} else if (a <= 1.55e-30) {
		tmp = t + (((y - a) * (x - t)) / 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 + ((z - y) * ((x - t) / a))
    if (a <= (-1.8d+47)) then
        tmp = t_1
    else if (a <= (-7.2d-80)) then
        tmp = y / ((a - z) / (t - x))
    else if (a <= 1.55d-30) then
        tmp = t + (((y - a) * (x - t)) / 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 + ((z - y) * ((x - t) / a));
	double tmp;
	if (a <= -1.8e+47) {
		tmp = t_1;
	} else if (a <= -7.2e-80) {
		tmp = y / ((a - z) / (t - x));
	} else if (a <= 1.55e-30) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / a))
	tmp = 0
	if a <= -1.8e+47:
		tmp = t_1
	elif a <= -7.2e-80:
		tmp = y / ((a - z) / (t - x))
	elif a <= 1.55e-30:
		tmp = t + (((y - a) * (x - t)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / a)))
	tmp = 0.0
	if (a <= -1.8e+47)
		tmp = t_1;
	elseif (a <= -7.2e-80)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (a <= 1.55e-30)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / a));
	tmp = 0.0;
	if (a <= -1.8e+47)
		tmp = t_1;
	elseif (a <= -7.2e-80)
		tmp = y / ((a - z) / (t - x));
	elseif (a <= 1.55e-30)
		tmp = t + (((y - a) * (x - t)) / 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[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+47], t$95$1, If[LessEqual[a, -7.2e-80], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e-30], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.80000000000000004e47 or 1.54999999999999995e-30 < a

   1. Initial program 87.5%

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

   2. Taylor expanded in a around inf 77.9%

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

   if -1.80000000000000004e47 < a < -7.2e-80

   1. Initial program 79.5%

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

   2. Taylor expanded in y around inf 67.2%

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

      1. div-sub 67.2%

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

      2. *-commutative 67.2%

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

      3. associate-*r/ 51.8%

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

      4. associate-/l* 67.3%

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

   4. Simplified 67.3%

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

   if -7.2e-80 < a < 1.54999999999999995e-30

   1. Initial program 69.6%

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

   2. Taylor expanded in z around inf 78.4%

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

      1. +-commutative 78.4%

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

      2. associate--l+ 78.4%

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

      3. associate-*r/ 78.4%

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

      4. associate-*r/ 78.4%

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

      5. div-sub 79.3%

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

      6. distribute-lft-out-- 79.3%

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

      7. mul-1-neg 79.3%

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

      8. distribute-neg-frac 79.3%

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

      9. unsub-neg 79.3%

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

      10. distribute-rgt-out-- 79.3%

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

   4. Simplified 79.3%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+47}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-30}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a}\\ \end{array} \]

Alternative 18: 45.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -4.5e+59)
     x
     (if (<= a -6.2e-268)
       t_1
       (if (<= a 3.8e-51) (* y (/ (- x t) z)) (if (<= a 2.6e+38) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -4.5e+59) {
		tmp = x;
	} else if (a <= -6.2e-268) {
		tmp = t_1;
	} else if (a <= 3.8e-51) {
		tmp = y * ((x - t) / z);
	} else if (a <= 2.6e+38) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-4.5d+59)) then
        tmp = x
    else if (a <= (-6.2d-268)) then
        tmp = t_1
    else if (a <= 3.8d-51) then
        tmp = y * ((x - t) / z)
    else if (a <= 2.6d+38) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -4.5e+59) {
		tmp = x;
	} else if (a <= -6.2e-268) {
		tmp = t_1;
	} else if (a <= 3.8e-51) {
		tmp = y * ((x - t) / z);
	} else if (a <= 2.6e+38) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -4.5e+59:
		tmp = x
	elif a <= -6.2e-268:
		tmp = t_1
	elif a <= 3.8e-51:
		tmp = y * ((x - t) / z)
	elif a <= 2.6e+38:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -4.5e+59)
		tmp = x;
	elseif (a <= -6.2e-268)
		tmp = t_1;
	elseif (a <= 3.8e-51)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 2.6e+38)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -4.5e+59)
		tmp = x;
	elseif (a <= -6.2e-268)
		tmp = t_1;
	elseif (a <= 3.8e-51)
		tmp = y * ((x - t) / z);
	elseif (a <= 2.6e+38)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+59], x, If[LessEqual[a, -6.2e-268], t$95$1, If[LessEqual[a, 3.8e-51], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+38], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.49999999999999959e59 or 2.5999999999999999e38 < a

   1. Initial program 89.6%

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

   2. Taylor expanded in a around inf 52.5%

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

   if -4.49999999999999959e59 < a < -6.1999999999999996e-268 or 3.80000000000000003e-51 < a < 2.5999999999999999e38

   1. Initial program 75.3%

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

   2. Taylor expanded in a around 0 44.7%

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

      1. +-commutative 44.7%

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

      2. mul-1-neg 44.7%

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

      3. unsub-neg 44.7%

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

      4. associate-/l* 48.9%

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

   4. Simplified 48.9%

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

   5. Taylor expanded in t around inf 50.0%

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

   if -6.1999999999999996e-268 < a < 3.80000000000000003e-51

   1. Initial program 68.1%

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

   2. Taylor expanded in a around 0 53.3%

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

      1. associate-*r/ 53.3%

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

      2. neg-mul-1 53.3%

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

   4. Simplified 53.3%

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

   5. Taylor expanded in y around inf 52.2%

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

      1. div-sub 52.2%

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

   7. Simplified 52.2%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-268}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 47.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-268}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ a x)))))
   (if (<= a -1.3e+60)
     t_1
     (if (<= a -5.2e-268)
       (* t (- 1.0 (/ y z)))
       (if (<= a 2.3e-62) (* y (/ (- x t) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / x));
	double tmp;
	if (a <= -1.3e+60) {
		tmp = t_1;
	} else if (a <= -5.2e-268) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 2.3e-62) {
		tmp = y * ((x - t) / 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 - (y / (a / x))
    if (a <= (-1.3d+60)) then
        tmp = t_1
    else if (a <= (-5.2d-268)) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 2.3d-62) then
        tmp = y * ((x - t) / 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 - (y / (a / x));
	double tmp;
	if (a <= -1.3e+60) {
		tmp = t_1;
	} else if (a <= -5.2e-268) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 2.3e-62) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (a / x))
	tmp = 0
	if a <= -1.3e+60:
		tmp = t_1
	elif a <= -5.2e-268:
		tmp = t * (1.0 - (y / z))
	elif a <= 2.3e-62:
		tmp = y * ((x - t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(a / x)))
	tmp = 0.0
	if (a <= -1.3e+60)
		tmp = t_1;
	elseif (a <= -5.2e-268)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 2.3e-62)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (a / x));
	tmp = 0.0;
	if (a <= -1.3e+60)
		tmp = t_1;
	elseif (a <= -5.2e-268)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 2.3e-62)
		tmp = y * ((x - t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e+60], t$95$1, If[LessEqual[a, -5.2e-268], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e-62], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.30000000000000004e60 or 2.3e-62 < a

   1. Initial program 86.2%

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

   2. Taylor expanded in z around 0 65.1%

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

   3. Taylor expanded in t around 0 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. associate-/l* 57.6%

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

   5. Simplified 57.6%

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

   if -1.30000000000000004e60 < a < -5.20000000000000005e-268

   1. Initial program 75.7%

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

   2. Taylor expanded in a around 0 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

      4. associate-/l* 57.5%

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

   4. Simplified 57.5%

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

   5. Taylor expanded in t around inf 52.8%

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

   if -5.20000000000000005e-268 < a < 2.3e-62

   1. Initial program 68.0%

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

   2. Taylor expanded in a around 0 55.5%

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

      1. associate-*r/ 55.5%

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

      2. neg-mul-1 55.5%

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

   4. Simplified 55.5%

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

   5. Taylor expanded in y around inf 52.9%

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

      1. div-sub 52.9%

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

   7. Simplified 52.9%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+60}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-268}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 20: 36.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-242}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.2e+49)
   x
   (if (<= a -1.3e-242)
     t
     (if (<= a 1.85e-51) (* y (/ x z)) (if (<= a 6.2e+37) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+49) {
		tmp = x;
	} else if (a <= -1.3e-242) {
		tmp = t;
	} else if (a <= 1.85e-51) {
		tmp = y * (x / z);
	} else if (a <= 6.2e+37) {
		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 <= (-6.2d+49)) then
        tmp = x
    else if (a <= (-1.3d-242)) then
        tmp = t
    else if (a <= 1.85d-51) then
        tmp = y * (x / z)
    else if (a <= 6.2d+37) 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 <= -6.2e+49) {
		tmp = x;
	} else if (a <= -1.3e-242) {
		tmp = t;
	} else if (a <= 1.85e-51) {
		tmp = y * (x / z);
	} else if (a <= 6.2e+37) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.2e+49:
		tmp = x
	elif a <= -1.3e-242:
		tmp = t
	elif a <= 1.85e-51:
		tmp = y * (x / z)
	elif a <= 6.2e+37:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e+49)
		tmp = x;
	elseif (a <= -1.3e-242)
		tmp = t;
	elseif (a <= 1.85e-51)
		tmp = Float64(y * Float64(x / z));
	elseif (a <= 6.2e+37)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.2e+49)
		tmp = x;
	elseif (a <= -1.3e-242)
		tmp = t;
	elseif (a <= 1.85e-51)
		tmp = y * (x / z);
	elseif (a <= 6.2e+37)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e+49], x, If[LessEqual[a, -1.3e-242], t, If[LessEqual[a, 1.85e-51], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+37], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.19999999999999985e49 or 6.2000000000000004e37 < a

   1. Initial program 89.8%

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

   2. Taylor expanded in a around inf 51.4%

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

   if -6.19999999999999985e49 < a < -1.30000000000000009e-242 or 1.84999999999999987e-51 < a < 6.2000000000000004e37

   1. Initial program 74.4%

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

   2. Taylor expanded in z around inf 36.4%

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

   if -1.30000000000000009e-242 < a < 1.84999999999999987e-51

   1. Initial program 69.0%

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

   2. Taylor expanded in a around 0 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

      4. associate-/l* 54.5%

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

   4. Simplified 54.5%

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

   5. Taylor expanded in x around -inf 42.1%

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

      1. expm1-log1p-u 27.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot x}{z}\right)\right)} \]

      2. expm1-udef 14.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot x}{z}\right)} - 1} \]

      3. associate-/l* 14.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{z}{x}}}\right)} - 1 \]

   7. Applied egg-rr 14.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{z}{x}}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 26.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{z}{x}}\right)\right)} \]

      2. expm1-log1p 43.4%

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

      3. associate-/r/ 40.7%

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

      4. *-commutative 40.7%

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

      5. associate-*r/ 42.1%

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

      6. *-commutative 42.1%

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

      7. associate-*r/ 43.4%

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

   9. Simplified 43.4%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-242}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 36.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-248}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.45e+50)
   x
   (if (<= a -5.2e-248)
     t
     (if (<= a 9.2e-51) (/ y (/ z x)) (if (<= a 1.02e+38) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.45e+50) {
		tmp = x;
	} else if (a <= -5.2e-248) {
		tmp = t;
	} else if (a <= 9.2e-51) {
		tmp = y / (z / x);
	} else if (a <= 1.02e+38) {
		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 <= (-1.45d+50)) then
        tmp = x
    else if (a <= (-5.2d-248)) then
        tmp = t
    else if (a <= 9.2d-51) then
        tmp = y / (z / x)
    else if (a <= 1.02d+38) 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 <= -1.45e+50) {
		tmp = x;
	} else if (a <= -5.2e-248) {
		tmp = t;
	} else if (a <= 9.2e-51) {
		tmp = y / (z / x);
	} else if (a <= 1.02e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.45e+50:
		tmp = x
	elif a <= -5.2e-248:
		tmp = t
	elif a <= 9.2e-51:
		tmp = y / (z / x)
	elif a <= 1.02e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.45e+50)
		tmp = x;
	elseif (a <= -5.2e-248)
		tmp = t;
	elseif (a <= 9.2e-51)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 1.02e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.45e+50)
		tmp = x;
	elseif (a <= -5.2e-248)
		tmp = t;
	elseif (a <= 9.2e-51)
		tmp = y / (z / x);
	elseif (a <= 1.02e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.45e+50], x, If[LessEqual[a, -5.2e-248], t, If[LessEqual[a, 9.2e-51], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e+38], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.45e50 or 1.02000000000000006e38 < a

   1. Initial program 89.8%

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

   2. Taylor expanded in a around inf 51.4%

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

   if -1.45e50 < a < -5.20000000000000013e-248 or 9.20000000000000007e-51 < a < 1.02000000000000006e38

   1. Initial program 74.4%

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

   2. Taylor expanded in z around inf 36.4%

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

   if -5.20000000000000013e-248 < a < 9.20000000000000007e-51

   1. Initial program 69.0%

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

   2. Taylor expanded in a around 0 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

      4. associate-/l* 54.5%

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

   4. Simplified 54.5%

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

   5. Taylor expanded in x around -inf 42.1%

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

      1. associate-/l* 43.4%

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

   7. Simplified 43.4%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-248}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 41.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e+73)
   x
   (if (<= a 3.2e-48) (* y (/ (- x t) z)) (if (<= a 1.42e+37) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e+73) {
		tmp = x;
	} else if (a <= 3.2e-48) {
		tmp = y * ((x - t) / z);
	} else if (a <= 1.42e+37) {
		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 <= (-7d+73)) then
        tmp = x
    else if (a <= 3.2d-48) then
        tmp = y * ((x - t) / z)
    else if (a <= 1.42d+37) 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 <= -7e+73) {
		tmp = x;
	} else if (a <= 3.2e-48) {
		tmp = y * ((x - t) / z);
	} else if (a <= 1.42e+37) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e+73:
		tmp = x
	elif a <= 3.2e-48:
		tmp = y * ((x - t) / z)
	elif a <= 1.42e+37:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e+73)
		tmp = x;
	elseif (a <= 3.2e-48)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 1.42e+37)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7e+73)
		tmp = x;
	elseif (a <= 3.2e-48)
		tmp = y * ((x - t) / z);
	elseif (a <= 1.42e+37)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e+73], x, If[LessEqual[a, 3.2e-48], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.42e+37], t, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.00000000000000004e73 or 1.4199999999999999e37 < a

   1. Initial program 90.2%

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

   2. Taylor expanded in a around inf 53.9%

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

   if -7.00000000000000004e73 < a < 3.1999999999999998e-48

   1. Initial program 72.1%

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

   2. Taylor expanded in a around 0 55.2%

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

      1. associate-*r/ 55.2%

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

      2. neg-mul-1 55.2%

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

   4. Simplified 55.2%

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

   5. Taylor expanded in y around inf 46.0%

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

      1. div-sub 46.1%

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

   7. Simplified 46.1%

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

   if 3.1999999999999998e-48 < a < 1.4199999999999999e37

   1. Initial program 73.9%

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

   2. Taylor expanded in z around inf 40.6%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23: 37.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.65e+50) x (if (<= a 1.45e+37) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.65e+50) {
		tmp = x;
	} else if (a <= 1.45e+37) {
		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 <= (-1.65d+50)) then
        tmp = x
    else if (a <= 1.45d+37) 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 <= -1.65e+50) {
		tmp = x;
	} else if (a <= 1.45e+37) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.65e+50:
		tmp = x
	elif a <= 1.45e+37:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.65e+50)
		tmp = x;
	elseif (a <= 1.45e+37)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.65e+50)
		tmp = x;
	elseif (a <= 1.45e+37)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.65e+50], x, If[LessEqual[a, 1.45e+37], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.65e50 or 1.44999999999999989e37 < a

   1. Initial program 89.8%

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

   2. Taylor expanded in a around inf 51.4%

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

   if -1.65e50 < a < 1.44999999999999989e37

   1. Initial program 72.0%

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

   2. Taylor expanded in z around inf 32.9%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 24.5% 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 78.8%

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

2. Taylor expanded in z around inf 24.6%

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

3. Final simplification 24.6%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023240 
(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)))))