Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 76.6% → 88.5%

Time: 11.5s

Alternatives: 16

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t - a}\\ t_2 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-70}:\\ \;\;\;\;\mathsf{fma}\left(z - t, t\_1, x + y\right)\\ \mathbf{elif}\;t\_2 \leq 10^{-234}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\left(x + y\right) - \frac{1}{\left(a - t\right) \cdot \frac{\frac{1}{y}}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t\_1 + \frac{x + \left(y - t \cdot t\_1\right)}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- t a))) (t_2 (- (+ x y) (/ (* y (- z t)) (- a t)))))
   (if (<= t_2 -2e-70)
     (fma (- z t) t_1 (+ x y))
     (if (<= t_2 1e-234)
       (+ x (* y (- (/ z t) (/ a t))))
       (if (<= t_2 5e+302)
         (- (+ x y) (/ 1.0 (* (- a t) (/ (/ 1.0 y) (- z t)))))
         (* z (+ t_1 (/ (+ x (- y (* t t_1))) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (t - a);
	double t_2 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -2e-70) {
		tmp = fma((z - t), t_1, (x + y));
	} else if (t_2 <= 1e-234) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else if (t_2 <= 5e+302) {
		tmp = (x + y) - (1.0 / ((a - t) * ((1.0 / y) / (z - t))));
	} else {
		tmp = z * (t_1 + ((x + (y - (t * t_1))) / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(t - a))
	t_2 = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e-70)
		tmp = fma(Float64(z - t), t_1, Float64(x + y));
	elseif (t_2 <= 1e-234)
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	elseif (t_2 <= 5e+302)
		tmp = Float64(Float64(x + y) - Float64(1.0 / Float64(Float64(a - t) * Float64(Float64(1.0 / y) / Float64(z - t)))));
	else
		tmp = Float64(z * Float64(t_1 + Float64(Float64(x + Float64(y - Float64(t * t_1))) / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-70], N[(N[(z - t), $MachinePrecision] * t$95$1 + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-234], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+302], N[(N[(x + y), $MachinePrecision] - N[(1.0 / N[(N[(a - t), $MachinePrecision] * N[(N[(1.0 / y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(t$95$1 + N[(N[(x + N[(y - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.99999999999999999e-70

   1. Initial program 78.9%

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

      1. sub-neg 78.9%

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

      2. +-commutative 78.9%

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

      3. distribute-frac-neg 78.9%

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

      4. distribute-rgt-neg-out 78.9%

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

      5. associate-/l* 87.8%

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

      6. fma-define 88.0%

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

      7. distribute-frac-neg 88.0%

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

      8. distribute-neg-frac2 88.0%

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

      9. sub-neg 88.0%

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

      10. distribute-neg-in 88.0%

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

      11. remove-double-neg 88.0%

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

      12. +-commutative 88.0%

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

      13. sub-neg 88.0%

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

   3. Simplified 88.0%

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

   if -1.99999999999999999e-70 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.9999999999999996e-235

   1. Initial program 24.9%

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

      1. sub-neg 24.9%

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

      2. +-commutative 24.9%

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

      3. distribute-frac-neg 24.9%

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

      4. distribute-rgt-neg-out 24.9%

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

      5. associate-/l* 25.1%

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

      6. fma-define 24.9%

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

      7. distribute-frac-neg 24.9%

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

      8. distribute-neg-frac2 24.9%

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

      9. sub-neg 24.9%

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

      10. distribute-neg-in 24.9%

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

      11. remove-double-neg 24.9%

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

      12. +-commutative 24.9%

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

      13. sub-neg 24.9%

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

   3. Simplified 24.9%

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

   5. Taylor expanded in t around inf 75.2%

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

      1. associate-+r+ 92.4%

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

      2. distribute-rgt1-in 92.4%

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

      3. metadata-eval 92.4%

         \[\leadsto \left(x + \left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      4. associate-/l* 92.5%

         \[\leadsto \left(x + \left(0 \cdot y + \color{blue}{y \cdot \frac{z}{t}}\right)\right) - \frac{a \cdot y}{t} \]

      5. associate-/l* 85.4%

         \[\leadsto \left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - \color{blue}{a \cdot \frac{y}{t}} \]

   7. Simplified 85.4%

      \[\leadsto \color{blue}{\left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - a \cdot \frac{y}{t}} \]

   8. Taylor expanded in y around 0 94.0%

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

   if 9.9999999999999996e-235 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 5e302

   1. Initial program 97.5%

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

      1. clear-num 97.5%

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

      2. inv-pow 97.5%

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

      3. *-commutative 97.5%

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

   4. Applied egg-rr 97.5%

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

      1. unpow-1 97.5%

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

      2. associate-/r* 93.1%

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

   6. Simplified 93.1%

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

      1. div-inv 93.1%

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

      2. *-un-lft-identity 93.1%

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

      3. times-frac 97.6%

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

   8. Applied egg-rr 97.6%

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

   if 5e302 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 40.5%

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

      1. sub-neg 40.5%

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

      2. +-commutative 40.5%

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

      3. distribute-frac-neg 40.5%

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

      4. distribute-rgt-neg-out 40.5%

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

      5. associate-/l* 69.0%

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

      6. fma-define 69.5%

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

      7. distribute-frac-neg 69.5%

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

      8. distribute-neg-frac2 69.5%

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

      9. sub-neg 69.5%

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

      10. distribute-neg-in 69.5%

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

      11. remove-double-neg 69.5%

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

      12. +-commutative 69.5%

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

      13. sub-neg 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in z around -inf 49.0%

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

      1. mul-1-neg 49.0%

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

      2. *-commutative 49.0%

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

      3. distribute-rgt-neg-in 49.0%

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

   7. Simplified 76.9%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-70}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 10^{-234}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\left(x + y\right) - \frac{1}{\left(a - t\right) \cdot \frac{\frac{1}{y}}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{y}{t - a} + \frac{x + \left(y - t \cdot \frac{y}{t - a}\right)}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ t_2 := \frac{y}{t - a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-163}:\\ \;\;\;\;\left(x + y\right) + \frac{-1}{\frac{\frac{a - t}{y}}{z - t}}\\ \mathbf{elif}\;t\_1 \leq 10^{-234}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\left(x + y\right) - \frac{1}{\left(a - t\right) \cdot \frac{\frac{1}{y}}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t\_2 + \frac{x + \left(y - t \cdot t\_2\right)}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y (- z t)) (- a t)))) (t_2 (/ y (- t a))))
   (if (<= t_1 -2e-163)
     (+ (+ x y) (/ -1.0 (/ (/ (- a t) y) (- z t))))
     (if (<= t_1 1e-234)
       (+ x (* y (- (/ z t) (/ a t))))
       (if (<= t_1 5e+302)
         (- (+ x y) (/ 1.0 (* (- a t) (/ (/ 1.0 y) (- z t)))))
         (* z (+ t_2 (/ (+ x (- y (* t t_2))) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double t_2 = y / (t - a);
	double tmp;
	if (t_1 <= -2e-163) {
		tmp = (x + y) + (-1.0 / (((a - t) / y) / (z - t)));
	} else if (t_1 <= 1e-234) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else if (t_1 <= 5e+302) {
		tmp = (x + y) - (1.0 / ((a - t) * ((1.0 / y) / (z - t))));
	} else {
		tmp = z * (t_2 + ((x + (y - (t * t_2))) / 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) :: t_2
    real(8) :: tmp
    t_1 = (x + y) - ((y * (z - t)) / (a - t))
    t_2 = y / (t - a)
    if (t_1 <= (-2d-163)) then
        tmp = (x + y) + ((-1.0d0) / (((a - t) / y) / (z - t)))
    else if (t_1 <= 1d-234) then
        tmp = x + (y * ((z / t) - (a / t)))
    else if (t_1 <= 5d+302) then
        tmp = (x + y) - (1.0d0 / ((a - t) * ((1.0d0 / y) / (z - t))))
    else
        tmp = z * (t_2 + ((x + (y - (t * t_2))) / 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) - ((y * (z - t)) / (a - t));
	double t_2 = y / (t - a);
	double tmp;
	if (t_1 <= -2e-163) {
		tmp = (x + y) + (-1.0 / (((a - t) / y) / (z - t)));
	} else if (t_1 <= 1e-234) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else if (t_1 <= 5e+302) {
		tmp = (x + y) - (1.0 / ((a - t) * ((1.0 / y) / (z - t))));
	} else {
		tmp = z * (t_2 + ((x + (y - (t * t_2))) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * (z - t)) / (a - t))
	t_2 = y / (t - a)
	tmp = 0
	if t_1 <= -2e-163:
		tmp = (x + y) + (-1.0 / (((a - t) / y) / (z - t)))
	elif t_1 <= 1e-234:
		tmp = x + (y * ((z / t) - (a / t)))
	elif t_1 <= 5e+302:
		tmp = (x + y) - (1.0 / ((a - t) * ((1.0 / y) / (z - t))))
	else:
		tmp = z * (t_2 + ((x + (y - (t * t_2))) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	t_2 = Float64(y / Float64(t - a))
	tmp = 0.0
	if (t_1 <= -2e-163)
		tmp = Float64(Float64(x + y) + Float64(-1.0 / Float64(Float64(Float64(a - t) / y) / Float64(z - t))));
	elseif (t_1 <= 1e-234)
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	elseif (t_1 <= 5e+302)
		tmp = Float64(Float64(x + y) - Float64(1.0 / Float64(Float64(a - t) * Float64(Float64(1.0 / y) / Float64(z - t)))));
	else
		tmp = Float64(z * Float64(t_2 + Float64(Float64(x + Float64(y - Float64(t * t_2))) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * (z - t)) / (a - t));
	t_2 = y / (t - a);
	tmp = 0.0;
	if (t_1 <= -2e-163)
		tmp = (x + y) + (-1.0 / (((a - t) / y) / (z - t)));
	elseif (t_1 <= 1e-234)
		tmp = x + (y * ((z / t) - (a / t)));
	elseif (t_1 <= 5e+302)
		tmp = (x + y) - (1.0 / ((a - t) * ((1.0 / y) / (z - t))));
	else
		tmp = z * (t_2 + ((x + (y - (t * t_2))) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-163], N[(N[(x + y), $MachinePrecision] + N[(-1.0 / N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-234], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+302], N[(N[(x + y), $MachinePrecision] - N[(1.0 / N[(N[(a - t), $MachinePrecision] * N[(N[(1.0 / y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(t$95$2 + N[(N[(x + N[(y - N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.99999999999999985e-163

   1. Initial program 78.8%

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

      1. clear-num 78.8%

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

      2. inv-pow 78.8%

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

      3. *-commutative 78.8%

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

   4. Applied egg-rr 78.8%

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

      1. unpow-1 78.8%

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

      2. associate-/r* 87.5%

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

   6. Simplified 87.5%

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

   if -1.99999999999999985e-163 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.9999999999999996e-235

   1. Initial program 17.9%

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

      1. sub-neg 17.9%

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

      2. +-commutative 17.9%

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

      3. distribute-frac-neg 17.9%

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

      4. distribute-rgt-neg-out 17.9%

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

      5. associate-/l* 18.1%

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

      6. fma-define 17.9%

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

      7. distribute-frac-neg 17.9%

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

      8. distribute-neg-frac2 17.9%

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

      9. sub-neg 17.9%

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

      10. distribute-neg-in 17.9%

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

      11. remove-double-neg 17.9%

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

      12. +-commutative 17.9%

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

      13. sub-neg 17.9%

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

   3. Simplified 17.9%

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

   5. Taylor expanded in t around inf 75.1%

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

      1. associate-+r+ 94.6%

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

      2. distribute-rgt1-in 94.6%

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

      3. metadata-eval 94.6%

         \[\leadsto \left(x + \left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      4. associate-/l* 94.8%

         \[\leadsto \left(x + \left(0 \cdot y + \color{blue}{y \cdot \frac{z}{t}}\right)\right) - \frac{a \cdot y}{t} \]

      5. associate-/l* 86.7%

         \[\leadsto \left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - \color{blue}{a \cdot \frac{y}{t}} \]

   7. Simplified 86.7%

      \[\leadsto \color{blue}{\left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - a \cdot \frac{y}{t}} \]

   8. Taylor expanded in y around 0 96.5%

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

   if 9.9999999999999996e-235 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 5e302

   1. Initial program 97.5%

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

      1. clear-num 97.5%

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

      2. inv-pow 97.5%

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

      3. *-commutative 97.5%

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

   4. Applied egg-rr 97.5%

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

      1. unpow-1 97.5%

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

      2. associate-/r* 93.1%

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

   6. Simplified 93.1%

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

      1. div-inv 93.1%

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

      2. *-un-lft-identity 93.1%

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

      3. times-frac 97.6%

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

   8. Applied egg-rr 97.6%

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

   if 5e302 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 40.5%

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

      1. sub-neg 40.5%

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

      2. +-commutative 40.5%

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

      3. distribute-frac-neg 40.5%

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

      4. distribute-rgt-neg-out 40.5%

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

      5. associate-/l* 69.0%

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

      6. fma-define 69.5%

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

      7. distribute-frac-neg 69.5%

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

      8. distribute-neg-frac2 69.5%

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

      9. sub-neg 69.5%

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

      10. distribute-neg-in 69.5%

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

      11. remove-double-neg 69.5%

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

      12. +-commutative 69.5%

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

      13. sub-neg 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in z around -inf 49.0%

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

      1. mul-1-neg 49.0%

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

      2. *-commutative 49.0%

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

      3. distribute-rgt-neg-in 49.0%

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

   7. Simplified 76.9%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-163}:\\ \;\;\;\;\left(x + y\right) + \frac{-1}{\frac{\frac{a - t}{y}}{z - t}}\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 10^{-234}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\left(x + y\right) - \frac{1}{\left(a - t\right) \cdot \frac{\frac{1}{y}}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{y}{t - a} + \frac{x + \left(y - t \cdot \frac{y}{t - a}\right)}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-163}:\\ \;\;\;\;\left(x + y\right) + \frac{-1}{\frac{\frac{a - t}{y}}{z - t}}\\ \mathbf{elif}\;t\_1 \leq 10^{-234} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{1}{\left(a - t\right) \cdot \frac{\frac{1}{y}}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y (- z t)) (- a t)))))
   (if (<= t_1 -2e-163)
     (+ (+ x y) (/ -1.0 (/ (/ (- a t) y) (- z t))))
     (if (or (<= t_1 1e-234) (not (<= t_1 5e+302)))
       (+ x (* y (- (/ z t) (/ a t))))
       (- (+ x y) (/ 1.0 (* (- a t) (/ (/ 1.0 y) (- z t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e-163) {
		tmp = (x + y) + (-1.0 / (((a - t) / y) / (z - t)));
	} else if ((t_1 <= 1e-234) || !(t_1 <= 5e+302)) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = (x + y) - (1.0 / ((a - t) * ((1.0 / y) / (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) - ((y * (z - t)) / (a - t))
    if (t_1 <= (-2d-163)) then
        tmp = (x + y) + ((-1.0d0) / (((a - t) / y) / (z - t)))
    else if ((t_1 <= 1d-234) .or. (.not. (t_1 <= 5d+302))) then
        tmp = x + (y * ((z / t) - (a / t)))
    else
        tmp = (x + y) - (1.0d0 / ((a - t) * ((1.0d0 / y) / (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) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e-163) {
		tmp = (x + y) + (-1.0 / (((a - t) / y) / (z - t)));
	} else if ((t_1 <= 1e-234) || !(t_1 <= 5e+302)) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = (x + y) - (1.0 / ((a - t) * ((1.0 / y) / (z - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -2e-163:
		tmp = (x + y) + (-1.0 / (((a - t) / y) / (z - t)))
	elif (t_1 <= 1e-234) or not (t_1 <= 5e+302):
		tmp = x + (y * ((z / t) - (a / t)))
	else:
		tmp = (x + y) - (1.0 / ((a - t) * ((1.0 / y) / (z - t))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -2e-163)
		tmp = Float64(Float64(x + y) + Float64(-1.0 / Float64(Float64(Float64(a - t) / y) / Float64(z - t))));
	elseif ((t_1 <= 1e-234) || !(t_1 <= 5e+302))
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	else
		tmp = Float64(Float64(x + y) - Float64(1.0 / Float64(Float64(a - t) * Float64(Float64(1.0 / y) / Float64(z - t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -2e-163)
		tmp = (x + y) + (-1.0 / (((a - t) / y) / (z - t)));
	elseif ((t_1 <= 1e-234) || ~((t_1 <= 5e+302)))
		tmp = x + (y * ((z / t) - (a / t)));
	else
		tmp = (x + y) - (1.0 / ((a - t) * ((1.0 / y) / (z - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-163], N[(N[(x + y), $MachinePrecision] + N[(-1.0 / N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, 1e-234], N[Not[LessEqual[t$95$1, 5e+302]], $MachinePrecision]], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(1.0 / N[(N[(a - t), $MachinePrecision] * N[(N[(1.0 / y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.99999999999999985e-163

   1. Initial program 78.8%

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

      1. clear-num 78.8%

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

      2. inv-pow 78.8%

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

      3. *-commutative 78.8%

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

   4. Applied egg-rr 78.8%

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

      1. unpow-1 78.8%

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

      2. associate-/r* 87.5%

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

   6. Simplified 87.5%

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

   if -1.99999999999999985e-163 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.9999999999999996e-235 or 5e302 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 30.1%

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

      1. sub-neg 30.1%

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

      2. +-commutative 30.1%

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

      3. distribute-frac-neg 30.1%

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

      4. distribute-rgt-neg-out 30.1%

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

      5. associate-/l* 45.6%

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

      6. fma-define 45.7%

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

      7. distribute-frac-neg 45.7%

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

      8. distribute-neg-frac2 45.7%

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

      9. sub-neg 45.7%

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

      10. distribute-neg-in 45.7%

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

      11. remove-double-neg 45.7%

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

      12. +-commutative 45.7%

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

      13. sub-neg 45.7%

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

   3. Simplified 45.7%

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

   5. Taylor expanded in t around inf 61.8%

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

      1. associate-+r+ 73.7%

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

      2. distribute-rgt1-in 73.7%

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

      3. metadata-eval 73.7%

         \[\leadsto \left(x + \left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      4. associate-/l* 76.8%

         \[\leadsto \left(x + \left(0 \cdot y + \color{blue}{y \cdot \frac{z}{t}}\right)\right) - \frac{a \cdot y}{t} \]

      5. associate-/l* 77.7%

         \[\leadsto \left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - \color{blue}{a \cdot \frac{y}{t}} \]

   7. Simplified 77.7%

      \[\leadsto \color{blue}{\left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - a \cdot \frac{y}{t}} \]

   8. Taylor expanded in y around 0 85.6%

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

   if 9.9999999999999996e-235 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 5e302

   1. Initial program 97.5%

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

      1. clear-num 97.5%

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

      2. inv-pow 97.5%

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

      3. *-commutative 97.5%

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

   4. Applied egg-rr 97.5%

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

      1. unpow-1 97.5%

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

      2. associate-/r* 93.1%

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

   6. Simplified 93.1%

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

      1. div-inv 93.1%

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

      2. *-un-lft-identity 93.1%

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

      3. times-frac 97.6%

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

   8. Applied egg-rr 97.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-163}:\\ \;\;\;\;\left(x + y\right) + \frac{-1}{\frac{\frac{a - t}{y}}{z - t}}\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 10^{-234} \lor \neg \left(\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{1}{\left(a - t\right) \cdot \frac{\frac{1}{y}}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-163}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{t - a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-234} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y (- z t)) (- a t)))))
   (if (<= t_1 -2e-163)
     (- (+ x y) (* (/ y (- t a)) (- t z)))
     (if (or (<= t_1 1e-234) (not (<= t_1 5e+302)))
       (+ x (* y (- (/ z t) (/ a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e-163) {
		tmp = (x + y) - ((y / (t - a)) * (t - z));
	} else if ((t_1 <= 1e-234) || !(t_1 <= 5e+302)) {
		tmp = x + (y * ((z / t) - (a / 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) - ((y * (z - t)) / (a - t))
    if (t_1 <= (-2d-163)) then
        tmp = (x + y) - ((y / (t - a)) * (t - z))
    else if ((t_1 <= 1d-234) .or. (.not. (t_1 <= 5d+302))) then
        tmp = x + (y * ((z / t) - (a / 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) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e-163) {
		tmp = (x + y) - ((y / (t - a)) * (t - z));
	} else if ((t_1 <= 1e-234) || !(t_1 <= 5e+302)) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -2e-163:
		tmp = (x + y) - ((y / (t - a)) * (t - z))
	elif (t_1 <= 1e-234) or not (t_1 <= 5e+302):
		tmp = x + (y * ((z / t) - (a / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -2e-163)
		tmp = Float64(Float64(x + y) - Float64(Float64(y / Float64(t - a)) * Float64(t - z)));
	elseif ((t_1 <= 1e-234) || !(t_1 <= 5e+302))
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -2e-163)
		tmp = (x + y) - ((y / (t - a)) * (t - z));
	elseif ((t_1 <= 1e-234) || ~((t_1 <= 5e+302)))
		tmp = x + (y * ((z / t) - (a / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-163], N[(N[(x + y), $MachinePrecision] - N[(N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, 1e-234], N[Not[LessEqual[t$95$1, 5e+302]], $MachinePrecision]], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.99999999999999985e-163

   1. Initial program 78.8%

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

      1. associate-/l* 87.4%

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

      2. *-commutative 87.4%

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

   4. Applied egg-rr 87.4%

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

   if -1.99999999999999985e-163 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.9999999999999996e-235 or 5e302 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 30.1%

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

      1. sub-neg 30.1%

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

      2. +-commutative 30.1%

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

      3. distribute-frac-neg 30.1%

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

      4. distribute-rgt-neg-out 30.1%

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

      5. associate-/l* 45.6%

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

      6. fma-define 45.7%

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

      7. distribute-frac-neg 45.7%

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

      8. distribute-neg-frac2 45.7%

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

      9. sub-neg 45.7%

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

      10. distribute-neg-in 45.7%

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

      11. remove-double-neg 45.7%

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

      12. +-commutative 45.7%

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

      13. sub-neg 45.7%

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

   3. Simplified 45.7%

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

   5. Taylor expanded in t around inf 61.8%

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

      1. associate-+r+ 73.7%

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

      2. distribute-rgt1-in 73.7%

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

      3. metadata-eval 73.7%

         \[\leadsto \left(x + \left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      4. associate-/l* 76.8%

         \[\leadsto \left(x + \left(0 \cdot y + \color{blue}{y \cdot \frac{z}{t}}\right)\right) - \frac{a \cdot y}{t} \]

      5. associate-/l* 77.7%

         \[\leadsto \left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - \color{blue}{a \cdot \frac{y}{t}} \]

   7. Simplified 77.7%

      \[\leadsto \color{blue}{\left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - a \cdot \frac{y}{t}} \]

   8. Taylor expanded in y around 0 85.6%

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

   if 9.9999999999999996e-235 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 5e302

   1. Initial program 97.5%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-163}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{t - a} \cdot \left(t - z\right)\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 10^{-234} \lor \neg \left(\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-163}:\\ \;\;\;\;\left(x + y\right) + \frac{-1}{\frac{\frac{a - t}{y}}{z - t}}\\ \mathbf{elif}\;t\_1 \leq 10^{-234} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y (- z t)) (- a t)))))
   (if (<= t_1 -2e-163)
     (+ (+ x y) (/ -1.0 (/ (/ (- a t) y) (- z t))))
     (if (or (<= t_1 1e-234) (not (<= t_1 5e+302)))
       (+ x (* y (- (/ z t) (/ a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e-163) {
		tmp = (x + y) + (-1.0 / (((a - t) / y) / (z - t)));
	} else if ((t_1 <= 1e-234) || !(t_1 <= 5e+302)) {
		tmp = x + (y * ((z / t) - (a / 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) - ((y * (z - t)) / (a - t))
    if (t_1 <= (-2d-163)) then
        tmp = (x + y) + ((-1.0d0) / (((a - t) / y) / (z - t)))
    else if ((t_1 <= 1d-234) .or. (.not. (t_1 <= 5d+302))) then
        tmp = x + (y * ((z / t) - (a / 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) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e-163) {
		tmp = (x + y) + (-1.0 / (((a - t) / y) / (z - t)));
	} else if ((t_1 <= 1e-234) || !(t_1 <= 5e+302)) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -2e-163:
		tmp = (x + y) + (-1.0 / (((a - t) / y) / (z - t)))
	elif (t_1 <= 1e-234) or not (t_1 <= 5e+302):
		tmp = x + (y * ((z / t) - (a / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -2e-163)
		tmp = Float64(Float64(x + y) + Float64(-1.0 / Float64(Float64(Float64(a - t) / y) / Float64(z - t))));
	elseif ((t_1 <= 1e-234) || !(t_1 <= 5e+302))
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -2e-163)
		tmp = (x + y) + (-1.0 / (((a - t) / y) / (z - t)));
	elseif ((t_1 <= 1e-234) || ~((t_1 <= 5e+302)))
		tmp = x + (y * ((z / t) - (a / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-163], N[(N[(x + y), $MachinePrecision] + N[(-1.0 / N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, 1e-234], N[Not[LessEqual[t$95$1, 5e+302]], $MachinePrecision]], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.99999999999999985e-163

   1. Initial program 78.8%

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

      1. clear-num 78.8%

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

      2. inv-pow 78.8%

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

      3. *-commutative 78.8%

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

   4. Applied egg-rr 78.8%

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

      1. unpow-1 78.8%

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

      2. associate-/r* 87.5%

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

   6. Simplified 87.5%

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

   if -1.99999999999999985e-163 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.9999999999999996e-235 or 5e302 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 30.1%

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

      1. sub-neg 30.1%

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

      2. +-commutative 30.1%

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

      3. distribute-frac-neg 30.1%

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

      4. distribute-rgt-neg-out 30.1%

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

      5. associate-/l* 45.6%

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

      6. fma-define 45.7%

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

      7. distribute-frac-neg 45.7%

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

      8. distribute-neg-frac2 45.7%

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

      9. sub-neg 45.7%

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

      10. distribute-neg-in 45.7%

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

      11. remove-double-neg 45.7%

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

      12. +-commutative 45.7%

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

      13. sub-neg 45.7%

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

   3. Simplified 45.7%

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

   5. Taylor expanded in t around inf 61.8%

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

      1. associate-+r+ 73.7%

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

      2. distribute-rgt1-in 73.7%

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

      3. metadata-eval 73.7%

         \[\leadsto \left(x + \left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      4. associate-/l* 76.8%

         \[\leadsto \left(x + \left(0 \cdot y + \color{blue}{y \cdot \frac{z}{t}}\right)\right) - \frac{a \cdot y}{t} \]

      5. associate-/l* 77.7%

         \[\leadsto \left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - \color{blue}{a \cdot \frac{y}{t}} \]

   7. Simplified 77.7%

      \[\leadsto \color{blue}{\left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - a \cdot \frac{y}{t}} \]

   8. Taylor expanded in y around 0 85.6%

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

   if 9.9999999999999996e-235 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 5e302

   1. Initial program 97.5%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-163}:\\ \;\;\;\;\left(x + y\right) + \frac{-1}{\frac{\frac{a - t}{y}}{z - t}}\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 10^{-234} \lor \neg \left(\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{-68}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-186}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= a -2.9e-68)
     (+ x y)
     (if (<= a -3.6e-91)
       (* y (/ (- z) a))
       (if (<= a -1.7e-149)
         x
         (if (<= a -4.1e-169)
           t_1
           (if (<= a -4.2e-286) x (if (<= a 1.45e-186) t_1 (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / t);
	double tmp;
	if (a <= -2.9e-68) {
		tmp = x + y;
	} else if (a <= -3.6e-91) {
		tmp = y * (-z / a);
	} else if (a <= -1.7e-149) {
		tmp = x;
	} else if (a <= -4.1e-169) {
		tmp = t_1;
	} else if (a <= -4.2e-286) {
		tmp = x;
	} else if (a <= 1.45e-186) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if (a <= (-2.9d-68)) then
        tmp = x + y
    else if (a <= (-3.6d-91)) then
        tmp = y * (-z / a)
    else if (a <= (-1.7d-149)) then
        tmp = x
    else if (a <= (-4.1d-169)) then
        tmp = t_1
    else if (a <= (-4.2d-286)) then
        tmp = x
    else if (a <= 1.45d-186) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / t);
	double tmp;
	if (a <= -2.9e-68) {
		tmp = x + y;
	} else if (a <= -3.6e-91) {
		tmp = y * (-z / a);
	} else if (a <= -1.7e-149) {
		tmp = x;
	} else if (a <= -4.1e-169) {
		tmp = t_1;
	} else if (a <= -4.2e-286) {
		tmp = x;
	} else if (a <= 1.45e-186) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / t)
	tmp = 0
	if a <= -2.9e-68:
		tmp = x + y
	elif a <= -3.6e-91:
		tmp = y * (-z / a)
	elif a <= -1.7e-149:
		tmp = x
	elif a <= -4.1e-169:
		tmp = t_1
	elif a <= -4.2e-286:
		tmp = x
	elif a <= 1.45e-186:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (a <= -2.9e-68)
		tmp = Float64(x + y);
	elseif (a <= -3.6e-91)
		tmp = Float64(y * Float64(Float64(-z) / a));
	elseif (a <= -1.7e-149)
		tmp = x;
	elseif (a <= -4.1e-169)
		tmp = t_1;
	elseif (a <= -4.2e-286)
		tmp = x;
	elseif (a <= 1.45e-186)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (a <= -2.9e-68)
		tmp = x + y;
	elseif (a <= -3.6e-91)
		tmp = y * (-z / a);
	elseif (a <= -1.7e-149)
		tmp = x;
	elseif (a <= -4.1e-169)
		tmp = t_1;
	elseif (a <= -4.2e-286)
		tmp = x;
	elseif (a <= 1.45e-186)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e-68], N[(x + y), $MachinePrecision], If[LessEqual[a, -3.6e-91], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.7e-149], x, If[LessEqual[a, -4.1e-169], t$95$1, If[LessEqual[a, -4.2e-286], x, If[LessEqual[a, 1.45e-186], t$95$1, N[(x + y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.9e-68 or 1.4500000000000001e-186 < a

   1. Initial program 73.7%

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

   3. Taylor expanded in a around inf 66.3%

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

      1. +-commutative 66.3%

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

   5. Simplified 66.3%

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

   if -2.9e-68 < a < -3.6e-91

   1. Initial program 85.9%

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

      1. sub-neg 85.9%

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

      2. +-commutative 85.9%

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

      3. distribute-frac-neg 85.9%

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

      4. distribute-rgt-neg-out 85.9%

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

      5. associate-/l* 86.2%

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

      6. fma-define 85.9%

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

      7. distribute-frac-neg 85.9%

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

      8. distribute-neg-frac2 85.9%

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

      9. sub-neg 85.9%

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

      10. distribute-neg-in 85.9%

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

      11. remove-double-neg 85.9%

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

      12. +-commutative 85.9%

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

      13. sub-neg 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in z around inf 99.8%

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

   6. Taylor expanded in t around 0 72.5%

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

      1. mul-1-neg 72.5%

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

      2. associate-/l* 71.9%

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

   8. Simplified 71.9%

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

   if -3.6e-91 < a < -1.6999999999999999e-149 or -4.0999999999999998e-169 < a < -4.19999999999999977e-286

   1. Initial program 67.6%

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

   3. Taylor expanded in x around inf 62.7%

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

   if -1.6999999999999999e-149 < a < -4.0999999999999998e-169 or -4.19999999999999977e-286 < a < 1.4500000000000001e-186

   1. Initial program 65.8%

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

      1. sub-neg 65.8%

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

      2. +-commutative 65.8%

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

      3. distribute-frac-neg 65.8%

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

      4. distribute-rgt-neg-out 65.8%

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

      5. associate-/l* 62.0%

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

      6. fma-define 62.5%

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

      7. distribute-frac-neg 62.5%

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

      8. distribute-neg-frac2 62.5%

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

      9. sub-neg 62.5%

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

      10. distribute-neg-in 62.5%

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

      11. remove-double-neg 62.5%

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

      12. +-commutative 62.5%

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

      13. sub-neg 62.5%

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

   3. Simplified 62.5%

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

   5. Taylor expanded in z around inf 69.3%

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

   6. Taylor expanded in t around inf 59.4%

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

      1. associate-*r/ 60.2%

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

   8. Simplified 60.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-68}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-169}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;a \leq -9 \cdot 10^{-68}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-189}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= a -9e-68)
     (+ x y)
     (if (<= a -3.4e-91)
       (/ (* y (- z)) a)
       (if (<= a -6e-150)
         x
         (if (<= a -5.5e-170)
           t_1
           (if (<= a -4.9e-286) x (if (<= a 3.6e-189) t_1 (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / t);
	double tmp;
	if (a <= -9e-68) {
		tmp = x + y;
	} else if (a <= -3.4e-91) {
		tmp = (y * -z) / a;
	} else if (a <= -6e-150) {
		tmp = x;
	} else if (a <= -5.5e-170) {
		tmp = t_1;
	} else if (a <= -4.9e-286) {
		tmp = x;
	} else if (a <= 3.6e-189) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if (a <= (-9d-68)) then
        tmp = x + y
    else if (a <= (-3.4d-91)) then
        tmp = (y * -z) / a
    else if (a <= (-6d-150)) then
        tmp = x
    else if (a <= (-5.5d-170)) then
        tmp = t_1
    else if (a <= (-4.9d-286)) then
        tmp = x
    else if (a <= 3.6d-189) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / t);
	double tmp;
	if (a <= -9e-68) {
		tmp = x + y;
	} else if (a <= -3.4e-91) {
		tmp = (y * -z) / a;
	} else if (a <= -6e-150) {
		tmp = x;
	} else if (a <= -5.5e-170) {
		tmp = t_1;
	} else if (a <= -4.9e-286) {
		tmp = x;
	} else if (a <= 3.6e-189) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / t)
	tmp = 0
	if a <= -9e-68:
		tmp = x + y
	elif a <= -3.4e-91:
		tmp = (y * -z) / a
	elif a <= -6e-150:
		tmp = x
	elif a <= -5.5e-170:
		tmp = t_1
	elif a <= -4.9e-286:
		tmp = x
	elif a <= 3.6e-189:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (a <= -9e-68)
		tmp = Float64(x + y);
	elseif (a <= -3.4e-91)
		tmp = Float64(Float64(y * Float64(-z)) / a);
	elseif (a <= -6e-150)
		tmp = x;
	elseif (a <= -5.5e-170)
		tmp = t_1;
	elseif (a <= -4.9e-286)
		tmp = x;
	elseif (a <= 3.6e-189)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (a <= -9e-68)
		tmp = x + y;
	elseif (a <= -3.4e-91)
		tmp = (y * -z) / a;
	elseif (a <= -6e-150)
		tmp = x;
	elseif (a <= -5.5e-170)
		tmp = t_1;
	elseif (a <= -4.9e-286)
		tmp = x;
	elseif (a <= 3.6e-189)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e-68], N[(x + y), $MachinePrecision], If[LessEqual[a, -3.4e-91], N[(N[(y * (-z)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -6e-150], x, If[LessEqual[a, -5.5e-170], t$95$1, If[LessEqual[a, -4.9e-286], x, If[LessEqual[a, 3.6e-189], t$95$1, N[(x + y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.99999999999999998e-68 or 3.60000000000000017e-189 < a

   1. Initial program 73.7%

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

   3. Taylor expanded in a around inf 66.3%

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

      1. +-commutative 66.3%

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

   5. Simplified 66.3%

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

   if -8.99999999999999998e-68 < a < -3.40000000000000027e-91

   1. Initial program 85.9%

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

      1. sub-neg 85.9%

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

      2. +-commutative 85.9%

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

      3. distribute-frac-neg 85.9%

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

      4. distribute-rgt-neg-out 85.9%

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

      5. associate-/l* 86.2%

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

      6. fma-define 85.9%

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

      7. distribute-frac-neg 85.9%

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

      8. distribute-neg-frac2 85.9%

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

      9. sub-neg 85.9%

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

      10. distribute-neg-in 85.9%

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

      11. remove-double-neg 85.9%

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

      12. +-commutative 85.9%

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

      13. sub-neg 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate-/l* 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in t around 0 72.5%

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

      1. associate-*r/ 72.5%

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

      2. mul-1-neg 72.5%

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

      3. distribute-rgt-neg-out 72.5%

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

   10. Simplified 72.5%

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

   if -3.40000000000000027e-91 < a < -6.0000000000000003e-150 or -5.50000000000000018e-170 < a < -4.9000000000000001e-286

   1. Initial program 67.6%

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

   3. Taylor expanded in x around inf 62.7%

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

   if -6.0000000000000003e-150 < a < -5.50000000000000018e-170 or -4.9000000000000001e-286 < a < 3.60000000000000017e-189

   1. Initial program 65.8%

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

      1. sub-neg 65.8%

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

      2. +-commutative 65.8%

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

      3. distribute-frac-neg 65.8%

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

      4. distribute-rgt-neg-out 65.8%

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

      5. associate-/l* 62.0%

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

      6. fma-define 62.5%

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

      7. distribute-frac-neg 62.5%

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

      8. distribute-neg-frac2 62.5%

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

      9. sub-neg 62.5%

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

      10. distribute-neg-in 62.5%

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

      11. remove-double-neg 62.5%

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

      12. +-commutative 62.5%

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

      13. sub-neg 62.5%

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

   3. Simplified 62.5%

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

   5. Taylor expanded in z around inf 69.3%

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

   6. Taylor expanded in t around inf 59.4%

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

      1. associate-*r/ 60.2%

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

   8. Simplified 60.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-68}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-189}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t - a}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-184}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- t a)))))
   (if (<= a -2.2e-67)
     (+ x y)
     (if (<= a -1.7e-92)
       t_1
       (if (<= a -4e-286) x (if (<= a 2.05e-184) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (a <= -2.2e-67) {
		tmp = x + y;
	} else if (a <= -1.7e-92) {
		tmp = t_1;
	} else if (a <= -4e-286) {
		tmp = x;
	} else if (a <= 2.05e-184) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (t - a))
    if (a <= (-2.2d-67)) then
        tmp = x + y
    else if (a <= (-1.7d-92)) then
        tmp = t_1
    else if (a <= (-4d-286)) then
        tmp = x
    else if (a <= 2.05d-184) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (a <= -2.2e-67) {
		tmp = x + y;
	} else if (a <= -1.7e-92) {
		tmp = t_1;
	} else if (a <= -4e-286) {
		tmp = x;
	} else if (a <= 2.05e-184) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (t - a))
	tmp = 0
	if a <= -2.2e-67:
		tmp = x + y
	elif a <= -1.7e-92:
		tmp = t_1
	elif a <= -4e-286:
		tmp = x
	elif a <= 2.05e-184:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(t - a)))
	tmp = 0.0
	if (a <= -2.2e-67)
		tmp = Float64(x + y);
	elseif (a <= -1.7e-92)
		tmp = t_1;
	elseif (a <= -4e-286)
		tmp = x;
	elseif (a <= 2.05e-184)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (t - a));
	tmp = 0.0;
	if (a <= -2.2e-67)
		tmp = x + y;
	elseif (a <= -1.7e-92)
		tmp = t_1;
	elseif (a <= -4e-286)
		tmp = x;
	elseif (a <= 2.05e-184)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e-67], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.7e-92], t$95$1, If[LessEqual[a, -4e-286], x, If[LessEqual[a, 2.05e-184], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.2000000000000001e-67 or 2.05e-184 < a

   1. Initial program 73.7%

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

   3. Taylor expanded in a around inf 66.3%

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

      1. +-commutative 66.3%

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

   5. Simplified 66.3%

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

   if -2.2000000000000001e-67 < a < -1.7000000000000001e-92 or -4.0000000000000002e-286 < a < 2.05e-184

   1. Initial program 67.4%

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

      1. sub-neg 67.4%

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

      2. +-commutative 67.4%

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

      3. distribute-frac-neg 67.4%

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

      4. distribute-rgt-neg-out 67.4%

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

      5. associate-/l* 63.6%

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

      6. fma-define 63.9%

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

      7. distribute-frac-neg 63.9%

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

      8. distribute-neg-frac2 63.9%

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

      9. sub-neg 63.9%

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

      10. distribute-neg-in 63.9%

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

      11. remove-double-neg 63.9%

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

      12. +-commutative 63.9%

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

      13. sub-neg 63.9%

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

   3. Simplified 63.9%

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

   5. Taylor expanded in z around inf 76.1%

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

      1. associate-/l* 74.5%

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

   7. Simplified 74.5%

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

   if -1.7000000000000001e-92 < a < -4.0000000000000002e-286

   1. Initial program 69.0%

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

   3. Taylor expanded in x around inf 58.5%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+43} \lor \neg \left(t \leq 9.8 \cdot 10^{+19}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{t - a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e+43) (not (<= t 9.8e+19)))
   (+ x (* y (- (/ z t) (/ a t))))
   (- (+ x y) (* (/ y (- t a)) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+43) || !(t <= 9.8e+19)) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = (x + y) - ((y / (t - a)) * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.1d+43)) .or. (.not. (t <= 9.8d+19))) then
        tmp = x + (y * ((z / t) - (a / t)))
    else
        tmp = (x + y) - ((y / (t - a)) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+43) || !(t <= 9.8e+19)) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = (x + y) - ((y / (t - a)) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e+43) or not (t <= 9.8e+19):
		tmp = x + (y * ((z / t) - (a / t)))
	else:
		tmp = (x + y) - ((y / (t - a)) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e+43) || !(t <= 9.8e+19))
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	else
		tmp = Float64(Float64(x + y) - Float64(Float64(y / Float64(t - a)) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.1e+43) || ~((t <= 9.8e+19)))
		tmp = x + (y * ((z / t) - (a / t)));
	else
		tmp = (x + y) - ((y / (t - a)) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.1e+43], N[Not[LessEqual[t, 9.8e+19]], $MachinePrecision]], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.10000000000000002e43 or 9.8e19 < t

   1. Initial program 49.0%

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

      1. sub-neg 49.0%

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

      2. +-commutative 49.0%

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

      3. distribute-frac-neg 49.0%

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

      4. distribute-rgt-neg-out 49.0%

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

      5. associate-/l* 62.2%

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

      6. fma-define 62.5%

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

      7. distribute-frac-neg 62.5%

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

      8. distribute-neg-frac2 62.5%

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

      9. sub-neg 62.5%

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

      10. distribute-neg-in 62.5%

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

      11. remove-double-neg 62.5%

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

      12. +-commutative 62.5%

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

      13. sub-neg 62.5%

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

   3. Simplified 62.5%

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

   5. Taylor expanded in t around inf 66.9%

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

      1. associate-+r+ 75.4%

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

      2. distribute-rgt1-in 75.4%

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

      3. metadata-eval 75.4%

         \[\leadsto \left(x + \left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      4. associate-/l* 79.8%

         \[\leadsto \left(x + \left(0 \cdot y + \color{blue}{y \cdot \frac{z}{t}}\right)\right) - \frac{a \cdot y}{t} \]

      5. associate-/l* 85.0%

         \[\leadsto \left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - \color{blue}{a \cdot \frac{y}{t}} \]

   7. Simplified 85.0%

      \[\leadsto \color{blue}{\left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - a \cdot \frac{y}{t}} \]

   8. Taylor expanded in y around 0 86.2%

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

   if -2.10000000000000002e43 < t < 9.8e19

   1. Initial program 88.4%

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

      1. associate-/l* 90.5%

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

      2. *-commutative 90.5%

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

   4. Applied egg-rr 90.5%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+43} \lor \neg \left(t \leq 9.8 \cdot 10^{+19}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{t - a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+42} \lor \neg \left(t \leq 4 \cdot 10^{-50}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.5e+42) (not (<= t 4e-50)))
   (+ x (* y (- (/ z t) (/ a t))))
   (- (+ x y) (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.5e+42) || !(t <= 4e-50)) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = (x + y) - (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.5d+42)) .or. (.not. (t <= 4d-50))) then
        tmp = x + (y * ((z / t) - (a / t)))
    else
        tmp = (x + y) - (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.5e+42) || !(t <= 4e-50)) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = (x + y) - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.5e+42) or not (t <= 4e-50):
		tmp = x + (y * ((z / t) - (a / t)))
	else:
		tmp = (x + y) - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.5e+42) || !(t <= 4e-50))
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	else
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.5e+42) || ~((t <= 4e-50)))
		tmp = x + (y * ((z / t) - (a / t)));
	else
		tmp = (x + y) - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.5e+42], N[Not[LessEqual[t, 4e-50]], $MachinePrecision]], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.50000000000000014e42 or 4.00000000000000003e-50 < t

   1. Initial program 53.3%

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

      1. sub-neg 53.3%

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

      2. +-commutative 53.3%

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

      3. distribute-frac-neg 53.3%

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

      4. distribute-rgt-neg-out 53.3%

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

      5. associate-/l* 66.2%

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

      6. fma-define 66.4%

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

      7. distribute-frac-neg 66.4%

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

      8. distribute-neg-frac2 66.4%

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

      9. sub-neg 66.4%

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

      10. distribute-neg-in 66.4%

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

      11. remove-double-neg 66.4%

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

      12. +-commutative 66.4%

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

      13. sub-neg 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in t around inf 67.8%

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

      1. associate-+r+ 75.0%

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

      2. distribute-rgt1-in 75.0%

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

      3. metadata-eval 75.0%

         \[\leadsto \left(x + \left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      4. associate-/l* 78.1%

         \[\leadsto \left(x + \left(0 \cdot y + \color{blue}{y \cdot \frac{z}{t}}\right)\right) - \frac{a \cdot y}{t} \]

      5. associate-/l* 82.5%

         \[\leadsto \left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - \color{blue}{a \cdot \frac{y}{t}} \]

   7. Simplified 82.5%

      \[\leadsto \color{blue}{\left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - a \cdot \frac{y}{t}} \]

   8. Taylor expanded in y around 0 83.6%

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

   if -1.50000000000000014e42 < t < 4.00000000000000003e-50

   1. Initial program 89.7%

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

   3. Taylor expanded in t around 0 82.9%

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

      1. +-commutative 82.9%

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

      2. associate-/l* 85.1%

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

   5. Simplified 85.1%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+42} \lor \neg \left(t \leq 4 \cdot 10^{-50}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.5e-14)
   (+ x y)
   (if (<= a -5e-286) x (if (<= a 2.8e-187) (* y (/ z t)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e-14) {
		tmp = x + y;
	} else if (a <= -5e-286) {
		tmp = x;
	} else if (a <= 2.8e-187) {
		tmp = y * (z / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.5d-14)) then
        tmp = x + y
    else if (a <= (-5d-286)) then
        tmp = x
    else if (a <= 2.8d-187) then
        tmp = y * (z / t)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e-14) {
		tmp = x + y;
	} else if (a <= -5e-286) {
		tmp = x;
	} else if (a <= 2.8e-187) {
		tmp = y * (z / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.5e-14:
		tmp = x + y
	elif a <= -5e-286:
		tmp = x
	elif a <= 2.8e-187:
		tmp = y * (z / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.5e-14)
		tmp = Float64(x + y);
	elseif (a <= -5e-286)
		tmp = x;
	elseif (a <= 2.8e-187)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.5e-14)
		tmp = x + y;
	elseif (a <= -5e-286)
		tmp = x;
	elseif (a <= 2.8e-187)
		tmp = y * (z / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.5e-14], N[(x + y), $MachinePrecision], If[LessEqual[a, -5e-286], x, If[LessEqual[a, 2.8e-187], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.5000000000000001e-14 or 2.8e-187 < a

   1. Initial program 73.5%

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

   3. Taylor expanded in a around inf 66.2%

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

      1. +-commutative 66.2%

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

   5. Simplified 66.2%

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

   if -6.5000000000000001e-14 < a < -5.00000000000000037e-286

   1. Initial program 72.3%

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

   3. Taylor expanded in x around inf 56.6%

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

   if -5.00000000000000037e-286 < a < 2.8e-187

   1. Initial program 63.2%

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

      1. sub-neg 63.2%

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

      2. +-commutative 63.2%

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

      3. distribute-frac-neg 63.2%

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

      4. distribute-rgt-neg-out 63.2%

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

      5. associate-/l* 58.5%

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

      6. fma-define 59.0%

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

      7. distribute-frac-neg 59.0%

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

      8. distribute-neg-frac2 59.0%

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

      9. sub-neg 59.0%

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

      10. distribute-neg-in 59.0%

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

      11. remove-double-neg 59.0%

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

      12. +-commutative 59.0%

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

      13. sub-neg 59.0%

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

   3. Simplified 59.0%

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

   5. Taylor expanded in z around inf 70.8%

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

   6. Taylor expanded in t around inf 58.3%

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

      1. associate-*r/ 59.3%

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

   8. Simplified 59.3%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1500000 \lor \neg \left(a \leq 2 \cdot 10^{+73}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1500000.0) (not (<= a 2e+73)))
   (+ x y)
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1500000.0) || !(a <= 2e+73)) {
		tmp = x + y;
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1500000.0d0)) .or. (.not. (a <= 2d+73))) then
        tmp = x + y
    else
        tmp = x - ((y * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1500000.0) || !(a <= 2e+73)) {
		tmp = x + y;
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1500000.0) or not (a <= 2e+73):
		tmp = x + y
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1500000.0) || !(a <= 2e+73))
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1500000.0) || ~((a <= 2e+73)))
		tmp = x + y;
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1500000.0], N[Not[LessEqual[a, 2e+73]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.5e6 or 1.99999999999999997e73 < a

   1. Initial program 75.3%

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

   3. Taylor expanded in a around inf 78.2%

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

      1. +-commutative 78.2%

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

   5. Simplified 78.2%

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

   if -1.5e6 < a < 1.99999999999999997e73

   1. Initial program 69.7%

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

   3. Taylor expanded in t around inf 74.4%

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

      1. associate--l+ 74.4%

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

      2. distribute-lft-out-- 74.4%

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

      3. div-sub 75.0%

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

      4. mul-1-neg 75.0%

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

      5. unsub-neg 75.0%

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

      6. *-commutative 75.0%

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

      7. distribute-lft-out-- 75.1%

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

   5. Simplified 75.1%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1500000 \lor \neg \left(a \leq 2 \cdot 10^{+73}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 82.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{-11} \lor \neg \left(a \leq 9 \cdot 10^{-22}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -9.8e-11) (not (<= a 9e-22)))
   (- (+ x y) (* y (/ z a)))
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.8e-11) || !(a <= 9e-22)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-9.8d-11)) .or. (.not. (a <= 9d-22))) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = x - ((y * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.8e-11) || !(a <= 9e-22)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -9.8e-11) or not (a <= 9e-22):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -9.8e-11) || !(a <= 9e-22))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -9.8e-11) || ~((a <= 9e-22)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -9.8e-11], N[Not[LessEqual[a, 9e-22]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.7999999999999998e-11 or 8.99999999999999973e-22 < a

   1. Initial program 76.2%

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

   3. Taylor expanded in t around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-/l* 88.3%

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

   5. Simplified 88.3%

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

   if -9.7999999999999998e-11 < a < 8.99999999999999973e-22

   1. Initial program 67.9%

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

   3. Taylor expanded in t around inf 77.8%

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

      1. associate--l+ 77.8%

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

      2. distribute-lft-out-- 77.8%

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

      3. div-sub 78.6%

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

      4. mul-1-neg 78.6%

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

      5. unsub-neg 78.6%

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

      6. *-commutative 78.6%

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

      7. distribute-lft-out-- 78.6%

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

   5. Simplified 78.6%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{-11} \lor \neg \left(a \leq 9 \cdot 10^{-22}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 76.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+18} \lor \neg \left(a \leq 9.5 \cdot 10^{-40}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.5e+18) (not (<= a 9.5e-40))) (+ x y) (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.5e+18) || !(a <= 9.5e-40)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.5d+18)) .or. (.not. (a <= 9.5d-40))) then
        tmp = x + y
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.5e+18) || !(a <= 9.5e-40)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.5e+18) or not (a <= 9.5e-40):
		tmp = x + y
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.5e+18) || !(a <= 9.5e-40))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.5e+18) || ~((a <= 9.5e-40)))
		tmp = x + y;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.5e+18], N[Not[LessEqual[a, 9.5e-40]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.5e18 or 9.5000000000000006e-40 < a

   1. Initial program 74.8%

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

   3. Taylor expanded in a around inf 73.1%

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

      1. +-commutative 73.1%

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

   5. Simplified 73.1%

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

   if -2.5e18 < a < 9.5000000000000006e-40

   1. Initial program 69.3%

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

      1. sub-neg 69.3%

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

      2. +-commutative 69.3%

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

      3. distribute-frac-neg 69.3%

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

      4. distribute-rgt-neg-out 69.3%

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

      5. associate-/l* 68.6%

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

      6. fma-define 68.7%

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

      7. distribute-frac-neg 68.7%

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

      8. distribute-neg-frac2 68.7%

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

      9. sub-neg 68.7%

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

      10. distribute-neg-in 68.7%

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

      11. remove-double-neg 68.7%

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

      12. +-commutative 68.7%

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

      13. sub-neg 68.7%

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

   3. Simplified 68.7%

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

   5. Taylor expanded in t around inf 68.1%

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

      1. associate-+r+ 77.6%

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

      2. distribute-rgt1-in 77.6%

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

      3. metadata-eval 77.6%

         \[\leadsto \left(x + \left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      4. associate-/l* 79.2%

         \[\leadsto \left(x + \left(0 \cdot y + \color{blue}{y \cdot \frac{z}{t}}\right)\right) - \frac{a \cdot y}{t} \]

      5. associate-/l* 75.3%

         \[\leadsto \left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - \color{blue}{a \cdot \frac{y}{t}} \]

   7. Simplified 75.3%

      \[\leadsto \color{blue}{\left(x + \left(0 \cdot y + y \cdot \frac{z}{t}\right)\right) - a \cdot \frac{y}{t}} \]

   8. Taylor expanded in a around 0 74.1%

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

      1. associate-*r/ 75.7%

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

   10. Simplified 75.7%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+18} \lor \neg \left(a \leq 9.5 \cdot 10^{-40}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 63.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-13} \lor \neg \left(a \leq 1.5 \cdot 10^{-128}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.1e-13) (not (<= a 1.5e-128))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.1e-13) || !(a <= 1.5e-128)) {
		tmp = x + y;
	} 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 <= (-1.1d-13)) .or. (.not. (a <= 1.5d-128))) then
        tmp = x + y
    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 <= -1.1e-13) || !(a <= 1.5e-128)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.1e-13) or not (a <= 1.5e-128):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.1e-13) || !(a <= 1.5e-128))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.1e-13) || ~((a <= 1.5e-128)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.1e-13], N[Not[LessEqual[a, 1.5e-128]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.09999999999999998e-13 or 1.49999999999999989e-128 < a

   1. Initial program 74.1%

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

   3. Taylor expanded in a around inf 68.3%

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

      1. +-commutative 68.3%

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

   5. Simplified 68.3%

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

   if -1.09999999999999998e-13 < a < 1.49999999999999989e-128

   1. Initial program 68.9%

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

   3. Taylor expanded in x around inf 47.8%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-13} \lor \neg \left(a \leq 1.5 \cdot 10^{-128}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.9%

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

3. Taylor expanded in x around inf 44.2%

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

4. Final simplification 44.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - 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) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - 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 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024067 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

  (- (+ x y) (/ (* (- z t) y) (- a t))))