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

Percentage Accurate: 76.8% → 90.4%

Time: 10.9s

Alternatives: 15

Speedup: 0.8×

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: 76.8% 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: 90.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ t_2 := \frac{y}{t - a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot \left(-\mathsf{fma}\left(-1, \frac{y - \left(t \cdot t\_2 - x\right)}{z}, \frac{y}{a - t}\right)\right)\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-244}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, t\_2, x + y\right)\\ \end{array} \end{array} \]

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 (- INFINITY))
     (* z (- (fma -1.0 (/ (- y (- (* t t_2) x)) z) (/ y (- a t)))))
     (if (<= t_1 -4e-284)
       t_1
       (if (<= t_1 1e-244)
         (- x (/ (* y (- a z)) t))
         (fma (- z t) t_2 (+ x y)))))))

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 <= -((double) INFINITY)) {
		tmp = z * -fma(-1.0, ((y - ((t * t_2) - x)) / z), (y / (a - t)));
	} else if (t_1 <= -4e-284) {
		tmp = t_1;
	} else if (t_1 <= 1e-244) {
		tmp = x - ((y * (a - z)) / t);
	} else {
		tmp = fma((z - t), t_2, (x + y));
	}
	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 <= Float64(-Inf))
		tmp = Float64(z * Float64(-fma(-1.0, Float64(Float64(y - Float64(Float64(t * t_2) - x)) / z), Float64(y / Float64(a - t)))));
	elseif (t_1 <= -4e-284)
		tmp = t_1;
	elseif (t_1 <= 1e-244)
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	else
		tmp = fma(Float64(z - t), t_2, Float64(x + y));
	end
	return 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, (-Infinity)], N[(z * (-N[(-1.0 * N[(N[(y - N[(N[(t * t$95$2), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[t$95$1, -4e-284], t$95$1, If[LessEqual[t$95$1, 1e-244], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * t$95$2 + N[(x + y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 37.3%

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

   3. Taylor expanded in z around -inf 53.2%

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

      1. mul-1-neg 53.2%

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

      2. distribute-rgt-neg-in 53.2%

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

      3. fma-neg 53.2%

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

   5. Simplified 95.1%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.00000000000000015e-284

   1. Initial program 96.2%

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

   if -4.00000000000000015e-284 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.9999999999999993e-245

   1. Initial program 7.7%

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

   3. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. distribute-lft-out-- 99.6%

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

      3. div-sub 99.6%

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

      4. mul-1-neg 99.6%

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

      5. unsub-neg 99.6%

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

      6. *-commutative 99.6%

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

      7. distribute-lft-out-- 99.6%

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

   5. Simplified 99.6%

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

   if 9.9999999999999993e-245 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 83.4%

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

      1. sub-neg 83.4%

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

      2. +-commutative 83.4%

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

      3. distribute-frac-neg 83.4%

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

      4. distribute-rgt-neg-out 83.4%

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

      5. associate-/l* 92.2%

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

      6. fma-define 92.3%

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

      7. distribute-frac-neg 92.3%

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

      8. distribute-neg-frac2 92.3%

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

      9. sub-neg 92.3%

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

      10. distribute-neg-in 92.3%

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

      11. remove-double-neg 92.3%

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

      12. +-commutative 92.3%

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

      13. sub-neg 92.3%

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

   3. Simplified 92.3%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;z \cdot \left(-\mathsf{fma}\left(-1, \frac{y - \left(t \cdot \frac{y}{t - a} - x\right)}{z}, \frac{y}{a - t}\right)\right)\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-284}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 10^{-244}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t - a}\\ t_2 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-284}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-244}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, t\_1, x + y\right)\\ \end{array} \end{array} \]

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 -4e-284)
     (+ (+ x y) (* (- z t) t_1))
     (if (<= t_2 1e-244)
       (- x (/ (* y (- a z)) t))
       (fma (- z t) t_1 (+ x y))))))

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 <= -4e-284) {
		tmp = (x + y) + ((z - t) * t_1);
	} else if (t_2 <= 1e-244) {
		tmp = x - ((y * (a - z)) / t);
	} else {
		tmp = fma((z - t), t_1, (x + y));
	}
	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 <= -4e-284)
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) * t_1));
	elseif (t_2 <= 1e-244)
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	else
		tmp = fma(Float64(z - t), t_1, Float64(x + y));
	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, -4e-284], N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-244], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * t$95$1 + N[(x + y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.00000000000000015e-284

   1. Initial program 81.8%

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

   3. Taylor expanded in y around 0 81.8%

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

      1. associate-*l/ 92.1%

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

   5. Simplified 92.1%

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

   if -4.00000000000000015e-284 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.9999999999999993e-245

   1. Initial program 7.7%

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

   3. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. distribute-lft-out-- 99.6%

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

      3. div-sub 99.6%

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

      4. mul-1-neg 99.6%

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

      5. unsub-neg 99.6%

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

      6. *-commutative 99.6%

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

      7. distribute-lft-out-- 99.6%

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

   5. Simplified 99.6%

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

   if 9.9999999999999993e-245 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 83.4%

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

      1. sub-neg 83.4%

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

      2. +-commutative 83.4%

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

      3. distribute-frac-neg 83.4%

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

      4. distribute-rgt-neg-out 83.4%

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

      5. associate-/l* 92.2%

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

      6. fma-define 92.3%

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

      7. distribute-frac-neg 92.3%

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

      8. distribute-neg-frac2 92.3%

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

      9. sub-neg 92.3%

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

      10. distribute-neg-in 92.3%

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

      11. remove-double-neg 92.3%

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

      12. +-commutative 92.3%

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

      13. sub-neg 92.3%

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

   3. Simplified 92.3%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-284}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 10^{-244}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-284} \lor \neg \left(t\_1 \leq 10^{-244}\right):\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y (- z t)) (- a t)))))
   (if (or (<= t_1 -4e-284) (not (<= t_1 1e-244)))
     (+ (+ x y) (* (- z t) (/ y (- t a))))
     (- x (/ (* y (- a 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 <= -4e-284) || !(t_1 <= 1e-244)) {
		tmp = (x + y) + ((z - t) * (y / (t - 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) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - ((y * (z - t)) / (a - t))
    if ((t_1 <= (-4d-284)) .or. (.not. (t_1 <= 1d-244))) then
        tmp = (x + y) + ((z - t) * (y / (t - 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 t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -4e-284) || !(t_1 <= 1e-244)) {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	} else {
		tmp = x - ((y * (a - 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 <= -4e-284) or not (t_1 <= 1e-244):
		tmp = (x + y) + ((z - t) * (y / (t - a)))
	else:
		tmp = x - ((y * (a - 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 <= -4e-284) || !(t_1 <= 1e-244))
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) * Float64(y / Float64(t - 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)
	t_1 = (x + y) - ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -4e-284) || ~((t_1 <= 1e-244)))
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	else
		tmp = x - ((y * (a - 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[Or[LessEqual[t$95$1, -4e-284], N[Not[LessEqual[t$95$1, 1e-244]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $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 (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.00000000000000015e-284 or 9.9999999999999993e-245 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 82.6%

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

   3. Taylor expanded in y around 0 82.6%

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

      1. associate-*l/ 92.1%

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

   5. Simplified 92.1%

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

   if -4.00000000000000015e-284 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.9999999999999993e-245

   1. Initial program 7.7%

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

   3. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. distribute-lft-out-- 99.6%

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

      3. div-sub 99.6%

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

      4. mul-1-neg 99.6%

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

      5. unsub-neg 99.6%

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

      6. *-commutative 99.6%

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

      7. distribute-lft-out-- 99.6%

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

   5. Simplified 99.6%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-284} \lor \neg \left(\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 10^{-244}\right):\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+18} \lor \neg \left(a \leq 2.6 \cdot 10^{-75}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.6e+18) (not (<= a 2.6e-75)))
   (+ x y)
   (+ x (* (/ y t) (+ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.6e+18) || !(a <= 2.6e-75)) {
		tmp = x + y;
	} else {
		tmp = x + ((y / t) * (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 ((a <= (-3.6d+18)) .or. (.not. (a <= 2.6d-75))) then
        tmp = x + y
    else
        tmp = x + ((y / t) * (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 ((a <= -3.6e+18) || !(a <= 2.6e-75)) {
		tmp = x + y;
	} else {
		tmp = x + ((y / t) * (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.6e+18) or not (a <= 2.6e-75):
		tmp = x + y
	else:
		tmp = x + ((y / t) * (z + a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.6e+18) || !(a <= 2.6e-75))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y / t) * Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.6e+18) || ~((a <= 2.6e-75)))
		tmp = x + y;
	else
		tmp = x + ((y / t) * (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.6e+18], N[Not[LessEqual[a, 2.6e-75]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.6e18 or 2.6e-75 < a

   1. Initial program 77.9%

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

   3. Taylor expanded in a around inf 73.7%

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

      1. +-commutative 73.7%

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

   5. Simplified 73.7%

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

   if -3.6e18 < a < 2.6e-75

   1. Initial program 77.8%

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

   3. Taylor expanded in t around inf 82.9%

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

      1. associate--l+ 82.9%

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

      2. mul-1-neg 82.9%

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

      3. associate-/l* 78.5%

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

      4. mul-1-neg 78.5%

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

      5. associate-/l* 79.7%

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

   5. Simplified 79.7%

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

      1. sub-neg 79.7%

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

      2. add-sqr-sqrt 64.3%

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

      3. sqrt-unprod 79.9%

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

      4. sqr-neg 79.9%

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

      5. sqrt-unprod 43.3%

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

      6. add-sqr-sqrt 80.9%

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

      7. remove-double-neg 80.9%

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

      8. clear-num 80.5%

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

      9. un-div-inv 80.5%

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

   7. Applied egg-rr 80.5%

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

      1. *-commutative 80.5%

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

      2. associate-/r/ 83.2%

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

      3. distribute-lft-out 86.0%

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

   9. Simplified 86.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+18} \lor \neg \left(a \leq 2.6 \cdot 10^{-75}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-86} \lor \neg \left(a \leq 2 \cdot 10^{-98}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2e-86) (not (<= a 2e-98)))
   (- (+ x y) (* y (/ z a)))
   (+ x (* (/ y t) (+ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2e-86) || !(a <= 2e-98)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + ((y / t) * (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 ((a <= (-2d-86)) .or. (.not. (a <= 2d-98))) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = x + ((y / t) * (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 ((a <= -2e-86) || !(a <= 2e-98)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + ((y / t) * (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2e-86) or not (a <= 2e-98):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x + ((y / t) * (z + a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2e-86) || !(a <= 2e-98))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(Float64(y / t) * Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2e-86) || ~((a <= 2e-98)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x + ((y / t) * (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2e-86], N[Not[LessEqual[a, 2e-98]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.00000000000000017e-86 or 1.99999999999999988e-98 < a

   1. Initial program 78.2%

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

   3. Taylor expanded in t around 0 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-/l* 85.7%

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

   5. Simplified 85.7%

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

   if -2.00000000000000017e-86 < a < 1.99999999999999988e-98

   1. Initial program 77.4%

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

   3. Taylor expanded in t around inf 88.8%

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

      1. associate--l+ 88.8%

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

      2. mul-1-neg 88.8%

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

      3. associate-/l* 83.5%

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

      4. mul-1-neg 83.5%

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

      5. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

      1. sub-neg 84.6%

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

      2. add-sqr-sqrt 67.5%

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

      3. sqrt-unprod 83.8%

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

      4. sqr-neg 83.8%

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

      5. sqrt-unprod 46.4%

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

      6. add-sqr-sqrt 84.9%

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

      7. remove-double-neg 84.9%

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

      8. clear-num 84.8%

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

      9. un-div-inv 84.8%

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

   7. Applied egg-rr 84.8%

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

      1. *-commutative 84.8%

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

      2. associate-/r/ 87.0%

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

      3. distribute-lft-out 90.4%

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

   9. Simplified 90.4%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-86} \lor \neg \left(a \leq 2 \cdot 10^{-98}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.26 \cdot 10^{-87} \lor \neg \left(a \leq 8.5 \cdot 10^{-98}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.26e-87) (not (<= a 8.5e-98)))
   (- (+ x y) (/ y (/ a z)))
   (+ x (* (/ y t) (+ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.26e-87) || !(a <= 8.5e-98)) {
		tmp = (x + y) - (y / (a / z));
	} else {
		tmp = x + ((y / t) * (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 ((a <= (-1.26d-87)) .or. (.not. (a <= 8.5d-98))) then
        tmp = (x + y) - (y / (a / z))
    else
        tmp = x + ((y / t) * (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 ((a <= -1.26e-87) || !(a <= 8.5e-98)) {
		tmp = (x + y) - (y / (a / z));
	} else {
		tmp = x + ((y / t) * (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.26e-87) or not (a <= 8.5e-98):
		tmp = (x + y) - (y / (a / z))
	else:
		tmp = x + ((y / t) * (z + a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.26e-87) || !(a <= 8.5e-98))
		tmp = Float64(Float64(x + y) - Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + Float64(Float64(y / t) * Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.26e-87) || ~((a <= 8.5e-98)))
		tmp = (x + y) - (y / (a / z));
	else
		tmp = x + ((y / t) * (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.26e-87], N[Not[LessEqual[a, 8.5e-98]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.26000000000000009e-87 or 8.4999999999999997e-98 < a

   1. Initial program 78.2%

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

   3. Taylor expanded in t around 0 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-/l* 85.7%

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

   5. Simplified 85.7%

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

      1. clear-num 85.7%

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

      2. un-div-inv 85.7%

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

   7. Applied egg-rr 85.7%

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

   if -1.26000000000000009e-87 < a < 8.4999999999999997e-98

   1. Initial program 77.4%

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

   3. Taylor expanded in t around inf 88.8%

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

      1. associate--l+ 88.8%

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

      2. mul-1-neg 88.8%

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

      3. associate-/l* 83.5%

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

      4. mul-1-neg 83.5%

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

      5. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

      1. sub-neg 84.6%

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

      2. add-sqr-sqrt 67.5%

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

      3. sqrt-unprod 83.8%

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

      4. sqr-neg 83.8%

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

      5. sqrt-unprod 46.4%

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

      6. add-sqr-sqrt 84.9%

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

      7. remove-double-neg 84.9%

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

      8. clear-num 84.8%

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

      9. un-div-inv 84.8%

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

   7. Applied egg-rr 84.8%

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

      1. *-commutative 84.8%

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

      2. associate-/r/ 87.0%

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

      3. distribute-lft-out 90.4%

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

   9. Simplified 90.4%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.26 \cdot 10^{-87} \lor \neg \left(a \leq 8.5 \cdot 10^{-98}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+135} \lor \neg \left(z \leq 2.9 \cdot 10^{+203}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e+135) (not (<= z 2.9e+203)))
   (* y (- 1.0 (/ z a)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+135) || !(z <= 2.9e+203)) {
		tmp = y * (1.0 - (z / a));
	} 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 ((z <= (-1.1d+135)) .or. (.not. (z <= 2.9d+203))) then
        tmp = y * (1.0d0 - (z / a))
    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 ((z <= -1.1e+135) || !(z <= 2.9e+203)) {
		tmp = y * (1.0 - (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e+135) or not (z <= 2.9e+203):
		tmp = y * (1.0 - (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e+135) || !(z <= 2.9e+203))
		tmp = Float64(y * Float64(1.0 - Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.1e+135) || ~((z <= 2.9e+203)))
		tmp = y * (1.0 - (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.1e+135], N[Not[LessEqual[z, 2.9e+203]], $MachinePrecision]], N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e135 or 2.90000000000000011e203 < z

   1. Initial program 69.8%

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

   3. Taylor expanded in x around 0 55.1%

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

      1. sub-neg 55.1%

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

      2. *-rgt-identity 55.1%

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

      3. associate-*r/ 73.6%

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

      4. distribute-rgt-neg-in 73.6%

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

      5. mul-1-neg 73.6%

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

      6. distribute-lft-in 73.6%

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

      7. mul-1-neg 73.6%

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

      8. unsub-neg 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in t around 0 51.7%

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

   if -1.1e135 < z < 2.90000000000000011e203

   1. Initial program 80.0%

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

   3. Taylor expanded in a around inf 72.8%

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

      1. +-commutative 72.8%

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

   5. Simplified 72.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+135} \lor \neg \left(z \leq 2.9 \cdot 10^{+203}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+107} \lor \neg \left(z \leq 1.1 \cdot 10^{+203}\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.7e+107) (not (<= z 1.1e+203))) (* y (/ z (- t a))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.7e+107) || !(z <= 1.1e+203)) {
		tmp = y * (z / (t - a));
	} 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 ((z <= (-3.7d+107)) .or. (.not. (z <= 1.1d+203))) then
        tmp = y * (z / (t - a))
    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 ((z <= -3.7e+107) || !(z <= 1.1e+203)) {
		tmp = y * (z / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.7e+107) or not (z <= 1.1e+203):
		tmp = y * (z / (t - a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.7e+107) || !(z <= 1.1e+203))
		tmp = Float64(y * Float64(z / Float64(t - a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.7e+107) || ~((z <= 1.1e+203)))
		tmp = y * (z / (t - a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.7e+107], N[Not[LessEqual[z, 1.1e+203]], $MachinePrecision]], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7e107 or 1.10000000000000002e203 < z

   1. Initial program 72.8%

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

      1. sub-neg 72.8%

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

      2. +-commutative 72.8%

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

      3. distribute-frac-neg 72.8%

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

      4. distribute-rgt-neg-out 72.8%

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

      5. associate-/l* 98.1%

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

      6. fma-define 98.1%

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

      7. distribute-frac-neg 98.1%

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

      8. distribute-neg-frac2 98.1%

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

      9. sub-neg 98.1%

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

      10. distribute-neg-in 98.1%

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

      11. remove-double-neg 98.1%

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

      12. +-commutative 98.1%

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

      13. sub-neg 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in z around inf 54.9%

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

      1. associate-/l* 66.0%

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

   7. Simplified 66.0%

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

   if -3.7e107 < z < 1.10000000000000002e203

   1. Initial program 79.4%

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

   3. Taylor expanded in a around inf 73.5%

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

      1. +-commutative 73.5%

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

   5. Simplified 73.5%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+107} \lor \neg \left(z \leq 1.1 \cdot 10^{+203}\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+106} \lor \neg \left(z \leq 2.1 \cdot 10^{+225}\right):\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.1e+106) (not (<= z 2.1e+225))) (* z (/ y (- t a))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.1e+106) || !(z <= 2.1e+225)) {
		tmp = z * (y / (t - a));
	} 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 ((z <= (-3.1d+106)) .or. (.not. (z <= 2.1d+225))) then
        tmp = z * (y / (t - a))
    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 ((z <= -3.1e+106) || !(z <= 2.1e+225)) {
		tmp = z * (y / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.1e+106) or not (z <= 2.1e+225):
		tmp = z * (y / (t - a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.1e+106) || !(z <= 2.1e+225))
		tmp = Float64(z * Float64(y / Float64(t - a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.1e+106) || ~((z <= 2.1e+225)))
		tmp = z * (y / (t - a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.1e+106], N[Not[LessEqual[z, 2.1e+225]], $MachinePrecision]], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0999999999999999e106 or 2.1e225 < z

   1. Initial program 75.9%

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

      1. sub-neg 75.9%

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

      2. +-commutative 75.9%

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

      3. distribute-frac-neg 75.9%

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

      4. distribute-rgt-neg-out 75.9%

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

      5. associate-/l* 99.8%

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

      6. fma-define 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. distribute-neg-frac2 99.7%

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

      9. sub-neg 99.7%

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

      10. distribute-neg-in 99.7%

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

      11. remove-double-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. sub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 54.7%

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

      1. *-commutative 54.7%

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

      2. *-un-lft-identity 54.7%

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

      3. times-frac 70.3%

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

   7. Applied egg-rr 70.3%

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

   8. Taylor expanded in z around 0 54.7%

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

      1. *-commutative 54.7%

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

      2. associate-/l* 70.3%

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

   10. Simplified 70.3%

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

   if -3.0999999999999999e106 < z < 2.1e225

   1. Initial program 78.4%

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

   3. Taylor expanded in a around inf 72.6%

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

      1. +-commutative 72.6%

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

   5. Simplified 72.6%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+106} \lor \neg \left(z \leq 2.1 \cdot 10^{+225}\right):\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+15} \lor \neg \left(a \leq 4.1 \cdot 10^{-75}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.2e+15) (not (<= a 4.1e-75))) (+ x y) (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.2e+15) || !(a <= 4.1e-75)) {
		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 <= (-6.2d+15)) .or. (.not. (a <= 4.1d-75))) 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 <= -6.2e+15) || !(a <= 4.1e-75)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.2e+15) or not (a <= 4.1e-75):
		tmp = x + y
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.2e+15) || !(a <= 4.1e-75))
		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 <= -6.2e+15) || ~((a <= 4.1e-75)))
		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, -6.2e+15], N[Not[LessEqual[a, 4.1e-75]], $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 < -6.2e15 or 4.10000000000000002e-75 < a

   1. Initial program 77.9%

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

   3. Taylor expanded in a around inf 73.7%

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

      1. +-commutative 73.7%

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

   5. Simplified 73.7%

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

   if -6.2e15 < a < 4.10000000000000002e-75

   1. Initial program 77.8%

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

   3. Taylor expanded in t around inf 82.9%

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

      1. associate--l+ 82.9%

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

      2. mul-1-neg 82.9%

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

      3. associate-/l* 78.5%

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

      4. mul-1-neg 78.5%

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

      5. associate-/l* 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in z around 0 82.9%

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

   7. Taylor expanded in z around inf 82.6%

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

      1. associate-*r/ 83.8%

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

   9. Simplified 83.8%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+15} \lor \neg \left(a \leq 4.1 \cdot 10^{-75}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+135} \lor \neg \left(z \leq 1.12 \cdot 10^{+227}\right):\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e+135) (not (<= z 1.12e+227))) (* z (/ (- y) a)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+135) || !(z <= 1.12e+227)) {
		tmp = z * (-y / a);
	} 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 ((z <= (-1.1d+135)) .or. (.not. (z <= 1.12d+227))) then
        tmp = z * (-y / a)
    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 ((z <= -1.1e+135) || !(z <= 1.12e+227)) {
		tmp = z * (-y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e+135) or not (z <= 1.12e+227):
		tmp = z * (-y / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e+135) || !(z <= 1.12e+227))
		tmp = Float64(z * Float64(Float64(-y) / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.1e+135) || ~((z <= 1.12e+227)))
		tmp = z * (-y / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.1e+135], N[Not[LessEqual[z, 1.12e+227]], $MachinePrecision]], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e135 or 1.1200000000000001e227 < z

   1. Initial program 72.5%

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

      1. sub-neg 72.5%

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

      2. +-commutative 72.5%

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

      3. distribute-frac-neg 72.5%

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

      4. distribute-rgt-neg-out 72.5%

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

      5. associate-/l* 99.7%

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

      6. fma-define 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. distribute-neg-frac2 99.7%

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

      9. sub-neg 99.7%

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

      10. distribute-neg-in 99.7%

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

      11. remove-double-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. sub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 54.2%

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

   6. Taylor expanded in t around 0 37.8%

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

      1. associate-*r/ 37.8%

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

      2. associate-*r* 37.8%

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

      3. neg-mul-1 37.8%

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

      4. *-commutative 37.8%

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

   8. Simplified 37.8%

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

      1. frac-2neg 37.8%

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

      2. distribute-frac-neg 37.8%

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

      3. add-sqr-sqrt 14.1%

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

      4. sqrt-unprod 19.3%

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

      5. sqr-neg 19.3%

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

      6. sqrt-unprod 5.1%

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

      7. add-sqr-sqrt 8.2%

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

      8. *-commutative 8.2%

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

      9. distribute-frac-neg2 8.2%

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

      10. distribute-frac-neg 8.2%

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

      11. *-commutative 8.2%

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

      12. distribute-rgt-neg-out 8.2%

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

      13. associate-/l* 8.2%

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

      14. add-sqr-sqrt 3.1%

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

      15. sqrt-unprod 24.9%

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

      16. sqr-neg 24.9%

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

      17. sqrt-unprod 24.0%

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

      18. add-sqr-sqrt 46.9%

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

   10. Applied egg-rr 46.9%

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

   if -1.1e135 < z < 1.1200000000000001e227

   1. Initial program 79.2%

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

   3. Taylor expanded in a around inf 71.7%

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

      1. +-commutative 71.7%

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

   5. Simplified 71.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+135} \lor \neg \left(z \leq 1.12 \cdot 10^{+227}\right):\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+135}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+226}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+135)
   (* (/ z a) (- y))
   (if (<= z 9.8e+226) (+ x y) (* z (/ (- y) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+135) {
		tmp = (z / a) * -y;
	} else if (z <= 9.8e+226) {
		tmp = x + y;
	} else {
		tmp = z * (-y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.1d+135)) then
        tmp = (z / a) * -y
    else if (z <= 9.8d+226) then
        tmp = x + y
    else
        tmp = z * (-y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+135) {
		tmp = (z / a) * -y;
	} else if (z <= 9.8e+226) {
		tmp = x + y;
	} else {
		tmp = z * (-y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e+135:
		tmp = (z / a) * -y
	elif z <= 9.8e+226:
		tmp = x + y
	else:
		tmp = z * (-y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+135)
		tmp = Float64(Float64(z / a) * Float64(-y));
	elseif (z <= 9.8e+226)
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(Float64(-y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e+135)
		tmp = (z / a) * -y;
	elseif (z <= 9.8e+226)
		tmp = x + y;
	else
		tmp = z * (-y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+135], N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[z, 9.8e+226], N[(x + y), $MachinePrecision], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e135

   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 t around 0 46.1%

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

      1. +-commutative 46.1%

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

      2. associate-/l* 65.1%

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

   5. Simplified 65.1%

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

   6. Taylor expanded in z around inf 34.0%

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

      1. associate-*r/ 34.0%

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

      2. neg-mul-1 34.0%

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

      3. distribute-rgt-neg-in 34.0%

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

      4. associate-*r/ 47.0%

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

   8. Simplified 47.0%

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

   if -1.1e135 < z < 9.8000000000000009e226

   1. Initial program 79.2%

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

   3. Taylor expanded in a around inf 71.7%

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

      1. +-commutative 71.7%

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

   5. Simplified 71.7%

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

   if 9.8000000000000009e226 < z

   1. Initial program 70.0%

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

      1. sub-neg 70.0%

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

      2. +-commutative 70.0%

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

      3. distribute-frac-neg 70.0%

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

      4. distribute-rgt-neg-out 70.0%

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

      5. associate-/l* 99.8%

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

      6. fma-define 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. distribute-neg-frac2 99.7%

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

      9. sub-neg 99.7%

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

      10. distribute-neg-in 99.7%

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

      11. remove-double-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. sub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 63.9%

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

   6. Taylor expanded in t around 0 45.5%

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

      1. associate-*r/ 45.5%

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

      2. associate-*r* 45.5%

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

      3. neg-mul-1 45.5%

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

      4. *-commutative 45.5%

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

   8. Simplified 45.5%

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

      1. frac-2neg 45.5%

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

      2. distribute-frac-neg 45.5%

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

      3. add-sqr-sqrt 13.5%

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

      4. sqrt-unprod 20.6%

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

      5. sqr-neg 20.6%

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

      6. sqrt-unprod 6.8%

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

      7. add-sqr-sqrt 8.2%

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

      8. *-commutative 8.2%

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

      9. distribute-frac-neg2 8.2%

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

      10. distribute-frac-neg 8.2%

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

      11. *-commutative 8.2%

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

      12. distribute-rgt-neg-out 8.2%

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

      13. associate-/l* 8.1%

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

      14. add-sqr-sqrt 1.2%

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

      15. sqrt-unprod 27.3%

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

      16. sqr-neg 27.3%

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

      17. sqrt-unprod 32.5%

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

      18. add-sqr-sqrt 46.8%

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

   10. Applied egg-rr 46.8%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+135}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+226}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y 3.1e+139) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 3.1e+139) {
		tmp = x;
	} else {
		tmp = 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 (y <= 3.1d+139) then
        tmp = x
    else
        tmp = 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 (y <= 3.1e+139) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 3.1e+139:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 3.1e+139)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 3.1e+139)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 3.1e+139], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 3.1e139

   1. Initial program 80.1%

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

   3. Taylor expanded in x around inf 59.0%

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

   if 3.1e139 < y

   1. Initial program 64.2%

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

   3. Taylor expanded in x around 0 64.2%

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

      1. sub-neg 64.2%

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

      2. *-rgt-identity 64.2%

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

      3. associate-*r/ 76.5%

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

      4. distribute-rgt-neg-in 76.5%

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

      5. mul-1-neg 76.5%

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

      6. distribute-lft-in 76.2%

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

      7. mul-1-neg 76.2%

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

      8. unsub-neg 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in t around 0 57.9%

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

   7. Taylor expanded in z around 0 33.8%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.5% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 77.9%

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

3. Taylor expanded in a around inf 63.6%

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

   1. +-commutative 63.6%

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

5. Simplified 63.6%

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

6. Final simplification 63.6%

   \[\leadsto x + y \]
7. Add Preprocessing

Alternative 15: 50.8% 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 77.9%

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

3. Taylor expanded in x around inf 52.2%

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

4. Final simplification 52.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 87.9% 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 2024059 
(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))))