Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Percentage Accurate: 97.2% → 99.9%

Time: 10.8s

Alternatives: 12

Speedup: 1.3×

Specification

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

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 - z) + 1.0d0) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

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 - z) + 1.0d0) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{a}{-1 + \left(z - t\right)}, y - z, x\right)\\ t_2 := \left(t - z\right) + 1\\ t_3 := \frac{y - z}{\frac{t\_2}{a}}\\ \mathbf{if}\;t\_3 \leq -4 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;x + \left(a \cdot \left(y - z\right)\right) \cdot \frac{-1}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ a (+ -1.0 (- z t))) (- y z) x))
        (t_2 (+ (- t z) 1.0))
        (t_3 (/ (- y z) (/ t_2 a))))
   (if (<= t_3 -4e-108)
     t_1
     (if (<= t_3 0.0) (+ x (* (* a (- y z)) (/ -1.0 t_2))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((a / (-1.0 + (z - t))), (y - z), x);
	double t_2 = (t - z) + 1.0;
	double t_3 = (y - z) / (t_2 / a);
	double tmp;
	if (t_3 <= -4e-108) {
		tmp = t_1;
	} else if (t_3 <= 0.0) {
		tmp = x + ((a * (y - z)) * (-1.0 / t_2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(a / Float64(-1.0 + Float64(z - t))), Float64(y - z), x)
	t_2 = Float64(Float64(t - z) + 1.0)
	t_3 = Float64(Float64(y - z) / Float64(t_2 / a))
	tmp = 0.0
	if (t_3 <= -4e-108)
		tmp = t_1;
	elseif (t_3 <= 0.0)
		tmp = Float64(x + Float64(Float64(a * Float64(y - z)) * Float64(-1.0 / t_2)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y - z), $MachinePrecision] / N[(t$95$2 / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -4e-108], t$95$1, If[LessEqual[t$95$3, 0.0], N[(x + N[(N[(a * N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) #s(literal 1 binary64)) a)) < -4.00000000000000016e-108 or -0.0 < (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) #s(literal 1 binary64)) a))

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. clear-num N/A

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

      6. associate-/r/ N/A

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

      7. lift-/.f64 N/A

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

      8. clear-num N/A

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

      9. distribute-lft-neg-in N/A

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

      10. clear-num N/A

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

      11. lift-/.f64 N/A

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

      12. distribute-frac-neg2 N/A

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

      13. lower-fma.f64 N/A

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

   4. Applied rewrites 99.9%

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

   if -4.00000000000000016e-108 < (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) #s(literal 1 binary64)) a)) < -0.0

   1. Initial program 85.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. associate-*l/ N/A

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

      5. div-inv N/A

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

      6. lift-+.f64 N/A

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

      7. flip3-+ N/A

         \[\leadsto x - \left(\left(y - z\right) \cdot a\right) \cdot \frac{1}{\color{blue}{\frac{{\left(t - z\right)}^{3} + {1}^{3}}{\left(t - z\right) \cdot \left(t - z\right) + \left(1 \cdot 1 - \left(t - z\right) \cdot 1\right)}}} \]

      8. clear-num N/A

         \[\leadsto x - \left(\left(y - z\right) \cdot a\right) \cdot \color{blue}{\frac{\left(t - z\right) \cdot \left(t - z\right) + \left(1 \cdot 1 - \left(t - z\right) \cdot 1\right)}{{\left(t - z\right)}^{3} + {1}^{3}}} \]

      9. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\left(\left(y - z\right) \cdot a\right) \cdot \frac{\left(t - z\right) \cdot \left(t - z\right) + \left(1 \cdot 1 - \left(t - z\right) \cdot 1\right)}{{\left(t - z\right)}^{3} + {1}^{3}}} \]

      10. lower-*.f64 N/A

          \[\leadsto x - \color{blue}{\left(\left(y - z\right) \cdot a\right)} \cdot \frac{\left(t - z\right) \cdot \left(t - z\right) + \left(1 \cdot 1 - \left(t - z\right) \cdot 1\right)}{{\left(t - z\right)}^{3} + {1}^{3}} \]

      11. clear-num N/A

          \[\leadsto x - \left(\left(y - z\right) \cdot a\right) \cdot \color{blue}{\frac{1}{\frac{{\left(t - z\right)}^{3} + {1}^{3}}{\left(t - z\right) \cdot \left(t - z\right) + \left(1 \cdot 1 - \left(t - z\right) \cdot 1\right)}}} \]

      12. flip3-+ N/A

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

      13. lift-+.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

      \[\leadsto x - \color{blue}{\left(\left(y - z\right) \cdot a\right) \cdot \frac{1}{\left(t - z\right) + 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \leq -4 \cdot 10^{-108}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{-1 + \left(z - t\right)}, y - z, x\right)\\ \mathbf{elif}\;\frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \leq 0:\\ \;\;\;\;x + \left(a \cdot \left(y - z\right)\right) \cdot \frac{-1}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{-1 + \left(z - t\right)}, y - z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+34}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-103}:\\ \;\;\;\;x - \frac{a \cdot y}{t}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\mathsf{fma}\left(y - z, -\mathsf{fma}\left(a, z, a\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e+34)
   (- x a)
   (if (<= z -7.6e-103)
     (- x (/ (* a y) t))
     (if (<= z 1.0) (fma (- y z) (- (fma a z a)) x) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+34) {
		tmp = x - a;
	} else if (z <= -7.6e-103) {
		tmp = x - ((a * y) / t);
	} else if (z <= 1.0) {
		tmp = fma((y - z), -fma(a, z, a), x);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e+34)
		tmp = Float64(x - a);
	elseif (z <= -7.6e-103)
		tmp = Float64(x - Float64(Float64(a * y) / t));
	elseif (z <= 1.0)
		tmp = fma(Float64(y - z), Float64(-fma(a, z, a)), x);
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e+34], N[(x - a), $MachinePrecision], If[LessEqual[z, -7.6e-103], N[(x - N[(N[(a * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(N[(y - z), $MachinePrecision] * (-N[(a * z + a), $MachinePrecision]) + x), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5999999999999996e34 or 1 < z

   1. Initial program 91.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 73.1

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

   5. Applied rewrites 73.1%

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

   if -4.5999999999999996e34 < z < -7.6000000000000001e-103

   1. Initial program 96.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.4

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

   5. Applied rewrites 79.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 79.2%

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

   if -7.6000000000000001e-103 < z < 1

   1. Initial program 98.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 76.8

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

   5. Applied rewrites 76.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y - z, \mathsf{neg}\left(\left(a + a \cdot z\right)\right), x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 76.4%

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

Alternative 3: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, \frac{y - z}{t}, x\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+158}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y - z}{z + -1}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- a) (/ (- y z) t) x)))
   (if (<= t -5e+160)
     t_1
     (if (<= t 2.9e+158) (fma a (/ (- y z) (+ z -1.0)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-a, ((y - z) / t), x);
	double tmp;
	if (t <= -5e+160) {
		tmp = t_1;
	} else if (t <= 2.9e+158) {
		tmp = fma(a, ((y - z) / (z + -1.0)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(-a), Float64(Float64(y - z) / t), x)
	tmp = 0.0
	if (t <= -5e+160)
		tmp = t_1;
	elseif (t <= 2.9e+158)
		tmp = fma(a, Float64(Float64(y - z) / Float64(z + -1.0)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-a) * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -5e+160], t$95$1, If[LessEqual[t, 2.9e+158], N[(a * N[(N[(y - z), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.0000000000000002e160 or 2.90000000000000024e158 < t

   1. Initial program 92.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 49.1

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

   5. Applied rewrites 49.1%

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

   6. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 89.9

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

   8. Applied rewrites 89.9%

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

   if -5.0000000000000002e160 < t < 2.90000000000000024e158

   1. Initial program 96.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 93.2

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

   5. Applied rewrites 93.2%

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

   6. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. distribute-neg-frac2 N/A

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

      9. mul-1-neg N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. sub-neg N/A

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

      13. mul-1-neg N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. neg-mul-1 N/A

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

      17. mul-1-neg N/A

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

      18. remove-double-neg N/A

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

      19. lower-+.f64 95.6

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

   8. Applied rewrites 95.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \frac{y - z}{-1 + z}, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y - z}{t}, x\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+158}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y - z}{z + -1}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y - z}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{a}{\frac{\left(t - z\right) + 1}{z - y}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (/ a (/ (+ (- t z) 1.0) (- z y)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (a / (((t - z) + 1.0) / (z - 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 + (a / (((t - z) + 1.0d0) / (z - y)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (a / (((t - z) + 1.0) / (z - y)));
}

Python

def code(x, y, z, t, a):
	return x + (a / (((t - z) + 1.0) / (z - y)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(a / Float64(Float64(Float64(t - z) + 1.0) / Float64(z - y))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (a / (((t - z) + 1.0) / (z - y)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(a / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.3%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. associate-/r/ N/A

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

   4. *-commutative N/A

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

   5. clear-num N/A

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

   6. un-div-inv N/A

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

   7. lower-/.f64 N/A

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

   8. lower-/.f64 99.3

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

4. Applied rewrites 99.3%

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

5. Final simplification 99.3%

   \[\leadsto x + \frac{a}{\frac{\left(t - z\right) + 1}{z - y}} \]
6. Add Preprocessing

Alternative 5: 86.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{a}{z}, x\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y}{-1 - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ a z) x)))
   (if (<= z -2.6e+56)
     t_1
     (if (<= z 4.8e+26) (fma a (/ y (- -1.0 t)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), (a / z), x);
	double tmp;
	if (z <= -2.6e+56) {
		tmp = t_1;
	} else if (z <= 4.8e+26) {
		tmp = fma(a, (y / (-1.0 - t)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(a / z), x)
	tmp = 0.0
	if (z <= -2.6e+56)
		tmp = t_1;
	elseif (z <= 4.8e+26)
		tmp = fma(a, Float64(y / Float64(-1.0 - t)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(a / z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -2.6e+56], t$95$1, If[LessEqual[z, 4.8e+26], N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.60000000000000011e56 or 4.80000000000000009e26 < z

   1. Initial program 90.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 87.5

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

   5. Applied rewrites 87.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 87.5%

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

   if -2.60000000000000011e56 < z < 4.80000000000000009e26

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. distribute-neg-frac2 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 91.5

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

   5. Applied rewrites 91.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \frac{y}{-1 - t}, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 85.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+62}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y}{-1 - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.85e+62)
   (- x a)
   (if (<= z 3.5e+27) (fma a (/ y (- -1.0 t)) x) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.85e+62) {
		tmp = x - a;
	} else if (z <= 3.5e+27) {
		tmp = fma(a, (y / (-1.0 - t)), x);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.85e+62)
		tmp = Float64(x - a);
	elseif (z <= 3.5e+27)
		tmp = fma(a, Float64(y / Float64(-1.0 - t)), x);
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.85e+62], N[(x - a), $MachinePrecision], If[LessEqual[z, 3.5e+27], N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85000000000000007e62 or 3.5000000000000002e27 < z

   1. Initial program 90.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 75.0

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

   5. Applied rewrites 75.0%

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

   if -1.85000000000000007e62 < z < 3.5000000000000002e27

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. distribute-neg-frac2 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 90.9

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

   5. Applied rewrites 90.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \frac{y}{-1 - t}, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 97.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{a}{-1 + \left(z - t\right)}, y - z, x\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (fma (/ a (+ -1.0 (- z t))) (- y z) x))

C

double code(double x, double y, double z, double t, double a) {
	return fma((a / (-1.0 + (z - t))), (y - z), x);
}

Julia

function code(x, y, z, t, a)
	return fma(Float64(a / Float64(-1.0 + Float64(z - t))), Float64(y - z), x)
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(a / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 95.3%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift--.f64 N/A

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

   2. sub-neg N/A

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

   3. +-commutative N/A

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

   4. lift-/.f64 N/A

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

   5. clear-num N/A

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

   6. associate-/r/ N/A

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

   7. lift-/.f64 N/A

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

   8. clear-num N/A

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

   9. distribute-lft-neg-in N/A

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

   10. clear-num N/A

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

   11. lift-/.f64 N/A

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

   12. distribute-frac-neg2 N/A

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

   13. lower-fma.f64 N/A

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

4. Applied rewrites 96.0%

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

5. Final simplification 96.0%

   \[\leadsto \mathsf{fma}\left(\frac{a}{-1 + \left(z - t\right)}, y - z, x\right) \]
6. Add Preprocessing

Alternative 8: 74.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+39}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\mathsf{fma}\left(y - z, -a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e+39) (- x a) (if (<= z 1.0) (fma (- y z) (- a) x) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+39) {
		tmp = x - a;
	} else if (z <= 1.0) {
		tmp = fma((y - z), -a, x);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e+39)
		tmp = Float64(x - a);
	elseif (z <= 1.0)
		tmp = fma(Float64(y - z), Float64(-a), x);
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e+39], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.0], N[(N[(y - z), $MachinePrecision] * (-a) + x), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.80000000000000001e39 or 1 < z

   1. Initial program 91.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 73.5

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

   5. Applied rewrites 73.5%

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

   if -2.80000000000000001e39 < z < 1

   1. Initial program 98.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 75.0

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

   5. Applied rewrites 75.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 72.9%

      \[\leadsto \mathsf{fma}\left(y - z, -a, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 72.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+62}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+26}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.85e+62) (- x a) (if (<= z 4.6e+26) (- x (* a y)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.85e+62) {
		tmp = x - a;
	} else if (z <= 4.6e+26) {
		tmp = x - (a * y);
	} else {
		tmp = x - 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 <= (-1.85d+62)) then
        tmp = x - a
    else if (z <= 4.6d+26) then
        tmp = x - (a * y)
    else
        tmp = x - 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 <= -1.85e+62) {
		tmp = x - a;
	} else if (z <= 4.6e+26) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.85e+62:
		tmp = x - a
	elif z <= 4.6e+26:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.85e+62)
		tmp = Float64(x - a);
	elseif (z <= 4.6e+26)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.85e+62)
		tmp = x - a;
	elseif (z <= 4.6e+26)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.85e+62], N[(x - a), $MachinePrecision], If[LessEqual[z, 4.6e+26], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85000000000000007e62 or 4.6000000000000001e26 < z

   1. Initial program 90.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 75.0

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

   5. Applied rewrites 75.0%

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

   if -1.85000000000000007e62 < z < 4.6000000000000001e26

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 74.5

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

   5. Applied rewrites 74.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 69.8%

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

Alternative 10: 66.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+34}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+26}:\\ \;\;\;\;-\left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e+34) (- x a) (if (<= z 4.6e+26) (- (- x)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+34) {
		tmp = x - a;
	} else if (z <= 4.6e+26) {
		tmp = -(-x);
	} else {
		tmp = x - 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 <= (-9d+34)) then
        tmp = x - a
    else if (z <= 4.6d+26) then
        tmp = -(-x)
    else
        tmp = x - 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 <= -9e+34) {
		tmp = x - a;
	} else if (z <= 4.6e+26) {
		tmp = -(-x);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9e+34:
		tmp = x - a
	elif z <= 4.6e+26:
		tmp = -(-x)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e+34)
		tmp = Float64(x - a);
	elseif (z <= 4.6e+26)
		tmp = Float64(-Float64(-x));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9e+34)
		tmp = x - a;
	elseif (z <= 4.6e+26)
		tmp = -(-x);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e+34], N[(x - a), $MachinePrecision], If[LessEqual[z, 4.6e+26], (-(-x)), N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.0000000000000001e34 or 4.6000000000000001e26 < z

   1. Initial program 91.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 73.1

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

   5. Applied rewrites 73.1%

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

   if -9.0000000000000001e34 < z < 4.6000000000000001e26

   1. Initial program 98.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 47.4

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

   5. Applied rewrites 47.4%

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

   6. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sub-neg N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

   8. Applied rewrites 86.3%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{neg}\left(-1 \cdot x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 61.1%

       \[\leadsto -\left(-x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 59.7% accurate, 8.8× speedup

Math

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

FPCore

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

C

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

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 - a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

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

   1. lower--.f64 59.0

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

5. Applied rewrites 59.0%

   \[\leadsto \color{blue}{x - a} \]
6. Add Preprocessing

Alternative 12: 16.8% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ -a \end{array} \]

FPCore

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

C

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

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 = -a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := (-a)

Derivation

1. Initial program 95.3%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

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

   1. lower--.f64 59.0

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

5. Applied rewrites 59.0%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 16.4%

   \[\leadsto -a \]
9. Add Preprocessing

Developer Target 1: 99.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\left(t - z\right) + 1} \cdot a \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (* (/ (- y z) (+ (- t z) 1.0)) a)))

C

double code(double x, double y, double z, double t, double a) {
	return x - (((y - z) / ((t - z) + 1.0)) * a);
}

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 - z) + 1.0d0)) * a)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - (((y - z) / ((t - z) + 1.0)) * a);
}

Python

def code(x, y, z, t, a):
	return x - (((y - z) / ((t - z) + 1.0)) * a)

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(Float64(y - z) / Float64(Float64(t - z) + 1.0)) * a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - (((y - z) / ((t - z) + 1.0)) * a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(N[(y - z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024238 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (/ (- y z) (+ (- t z) 1)) a)))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))