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

Percentage Accurate: 77.2% → 87.8%

Time: 9.7s

Alternatives: 12

Speedup: 0.9×

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: 77.2% 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: 87.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+69}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(t - z\right), \frac{-1}{t - a}, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y t) (- z a) x)))
   (if (<= t -6.5e+152)
     t_1
     (if (<= t 1.32e+69) (fma (* y (- t z)) (/ -1.0 (- t a)) (+ y x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / t), (z - a), x);
	double tmp;
	if (t <= -6.5e+152) {
		tmp = t_1;
	} else if (t <= 1.32e+69) {
		tmp = fma((y * (t - z)), (-1.0 / (t - a)), (y + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / t), Float64(z - a), x)
	tmp = 0.0
	if (t <= -6.5e+152)
		tmp = t_1;
	elseif (t <= 1.32e+69)
		tmp = fma(Float64(y * Float64(t - z)), Float64(-1.0 / Float64(t - a)), Float64(y + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -6.5e+152], t$95$1, If[LessEqual[t, 1.32e+69], N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.4999999999999997e152 or 1.32e69 < t

   1. Initial program 56.1%

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

   3. Taylor expanded in t around inf

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. associate-+r+ N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. distribute-rgt-out-- N/A

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

      13. accelerator-lowering-fma.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. --lowering--.f64 89.4

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

   5. Simplified 89.4%

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

   if -6.4999999999999997e152 < t < 1.32e69

   1. Initial program 88.8%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. div-inv N/A

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

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

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

      5. accelerator-lowering-fma.f64 N/A

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

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

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

      7. *-lowering-*.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. neg-lowering-neg.f64 N/A

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. +-lowering-+.f64 89.0

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

   4. Applied egg-rr 89.0%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+69}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(t - z\right), \frac{-1}{t - a}, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+64}:\\ \;\;\;\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y t) (- z a) x)))
   (if (<= t -3.2e+153)
     t_1
     (if (<= t 7.5e+64) (+ (+ y x) (/ (* y (- t z)) (- a t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / t), (z - a), x);
	double tmp;
	if (t <= -3.2e+153) {
		tmp = t_1;
	} else if (t <= 7.5e+64) {
		tmp = (y + x) + ((y * (t - z)) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / t), Float64(z - a), x)
	tmp = 0.0
	if (t <= -3.2e+153)
		tmp = t_1;
	elseif (t <= 7.5e+64)
		tmp = Float64(Float64(y + x) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -3.2e+153], t$95$1, If[LessEqual[t, 7.5e+64], N[(N[(y + x), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2000000000000001e153 or 7.5000000000000005e64 < t

   1. Initial program 56.1%

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

   3. Taylor expanded in t around inf

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. associate-+r+ N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. distribute-rgt-out-- N/A

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

      13. accelerator-lowering-fma.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. --lowering--.f64 89.4

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

   5. Simplified 89.4%

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

   if -3.2000000000000001e153 < t < 7.5000000000000005e64

   1. Initial program 88.8%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+153}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+64}:\\ \;\;\;\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.16 \cdot 10^{-91}:\\ \;\;\;\;\left(y + x\right) - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.16e-91)
   (- (+ y x) (* z (/ y a)))
   (if (<= a 6.8e-30) (+ x (/ (* y (- z a)) t)) (fma y (- 1.0 (/ z a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.16e-91) {
		tmp = (y + x) - (z * (y / a));
	} else if (a <= 6.8e-30) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = fma(y, (1.0 - (z / a)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.16e-91)
		tmp = Float64(Float64(y + x) - Float64(z * Float64(y / a)));
	elseif (a <= 6.8e-30)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = fma(y, Float64(1.0 - Float64(z / a)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.16e-91], N[(N[(y + x), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e-30], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.15999999999999994e-91

   1. Initial program 81.7%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 87.4

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

   5. Simplified 87.4%

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

   if -1.15999999999999994e-91 < a < 6.8000000000000006e-30

   1. Initial program 74.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. div-inv N/A

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

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

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

      5. accelerator-lowering-fma.f64 N/A

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

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

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

      7. *-lowering-*.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. neg-lowering-neg.f64 N/A

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. +-lowering-+.f64 74.7

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

   4. Applied egg-rr 74.7%

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

   5. Taylor expanded in t around inf

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

      1. associate-+r+ N/A

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

      2. distribute-rgt1-in N/A

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

      3. metadata-eval N/A

         \[\leadsto x + \left(\color{blue}{0} \cdot y + -1 \cdot \frac{-1 \cdot \left(y \cdot z\right) - -1 \cdot \left(a \cdot y\right)}{t}\right) \]

      4. mul0-lft N/A

         \[\leadsto x + \left(\color{blue}{0} + -1 \cdot \frac{-1 \cdot \left(y \cdot z\right) - -1 \cdot \left(a \cdot y\right)}{t}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + 0\right) + -1 \cdot \frac{-1 \cdot \left(y \cdot z\right) - -1 \cdot \left(a \cdot y\right)}{t}} \]

      6. +-rgt-identity N/A

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

      7. +-lowering-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. distribute-lft-out-- N/A

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

      10. mul-1-neg N/A

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

      11. distribute-frac-neg N/A

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

      12. remove-double-neg N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-commutative N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-lowering-*.f64 N/A

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

      17. --lowering--.f64 89.0

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

   7. Simplified 89.0%

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

   if 6.8000000000000006e-30 < a

   1. Initial program 81.9%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

      5. distribute-lft-out-- N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. /-lowering-/.f64 86.7

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

   5. Simplified 86.7%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.16 \cdot 10^{-91}:\\ \;\;\;\;\left(y + x\right) - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 1 - \frac{z}{a}, x\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (- 1.0 (/ z a)) x)))
   (if (<= a -3.5e-91) t_1 (if (<= a 8e-30) (+ x (/ (* y (- z a)) t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (1.0 - (z / a)), x);
	double tmp;
	if (a <= -3.5e-91) {
		tmp = t_1;
	} else if (a <= 8e-30) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(1.0 - Float64(z / a)), x)
	tmp = 0.0
	if (a <= -3.5e-91)
		tmp = t_1;
	elseif (a <= 8e-30)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -3.5e-91], t$95$1, If[LessEqual[a, 8e-30], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.4999999999999999e-91 or 8.000000000000001e-30 < a

   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 t around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

      5. distribute-lft-out-- N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. /-lowering-/.f64 87.0

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

   5. Simplified 87.0%

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

   if -3.4999999999999999e-91 < a < 8.000000000000001e-30

   1. Initial program 74.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. div-inv N/A

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

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

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

      5. accelerator-lowering-fma.f64 N/A

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

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

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

      7. *-lowering-*.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. neg-lowering-neg.f64 N/A

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. +-lowering-+.f64 74.7

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

   4. Applied egg-rr 74.7%

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

   5. Taylor expanded in t around inf

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

      1. associate-+r+ N/A

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

      2. distribute-rgt1-in N/A

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

      3. metadata-eval N/A

         \[\leadsto x + \left(\color{blue}{0} \cdot y + -1 \cdot \frac{-1 \cdot \left(y \cdot z\right) - -1 \cdot \left(a \cdot y\right)}{t}\right) \]

      4. mul0-lft N/A

         \[\leadsto x + \left(\color{blue}{0} + -1 \cdot \frac{-1 \cdot \left(y \cdot z\right) - -1 \cdot \left(a \cdot y\right)}{t}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + 0\right) + -1 \cdot \frac{-1 \cdot \left(y \cdot z\right) - -1 \cdot \left(a \cdot y\right)}{t}} \]

      6. +-rgt-identity N/A

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

      7. +-lowering-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. distribute-lft-out-- N/A

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

      10. mul-1-neg N/A

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

      11. distribute-frac-neg N/A

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

      12. remove-double-neg N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-commutative N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-lowering-*.f64 N/A

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

      17. --lowering--.f64 89.0

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

   7. Simplified 89.0%

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

Alternative 5: 83.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 1 - \frac{z}{a}, x\right)\\ \mathbf{if}\;a \leq -7 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-30}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (- 1.0 (/ z a)) x)))
   (if (<= a -7e-90) t_1 (if (<= a 5.9e-30) (fma (/ y t) (- z a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (1.0 - (z / a)), x);
	double tmp;
	if (a <= -7e-90) {
		tmp = t_1;
	} else if (a <= 5.9e-30) {
		tmp = fma((y / t), (z - a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(1.0 - Float64(z / a)), x)
	tmp = 0.0
	if (a <= -7e-90)
		tmp = t_1;
	elseif (a <= 5.9e-30)
		tmp = fma(Float64(y / t), Float64(z - a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -7e-90], t$95$1, If[LessEqual[a, 5.9e-30], N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.9999999999999997e-90 or 5.89999999999999979e-30 < a

   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 t around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

      5. distribute-lft-out-- N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. /-lowering-/.f64 87.0

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

   5. Simplified 87.0%

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

   if -6.9999999999999997e-90 < a < 5.89999999999999979e-30

   1. Initial program 74.4%

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

   3. Taylor expanded in t around inf

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. associate-+r+ N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. distribute-rgt-out-- N/A

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

      13. accelerator-lowering-fma.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. --lowering--.f64 85.5

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

   5. Simplified 85.5%

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

Alternative 6: 83.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 1 - \frac{z}{a}, x\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-30}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (- 1.0 (/ z a)) x)))
   (if (<= a -2.7e-89) t_1 (if (<= a 5.9e-30) (fma y (/ z t) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (1.0 - (z / a)), x);
	double tmp;
	if (a <= -2.7e-89) {
		tmp = t_1;
	} else if (a <= 5.9e-30) {
		tmp = fma(y, (z / t), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(1.0 - Float64(z / a)), x)
	tmp = 0.0
	if (a <= -2.7e-89)
		tmp = t_1;
	elseif (a <= 5.9e-30)
		tmp = fma(y, Float64(z / t), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.7e-89], t$95$1, If[LessEqual[a, 5.9e-30], N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.69999999999999988e-89 or 5.89999999999999979e-30 < a

   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 t around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

      5. distribute-lft-out-- N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. /-lowering-/.f64 87.0

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

   5. Simplified 87.0%

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

   if -2.69999999999999988e-89 < a < 5.89999999999999979e-30

   1. Initial program 74.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. div-inv N/A

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

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

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

      5. accelerator-lowering-fma.f64 N/A

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

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

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

      7. *-lowering-*.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. neg-lowering-neg.f64 N/A

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. +-lowering-+.f64 74.7

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

   4. Applied egg-rr 74.7%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. associate-+r+ N/A

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

      12. distribute-rgt1-in N/A

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

      13. metadata-eval N/A

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

      14. mul0-lft N/A

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

      15. +-lft-identity N/A

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

      16. associate-/l* N/A

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

      17. accelerator-lowering-fma.f64 N/A

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

      18. /-lowering-/.f64 85.0

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

   7. Simplified 85.0%

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

Alternative 7: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.8e-41) (+ y x) (if (<= a 3.4e+84) (fma y (/ z t) x) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e-41) {
		tmp = y + x;
	} else if (a <= 3.4e+84) {
		tmp = fma(y, (z / t), x);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.8e-41)
		tmp = Float64(y + x);
	elseif (a <= 3.4e+84)
		tmp = fma(y, Float64(z / t), x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.8e-41], N[(y + x), $MachinePrecision], If[LessEqual[a, 3.4e+84], N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.79999999999999955e-41 or 3.3999999999999998e84 < a

   1. Initial program 83.1%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 79.3

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

   5. Simplified 79.3%

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

   if -5.79999999999999955e-41 < a < 3.3999999999999998e84

   1. Initial program 75.0%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. div-inv N/A

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

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

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

      5. accelerator-lowering-fma.f64 N/A

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

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

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

      7. *-lowering-*.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. neg-lowering-neg.f64 N/A

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. +-lowering-+.f64 75.2

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

   4. Applied egg-rr 75.2%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. associate-+r+ N/A

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

      12. distribute-rgt1-in N/A

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

      13. metadata-eval N/A

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

      14. mul0-lft N/A

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

      15. +-lft-identity N/A

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

      16. associate-/l* N/A

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

      17. accelerator-lowering-fma.f64 N/A

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

      18. /-lowering-/.f64 77.7

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

   7. Simplified 77.7%

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

Alternative 8: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-127}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 4.45 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.85e-127) (+ y x) (if (<= a 4.45e-299) (* y (/ z t)) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.85e-127) {
		tmp = y + x;
	} else if (a <= 4.45e-299) {
		tmp = y * (z / t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.85d-127)) then
        tmp = y + x
    else if (a <= 4.45d-299) then
        tmp = y * (z / t)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.85e-127) {
		tmp = y + x;
	} else if (a <= 4.45e-299) {
		tmp = y * (z / t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.85e-127:
		tmp = y + x
	elif a <= 4.45e-299:
		tmp = y * (z / t)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.85e-127)
		tmp = Float64(y + x);
	elseif (a <= 4.45e-299)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.85e-127)
		tmp = y + x;
	elseif (a <= 4.45e-299)
		tmp = y * (z / t);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.85e-127], N[(y + x), $MachinePrecision], If[LessEqual[a, 4.45e-299], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8500000000000002e-127 or 4.4500000000000002e-299 < a

   1. Initial program 79.1%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 67.0

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

   5. Simplified 67.0%

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

   if -1.8500000000000002e-127 < a < 4.4500000000000002e-299

   1. Initial program 78.3%

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

   3. Taylor expanded in x around 0

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

      1. *-rgt-identity N/A

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

      2. associate-/l* N/A

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

      3. distribute-lft-out-- N/A

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

      4. unsub-neg N/A

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. distribute-rgt-in N/A

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

      8. *-lft-identity N/A

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

      9. mul-1-neg N/A

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

      10. distribute-lft-neg-out N/A

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

      11. *-commutative N/A

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

      12. associate-/l* N/A

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

      13. *-commutative N/A

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

      14. associate-/l* N/A

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

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

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

      16. mul-1-neg N/A

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

      17. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 50.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. sub-neg N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. distribute-lft-out N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. associate-+r+ N/A

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

      11. distribute-rgt1-in N/A

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

      12. metadata-eval N/A

          \[\leadsto \color{blue}{0} \cdot y + \frac{y \cdot z}{t} \]

      13. mul0-lft N/A

          \[\leadsto \color{blue}{0} + \frac{y \cdot z}{t} \]

      14. +-lft-identity N/A

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

      15. associate-/l* N/A

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

      16. *-lowering-*.f64 N/A

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

      17. /-lowering-/.f64 62.6

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

   8. Simplified 62.6%

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

Alternative 9: 52.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+188}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1e+188) y (if (<= y 1.5e+35) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1e+188) {
		tmp = y;
	} else if (y <= 1.5e+35) {
		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 <= (-1d+188)) then
        tmp = y
    else if (y <= 1.5d+35) 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 <= -1e+188) {
		tmp = y;
	} else if (y <= 1.5e+35) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1e+188:
		tmp = y
	elif y <= 1.5e+35:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1e+188)
		tmp = y;
	elseif (y <= 1.5e+35)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1e+188)
		tmp = y;
	elseif (y <= 1.5e+35)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1e+188], y, If[LessEqual[y, 1.5e+35], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1e188 or 1.49999999999999995e35 < y

   1. Initial program 64.5%

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

   3. Taylor expanded in x around 0

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

      1. *-rgt-identity N/A

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

      2. associate-/l* N/A

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

      3. distribute-lft-out-- N/A

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

      4. unsub-neg N/A

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. distribute-rgt-in N/A

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

      8. *-lft-identity N/A

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

      9. mul-1-neg N/A

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

      10. distribute-lft-neg-out N/A

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

      11. *-commutative N/A

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

      12. associate-/l* N/A

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

      13. *-commutative N/A

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

      14. associate-/l* N/A

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

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

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

      16. mul-1-neg N/A

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

      17. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 72.4%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 31.8%

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

   if -1e188 < y < 1.49999999999999995e35

   1. Initial program 85.4%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 65.0%

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

Alternative 10: 62.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+176}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t -7e+176) x (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+176) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7d+176)) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+176) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7e+176:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e+176)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7e+176)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e+176], x, N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.00000000000000005e176

   1. Initial program 44.5%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 60.1%

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

   if -7.00000000000000005e176 < t

   1. Initial program 83.7%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 64.0

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

   5. Simplified 64.0%

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

Alternative 11: 51.6% accurate, 29.0× 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 79.0%

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

3. Taylor expanded in x around inf

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

5. Simplified 48.8%

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

Alternative 12: 2.7% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 79.0%

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

3. Taylor expanded in x around 0

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

   1. *-rgt-identity N/A

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

   2. associate-/l* N/A

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

   3. distribute-lft-out-- N/A

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

   4. unsub-neg N/A

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

   5. mul-1-neg N/A

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

   6. +-commutative N/A

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

   7. distribute-rgt-in N/A

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

   8. *-lft-identity N/A

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

   9. mul-1-neg N/A

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

   10. distribute-lft-neg-out N/A

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

   11. *-commutative N/A

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

   12. associate-/l* N/A

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

   13. *-commutative N/A

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

   14. associate-/l* N/A

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

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

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

   16. mul-1-neg N/A

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

   17. accelerator-lowering-fma.f64 N/A

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

5. Simplified 42.7%

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

6. Taylor expanded in t around inf

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

   1. distribute-rgt1-in N/A

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

   2. metadata-eval N/A

      \[\leadsto \color{blue}{0} \cdot y \]

   3. mul0-lft 2.8

      \[\leadsto \color{blue}{0} \]

8. Simplified 2.8%

   \[\leadsto \color{blue}{0} \]
9. Add Preprocessing

Developer Target 1: 88.3% 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 2024205 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -13664970889390727/100000000000000000000000) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 14754293444577233/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)))))

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