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

Percentage Accurate: 85.2% → 98.2%

Time: 10.7s

Alternatives: 11

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - z) * t) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - z) * t) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

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

      \[\leadsto \mathsf{fma.f64}\left(\left(\frac{y - z}{a - z}\right), \color{blue}{t}, x\right) \]

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

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(a - z\right)\right), t, x\right) \]

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

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(a - z\right)\right), t, x\right) \]

   8. --lowering--.f64 99.2%

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right), t, x\right) \]

4. Applied egg-rr 99.2%

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

Alternative 2: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{z}, t, x\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) z) t x)))
   (if (<= z -2e-45) t_1 (if (<= z 1.35e-23) (fma t (/ (- y z) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - y) / z), t, x);
	double tmp;
	if (z <= -2e-45) {
		tmp = t_1;
	} else if (z <= 1.35e-23) {
		tmp = fma(t, ((y - z) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / z), t, x)
	tmp = 0.0
	if (z <= -2e-45)
		tmp = t_1;
	elseif (z <= 1.35e-23)
		tmp = fma(t, Float64(Float64(y - z) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * t + x), $MachinePrecision]}, If[LessEqual[z, -2e-45], t$95$1, If[LessEqual[z, 1.35e-23], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.99999999999999997e-45 or 1.34999999999999992e-23 < z

   1. Initial program 77.3%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(\left(\frac{y - z}{a - z}\right), \color{blue}{t}, x\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(a - z\right)\right), t, x\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(a - z\right)\right), t, x\right) \]

      8. --lowering--.f64 99.9%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right), t, x\right) \]

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma.f64}\left(\color{blue}{\left(-1 \cdot \frac{y - z}{z}\right)}, t, x\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\frac{-1 \cdot \left(y - z\right)}{z}\right), t, x\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(y - z\right)\right), z\right), t, x\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(y - z\right)\right)\right), z\right), t, x\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), z\right), t, x\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(y + -1 \cdot z\right)\right)\right), z\right), t, x\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(-1 \cdot z + y\right)\right)\right), z\right), t, x\right) \]

      7. distribute-neg-in N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(-1 \cdot z\right)\right) + \left(\mathsf{neg}\left(y\right)\right)\right), z\right), t, x\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right)\right), z\right), t, x\right) \]

      9. remove-double-neg N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(z + \left(\mathsf{neg}\left(y\right)\right)\right), z\right), t, x\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(z - y\right), z\right), t, x\right) \]

      11. --lowering--.f64 89.3%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), z\right), t, x\right) \]

   7. Simplified 89.3%

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

   if -1.99999999999999997e-45 < z < 1.34999999999999992e-23

   1. Initial program 95.2%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(\frac{y - z}{a}\right)}, x\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{a}\right), x\right) \]

      5. --lowering--.f64 88.1%

         \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), a\right), x\right) \]

   5. Simplified 88.1%

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

Alternative 3: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, 1 - \frac{y}{z}, x\right)\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.65 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma t (- 1.0 (/ y z)) x)))
   (if (<= z -2.35e-46) t_1 (if (<= z 3.65e-23) (fma t (/ (- y z) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, (1.0 - (y / z)), x);
	double tmp;
	if (z <= -2.35e-46) {
		tmp = t_1;
	} else if (z <= 3.65e-23) {
		tmp = fma(t, ((y - z) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(1.0 - Float64(y / z)), x)
	tmp = 0.0
	if (z <= -2.35e-46)
		tmp = t_1;
	elseif (z <= 3.65e-23)
		tmp = fma(t, Float64(Float64(y - z) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -2.35e-46], t$95$1, If[LessEqual[z, 3.65e-23], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.34999999999999983e-46 or 3.65000000000000002e-23 < z

   1. Initial program 77.3%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}, x\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 - \color{blue}{\frac{y - z}{z}}\right), x\right) \]

      7. div-sub N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right), x\right) \]

      8. *-inverses N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 - \left(\frac{y}{z} - 1\right)\right), x\right) \]

      9. associate-+l- N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right), x\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right), x\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(-1 \cdot \frac{y}{z} + 1\right), x\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right), x\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right), x\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(1 - \color{blue}{\frac{y}{z}}\right), x\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right), x\right) \]

      16. /-lowering-/.f64 89.3%

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right), x\right) \]

   5. Simplified 89.3%

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

   if -2.34999999999999983e-46 < z < 3.65000000000000002e-23

   1. Initial program 95.2%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(\frac{y - z}{a}\right)}, x\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{a}\right), x\right) \]

      5. --lowering--.f64 88.1%

         \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), a\right), x\right) \]

   5. Simplified 88.1%

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

Alternative 4: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, 1 - \frac{y}{z}, x\right)\\ \mathbf{if}\;z \leq -1.66 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-48}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma t (- 1.0 (/ y z)) x)))
   (if (<= z -1.66e-47) t_1 (if (<= z 2.8e-48) (fma t (/ y a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, (1.0 - (y / z)), x);
	double tmp;
	if (z <= -1.66e-47) {
		tmp = t_1;
	} else if (z <= 2.8e-48) {
		tmp = fma(t, (y / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(1.0 - Float64(y / z)), x)
	tmp = 0.0
	if (z <= -1.66e-47)
		tmp = t_1;
	elseif (z <= 2.8e-48)
		tmp = fma(t, Float64(y / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.66e-47], t$95$1, If[LessEqual[z, 2.8e-48], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65999999999999998e-47 or 2.80000000000000005e-48 < z

   1. Initial program 78.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}, x\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 - \color{blue}{\frac{y - z}{z}}\right), x\right) \]

      7. div-sub N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right), x\right) \]

      8. *-inverses N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 - \left(\frac{y}{z} - 1\right)\right), x\right) \]

      9. associate-+l- N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right), x\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right), x\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(-1 \cdot \frac{y}{z} + 1\right), x\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right), x\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right), x\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(1 - \color{blue}{\frac{y}{z}}\right), x\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right), x\right) \]

      16. /-lowering-/.f64 87.3%

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right), x\right) \]

   5. Simplified 87.3%

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

   if -1.65999999999999998e-47 < z < 2.80000000000000005e-48

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(\frac{y}{a}\right)}, x\right) \]

      4. /-lowering-/.f64 86.6%

         \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{a}\right), x\right) \]

   5. Simplified 86.6%

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

Alternative 5: 75.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-45}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-36}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e-45) (+ t x) (if (<= z 3.1e-36) (fma t (/ y a) x) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e-45) {
		tmp = t + x;
	} else if (z <= 3.1e-36) {
		tmp = fma(t, (y / a), x);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e-45)
		tmp = Float64(t + x);
	elseif (z <= 3.1e-36)
		tmp = fma(t, Float64(y / a), x);
	else
		tmp = Float64(t + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e-45], N[(t + x), $MachinePrecision], If[LessEqual[z, 3.1e-36], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.19999999999999967e-45 or 3.0999999999999999e-36 < z

   1. Initial program 78.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 75.9%

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

   if -9.19999999999999967e-45 < z < 3.0999999999999999e-36

   1. Initial program 94.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(\frac{y}{a}\right)}, x\right) \]

      4. /-lowering-/.f64 85.5%

         \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{a}\right), x\right) \]

   5. Simplified 85.5%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-45}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-36}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+85}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= y -2.5e+179) t_1 (if (<= y 6e+85) (+ t x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (y <= -2.5e+179) {
		tmp = t_1;
	} else if (y <= 6e+85) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (y <= (-2.5d+179)) then
        tmp = t_1
    else if (y <= 6d+85) then
        tmp = t + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (y <= -2.5e+179) {
		tmp = t_1;
	} else if (y <= 6e+85) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if y <= -2.5e+179:
		tmp = t_1
	elif y <= 6e+85:
		tmp = t + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (y <= -2.5e+179)
		tmp = t_1;
	elseif (y <= 6e+85)
		tmp = Float64(t + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (y <= -2.5e+179)
		tmp = t_1;
	elseif (y <= 6e+85)
		tmp = t + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+179], t$95$1, If[LessEqual[y, 6e+85], N[(t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5e179 or 6.0000000000000001e85 < y

   1. Initial program 85.4%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot y\right), \color{blue}{\left(a - z\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, y\right), \left(\color{blue}{a} - z\right)\right) \]

      3. --lowering--.f64 65.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, y\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 65.3%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a - z}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{\left(a - z\right)}\right)\right) \]

      5. --lowering--.f64 68.0%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 68.0%

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

   8. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 44.0%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right) \]

   10. Simplified 44.0%

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

       1. associate-*r/ N/A

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

       2. *-commutative N/A

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

       3. associate-/l* N/A

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

       4. *-commutative N/A

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

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

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{t}\right) \]

       6. /-lowering-/.f64 48.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), t\right) \]

   12. Applied egg-rr 48.4%

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

   if -2.5e179 < y < 6.0000000000000001e85

   1. Initial program 85.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 73.6%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+179}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+85}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+85}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t a))))
   (if (<= y -1.5e+179) t_1 (if (<= y 3.1e+85) (+ t x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (y <= -1.5e+179) {
		tmp = t_1;
	} else if (y <= 3.1e+85) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / a)
    if (y <= (-1.5d+179)) then
        tmp = t_1
    else if (y <= 3.1d+85) then
        tmp = t + x
    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 * (t / a);
	double tmp;
	if (y <= -1.5e+179) {
		tmp = t_1;
	} else if (y <= 3.1e+85) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / a)
	tmp = 0
	if y <= -1.5e+179:
		tmp = t_1
	elif y <= 3.1e+85:
		tmp = t + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / a))
	tmp = 0.0
	if (y <= -1.5e+179)
		tmp = t_1;
	elseif (y <= 3.1e+85)
		tmp = Float64(t + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / a);
	tmp = 0.0;
	if (y <= -1.5e+179)
		tmp = t_1;
	elseif (y <= 3.1e+85)
		tmp = t + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+179], t$95$1, If[LessEqual[y, 3.1e+85], N[(t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4999999999999999e179 or 3.10000000000000011e85 < y

   1. Initial program 85.4%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot y\right), \color{blue}{\left(a - z\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, y\right), \left(\color{blue}{a} - z\right)\right) \]

      3. --lowering--.f64 65.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, y\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 65.3%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a - z}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{\left(a - z\right)}\right)\right) \]

      5. --lowering--.f64 68.0%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 68.0%

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

   8. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 44.0%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right) \]

   10. Simplified 44.0%

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

   if -1.4999999999999999e179 < y < 3.10000000000000011e85

   1. Initial program 85.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 73.6%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+85}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 96.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

   1. +-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

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

      \[\leadsto \mathsf{fma.f64}\left(\left(\frac{t}{a - z}\right), \color{blue}{\left(y - z\right)}, x\right) \]

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

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(t, \left(a - z\right)\right), \left(\color{blue}{y} - z\right), x\right) \]

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

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, z\right)\right), \left(y - z\right), x\right) \]

   7. --lowering--.f64 94.1%

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, z\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right), x\right) \]

4. Applied egg-rr 94.1%

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

Alternative 9: 51.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+145}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.1e+145) t (if (<= t 1.4e+60) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e+145) {
		tmp = t;
	} else if (t <= 1.4e+60) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.1d+145)) then
        tmp = t
    else if (t <= 1.4d+60) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e+145) {
		tmp = t;
	} else if (t <= 1.4e+60) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.1e+145:
		tmp = t
	elif t <= 1.4e+60:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.1e+145)
		tmp = t;
	elseif (t <= 1.4e+60)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.1e+145)
		tmp = t;
	elseif (t <= 1.4e+60)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.1e+145], t, If[LessEqual[t, 1.4e+60], x, t]]

Derivation

1. Split input into 2 regimes

2. if t < -1.10000000000000004e145 or 1.4e60 < t

   1. Initial program 70.3%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(y - z\right)\right), \color{blue}{\left(a - z\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(y - z\right)\right), \left(\color{blue}{a} - z\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \left(a - z\right)\right) \]

      4. --lowering--.f64 56.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 56.5%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 34.2%

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

   if -1.10000000000000004e145 < t < 1.4e60

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 63.3%

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

Alternative 10: 61.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 6 \cdot 10^{+205}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 6e+205) (+ t x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 6e+205) {
		tmp = t + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 6d+205) then
        tmp = t + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 6e+205) {
		tmp = t + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 6e+205:
		tmp = t + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 6e+205)
		tmp = Float64(t + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 6e+205)
		tmp = t + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 6e+205], N[(t + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 5.9999999999999999e205

   1. Initial program 85.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 62.7%

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

   if 5.9999999999999999e205 < a

   1. Initial program 87.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 70.6%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 6 \cdot 10^{+205}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 18.6% accurate, 26.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

3. Taylor expanded in x around 0

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

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(y - z\right)\right), \color{blue}{\left(a - z\right)}\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(y - z\right)\right), \left(\color{blue}{a} - z\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \left(a - z\right)\right) \]

   4. --lowering--.f64 43.7%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

5. Simplified 43.7%

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

6. Taylor expanded in z around inf

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

8. Simplified 21.6%

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

Developer Target 1: 99.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024193 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -10682974490174067/10000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 312887599100691/80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t)))))

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