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

Percentage Accurate: 84.8% → 99.7%

Time: 9.6s

Alternatives: 12

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: 84.8% 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: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ t_2 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+293}:\\ \;\;\;\;t\_2 + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t (- a z)) (- y z) x)) (t_2 (/ (* (- y z) t) (- a z))))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 2e+293) (+ t_2 x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / (a - z)), (y - z), x);
	double t_2 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 2e+293) {
		tmp = t_2 + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / Float64(a - z)), Float64(y - z), x)
	t_2 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 2e+293)
		tmp = Float64(t_2 + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 2e+293], N[(t$95$2 + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 1.9999999999999998e293 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 44.3%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 1.9999999999999998e293

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 2 \cdot 10^{+293}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, t, x\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, 1 - \frac{y}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+27)
   (fma (/ z (- z a)) t x)
   (if (<= z 2.9e+31) (+ x (/ (* y t) (- a z))) (fma t (- 1.0 (/ y z)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+27) {
		tmp = fma((z / (z - a)), t, x);
	} else if (z <= 2.9e+31) {
		tmp = x + ((y * t) / (a - z));
	} else {
		tmp = fma(t, (1.0 - (y / z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+27)
		tmp = fma(Float64(z / Float64(z - a)), t, x);
	elseif (z <= 2.9e+31)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	else
		tmp = fma(t, Float64(1.0 - Float64(y / z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+27], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[z, 2.9e+31], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999997e27

   1. Initial program 86.7%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 91.4

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

   4. Applied egg-rr 91.4%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

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

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

      7. --lowering--.f64 89.6

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

   7. Simplified 89.6%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. distribute-frac-neg2 N/A

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

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

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

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

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\frac{z}{0 - \color{blue}{\left(a + \left(\mathsf{neg}\left(z\right)\right)\right)}}, t, x\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + a\right)}}, t, x\right) \]

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. --lowering--.f64 89.6

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

   9. Applied egg-rr 89.6%

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

   if -9.4999999999999997e27 < z < 2.9e31

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 87.3%

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

   if 2.9e31 < z

   1. Initial program 79.1%

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

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. neg-sub0 N/A

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

      7. div-sub N/A

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

      8. *-inverses N/A

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

      9. associate-+l- N/A

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

      10. neg-sub0 N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

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

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

      16. /-lowering-/.f64 93.1

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

   5. Simplified 93.1%

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

Alternative 3: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-52}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, t, x\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, 1 - \frac{y}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e-52)
   (fma (/ z (- z a)) t x)
   (if (<= z 2e+36) (fma t (/ (- y z) a) x) (fma t (- 1.0 (/ y z)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e-52) {
		tmp = fma((z / (z - a)), t, x);
	} else if (z <= 2e+36) {
		tmp = fma(t, ((y - z) / a), x);
	} else {
		tmp = fma(t, (1.0 - (y / z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e-52)
		tmp = fma(Float64(z / Float64(z - a)), t, x);
	elseif (z <= 2e+36)
		tmp = fma(t, Float64(Float64(y - z) / a), x);
	else
		tmp = fma(t, Float64(1.0 - Float64(y / z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e-52], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[z, 2e+36], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5e-52

   1. Initial program 87.7%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 90.3

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

   4. Applied egg-rr 90.3%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

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

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

      7. --lowering--.f64 85.9

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

   7. Simplified 85.9%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. distribute-frac-neg2 N/A

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

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

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

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

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\frac{z}{0 - \color{blue}{\left(a + \left(\mathsf{neg}\left(z\right)\right)\right)}}, t, x\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + a\right)}}, t, x\right) \]

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. --lowering--.f64 85.9

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

   9. Applied egg-rr 85.9%

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

   if -4.5e-52 < z < 2.00000000000000008e36

   1. Initial program 94.7%

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

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 87.6

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

   5. Simplified 87.6%

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

   if 2.00000000000000008e36 < z

   1. Initial program 79.1%

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

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. neg-sub0 N/A

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

      7. div-sub N/A

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

      8. *-inverses N/A

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

      9. associate-+l- N/A

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

      10. neg-sub0 N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

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

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

      16. /-lowering-/.f64 93.1

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

   5. Simplified 93.1%

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

Alternative 4: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, 1 - \frac{y}{z}, x\right)\\ \mathbf{if}\;z \leq -95000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma t (- 1.0 (/ y z)) x)))
   (if (<= z -95000000.0)
     t_1
     (if (<= z 1.3e+33) (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 <= -95000000.0) {
		tmp = t_1;
	} else if (z <= 1.3e+33) {
		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 <= -95000000.0)
		tmp = t_1;
	elseif (z <= 1.3e+33)
		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, -95000000.0], t$95$1, If[LessEqual[z, 1.3e+33], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5e7 or 1.2999999999999999e33 < z

   1. Initial program 83.6%

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

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. neg-sub0 N/A

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

      7. div-sub N/A

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

      8. *-inverses N/A

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

      9. associate-+l- N/A

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

      10. neg-sub0 N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

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

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

      16. /-lowering-/.f64 89.8

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

   5. Simplified 89.8%

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

   if -9.5e7 < z < 1.2999999999999999e33

   1. Initial program 94.3%

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

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 86.7

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

   5. Simplified 86.7%

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

Alternative 5: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, 1 - \frac{y}{z}, x\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma t (- 1.0 (/ y z)) x)))
   (if (<= z -2.4e+63) t_1 (if (<= z 2.7e-21) (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 <= -2.4e+63) {
		tmp = t_1;
	} else if (z <= 2.7e-21) {
		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 <= -2.4e+63)
		tmp = t_1;
	elseif (z <= 2.7e-21)
		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, -2.4e+63], t$95$1, If[LessEqual[z, 2.7e-21], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e63 or 2.7000000000000001e-21 < z

   1. Initial program 82.7%

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

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. neg-sub0 N/A

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

      7. div-sub N/A

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

      8. *-inverses N/A

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

      9. associate-+l- N/A

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

      10. neg-sub0 N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

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

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

      16. /-lowering-/.f64 89.2

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

   5. Simplified 89.2%

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

   if -2.4e63 < z < 2.7000000000000001e-21

   1. Initial program 95.0%

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

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 84.5

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

   5. Simplified 84.5%

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

Alternative 6: 77.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+70}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e+70) (+ t x) (if (<= z 1.6e+64) (fma t (/ y a) x) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+70) {
		tmp = t + x;
	} else if (z <= 1.6e+64) {
		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 <= -2.8e+70)
		tmp = Float64(t + x);
	elseif (z <= 1.6e+64)
		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, -2.8e+70], N[(t + x), $MachinePrecision], If[LessEqual[z, 1.6e+64], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999999e70 or 1.60000000000000009e64 < z

   1. Initial program 81.7%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 80.4%

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

   if -2.7999999999999999e70 < z < 1.60000000000000009e64

   1. Initial program 94.8%

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

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 81.8

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

   5. Simplified 81.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+70}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-99}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e-99)
   (+ t x)
   (if (<= z 1.1e-204) (* y (/ t a)) (if (<= z 2.9e+32) x (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-99) {
		tmp = t + x;
	} else if (z <= 1.1e-204) {
		tmp = y * (t / a);
	} else if (z <= 2.9e+32) {
		tmp = x;
	} else {
		tmp = t + 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 (z <= (-5.5d-99)) then
        tmp = t + x
    else if (z <= 1.1d-204) then
        tmp = y * (t / a)
    else if (z <= 2.9d+32) then
        tmp = x
    else
        tmp = t + 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 (z <= -5.5e-99) {
		tmp = t + x;
	} else if (z <= 1.1e-204) {
		tmp = y * (t / a);
	} else if (z <= 2.9e+32) {
		tmp = x;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e-99:
		tmp = t + x
	elif z <= 1.1e-204:
		tmp = y * (t / a)
	elif z <= 2.9e+32:
		tmp = x
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e-99)
		tmp = Float64(t + x);
	elseif (z <= 1.1e-204)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 2.9e+32)
		tmp = x;
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e-99)
		tmp = t + x;
	elseif (z <= 1.1e-204)
		tmp = y * (t / a);
	elseif (z <= 2.9e+32)
		tmp = x;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e-99], N[(t + x), $MachinePrecision], If[LessEqual[z, 1.1e-204], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+32], x, N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.49999999999999991e-99 or 2.90000000000000003e32 < z

   1. Initial program 85.2%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 74.3%

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

   if -5.49999999999999991e-99 < z < 1.0999999999999999e-204

   1. Initial program 92.6%

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

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

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

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

      3. --lowering--.f64 53.9

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

   5. Simplified 53.9%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 53.6%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 59.3

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

   10. Applied egg-rr 59.3%

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

   if 1.0999999999999999e-204 < z < 2.90000000000000003e32

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 62.5%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-99}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-100}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-203}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e-100)
   (+ t x)
   (if (<= z 1.08e-203) (* t (/ y a)) (if (<= z 2.45e+32) x (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e-100) {
		tmp = t + x;
	} else if (z <= 1.08e-203) {
		tmp = t * (y / a);
	} else if (z <= 2.45e+32) {
		tmp = x;
	} else {
		tmp = t + 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 (z <= (-3.2d-100)) then
        tmp = t + x
    else if (z <= 1.08d-203) then
        tmp = t * (y / a)
    else if (z <= 2.45d+32) then
        tmp = x
    else
        tmp = t + 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 (z <= -3.2e-100) {
		tmp = t + x;
	} else if (z <= 1.08e-203) {
		tmp = t * (y / a);
	} else if (z <= 2.45e+32) {
		tmp = x;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e-100:
		tmp = t + x
	elif z <= 1.08e-203:
		tmp = t * (y / a)
	elif z <= 2.45e+32:
		tmp = x
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e-100)
		tmp = Float64(t + x);
	elseif (z <= 1.08e-203)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 2.45e+32)
		tmp = x;
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e-100)
		tmp = t + x;
	elseif (z <= 1.08e-203)
		tmp = t * (y / a);
	elseif (z <= 2.45e+32)
		tmp = x;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e-100], N[(t + x), $MachinePrecision], If[LessEqual[z, 1.08e-203], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+32], x, N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.20000000000000017e-100 or 2.4500000000000001e32 < z

   1. Initial program 85.2%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 74.3%

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

   if -3.20000000000000017e-100 < z < 1.07999999999999997e-203

   1. Initial program 92.6%

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

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 91.9

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

   5. Simplified 91.9%

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

   6. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

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

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

      3. /-lowering-/.f64 59.3

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

   8. Simplified 59.3%

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

   if 1.07999999999999997e-203 < z < 2.4500000000000001e32

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 62.5%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-100}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-203}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 96.1% 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 89.2%

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

   1. +-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

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

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

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

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

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

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

   7. --lowering--.f64 94.2

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

4. Applied egg-rr 94.2%

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

Alternative 10: 64.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.3 \cdot 10^{-69}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.3e-69) (+ t x) (if (<= z 3.9e+31) x (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.3e-69) {
		tmp = t + x;
	} else if (z <= 3.9e+31) {
		tmp = x;
	} else {
		tmp = t + 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 (z <= (-8.3d-69)) then
        tmp = t + x
    else if (z <= 3.9d+31) then
        tmp = x
    else
        tmp = t + 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 (z <= -8.3e-69) {
		tmp = t + x;
	} else if (z <= 3.9e+31) {
		tmp = x;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.3e-69:
		tmp = t + x
	elif z <= 3.9e+31:
		tmp = x
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.3e-69)
		tmp = Float64(t + x);
	elseif (z <= 3.9e+31)
		tmp = x;
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.3e-69)
		tmp = t + x;
	elseif (z <= 3.9e+31)
		tmp = x;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.3e-69], N[(t + x), $MachinePrecision], If[LessEqual[z, 3.9e+31], x, N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.3000000000000004e-69 or 3.89999999999999999e31 < z

   1. Initial program 84.2%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 76.2%

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

   if -8.3000000000000004e-69 < z < 3.89999999999999999e31

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 49.8%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.3 \cdot 10^{-69}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-207}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.4e-167) x (if (<= x 1.4e-207) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.4e-167) {
		tmp = x;
	} else if (x <= 1.4e-207) {
		tmp = t;
	} 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 (x <= (-2.4d-167)) then
        tmp = x
    else if (x <= 1.4d-207) then
        tmp = t
    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 (x <= -2.4e-167) {
		tmp = x;
	} else if (x <= 1.4e-207) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.4e-167:
		tmp = x
	elif x <= 1.4e-207:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.4e-167)
		tmp = x;
	elseif (x <= 1.4e-207)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.4e-167)
		tmp = x;
	elseif (x <= 1.4e-207)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.4e-167], x, If[LessEqual[x, 1.4e-207], t, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.39999999999999993e-167 or 1.39999999999999996e-207 < x

   1. Initial program 89.4%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 61.5%

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

   if -2.39999999999999993e-167 < x < 1.39999999999999996e-207

   1. Initial program 88.7%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 40.2%

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

   6. Taylor expanded in x around 0

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

   8. Simplified 37.1%

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

Alternative 12: 18.9% 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 89.2%

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

3. Taylor expanded in z around inf

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

5. Simplified 56.6%

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

6. Taylor expanded in x around 0

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

8. Simplified 19.3%

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

Developer Target 1: 99.3% 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 2024196 
(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))))