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

Percentage Accurate: 85.1% → 96.4%

Time: 7.7s

Alternatives: 10

Speedup: 0.7×

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: 85.1% 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: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{a - z} \cdot \left(y - z\right)\\ t_2 := \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+288}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, t \cdot y\right)}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ t (- a z)) (- y z))) (t_2 (/ (* t (- y z)) (- a z))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 2e+288) (+ (/ (fma (- z) t (* t y)) (- a z)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / (a - z)) * (y - z);
	double t_2 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 2e+288) {
		tmp = (fma(-z, t, (t * y)) / (a - z)) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / Float64(a - z)) * Float64(y - z))
	t_2 = Float64(Float64(t * Float64(y - z)) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 2e+288)
		tmp = Float64(Float64(fma(Float64(-z), t, Float64(t * y)) / Float64(a - z)) + 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]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 2e+288], N[(N[(N[((-z) * t + N[(t * y), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + 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 2e288 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 34.7%

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

   3. Taylor expanded in t around inf

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

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

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

      2. associate-/l* N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-*r/ N/A

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

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

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 86.7

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

   5. Applied rewrites 86.7%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 2e288

   1. Initial program 99.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-rgt-in N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 99.8

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

   4. Applied rewrites 99.8%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq -\infty:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq 2 \cdot 10^{+288}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, t \cdot y\right)}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{a - z} \cdot \left(y - z\right)\\ t_2 := \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+288}:\\ \;\;\;\;x + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ t (- a z)) (- y z))) (t_2 (/ (* t (- y z)) (- a z))))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 2e+288) (+ x t_2) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / (a - z)) * (y - z);
	double t_2 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 2e+288) {
		tmp = x + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / (a - z)) * (y - z);
	double t_2 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 2e+288) {
		tmp = x + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t / (a - z)) * (y - z)
	t_2 = (t * (y - z)) / (a - z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 2e+288:
		tmp = x + t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / Float64(a - z)) * Float64(y - z))
	t_2 = Float64(Float64(t * Float64(y - z)) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 2e+288)
		tmp = Float64(x + t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t / (a - z)) * (y - z);
	t_2 = (t * (y - z)) / (a - z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 2e+288)
		tmp = x + t_2;
	else
		tmp = t_1;
	end
	tmp_2 = 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]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 2e+288], N[(x + t$95$2), $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 2e288 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 34.7%

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

   3. Taylor expanded in t around inf

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

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

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

      2. associate-/l* N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-*r/ N/A

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

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

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 86.7

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

   5. Applied rewrites 86.7%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 2e288

   1. Initial program 99.8%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq -\infty:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq 2 \cdot 10^{+288}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, \frac{z}{a - z}, x\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 780000:\\ \;\;\;\;\frac{t \cdot y}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t) (/ z (- a z)) x)))
   (if (<= z -6.8e+64)
     t_1
     (if (<= z 780000.0) (+ (/ (* t y) (- a z)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-t, (z / (a - z)), x);
	double tmp;
	if (z <= -6.8e+64) {
		tmp = t_1;
	} else if (z <= 780000.0) {
		tmp = ((t * y) / (a - z)) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(-t), Float64(z / Float64(a - z)), x)
	tmp = 0.0
	if (z <= -6.8e+64)
		tmp = t_1;
	elseif (z <= 780000.0)
		tmp = Float64(Float64(Float64(t * y) / Float64(a - z)) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -6.8e+64], t$95$1, If[LessEqual[z, 780000.0], N[(N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8000000000000003e64 or 7.8e5 < z

   1. Initial program 68.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 94.2

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

   5. Applied rewrites 94.2%

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

   if -6.8000000000000003e64 < z < 7.8e5

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 87.0

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

   5. Applied rewrites 87.0%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{z}{a - z}, x\right)\\ \mathbf{elif}\;z \leq 780000:\\ \;\;\;\;\frac{t \cdot y}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{z}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - z}{a}, t, x\right)\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-63}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{y}{z}, t\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- y z) a) t x)))
   (if (<= a -3.6e+16)
     t_1
     (if (<= a 2.35e-63) (+ (fma (- t) (/ y z) t) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((y - z) / a), t, x);
	double tmp;
	if (a <= -3.6e+16) {
		tmp = t_1;
	} else if (a <= 2.35e-63) {
		tmp = fma(-t, (y / z), t) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(y - z) / a), t, x)
	tmp = 0.0
	if (a <= -3.6e+16)
		tmp = t_1;
	elseif (a <= 2.35e-63)
		tmp = Float64(fma(Float64(-t), Float64(y / z), t) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * t + x), $MachinePrecision]}, If[LessEqual[a, -3.6e+16], t$95$1, If[LessEqual[a, 2.35e-63], N[(N[((-t) * N[(y / z), $MachinePrecision] + t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.6e16 or 2.35e-63 < a

   1. Initial program 83.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 86.9

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

   5. Applied rewrites 86.9%

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

   if -3.6e16 < a < 2.35e-63

   1. Initial program 82.8%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. associate--r+ N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. div-sub N/A

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

      7. lower--.f64 N/A

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

      8. div-sub N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. associate-/l* N/A

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

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

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 85.1

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

   5. Applied rewrites 85.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 85.5%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a}, t, x\right)\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-63}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{y}{z}, t\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a}, t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - z}{a}, t, x\right)\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-63}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- y z) a) t x)))
   (if (<= a -3.6e+16)
     t_1
     (if (<= a 2.35e-63) (fma (- 1.0 (/ y z)) t x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((y - z) / a), t, x);
	double tmp;
	if (a <= -3.6e+16) {
		tmp = t_1;
	} else if (a <= 2.35e-63) {
		tmp = fma((1.0 - (y / z)), t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(y - z) / a), t, x)
	tmp = 0.0
	if (a <= -3.6e+16)
		tmp = t_1;
	elseif (a <= 2.35e-63)
		tmp = fma(Float64(1.0 - Float64(y / z)), t, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * t + x), $MachinePrecision]}, If[LessEqual[a, -3.6e+16], t$95$1, If[LessEqual[a, 2.35e-63], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.6e16 or 2.35e-63 < a

   1. Initial program 83.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 86.9

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

   5. Applied rewrites 86.9%

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

   if -3.6e16 < a < 2.35e-63

   1. Initial program 82.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

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

      8. div-sub N/A

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

      9. *-inverses N/A

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

      10. associate-+l- N/A

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

      11. neg-sub0 N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. mul-1-neg N/A

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

      15. unsub-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower-/.f64 85.4

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

   5. Applied rewrites 85.4%

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

Alternative 6: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \mathbf{if}\;z \leq -1.86 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-33}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (/ y z)) t x)))
   (if (<= z -1.86e-81) t_1 (if (<= z 1.22e-33) (fma y (/ t a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((1.0 - (y / z)), t, x);
	double tmp;
	if (z <= -1.86e-81) {
		tmp = t_1;
	} else if (z <= 1.22e-33) {
		tmp = fma(y, (t / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(1.0 - Float64(y / z)), t, x)
	tmp = 0.0
	if (z <= -1.86e-81)
		tmp = t_1;
	elseif (z <= 1.22e-33)
		tmp = fma(y, Float64(t / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision]}, If[LessEqual[z, -1.86e-81], t$95$1, If[LessEqual[z, 1.22e-33], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8600000000000001e-81 or 1.22e-33 < z

   1. Initial program 76.4%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

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

      8. div-sub N/A

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

      9. *-inverses N/A

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

      10. associate-+l- N/A

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

      11. neg-sub0 N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. mul-1-neg N/A

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

      15. unsub-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower-/.f64 85.5

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

   5. Applied rewrites 85.5%

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

   if -1.8600000000000001e-81 < z < 1.22e-33

   1. Initial program 94.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-rgt-in N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 94.2

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

   4. Applied rewrites 94.2%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 81.8

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

   7. Applied rewrites 81.8%

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

Alternative 7: 76.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+17}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 260000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.85e+17)
   (+ x t)
   (if (<= z 260000000.0) (fma y (/ t a) x) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.85e+17) {
		tmp = x + t;
	} else if (z <= 260000000.0) {
		tmp = fma(y, (t / a), x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.85e+17)
		tmp = Float64(x + t);
	elseif (z <= 260000000.0)
		tmp = fma(y, Float64(t / a), x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.85e+17], N[(x + t), $MachinePrecision], If[LessEqual[z, 260000000.0], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.85e17 or 2.6e8 < z

   1. Initial program 70.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 81.7

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

   5. Applied rewrites 81.7%

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

   if -2.85e17 < z < 2.6e8

   1. Initial program 94.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-rgt-in N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 94.9

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

   4. Applied rewrites 94.9%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 75.5

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

   7. Applied rewrites 75.5%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+17}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 260000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+17}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 8000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.85e+17)
   (+ x t)
   (if (<= z 8000000000.0) (fma (/ y a) t x) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.85e+17) {
		tmp = x + t;
	} else if (z <= 8000000000.0) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.85e+17)
		tmp = Float64(x + t);
	elseif (z <= 8000000000.0)
		tmp = fma(Float64(y / a), t, x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.85e+17], N[(x + t), $MachinePrecision], If[LessEqual[z, 8000000000.0], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.85e17 or 8e9 < z

   1. Initial program 70.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 81.7

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

   5. Applied rewrites 81.7%

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

   if -2.85e17 < z < 8e9

   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

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 74.1

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

   5. Applied rewrites 74.1%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+17}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 8000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{+205}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 5.2e+205) (+ x t) (* (/ t a) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 5.2e+205) {
		tmp = x + t;
	} else {
		tmp = (t / a) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 5.2d+205) then
        tmp = x + t
    else
        tmp = (t / a) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 5.2e+205) {
		tmp = x + t;
	} else {
		tmp = (t / a) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 5.2e+205:
		tmp = x + t
	else:
		tmp = (t / a) * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 5.2e+205)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(t / a) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 5.2e+205)
		tmp = x + t;
	else
		tmp = (t / a) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 5.2e+205], N[(x + t), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.1999999999999998e205

   1. Initial program 83.4%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 63.4

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

   5. Applied rewrites 63.4%

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

   if 5.1999999999999998e205 < y

   1. Initial program 82.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 73.7

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

   5. Applied rewrites 73.7%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 55.4%

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

   10. Applied rewrites 61.9%

       \[\leadsto \frac{t}{a} \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{+205}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.7% accurate, 6.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.3%

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

3. Taylor expanded in z around inf

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

   1. lower-+.f64 59.8

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

5. Applied rewrites 59.8%

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

6. Final simplification 59.8%

   \[\leadsto x + t \]
7. 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 2024254 
(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))))