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

Percentage Accurate: 85.7% → 98.2%

Time: 4.4s

Alternatives: 14

Speedup: 1.0×

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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: 85.7% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.7%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift--.f64 N/A

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

   6. *-commutative N/A

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

   7. +-commutative N/A

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

   8. associate-/l* N/A

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

   9. sub-div N/A

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

   10. *-commutative N/A

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

   11. lower-fma.f64 N/A

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

   12. sub-div N/A

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

   13. lower-/.f64 N/A

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

   14. lift--.f64 N/A

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

   15. lift--.f64 98.2

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

3. Applied rewrites 98.2%

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

Alternative 2: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, 1 - \frac{y}{z}, x\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 42000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma t (- 1.0 (/ y z)) x)))
   (if (<= z -9e+34) t_1 (if (<= z 42000000.0) (fma (/ y (- a z)) t 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 <= -9e+34) {
		tmp = t_1;
	} else if (z <= 42000000.0) {
		tmp = fma((y / (a - z)), t, 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 <= -9e+34)
		tmp = t_1;
	elseif (z <= 42000000.0)
		tmp = fma(Float64(y / Float64(a - z)), t, 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, -9e+34], t$95$1, If[LessEqual[z, 42000000.0], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.0000000000000001e34 or 4.2e7 < z

   1. Initial program 74.4%

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

   2. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. metadata-eval N/A

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

      4. times-frac N/A

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. frac-2neg N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 65.9

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

   4. Applied rewrites 65.9%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 87.0

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

   7. Applied rewrites 87.0%

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

   if -9.0000000000000001e34 < z < 4.2e7

   1. Initial program 95.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 96.7

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

   3. Applied rewrites 96.7%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 87.9%

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

Alternative 3: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, 1 - \frac{y}{z}, x\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma t (- 1.0 (/ y z)) x)))
   (if (<= z -3e+33) t_1 (if (<= z 3.7e-24) (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 <= -3e+33) {
		tmp = t_1;
	} else if (z <= 3.7e-24) {
		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 <= -3e+33)
		tmp = t_1;
	elseif (z <= 3.7e-24)
		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, -3e+33], t$95$1, If[LessEqual[z, 3.7e-24], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999984e33 or 3.69999999999999981e-24 < z

   1. Initial program 75.5%

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

   2. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. metadata-eval N/A

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

      4. times-frac N/A

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. frac-2neg N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 66.2

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

   4. Applied rewrites 66.2%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 86.3

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

   7. Applied rewrites 86.3%

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

   if -2.99999999999999984e33 < z < 3.69999999999999981e-24

   1. Initial program 95.5%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 80.6

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

   4. Applied rewrites 80.6%

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

Alternative 4: 81.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, 1 - \frac{y}{z}, x\right)\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma t (- 1.0 (/ y z)) x)))
   (if (<= z -2.45e+33) t_1 (if (<= z 3.7e-24) (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 <= -2.45e+33) {
		tmp = t_1;
	} else if (z <= 3.7e-24) {
		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 <= -2.45e+33)
		tmp = t_1;
	elseif (z <= 3.7e-24)
		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, -2.45e+33], t$95$1, If[LessEqual[z, 3.7e-24], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45000000000000007e33 or 3.69999999999999981e-24 < z

   1. Initial program 75.5%

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

   2. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. metadata-eval N/A

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

      4. times-frac N/A

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. frac-2neg N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 66.2

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

   4. Applied rewrites 66.2%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 86.3

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

   7. Applied rewrites 86.3%

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

   if -2.45000000000000007e33 < z < 3.69999999999999981e-24

   1. Initial program 95.5%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 77.6

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

   4. Applied rewrites 77.6%

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

Alternative 5: 76.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+34}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+94}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+34)
   (+ x t)
   (if (<= z 1.2e-78)
     (fma t (/ y a) x)
     (if (<= z 2.3e+94) (- x (/ (* y t) z)) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+34) {
		tmp = x + t;
	} else if (z <= 1.2e-78) {
		tmp = fma(t, (y / a), x);
	} else if (z <= 2.3e+94) {
		tmp = x - ((y * t) / z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+34)
		tmp = Float64(x + t);
	elseif (z <= 1.2e-78)
		tmp = fma(t, Float64(y / a), x);
	elseif (z <= 2.3e+94)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+34], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.2e-78], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 2.3e+94], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000003e34 or 2.3e94 < z

   1. Initial program 71.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 80.7%

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

   if -8.5000000000000003e34 < z < 1.2e-78

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 78.7

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

   4. Applied rewrites 78.7%

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

   if 1.2e-78 < z < 2.3e94

   1. Initial program 92.1%

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

   2. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. metadata-eval N/A

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

      4. times-frac N/A

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. frac-2neg N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 67.2

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

   4. Applied rewrites 67.2%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 59.3%

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

Alternative 6: 76.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+34}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;z \leq 1500000000:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+34)
   (+ x t)
   (if (<= z 8.6e-24)
     (fma t (/ y a) x)
     (if (<= z 1500000000.0) (* y (/ t (- a z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+34) {
		tmp = x + t;
	} else if (z <= 8.6e-24) {
		tmp = fma(t, (y / a), x);
	} else if (z <= 1500000000.0) {
		tmp = y * (t / (a - z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+34)
		tmp = Float64(x + t);
	elseif (z <= 8.6e-24)
		tmp = fma(t, Float64(y / a), x);
	elseif (z <= 1500000000.0)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+34], N[(x + t), $MachinePrecision], If[LessEqual[z, 8.6e-24], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1500000000.0], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000003e34 or 1.5e9 < z

   1. Initial program 74.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 77.6%

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

   if -8.5000000000000003e34 < z < 8.6000000000000006e-24

   1. Initial program 95.5%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 77.5

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

   4. Applied rewrites 77.5%

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

   if 8.6000000000000006e-24 < z < 1.5e9

   1. Initial program 96.3%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 49.4

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

   4. Applied rewrites 49.4%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 29.4%

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

Alternative 7: 76.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+34}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;z \leq 1500000000:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+34)
   (+ x t)
   (if (<= z 4.5e-31)
     (fma t (/ y a) x)
     (if (<= z 1500000000.0) (* t (/ y (- a z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+34) {
		tmp = x + t;
	} else if (z <= 4.5e-31) {
		tmp = fma(t, (y / a), x);
	} else if (z <= 1500000000.0) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+34)
		tmp = Float64(x + t);
	elseif (z <= 4.5e-31)
		tmp = fma(t, Float64(y / a), x);
	elseif (z <= 1500000000.0)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+34], N[(x + t), $MachinePrecision], If[LessEqual[z, 4.5e-31], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1500000000.0], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000003e34 or 1.5e9 < z

   1. Initial program 74.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 77.6%

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

   if -8.5000000000000003e34 < z < 4.5000000000000004e-31

   1. Initial program 95.5%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 77.7

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

   4. Applied rewrites 77.7%

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

   if 4.5000000000000004e-31 < z < 1.5e9

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 31.4

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

   4. Applied rewrites 31.4%

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

Alternative 8: 76.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+34}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+34)
   (+ x t)
   (if (<= z 8.6e-24)
     (fma t (/ y a) x)
     (if (<= z 9.5e+15) (* t (- 1.0 (/ y z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+34) {
		tmp = x + t;
	} else if (z <= 8.6e-24) {
		tmp = fma(t, (y / a), x);
	} else if (z <= 9.5e+15) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+34)
		tmp = Float64(x + t);
	elseif (z <= 8.6e-24)
		tmp = fma(t, Float64(y / a), x);
	elseif (z <= 9.5e+15)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+34], N[(x + t), $MachinePrecision], If[LessEqual[z, 8.6e-24], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 9.5e+15], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000003e34 or 9.5e15 < z

   1. Initial program 74.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 77.9%

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

   if -8.5000000000000003e34 < z < 8.6000000000000006e-24

   1. Initial program 95.5%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 77.5

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

   4. Applied rewrites 77.5%

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

   if 8.6000000000000006e-24 < z < 9.5e15

   1. Initial program 95.7%

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

   2. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. metadata-eval N/A

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

      4. times-frac N/A

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. frac-2neg N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 69.9

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

   4. Applied rewrites 69.9%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 31.0

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

   7. Applied rewrites 31.0%

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

Alternative 9: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+34}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;z \leq 800000000:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+34)
   (+ x t)
   (if (<= z 4.5e-31)
     (fma t (/ y a) x)
     (if (<= z 800000000.0) (* t (/ y (- z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+34) {
		tmp = x + t;
	} else if (z <= 4.5e-31) {
		tmp = fma(t, (y / a), x);
	} else if (z <= 800000000.0) {
		tmp = t * (y / -z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+34)
		tmp = Float64(x + t);
	elseif (z <= 4.5e-31)
		tmp = fma(t, Float64(y / a), x);
	elseif (z <= 800000000.0)
		tmp = Float64(t * Float64(y / Float64(-z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+34], N[(x + t), $MachinePrecision], If[LessEqual[z, 4.5e-31], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 800000000.0], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000003e34 or 8e8 < z

   1. Initial program 74.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 77.6%

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

   if -8.5000000000000003e34 < z < 4.5000000000000004e-31

   1. Initial program 95.5%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 77.7

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

   4. Applied rewrites 77.7%

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

   if 4.5000000000000004e-31 < z < 8e8

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 31.4

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

   4. Applied rewrites 31.4%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 21.2

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

   7. Applied rewrites 21.2%

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

Alternative 10: 62.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -105000000:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 800000000:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -105000000.0)
   (+ x t)
   (if (<= z 4.5e-31) x (if (<= z 800000000.0) (* t (/ y (- z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -105000000.0) {
		tmp = x + t;
	} else if (z <= 4.5e-31) {
		tmp = x;
	} else if (z <= 800000000.0) {
		tmp = t * (y / -z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 <= (-105000000.0d0)) then
        tmp = x + t
    else if (z <= 4.5d-31) then
        tmp = x
    else if (z <= 800000000.0d0) then
        tmp = t * (y / -z)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -105000000.0) {
		tmp = x + t;
	} else if (z <= 4.5e-31) {
		tmp = x;
	} else if (z <= 800000000.0) {
		tmp = t * (y / -z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -105000000.0:
		tmp = x + t
	elif z <= 4.5e-31:
		tmp = x
	elif z <= 800000000.0:
		tmp = t * (y / -z)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -105000000.0)
		tmp = Float64(x + t);
	elseif (z <= 4.5e-31)
		tmp = x;
	elseif (z <= 800000000.0)
		tmp = Float64(t * Float64(y / Float64(-z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -105000000.0)
		tmp = x + t;
	elseif (z <= 4.5e-31)
		tmp = x;
	elseif (z <= 800000000.0)
		tmp = t * (y / -z);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -105000000.0], N[(x + t), $MachinePrecision], If[LessEqual[z, 4.5e-31], x, If[LessEqual[z, 800000000.0], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e8 or 8e8 < z

   1. Initial program 75.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 76.8%

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

   if -1.05e8 < z < 4.5000000000000004e-31

   1. Initial program 95.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 49.3%

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

   if 4.5000000000000004e-31 < z < 8e8

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 31.4

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

   4. Applied rewrites 31.4%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 21.2

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

   7. Applied rewrites 21.2%

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

Alternative 11: 61.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -105000000:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 800000000:\\ \;\;\;\;\frac{\left(-t\right) \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -105000000.0)
   (+ x t)
   (if (<= z 4.5e-31) x (if (<= z 800000000.0) (/ (* (- t) y) z) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -105000000.0) {
		tmp = x + t;
	} else if (z <= 4.5e-31) {
		tmp = x;
	} else if (z <= 800000000.0) {
		tmp = (-t * y) / z;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 <= (-105000000.0d0)) then
        tmp = x + t
    else if (z <= 4.5d-31) then
        tmp = x
    else if (z <= 800000000.0d0) then
        tmp = (-t * y) / z
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -105000000.0) {
		tmp = x + t;
	} else if (z <= 4.5e-31) {
		tmp = x;
	} else if (z <= 800000000.0) {
		tmp = (-t * y) / z;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -105000000.0:
		tmp = x + t
	elif z <= 4.5e-31:
		tmp = x
	elif z <= 800000000.0:
		tmp = (-t * y) / z
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -105000000.0)
		tmp = Float64(x + t);
	elseif (z <= 4.5e-31)
		tmp = x;
	elseif (z <= 800000000.0)
		tmp = Float64(Float64(Float64(-t) * y) / z);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -105000000.0)
		tmp = x + t;
	elseif (z <= 4.5e-31)
		tmp = x;
	elseif (z <= 800000000.0)
		tmp = (-t * y) / z;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -105000000.0], N[(x + t), $MachinePrecision], If[LessEqual[z, 4.5e-31], x, If[LessEqual[z, 800000000.0], N[(N[((-t) * y), $MachinePrecision] / z), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e8 or 8e8 < z

   1. Initial program 75.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 76.8%

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

   if -1.05e8 < z < 4.5000000000000004e-31

   1. Initial program 95.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 49.3%

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

   if 4.5000000000000004e-31 < z < 8e8

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 31.4

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

   4. Applied rewrites 31.4%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 21.3

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

   7. Applied rewrites 21.3%

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

Alternative 12: 61.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -105000000:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 112000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -105000000.0) (+ x t) (if (<= z 112000000.0) x (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -105000000.0) {
		tmp = x + t;
	} else if (z <= 112000000.0) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 <= (-105000000.0d0)) then
        tmp = x + t
    else if (z <= 112000000.0d0) then
        tmp = x
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -105000000.0) {
		tmp = x + t;
	} else if (z <= 112000000.0) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -105000000.0:
		tmp = x + t
	elif z <= 112000000.0:
		tmp = x
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -105000000.0)
		tmp = Float64(x + t);
	elseif (z <= 112000000.0)
		tmp = x;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -105000000.0)
		tmp = x + t;
	elseif (z <= 112000000.0)
		tmp = x;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -105000000.0], N[(x + t), $MachinePrecision], If[LessEqual[z, 112000000.0], x, N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e8 or 1.12e8 < z

   1. Initial program 75.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 76.8%

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

   if -1.05e8 < z < 1.12e8

   1. Initial program 95.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 49.4%

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

Alternative 13: 54.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\\ \mathbf{elif}\;t\_1 \leq 10^{+168}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 (- INFINITY)) t (if (<= t_1 1e+168) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t;
	} else if (t_1 <= 1e+168) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t;
	} else if (t_1 <= 1e+168) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t
	elif t_1 <= 1e+168:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t;
	elseif (t_1 <= 1e+168)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t;
	elseif (t_1 <= 1e+168)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t, If[LessEqual[t$95$1, 1e+168], x, t]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 9.9999999999999993e167 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 48.9%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 85.4

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

   4. Applied rewrites 85.4%

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

   5. Taylor expanded in z around inf

      \[\leadsto t \]
   6. Step-by-step derivation

   7. Applied rewrites 29.3%

      \[\leadsto t \]

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 9.9999999999999993e167

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 63.6%

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

Alternative 14: 49.9% accurate, 15.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.7%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 49.9%

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

Reproduce

herbie shell --seed 2025120 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64
  (+ x (/ (* (- y z) t) (- a z))))