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

Percentage Accurate: 85.1% → 99.4%

Time: 6.2s

Alternatives: 10

Speedup: 0.3×

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: 85.1% 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

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: 99.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot t}{a - z}\\ t_2 := \sqrt[3]{y - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+301}\right):\\ \;\;\;\;\mathsf{fma}\left({t\_2}^{2}, t\_2 \cdot \frac{t}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) t) (- a z)))) (t_2 (cbrt (- y z))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+301)))
     (fma (pow t_2 2.0) (* t_2 (/ t (- a z))) x)
     t_1)))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * t) / (a - z));
	double t_2 = cbrt((y - z));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+301)) {
		tmp = fma(pow(t_2, 2.0), (t_2 * (t / (a - z))), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)))
	t_2 = cbrt(Float64(y - z))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+301))
		tmp = fma((t_2 ^ 2.0), Float64(t_2 * Float64(t / Float64(a - z))), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(y - z), $MachinePrecision], 1/3], $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+301]], $MachinePrecision]], N[(N[Power[t$95$2, 2.0], $MachinePrecision] * N[(t$95$2 * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))) < -inf.0 or 1.00000000000000005e301 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

   1. Initial program 29.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. add-cube-cbrt N/A

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \sqrt[3]{y - z}\right)} \cdot \frac{t}{a - z} + x \]

      7. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \left(\sqrt[3]{y - z} \cdot \frac{t}{a - z}\right)} + x \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right)} \]

      9. pow2 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{y - z}\right)}^{2}}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right) \]

      10. lower-pow.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{y - z}\right)}^{2}}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right) \]

      11. lower-cbrt.f64 N/A

          \[\leadsto \mathsf{fma}\left({\color{blue}{\left(\sqrt[3]{y - z}\right)}}^{2}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{y - z}\right)}^{2}, \color{blue}{\sqrt[3]{y - z} \cdot \frac{t}{a - z}}, x\right) \]

      13. lower-cbrt.f64 N/A

          \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{y - z}\right)}^{2}, \color{blue}{\sqrt[3]{y - z}} \cdot \frac{t}{a - z}, x\right) \]

      14. lower-/.f64 98.6

          \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{y - z}\right)}^{2}, \sqrt[3]{y - z} \cdot \color{blue}{\frac{t}{a - z}}, x\right) \]

   4. Applied rewrites 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{y - z}\right)}^{2}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right)} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))) < 1.00000000000000005e301

   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 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty \lor \neg \left(x + \frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+301}\right):\\ \;\;\;\;\mathsf{fma}\left({\left(\sqrt[3]{y - z}\right)}^{2}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{a - z} \cdot \left(y - z\right)\\ t_2 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_2 \leq -500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+71}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a - z}, -t, x\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+301}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ t (- a z)) (- y z))) (t_2 (/ (* (- y z) t) (- a z))))
   (if (<= t_2 -500000000000.0)
     t_1
     (if (<= t_2 1e+71)
       (fma (/ z (- a z)) (- t) x)
       (if (<= t_2 1e+301) (+ x (/ (* y t) (- a z))) 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 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -500000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+71) {
		tmp = fma((z / (a - z)), -t, x);
	} else if (t_2 <= 1e+301) {
		tmp = x + ((y * t) / (a - z));
	} 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(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= -500000000000.0)
		tmp = t_1;
	elseif (t_2 <= 1e+71)
		tmp = fma(Float64(z / Float64(a - z)), Float64(-t), x);
	elseif (t_2 <= 1e+301)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	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[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -500000000000.0], t$95$1, If[LessEqual[t$95$2, 1e+71], N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] * (-t) + x), $MachinePrecision], If[LessEqual[t$95$2, 1e+301], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -5e11 or 1.00000000000000005e301 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 53.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 90.8%

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

   if -5e11 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 1e71

   1. Initial program 99.9%

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

   5. Applied rewrites 90.7%

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

   if 1e71 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 1.00000000000000005e301

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 83.6%

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

Alternative 3: 95.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+177} \lor \neg \left(t\_1 \leq 10^{+301}\right):\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (or (<= t_1 -5e+177) (not (<= t_1 1e+301)))
     (* (/ t (- a z)) (- y z))
     (+ x t_1))))

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 <= -5e+177) || !(t_1 <= 1e+301)) {
		tmp = (t / (a - z)) * (y - z);
	} else {
		tmp = x + t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = ((y - z) * t) / (a - z)
    if ((t_1 <= (-5d+177)) .or. (.not. (t_1 <= 1d+301))) then
        tmp = (t / (a - z)) * (y - z)
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -5e+177) || !(t_1 <= 1e+301)) {
		tmp = (t / (a - z)) * (y - z);
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if (t_1 <= -5e+177) or not (t_1 <= 1e+301):
		tmp = (t / (a - z)) * (y - z)
	else:
		tmp = x + t_1
	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 <= -5e+177) || !(t_1 <= 1e+301))
		tmp = Float64(Float64(t / Float64(a - z)) * Float64(y - z));
	else
		tmp = Float64(x + t_1);
	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 <= -5e+177) || ~((t_1 <= 1e+301)))
		tmp = (t / (a - z)) * (y - z);
	else
		tmp = x + t_1;
	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[Or[LessEqual[t$95$1, -5e+177], N[Not[LessEqual[t$95$1, 1e+301]], $MachinePrecision]], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -5.0000000000000003e177 or 1.00000000000000005e301 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 36.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 92.2%

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

   if -5.0000000000000003e177 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 1.00000000000000005e301

   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 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -5 \cdot 10^{+177} \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+301}\right):\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -500000000000 \lor \neg \left(t\_1 \leq 10^{+60}\right):\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a - z}, -t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (or (<= t_1 -500000000000.0) (not (<= t_1 1e+60)))
     (* (/ t (- a z)) (- y z))
     (fma (/ z (- a z)) (- t) x))))

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 <= -500000000000.0) || !(t_1 <= 1e+60)) {
		tmp = (t / (a - z)) * (y - z);
	} else {
		tmp = fma((z / (a - z)), -t, x);
	}
	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 <= -500000000000.0) || !(t_1 <= 1e+60))
		tmp = Float64(Float64(t / Float64(a - z)) * Float64(y - z));
	else
		tmp = fma(Float64(z / Float64(a - z)), Float64(-t), x);
	end
	return 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[Or[LessEqual[t$95$1, -500000000000.0], N[Not[LessEqual[t$95$1, 1e+60]], $MachinePrecision]], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] * (-t) + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -5e11 or 9.9999999999999995e59 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 62.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 84.4%

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

   if -5e11 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 9.9999999999999995e59

   1. Initial program 99.9%

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

   5. Applied rewrites 91.2%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -500000000000 \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+60}\right):\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a - z}, -t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-132} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-123}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (or (<= t_1 -1e-132) (not (<= t_1 2e-123))) (+ x t) x)))

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 <= -1e-132) || !(t_1 <= 2e-123)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = ((y - z) * t) / (a - z)
    if ((t_1 <= (-1d-132)) .or. (.not. (t_1 <= 2d-123))) then
        tmp = x + t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -1e-132) || !(t_1 <= 2e-123)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if (t_1 <= -1e-132) or not (t_1 <= 2e-123):
		tmp = x + t
	else:
		tmp = x
	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 <= -1e-132) || !(t_1 <= 2e-123))
		tmp = Float64(x + t);
	else
		tmp = x;
	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 <= -1e-132) || ~((t_1 <= 2e-123)))
		tmp = x + t;
	else
		tmp = x;
	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[Or[LessEqual[t$95$1, -1e-132], N[Not[LessEqual[t$95$1, 2e-123]], $MachinePrecision]], N[(x + t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -9.9999999999999999e-133 or 2.0000000000000001e-123 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 76.1%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 53.7%

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

   if -9.9999999999999999e-133 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 2.0000000000000001e-123

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 90.4%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -1 \cdot 10^{-132} \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 2 \cdot 10^{-123}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.012 \lor \neg \left(a \leq 4.2\right):\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.012) (not (<= a 4.2)))
   (fma t (/ (- y z) a) x)
   (fma (/ (- z y) z) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.012) || !(a <= 4.2)) {
		tmp = fma(t, ((y - z) / a), x);
	} else {
		tmp = fma(((z - y) / z), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.012) || !(a <= 4.2))
		tmp = fma(t, Float64(Float64(y - z) / a), x);
	else
		tmp = fma(Float64(Float64(z - y) / z), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.012], N[Not[LessEqual[a, 4.2]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.012 or 4.20000000000000018 < a

   1. Initial program 85.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. add-cube-cbrt N/A

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \sqrt[3]{y - z}\right)} \cdot \frac{t}{a - z} + x \]

      7. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \left(\sqrt[3]{y - z} \cdot \frac{t}{a - z}\right)} + x \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right)} \]

      9. pow2 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{y - z}\right)}^{2}}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right) \]

      10. lower-pow.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{y - z}\right)}^{2}}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right) \]

      11. lower-cbrt.f64 N/A

          \[\leadsto \mathsf{fma}\left({\color{blue}{\left(\sqrt[3]{y - z}\right)}}^{2}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{y - z}\right)}^{2}, \color{blue}{\sqrt[3]{y - z} \cdot \frac{t}{a - z}}, x\right) \]

      13. lower-cbrt.f64 N/A

          \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{y - z}\right)}^{2}, \color{blue}{\sqrt[3]{y - z}} \cdot \frac{t}{a - z}, x\right) \]

      14. lower-/.f64 95.9

          \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{y - z}\right)}^{2}, \sqrt[3]{y - z} \cdot \color{blue}{\frac{t}{a - z}}, x\right) \]

   4. Applied rewrites 95.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{y - z}\right)}^{2}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right)} \]

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 85.0%

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

   if -0.012 < a < 4.20000000000000018

   1. Initial program 82.7%

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

   3. Taylor expanded in a around 0

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

   5. Applied rewrites 87.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.012 \lor \neg \left(a \leq 4.2\right):\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z}, t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+69} \lor \neg \left(z \leq 1.45 \cdot 10^{-25}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e+69) (not (<= z 1.45e-25)))
   (+ x t)
   (fma (- y z) (/ t a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+69) || !(z <= 1.45e-25)) {
		tmp = x + t;
	} else {
		tmp = fma((y - z), (t / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e+69) || !(z <= 1.45e-25))
		tmp = Float64(x + t);
	else
		tmp = fma(Float64(y - z), Float64(t / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e+69], N[Not[LessEqual[z, 1.45e-25]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000008e69 or 1.45e-25 < z

   1. Initial program 72.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 79.9%

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

   if -1.15000000000000008e69 < z < 1.45e-25

   1. Initial program 94.9%

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

   5. Applied rewrites 78.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+69} \lor \neg \left(z \leq 1.45 \cdot 10^{-25}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+68} \lor \neg \left(z \leq 1.45 \cdot 10^{-25}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.5e+68) (not (<= z 1.45e-25)))
   (+ x t)
   (fma t (/ (- y z) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+68) || !(z <= 1.45e-25)) {
		tmp = x + t;
	} else {
		tmp = fma(t, ((y - z) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.5e+68) || !(z <= 1.45e-25))
		tmp = Float64(x + t);
	else
		tmp = fma(t, Float64(Float64(y - z) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.5e+68], N[Not[LessEqual[z, 1.45e-25]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.49999999999999966e68 or 1.45e-25 < z

   1. Initial program 72.7%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 79.3%

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

   if -8.49999999999999966e68 < z < 1.45e-25

   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

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. add-cube-cbrt N/A

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \sqrt[3]{y - z}\right)} \cdot \frac{t}{a - z} + x \]

      7. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \left(\sqrt[3]{y - z} \cdot \frac{t}{a - z}\right)} + x \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right)} \]

      9. pow2 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{y - z}\right)}^{2}}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right) \]

      10. lower-pow.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{y - z}\right)}^{2}}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right) \]

      11. lower-cbrt.f64 N/A

          \[\leadsto \mathsf{fma}\left({\color{blue}{\left(\sqrt[3]{y - z}\right)}}^{2}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{y - z}\right)}^{2}, \color{blue}{\sqrt[3]{y - z} \cdot \frac{t}{a - z}}, x\right) \]

      13. lower-cbrt.f64 N/A

          \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{y - z}\right)}^{2}, \color{blue}{\sqrt[3]{y - z}} \cdot \frac{t}{a - z}, x\right) \]

      14. lower-/.f64 96.6

          \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{y - z}\right)}^{2}, \sqrt[3]{y - z} \cdot \color{blue}{\frac{t}{a - z}}, x\right) \]

   4. Applied rewrites 96.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{y - z}\right)}^{2}, \sqrt[3]{y - z} \cdot \frac{t}{a - z}, x\right)} \]

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 78.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+68} \lor \neg \left(z \leq 1.45 \cdot 10^{-25}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+21} \lor \neg \left(z \leq 1.18 \cdot 10^{-25}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.2e+21) (not (<= z 1.18e-25))) (+ x t) (fma (/ y a) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.2e+21) || !(z <= 1.18e-25)) {
		tmp = x + t;
	} else {
		tmp = fma((y / a), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.2e+21) || !(z <= 1.18e-25))
		tmp = Float64(x + t);
	else
		tmp = fma(Float64(y / a), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.2e+21], N[Not[LessEqual[z, 1.18e-25]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e21 or 1.1800000000000001e-25 < z

   1. Initial program 74.1%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 76.8%

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

   if -6.2e21 < z < 1.1800000000000001e-25

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 77.9%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+21} \lor \neg \left(z \leq 1.18 \cdot 10^{-25}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.1% accurate, 26.0× speedup

Math

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

FPCore

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

C

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

Fortran

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 84.1%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 49.4%

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

Developer Target 1: 99.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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) :: 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 2025021 
(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))))