Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 69.5% → 91.2%

Time: 9.2s

Alternatives: 13

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(y - z, t\_1, x\right)\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-217}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}, -1, t\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     (fma (- y z) t_1 x)
     (if (<= t_2 -2e-217)
       t_2
       (if (<= t_2 0.0)
         (fma (/ (* (- t x) (- y a)) z) -1.0 t)
         (if (<= t_2 5e+305) t_2 (+ (* (- y z) t_1) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma((y - z), t_1, x);
	} else if (t_2 <= -2e-217) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = fma((((t - x) * (y - a)) / z), -1.0, t);
	} else if (t_2 <= 5e+305) {
		tmp = t_2;
	} else {
		tmp = ((y - z) * t_1) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(Float64(y - z), t_1, x);
	elseif (t_2 <= -2e-217)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = fma(Float64(Float64(Float64(t - x) * Float64(y - a)) / z), -1.0, t);
	elseif (t_2 <= 5e+305)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(y - z) * t_1) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision], If[LessEqual[t$95$2, -2e-217], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * -1.0 + t), $MachinePrecision], If[LessEqual[t$95$2, 5e+305], t$95$2, N[(N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision] + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 38.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 76.9

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

   4. Applied rewrites 76.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2.00000000000000016e-217 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.00000000000000009e305

   1. Initial program 98.3%

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

   if -2.00000000000000016e-217 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 8.8%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   5. Applied rewrites 99.6%

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

   if 5.00000000000000009e305 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 47.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. associate-/l* N/A

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

      10. sub-div N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-div N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. lift--.f64 86.3

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

   4. Applied rewrites 86.3%

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

Alternative 2: 91.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-217}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}, -1, t\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-217)
       t_2
       (if (<= t_2 0.0)
         (fma (/ (* (- t x) (- y a)) z) -1.0 t)
         (if (<= t_2 5e+305) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-217) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = fma((((t - x) * (y - a)) / z), -1.0, t);
	} else if (t_2 <= 5e+305) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-217)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = fma(Float64(Float64(Float64(t - x) * Float64(y - a)) / z), -1.0, t);
	elseif (t_2 <= 5e+305)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-217], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * -1.0 + t), $MachinePrecision], If[LessEqual[t$95$2, 5e+305], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 5.00000000000000009e305 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 42.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 81.6

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

   4. Applied rewrites 81.6%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2.00000000000000016e-217 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.00000000000000009e305

   1. Initial program 98.3%

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

   if -2.00000000000000016e-217 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 8.8%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   5. Applied rewrites 99.6%

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

Alternative 3: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+102} \lor \neg \left(z \leq 6.4 \cdot 10^{+143}\right):\\ \;\;\;\;\mathsf{fma}\left(-y, \frac{t - x}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+102) (not (<= z 6.4e+143)))
   (fma (- y) (/ (- t x) z) t)
   (fma (- y z) (/ (- t x) (- a z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+102) || !(z <= 6.4e+143)) {
		tmp = fma(-y, ((t - x) / z), t);
	} else {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+102) || !(z <= 6.4e+143))
		tmp = fma(Float64(-y), Float64(Float64(t - x) / z), t);
	else
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+102], N[Not[LessEqual[z, 6.4e+143]], $MachinePrecision]], N[((-y) * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4999999999999999e102 or 6.40000000000000033e143 < z

   1. Initial program 33.2%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 52.1

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

   5. Applied rewrites 52.1%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 80.5

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

   8. Applied rewrites 80.5%

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

   if -1.4999999999999999e102 < z < 6.40000000000000033e143

   1. Initial program 85.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 86.0

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

   4. Applied rewrites 86.0%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+102} \lor \neg \left(z \leq 6.4 \cdot 10^{+143}\right):\\ \;\;\;\;\mathsf{fma}\left(-y, \frac{t - x}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+102}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}, -1, t\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, \frac{t - x}{z}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+102)
   (fma (/ (* (- t x) (- y a)) z) -1.0 t)
   (if (<= z 6.4e+143)
     (fma (- y z) (/ (- t x) (- a z)) x)
     (fma (- y) (/ (- t x) z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+102) {
		tmp = fma((((t - x) * (y - a)) / z), -1.0, t);
	} else if (z <= 6.4e+143) {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	} else {
		tmp = fma(-y, ((t - x) / z), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+102)
		tmp = fma(Float64(Float64(Float64(t - x) * Float64(y - a)) / z), -1.0, t);
	elseif (z <= 6.4e+143)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	else
		tmp = fma(Float64(-y), Float64(Float64(t - x) / z), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+102], N[(N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * -1.0 + t), $MachinePrecision], If[LessEqual[z, 6.4e+143], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[((-y) * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4999999999999999e102

   1. Initial program 43.9%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   5. Applied rewrites 79.9%

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

   if -1.4999999999999999e102 < z < 6.40000000000000033e143

   1. Initial program 85.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 86.0

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

   4. Applied rewrites 86.0%

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

   if 6.40000000000000033e143 < z

   1. Initial program 23.6%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 44.8

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

   5. Applied rewrites 44.8%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 81.2

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

   8. Applied rewrites 81.2%

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

Alternative 5: 72.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+74} \lor \neg \left(z \leq 5.6 \cdot 10^{+76}\right):\\ \;\;\;\;\mathsf{fma}\left(-y, \frac{t - x}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e+74) (not (<= z 5.6e+76)))
   (fma (- y) (/ (- t x) z) t)
   (fma (- t x) (/ (- y z) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e+74) || !(z <= 5.6e+76)) {
		tmp = fma(-y, ((t - x) / z), t);
	} else {
		tmp = fma((t - x), ((y - z) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e+74) || !(z <= 5.6e+76))
		tmp = fma(Float64(-y), Float64(Float64(t - x) / z), t);
	else
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.8e+74], N[Not[LessEqual[z, 5.6e+76]], $MachinePrecision]], N[((-y) * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.80000000000000017e74 or 5.5999999999999997e76 < z

   1. Initial program 37.1%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 53.8

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

   5. Applied rewrites 53.8%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 78.3

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

   8. Applied rewrites 78.3%

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

   if -4.80000000000000017e74 < z < 5.5999999999999997e76

   1. Initial program 87.9%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 75.5

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

   5. Applied rewrites 75.5%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+74} \lor \neg \left(z \leq 5.6 \cdot 10^{+76}\right):\\ \;\;\;\;\mathsf{fma}\left(-y, \frac{t - x}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -54000000000 \lor \neg \left(z \leq 1.25 \cdot 10^{-43}\right):\\ \;\;\;\;\mathsf{fma}\left(-y, \frac{t - x}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -54000000000.0) (not (<= z 1.25e-43)))
   (fma (- y) (/ (- t x) z) t)
   (fma y (/ (- t x) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -54000000000.0) || !(z <= 1.25e-43)) {
		tmp = fma(-y, ((t - x) / z), t);
	} else {
		tmp = fma(y, ((t - x) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -54000000000.0) || !(z <= 1.25e-43))
		tmp = fma(Float64(-y), Float64(Float64(t - x) / z), t);
	else
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -54000000000.0], N[Not[LessEqual[z, 1.25e-43]], $MachinePrecision]], N[((-y) * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4e10 or 1.25000000000000005e-43 < z

   1. Initial program 48.5%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 49.4

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

   5. Applied rewrites 49.4%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 68.9

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

   8. Applied rewrites 68.9%

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

   if -5.4e10 < z < 1.25000000000000005e-43

   1. Initial program 91.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 72.7

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

   5. Applied rewrites 72.7%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -54000000000 \lor \neg \left(z \leq 1.25 \cdot 10^{-43}\right):\\ \;\;\;\;\mathsf{fma}\left(-y, \frac{t - x}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+74} \lor \neg \left(z \leq 2.1 \cdot 10^{+32}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.9e+74) (not (<= z 2.1e+32)))
   (* (- t) (/ (- y z) z))
   (fma y (/ (- t x) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.9e+74) || !(z <= 2.1e+32)) {
		tmp = -t * ((y - z) / z);
	} else {
		tmp = fma(y, ((t - x) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.9e+74) || !(z <= 2.1e+32))
		tmp = Float64(Float64(-t) * Float64(Float64(y - z) / z));
	else
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.9e+74], N[Not[LessEqual[z, 2.1e+32]], $MachinePrecision]], N[((-t) * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.90000000000000008e74 or 2.1000000000000001e32 < z

   1. Initial program 42.1%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 52.3

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

   5. Applied rewrites 52.3%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 57.9

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

   8. Applied rewrites 57.9%

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

   if -3.90000000000000008e74 < z < 2.1000000000000001e32

   1. Initial program 88.3%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 66.4

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

   5. Applied rewrites 66.4%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+74} \lor \neg \left(z \leq 2.1 \cdot 10^{+32}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+74}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y - z}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} - 1\right) \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.9e+74)
   (* (- t) (/ (- y z) z))
   (if (<= z 2.1e+32) (fma y (/ (- t x) a) x) (* (- (/ y z) 1.0) (- t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.9e+74) {
		tmp = -t * ((y - z) / z);
	} else if (z <= 2.1e+32) {
		tmp = fma(y, ((t - x) / a), x);
	} else {
		tmp = ((y / z) - 1.0) * -t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.9e+74)
		tmp = Float64(Float64(-t) * Float64(Float64(y - z) / z));
	elseif (z <= 2.1e+32)
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	else
		tmp = Float64(Float64(Float64(y / z) - 1.0) * Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.9e+74], N[((-t) * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+32], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(y / z), $MachinePrecision] - 1.0), $MachinePrecision] * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.90000000000000008e74

   1. Initial program 45.3%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 59.2

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

   5. Applied rewrites 59.2%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 61.4

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

   8. Applied rewrites 61.4%

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

   if -3.90000000000000008e74 < z < 2.1000000000000001e32

   1. Initial program 88.3%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 66.4

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

   5. Applied rewrites 66.4%

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

   if 2.1000000000000001e32 < z

   1. Initial program 39.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 47.5

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

   5. Applied rewrites 47.5%

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

   6. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 55.5

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

   8. Applied rewrites 55.5%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+74}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y - z}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} - 1\right) \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+75) t (if (<= z 3.8e+143) (fma y (/ (- t x) a) x) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+75) {
		tmp = t;
	} else if (z <= 3.8e+143) {
		tmp = fma(y, ((t - x) / a), x);
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+75)
		tmp = t;
	elseif (z <= 3.8e+143)
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+75], t, If[LessEqual[z, 3.8e+143], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e75 or 3.8e143 < z

   1. Initial program 34.7%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 54.0%

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

   if -1.2e75 < z < 3.8e143

   1. Initial program 86.4%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 63.6

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

   5. Applied rewrites 63.6%

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

Alternative 10: 41.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+75} \lor \neg \left(z \leq 7 \cdot 10^{+32}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e+75) (not (<= z 7e+32))) t (* (- t x) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+75) || !(z <= 7e+32)) {
		tmp = t;
	} else {
		tmp = (t - x) * (y / a);
	}
	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 <= (-1.2d+75)) .or. (.not. (z <= 7d+32))) then
        tmp = t
    else
        tmp = (t - x) * (y / a)
    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 <= -1.2e+75) || !(z <= 7e+32)) {
		tmp = t;
	} else {
		tmp = (t - x) * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e+75) or not (z <= 7e+32):
		tmp = t
	else:
		tmp = (t - x) * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e+75) || !(z <= 7e+32))
		tmp = t;
	else
		tmp = Float64(Float64(t - x) * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.2e+75) || ~((z <= 7e+32)))
		tmp = t;
	else
		tmp = (t - x) * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e+75], N[Not[LessEqual[z, 7e+32]], $MachinePrecision]], t, N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e75 or 7.0000000000000002e32 < z

   1. Initial program 42.1%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 48.8%

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

   if -1.2e75 < z < 7.0000000000000002e32

   1. Initial program 88.3%

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

   3. Taylor expanded in y around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 57.0

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

   5. Applied rewrites 57.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 42.8%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lower-/.f64 44.5

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

   10. Applied rewrites 44.5%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+75} \lor \neg \left(z \leq 7 \cdot 10^{+32}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+75} \lor \neg \left(z \leq 5.2 \cdot 10^{+32}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e+75) (not (<= z 5.2e+32))) t (* t (/ y (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+75) || !(z <= 5.2e+32)) {
		tmp = t;
	} else {
		tmp = t * (y / (a - z));
	}
	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 <= (-1.2d+75)) .or. (.not. (z <= 5.2d+32))) then
        tmp = t
    else
        tmp = t * (y / (a - z))
    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 <= -1.2e+75) || !(z <= 5.2e+32)) {
		tmp = t;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e+75) or not (z <= 5.2e+32):
		tmp = t
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e+75) || !(z <= 5.2e+32))
		tmp = t;
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.2e+75) || ~((z <= 5.2e+32)))
		tmp = t;
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e+75], N[Not[LessEqual[z, 5.2e+32]], $MachinePrecision]], t, N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e75 or 5.2000000000000004e32 < z

   1. Initial program 42.1%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 48.8%

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

   if -1.2e75 < z < 5.2000000000000004e32

   1. Initial program 88.3%

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

   3. Taylor expanded in y around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 57.0

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

   5. Applied rewrites 57.0%

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

   6. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 33.0

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

   8. Applied rewrites 33.0%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+75} \lor \neg \left(z \leq 5.2 \cdot 10^{+32}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -90000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -90000000000.0) x (if (<= a 1.55e-7) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -90000000000.0) {
		tmp = x;
	} else if (a <= 1.55e-7) {
		tmp = 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) :: tmp
    if (a <= (-90000000000.0d0)) then
        tmp = x
    else if (a <= 1.55d-7) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -90000000000.0) {
		tmp = x;
	} else if (a <= 1.55e-7) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -90000000000.0:
		tmp = x
	elif a <= 1.55e-7:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -90000000000.0)
		tmp = x;
	elseif (a <= 1.55e-7)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -90000000000.0)
		tmp = x;
	elseif (a <= 1.55e-7)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -90000000000.0], x, If[LessEqual[a, 1.55e-7], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -9e10 or 1.55e-7 < a

   1. Initial program 69.6%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 43.1%

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

   if -9e10 < a < 1.55e-7

   1. Initial program 71.4%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 32.6%

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

Alternative 13: 24.4% accurate, 29.0× speedup

Math

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

FPCore

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

C

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

Fortran

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 = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.6%

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

3. Taylor expanded in z around inf

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

5. Applied rewrites 23.4%

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

Developer Target 1: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} 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 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2025037 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -125361310560950360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- t (* (/ y z) (- t x))) (if (< z 44467023691138110000000000000000000000000000000000000000000000000) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x))))))

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