Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B

Percentage Accurate: 81.7% → 99.7%

Time: 2.1s

Alternatives: 3

Speedup: 1.9×

Specification

Math

\[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (* x (/ (* (/ y z) t) t)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	x * (((y / z) * t) / t)
END code

Initial Program: 81.7% accurate, 1.0× speedup

Math

\[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (* x (/ (* (/ y z) t) t)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	x * (((y / z) * t) / t)
END code

Alternative 1: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\left|x\right|, \left|y\right|\right)\\ t_2 := \frac{t\_1}{\left|z\right|}\\ t_3 := \mathsf{min}\left(\left|x\right|, \left|y\right|\right)\\ \mathsf{copysign}\left(1, x\right) \cdot \left(\mathsf{copysign}\left(1, y\right) \cdot \left(\mathsf{copysign}\left(1, z\right) \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq 5 \cdot 10^{+265}:\\ \;\;\;\;t\_3 \cdot t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{\frac{\left|z\right|}{t\_3}}\\ \end{array}\right)\right) \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fabs x) (fabs y)))
       (t_2 (/ t_1 (fabs z)))
       (t_3 (fmin (fabs x) (fabs y))))
  (*
   (copysign 1.0 x)
   (*
    (copysign 1.0 y)
    (*
     (copysign 1.0 z)
     (if (<= t_2 5e+265) (* t_3 t_2) (/ t_1 (/ (fabs z) t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fabs(x), fabs(y));
	double t_2 = t_1 / fabs(z);
	double t_3 = fmin(fabs(x), fabs(y));
	double tmp;
	if (t_2 <= 5e+265) {
		tmp = t_3 * t_2;
	} else {
		tmp = t_1 / (fabs(z) / t_3);
	}
	return copysign(1.0, x) * (copysign(1.0, y) * (copysign(1.0, z) * tmp));
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(Math.abs(x), Math.abs(y));
	double t_2 = t_1 / Math.abs(z);
	double t_3 = fmin(Math.abs(x), Math.abs(y));
	double tmp;
	if (t_2 <= 5e+265) {
		tmp = t_3 * t_2;
	} else {
		tmp = t_1 / (Math.abs(z) / t_3);
	}
	return Math.copySign(1.0, x) * (Math.copySign(1.0, y) * (Math.copySign(1.0, z) * tmp));
}

Python

def code(x, y, z, t):
	t_1 = fmax(math.fabs(x), math.fabs(y))
	t_2 = t_1 / math.fabs(z)
	t_3 = fmin(math.fabs(x), math.fabs(y))
	tmp = 0
	if t_2 <= 5e+265:
		tmp = t_3 * t_2
	else:
		tmp = t_1 / (math.fabs(z) / t_3)
	return math.copysign(1.0, x) * (math.copysign(1.0, y) * (math.copysign(1.0, z) * tmp))

Julia

function code(x, y, z, t)
	t_1 = fmax(abs(x), abs(y))
	t_2 = Float64(t_1 / abs(z))
	t_3 = fmin(abs(x), abs(y))
	tmp = 0.0
	if (t_2 <= 5e+265)
		tmp = Float64(t_3 * t_2);
	else
		tmp = Float64(t_1 / Float64(abs(z) / t_3));
	end
	return Float64(copysign(1.0, x) * Float64(copysign(1.0, y) * Float64(copysign(1.0, z) * tmp)))
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(abs(x), abs(y));
	t_2 = t_1 / abs(z);
	t_3 = min(abs(x), abs(y));
	tmp = 0.0;
	if (t_2 <= 5e+265)
		tmp = t_3 * t_2;
	else
		tmp = t_1 / (abs(z) / t_3);
	end
	tmp_2 = (sign(x) * abs(1.0)) * ((sign(y) * abs(1.0)) * ((sign(z) * abs(1.0)) * tmp));
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Abs[x], $MachinePrecision], N[Abs[y], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[Abs[z], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Abs[x], $MachinePrecision], N[Abs[y], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$2, 5e+265], N[(t$95$3 * t$95$2), $MachinePrecision], N[(t$95$1 / N[(N[Abs[z], $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 y z) < 5.0000000000000002e265

   1. Initial program 81.7%

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

   3. Applied rewrites 92.5%

      \[\leadsto x \cdot \frac{y}{z} \]

   if 5.0000000000000002e265 < (/.f64 y z)

   1. Initial program 81.7%

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

   3. Applied rewrites 91.6%

      \[\leadsto \frac{1}{\frac{z}{x \cdot y}} \]
   4. Step-by-step derivation

   5. Applied rewrites 91.8%

      \[\leadsto \frac{y}{\frac{z}{x}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\left|x\right|, \left|y\right|\right)\\ t_2 := \frac{t\_1}{\left|z\right|}\\ t_3 := \mathsf{min}\left(\left|x\right|, \left|y\right|\right)\\ \mathsf{copysign}\left(1, x\right) \cdot \left(\mathsf{copysign}\left(1, y\right) \cdot \left(\mathsf{copysign}\left(1, z\right) \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq 5 \cdot 10^{+265}:\\ \;\;\;\;t\_3 \cdot t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_3 \cdot t\_1}{\left|z\right|}\\ \end{array}\right)\right) \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fabs x) (fabs y)))
       (t_2 (/ t_1 (fabs z)))
       (t_3 (fmin (fabs x) (fabs y))))
  (*
   (copysign 1.0 x)
   (*
    (copysign 1.0 y)
    (*
     (copysign 1.0 z)
     (if (<= t_2 5e+265) (* t_3 t_2) (/ (* t_3 t_1) (fabs z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fabs(x), fabs(y));
	double t_2 = t_1 / fabs(z);
	double t_3 = fmin(fabs(x), fabs(y));
	double tmp;
	if (t_2 <= 5e+265) {
		tmp = t_3 * t_2;
	} else {
		tmp = (t_3 * t_1) / fabs(z);
	}
	return copysign(1.0, x) * (copysign(1.0, y) * (copysign(1.0, z) * tmp));
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(Math.abs(x), Math.abs(y));
	double t_2 = t_1 / Math.abs(z);
	double t_3 = fmin(Math.abs(x), Math.abs(y));
	double tmp;
	if (t_2 <= 5e+265) {
		tmp = t_3 * t_2;
	} else {
		tmp = (t_3 * t_1) / Math.abs(z);
	}
	return Math.copySign(1.0, x) * (Math.copySign(1.0, y) * (Math.copySign(1.0, z) * tmp));
}

Python

def code(x, y, z, t):
	t_1 = fmax(math.fabs(x), math.fabs(y))
	t_2 = t_1 / math.fabs(z)
	t_3 = fmin(math.fabs(x), math.fabs(y))
	tmp = 0
	if t_2 <= 5e+265:
		tmp = t_3 * t_2
	else:
		tmp = (t_3 * t_1) / math.fabs(z)
	return math.copysign(1.0, x) * (math.copysign(1.0, y) * (math.copysign(1.0, z) * tmp))

Julia

function code(x, y, z, t)
	t_1 = fmax(abs(x), abs(y))
	t_2 = Float64(t_1 / abs(z))
	t_3 = fmin(abs(x), abs(y))
	tmp = 0.0
	if (t_2 <= 5e+265)
		tmp = Float64(t_3 * t_2);
	else
		tmp = Float64(Float64(t_3 * t_1) / abs(z));
	end
	return Float64(copysign(1.0, x) * Float64(copysign(1.0, y) * Float64(copysign(1.0, z) * tmp)))
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(abs(x), abs(y));
	t_2 = t_1 / abs(z);
	t_3 = min(abs(x), abs(y));
	tmp = 0.0;
	if (t_2 <= 5e+265)
		tmp = t_3 * t_2;
	else
		tmp = (t_3 * t_1) / abs(z);
	end
	tmp_2 = (sign(x) * abs(1.0)) * ((sign(y) * abs(1.0)) * ((sign(z) * abs(1.0)) * tmp));
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Abs[x], $MachinePrecision], N[Abs[y], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[Abs[z], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Abs[x], $MachinePrecision], N[Abs[y], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$2, 5e+265], N[(t$95$3 * t$95$2), $MachinePrecision], N[(N[(t$95$3 * t$95$1), $MachinePrecision] / N[Abs[z], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 y z) < 5.0000000000000002e265

   1. Initial program 81.7%

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

   3. Applied rewrites 92.5%

      \[\leadsto x \cdot \frac{y}{z} \]

   if 5.0000000000000002e265 < (/.f64 y z)

   1. Initial program 81.7%

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 92.1%

      \[\leadsto \frac{x \cdot y}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 92.1% accurate, 1.9× speedup

Math

\[\frac{x \cdot y}{z} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (/ (* x y) z))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	(x * y) / z
END code

Derivation

1. Initial program 81.7%

   \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]

2. Taylor expanded in x around 0

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

4. Applied rewrites 92.1%

   \[\leadsto \frac{x \cdot y}{z} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))