\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

↓

\[\frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}}\]

\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}

↓

\frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}}

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r434198 = x;
        double r434199 = y;
        double r434200 = 2.0;
        double r434201 = z;
        double r434202 = t;
        double r434203 = a;
        double r434204 = r434202 + r434203;
        double r434205 = sqrt(r434204);
        double r434206 = r434201 * r434205;
        double r434207 = r434206 / r434202;
        double r434208 = b;
        double r434209 = c;
        double r434210 = r434208 - r434209;
        double r434211 = 5.0;
        double r434212 = 6.0;
        double r434213 = r434211 / r434212;
        double r434214 = r434203 + r434213;
        double r434215 = 3.0;
        double r434216 = r434202 * r434215;
        double r434217 = r434200 / r434216;
        double r434218 = r434214 - r434217;
        double r434219 = r434210 * r434218;
        double r434220 = r434207 - r434219;
        double r434221 = r434200 * r434220;
        double r434222 = exp(r434221);
        double r434223 = r434199 * r434222;
        double r434224 = r434198 + r434223;
        double r434225 = r434198 / r434224;
        return r434225;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r434226 = x;
        double r434227 = y;
        double r434228 = 2.0;
        double r434229 = z;
        double r434230 = t;
        double r434231 = a;
        double r434232 = r434230 + r434231;
        double r434233 = sqrt(r434232);
        double r434234 = r434229 * r434233;
        double r434235 = r434234 / r434230;
        double r434236 = b;
        double r434237 = c;
        double r434238 = r434236 - r434237;
        double r434239 = 5.0;
        double r434240 = 6.0;
        double r434241 = r434239 / r434240;
        double r434242 = r434231 + r434241;
        double r434243 = 3.0;
        double r434244 = r434230 * r434243;
        double r434245 = r434228 / r434244;
        double r434246 = r434242 - r434245;
        double r434247 = r434238 * r434246;
        double r434248 = r434235 - r434247;
        double r434249 = exp(r434248);
        double r434250 = log(r434249);
        double r434251 = r434228 * r434250;
        double r434252 = exp(r434251);
        double r434253 = r434227 * r434252;
        double r434254 = r434226 + r434253;
        double r434255 = r434226 / r434254;
        return r434255;
}

Target

Original	3.8
Target	3.1
Herbie	3.8

\[\begin{array}{l} \mathbf{if}\;t \lt -2.118326644891581057561884576920117070548 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.8333333333333333703407674875052180141211 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t \lt 5.196588770651547088010424937268931048836 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(3 \cdot t\right) \cdot \left(a - \frac{5}{6}\right)\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot \left(a - \frac{5}{6}\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array}\]

Derivation

Initial program 3.8
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Using strategy rm
Applied add-log-exp8.0
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}\right)}}\]
Applied add-log-exp16.3
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\log \left(e^{\frac{z \cdot \sqrt{t + a}}{t}}\right)} - \log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)\right)}}\]
Applied diff-log16.3
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\log \left(\frac{e^{\frac{z \cdot \sqrt{t + a}}{t}}}{e^{\left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}}\right)}}}\]
Simplified3.8
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \color{blue}{\left(e^{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}}}\]
Final simplification3.8
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}}\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64

  :herbie-target
  (if (< t -2.118326644891581e-50) (/ x (+ x (* y (exp (* 2 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b))))))) (if (< t 5.196588770651547e-123) (/ x (+ x (* y (exp (* 2 (/ (- (* (* z (sqrt (+ t a))) (* (* 3 t) (- a (/ 5 6)))) (* (- (* (+ (/ 5 6) a) (* 3 t)) 2) (* (- a (/ 5 6)) (* (- b c) t)))) (* (* (* t t) 3) (- a (/ 5 6))))))))) (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3))))))))))))

  (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3)))))))))))

Error

Try it out

Target

Derivation

Reproduce

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