Average Error: 1.8 → 0.9
Time: 1.5m
Precision: 64
Internal Precision: 128
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{6 + \left(1 - z\right)}\right)\right) + \left(e^{\log \left(\frac{\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(\left(2 - z\right) \cdot 0.9999999999998099 + -1259.1392167224028\right) + \frac{676.5203681218851 \cdot \left(2 - z\right)}{1 - z}\right)}{\left(1 + \left(1 - z\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)}\right)} + \frac{-176.6150291621406 \cdot \left(3 - z\right) + 771.3234287776531 \cdot \left(4 - z\right)}{\left(4 - z\right) \cdot \left(3 - z\right)}\right)\right) \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \left(\sqrt{2} \cdot \sqrt{\pi}\right)\right)\right)\]

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.8

    \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

  2. Simplified0.6

    \[\leadsto \color{blue}{\left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)}\]
  3. Using strategy rm

  4. Applied add-exp-log0.9

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(\color{blue}{e^{\log \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)}} + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
  5. Using strategy rm

  6. Applied frac-add1.3

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(e^{\log \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)} + \color{blue}{\frac{771.3234287776531 \cdot \left(5 - \left(z + 1\right)\right) + \left(1 - \left(z + -2\right)\right) \cdot -176.6150291621406}{\left(1 - \left(z + -2\right)\right) \cdot \left(5 - \left(z + 1\right)\right)}}\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]

  7. Simplified1.3

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(e^{\log \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)} + \frac{\color{blue}{\left(4 - z\right) \cdot 771.3234287776531 + \left(3 - z\right) \cdot -176.6150291621406}}{\left(1 - \left(z + -2\right)\right) \cdot \left(5 - \left(z + 1\right)\right)}\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]

  8. Simplified1.3

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(e^{\log \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)} + \frac{\left(4 - z\right) \cdot 771.3234287776531 + \left(3 - z\right) \cdot -176.6150291621406}{\color{blue}{\left(4 - z\right) \cdot \left(3 - z\right)}}\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
  9. Using strategy rm

  10. Applied sqrt-prod0.9

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\color{blue}{\left(\sqrt{2} \cdot \sqrt{\pi}\right)} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(e^{\log \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)} + \frac{\left(4 - z\right) \cdot 771.3234287776531 + \left(3 - z\right) \cdot -176.6150291621406}{\left(4 - z\right) \cdot \left(3 - z\right)}\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
  11. Using strategy rm

  12. Applied flip-+0.9

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\left(\sqrt{2} \cdot \sqrt{\pi}\right) \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(e^{\log \left(\color{blue}{\frac{0.9999999999998099 \cdot 0.9999999999998099 - \frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}}{0.9999999999998099 - \frac{676.5203681218851}{1 - z}}} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)} + \frac{\left(4 - z\right) \cdot 771.3234287776531 + \left(3 - z\right) \cdot -176.6150291621406}{\left(4 - z\right) \cdot \left(3 - z\right)}\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]

  13. Applied frac-add1.6

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\left(\sqrt{2} \cdot \sqrt{\pi}\right) \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(e^{\log \color{blue}{\left(\frac{\left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(1 - z\right) + 1\right) + \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot -1259.1392167224028}{\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(1 - z\right) + 1\right)}\right)}} + \frac{\left(4 - z\right) \cdot 771.3234287776531 + \left(3 - z\right) \cdot -176.6150291621406}{\left(4 - z\right) \cdot \left(3 - z\right)}\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]

  14. Simplified0.9

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\left(\sqrt{2} \cdot \sqrt{\pi}\right) \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(e^{\log \left(\frac{\color{blue}{\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \left(\frac{676.5203681218851 \cdot \left(2 - z\right)}{1 - z} + \left(\left(2 - z\right) \cdot 0.9999999999998099 + -1259.1392167224028\right)\right)}}{\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(1 - z\right) + 1\right)}\right)} + \frac{\left(4 - z\right) \cdot 771.3234287776531 + \left(3 - z\right) \cdot -176.6150291621406}{\left(4 - z\right) \cdot \left(3 - z\right)}\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]

  15. Final simplification0.9

    \[\leadsto \left(\left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{6 + \left(1 - z\right)}\right)\right) + \left(e^{\log \left(\frac{\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(\left(2 - z\right) \cdot 0.9999999999998099 + -1259.1392167224028\right) + \frac{676.5203681218851 \cdot \left(2 - z\right)}{1 - z}\right)}{\left(1 + \left(1 - z\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)}\right)} + \frac{-176.6150291621406 \cdot \left(3 - z\right) + 771.3234287776531 \cdot \left(4 - z\right)}{\left(4 - z\right) \cdot \left(3 - z\right)}\right)\right) \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \left(\sqrt{2} \cdot \sqrt{\pi}\right)\right)\right)\]

Reproduce

herbie shell --seed 2019004 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- (- 1 z) 1) 7) 0.5) (+ (- (- 1 z) 1) 0.5))) (exp (- (+ (+ (- (- 1 z) 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1 z) 1) 1))) (/ -1259.1392167224028 (+ (- (- 1 z) 1) 2))) (/ 771.3234287776531 (+ (- (- 1 z) 1) 3))) (/ -176.6150291621406 (+ (- (- 1 z) 1) 4))) (/ 12.507343278686905 (+ (- (- 1 z) 1) 5))) (/ -0.13857109526572012 (+ (- (- 1 z) 1) 6))) (/ 9.984369578019572e-06 (+ (- (- 1 z) 1) 7))) (/ 1.5056327351493116e-07 (+ (- (- 1 z) 1) 8))))))

Details

Time bar (total: 1.4m)Debug log

sample2.0s

Algorithm
intervals

simplify118.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

118.0ms
(* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- (- 1 z) 1) 7) 0.5) (+ (- (- 1 z) 1) 0.5))) (exp (- (+ (+ (- (- 1 z) 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1 z) 1) 1))) (/ -1259.1392167224028 (+ (- (- 1 z) 1) 2))) (/ 771.3234287776531 (+ (- (- 1 z) 1) 3))) (/ -176.6150291621406 (+ (- (- 1 z) 1) 4))) (/ 12.507343278686905 (+ (- (- 1 z) 1) 5))) (/ -0.13857109526572012 (+ (- (- 1 z) 1) 6))) (/ 9.984369578019572e-06 (+ (- (- 1 z) 1) 7))) (/ 1.5056327351493116e-07 (+ (- (- 1 z) 1) 8)))))

prune87.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize186.0ms

Local error

Found 4 expressions with local error:

2.6b
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
1.0b
(sqrt (* 2 PI))
1.0b
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
1.0b
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Counts
4 → 50
Calls

4 calls. Slowest were:

10.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
6.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
5.0ms
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))

series63.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

22.0ms
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))
21.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
20.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify4.5s

Counts
25 → 60
Calls

25 calls. Slowest were:

955.0ms
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))
659.0ms
(+ (* (- (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z)))) (+ (- 1 z) 1)) (* (- 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) -1259.1392167224028))
430.0ms
(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1 z)) 3)) (+ (- 1 z) 1)) (* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) -1259.1392167224028))

prune2.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

2.6b
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
1.5b
(exp (log (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))))
1.0b
(sqrt (* 2 PI))
1.0b
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
4 → 57
Calls

4 calls. Slowest were:

6.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
6.0ms
(exp (log (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))))
4.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series74.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

26.0ms
(exp (log (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))))
24.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
23.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
0.0ms
(sqrt (* 2 PI))

simplify4.3s

Counts
33 → 67
Calls

33 calls. Slowest were:

618.0ms
(+ (* (- (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z)))) (+ (- 1 z) 1)) (* (- 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) -1259.1392167224028))
482.0ms
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))
476.0ms
(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1 z)) 3)) (+ (- 1 z) 1)) (* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) -1259.1392167224028))

prune3.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize55.0ms

Local error

Found 4 expressions with local error:

2.6b
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
1.5b
(exp (log (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))))
1.0b
(sqrt (* 2 PI))
1.0b
(/ (+ (* (- 4 z) 771.3234287776531) (* (- 3 z) -176.6150291621406)) (* (- 4 z) (- 3 z)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Counts
4 → 79
Calls

4 calls. Slowest were:

16.0ms
(/ (+ (* (- 4 z) 771.3234287776531) (* (- 3 z) -176.6150291621406)) (* (- 4 z) (- 3 z)))
10.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
9.0ms
(exp (log (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))))

series65.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

24.0ms
(/ (+ (* (- 4 z) 771.3234287776531) (* (- 3 z) -176.6150291621406)) (* (- 4 z) (- 3 z)))
21.0ms
(exp (log (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))))
20.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify7.6s

Counts
57 → 89
Calls

57 calls. Slowest were:

513.0ms
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))
501.0ms
(+ (* (* (- (* 4 4) (* z z)) 771.3234287776531) (+ (* 3 3) (+ (* z z) (* 3 z)))) (* (+ 4 z) (* (- (pow 3 3) (pow z 3)) -176.6150291621406)))
448.0ms
(+ (* (- (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z)))) (+ (- 1 z) 1)) (* (- 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) -1259.1392167224028))

prune4.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

2.6b
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
1.5b
(exp (log (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))))
1.0b
(sqrt PI)
1.0b
(/ (+ (* (- 4 z) 771.3234287776531) (* (- 3 z) -176.6150291621406)) (* (- 4 z) (- 3 z)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Counts
4 → 78
Calls

4 calls. Slowest were:

32.0ms
(/ (+ (* (- 4 z) 771.3234287776531) (* (- 3 z) -176.6150291621406)) (* (- 4 z) (- 3 z)))
12.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
12.0ms
(exp (log (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))))

series79.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

34.0ms
(/ (+ (* (- 4 z) 771.3234287776531) (* (- 3 z) -176.6150291621406)) (* (- 4 z) (- 3 z)))
26.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
19.0ms
(exp (log (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))))
0.0ms
(sqrt PI)

simplify7.2s

Counts
56 → 88
Calls

56 calls. Slowest were:

578.0ms
(+ (* (- (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z)))) (+ (- 1 z) 1)) (* (- 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) -1259.1392167224028))
549.0ms
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))
451.0ms
(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1 z)) 3)) (+ (- 1 z) 1)) (* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) -1259.1392167224028))

prune4.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes578.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch11.0ms

end0.0ms

sample43.1s

Algorithm
intervals