Average Error: 1.8 → 0.6
Time: 2.8m
Precision: 64
Internal Precision: 128
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(\log \left(e^{\frac{\left(0.9999999999998099 - \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\left(\left(1 - z\right) \cdot 0.9999999999998099 + 676.5203681218851\right) + \frac{\left(1 - z\right) \cdot -1259.1392167224028}{2 - z}\right)}{\left(0.9999999999998099 - \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(1 - z\right)}}\right) + \left(\frac{-176.6150291621406}{5 - \left(z + 1\right)} + \frac{771.3234287776531}{1 - \left(-2 + z\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{6 + \left(1 - z\right)}\right)\right)\right)\]

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. Initial simplification0.6

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

  4. Applied add-log-exp0.7

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

  5. Applied add-log-exp0.8

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

  6. Applied sum-log0.8

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

  7. Simplified0.6

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

  9. Applied flip-+0.6

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

  10. Applied frac-add1.4

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

  11. Simplified0.6

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

  12. Final simplification0.6

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

Reproduce

herbie shell --seed 2018362 
(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: 1.3m)Debug log

start2.5s

Algorithm
intervals

setup331.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize147.0ms

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)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Counts
4 → 66
Calls

4 calls. Slowest were:

47.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
6.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
4.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series145.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

73.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
40.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
32.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify21.5s

Counts
49 → 76
Calls

49 calls. Slowest were:

1.6s
(* (exp (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))) (exp (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6)))))
1.5s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
1.5s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

prune6.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize59.0ms

Local error

Found 4 expressions with local error:

3.3b
(exp (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 676.5203681218851 (- 1 z))))
2.5b
(+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 676.5203681218851 (- 1 z)))
1.0b
(sqrt (* 2 PI))
1.0b
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Counts
4 → 51
Calls

4 calls. Slowest were:

30.0ms
(exp (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 676.5203681218851 (- 1 z))))
11.0ms
(+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 676.5203681218851 (- 1 z)))
9.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series105.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

40.0ms
(exp (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 676.5203681218851 (- 1 z))))
37.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
27.0ms
(+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 676.5203681218851 (- 1 z)))
0.0ms
(sqrt (* 2 PI))

simplify2.7s

Counts
28 → 61
Calls

28 calls. Slowest were:

357.0ms
(- (+ (* 4116.070392404628 (/ 1 (pow z 3))) (+ (* 1607.5101696843972 (/ 1 (pow z 2))) (* 594.7083996155126 (/ 1 z)))))
268.0ms
(- (+ (* 4116.070392404628 (/ 1 (pow z 3))) (+ (* 1607.5101696843972 (/ 1 (pow z 2))) (* 594.7083996155126 (/ 1 z)))))
261.0ms
(+ (* (- (* 0.9999999999998099 0.9999999999998099) (* (/ -1259.1392167224028 (- 2 z)) (/ -1259.1392167224028 (- 2 z)))) (- 1 z)) (* (- 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) 676.5203681218851))

prune5.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize99.0ms

Local error

Found 4 expressions with local error:

3.3b
(exp (/ (* (+ (/ (* (- 1 z) -1259.1392167224028) (- 2 z)) (+ (* 0.9999999999998099 (- 1 z)) 676.5203681218851)) (- 0.9999999999998099 (/ -1259.1392167224028 (- 2 z)))) (* (- 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (- 1 z))))
2.6b
(+ (/ (* (- 1 z) -1259.1392167224028) (- 2 z)) (+ (* 0.9999999999998099 (- 1 z)) 676.5203681218851))
1.0b
(sqrt (* 2 PI))
1.0b
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Counts
4 → 58
Calls

4 calls. Slowest were:

20.0ms
(+ (/ (* (- 1 z) -1259.1392167224028) (- 2 z)) (+ (* 0.9999999999998099 (- 1 z)) 676.5203681218851))
14.0ms
(exp (/ (* (+ (/ (* (- 1 z) -1259.1392167224028) (- 2 z)) (+ (* 0.9999999999998099 (- 1 z)) 676.5203681218851)) (- 0.9999999999998099 (/ -1259.1392167224028 (- 2 z)))) (* (- 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (- 1 z))))
9.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series160.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

82.0ms
(exp (/ (* (+ (/ (* (- 1 z) -1259.1392167224028) (- 2 z)) (+ (* 0.9999999999998099 (- 1 z)) 676.5203681218851)) (- 0.9999999999998099 (/ -1259.1392167224028 (- 2 z)))) (* (- 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (- 1 z))))
40.0ms
(+ (/ (* (- 1 z) -1259.1392167224028) (- 2 z)) (+ (* 0.9999999999998099 (- 1 z)) 676.5203681218851))
37.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
0.0ms
(sqrt (* 2 PI))

simplify6.7s

Counts
35 → 68
Calls

35 calls. Slowest were:

521.0ms
(* (- 1 (+ z -2)) (- 5 (+ z 1)))
433.0ms
(+ (* (* (- 1 z) -1259.1392167224028) (- (* 0.9999999999998099 (- 1 z)) 676.5203681218851)) (* (- 2 z) (- (* (* 0.9999999999998099 (- 1 z)) (* 0.9999999999998099 (- 1 z))) (* 676.5203681218851 676.5203681218851))))
379.0ms
(exp (/ (+ (/ (* (- 1 z) -1259.1392167224028) (- 2 z)) (+ (* 0.9999999999998099 (- 1 z)) 676.5203681218851)) (- 0.9999999999998099 (/ -1259.1392167224028 (- 2 z)))))

prune6.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize48.0ms

Local error

Found 4 expressions with local error:

2.6b
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
1.0b
(sqrt 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)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

66.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
12.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
9.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series117.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

50.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
35.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
32.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt PI)

simplify21.2s

Counts
48 → 75
Calls

48 calls. Slowest were:

1.6s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
1.6s
(* (* (exp (/ -0.13857109526572012 (- 7 (+ z 1)))) (exp (/ 12.507343278686905 (- 6 (+ z 1))))) (exp (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6)))))
1.5s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

prune6.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes408.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch18.0ms