Average Error: 1.8 → 0.6
Time: 2.2m
Precision: 64
Internal Precision: 128
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \left(\sqrt{2} \cdot \sqrt{\pi}\right)\right)\right) \cdot \left(\left(\left(\frac{-176.6150291621406}{5 - \left(z + 1\right)} + \frac{771.3234287776531}{1 - \left(-2 + z\right)}\right) + \left(\sqrt[3]{\frac{-1259.1392167224028}{1 + \left(1 - z\right)} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)} \cdot \sqrt[3]{\frac{-1259.1392167224028}{1 + \left(1 - z\right)} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)}\right) \cdot \sqrt[3]{\frac{\left(\frac{676.5203681218851 \cdot \left(2 - z\right)}{1 - z} + \left(-1259.1392167224028 + \left(2 - z\right) \cdot 0.9999999999998099\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)}{\left(1 + \left(1 - z\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)}}\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(-7 + z\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{6 + \left(1 - z\right)}\right)\right)\right)\]

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. 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 sqrt-prod1.0

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

  6. Applied add-cube-cbrt0.6

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

  8. Applied flip-+0.6

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

  9. Applied frac-add1.0

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

  10. Simplified0.6

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

  11. Final simplification0.6

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

Reproduce

herbie shell --seed 2019007 
(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: 2.1m)Debug log

sample2.0s

Algorithm
intervals

simplify160.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

160.0ms
(* (/ 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)))))

prune75.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize185.0ms

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
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ 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))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Counts
4 → 66
Calls

4 calls. Slowest were:

68.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
13.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
10.0ms
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))

series127.0ms

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))))
30.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
24.0ms
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))
0.0ms
(sqrt (* 2 PI))

simplify19.8s

Counts
49 → 76
Calls

49 calls. Slowest were:

1.6s
(* (* (exp (/ -0.13857109526572012 (- 7 (+ z 1)))) (exp (/ 12.507343278686905 (- 6 (+ z 1))))) (* (exp (/ 1.5056327351493116e-07 (- 1 (+ z -7)))) (exp (/ 9.984369578019572e-06 (+ (- 1 z) 6)))))
1.4s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
1.4s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

prune3.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize79.0ms

Local error

Found 4 expressions with local error:

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

rewrite474.0ms

Algorithm
rewrite-expression-head
Counts
4 → 66
Calls

4 calls. Slowest were:

396.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
67.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
9.0ms
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))

series141.0ms

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))))
42.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
25.0ms
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))
0.0ms
(sqrt (* 2 PI))

simplify18.7s

Counts
49 → 76
Calls

49 calls. Slowest were:

1.5s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
1.4s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
1.4s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

prune4.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize37.0ms

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
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ 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))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

44.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
7.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
5.0ms
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))

series131.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

71.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
33.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
26.0ms
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))
0.0ms
(sqrt PI)

simplify18.6s

Counts
48 → 75
Calls

48 calls. Slowest were:

1.4s
(* (* (exp (/ -0.13857109526572012 (- 7 (+ z 1)))) (exp (/ 12.507343278686905 (- 6 (+ z 1))))) (* (exp (/ 1.5056327351493116e-07 (- 1 (+ z -7)))) (exp (/ 9.984369578019572e-06 (+ (- 1 z) 6)))))
1.4s
(* (exp (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))) (exp (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6)))))
1.4s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

prune3.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

2.6b
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
2.6b
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
2.6b
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
1.0b
(sqrt PI)

rewrite40.0ms

Algorithm
rewrite-expression-head
Counts
4 → 53
Calls

4 calls. Slowest were:

13.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
13.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
13.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))

series477.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

412.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
32.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
32.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt PI)

simplify5.9s

Counts
27 → 63
Calls

27 calls. Slowest were:

637.0ms
(+ (* (- (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z)))) (+ (- 1 z) 1)) (* (- 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) -1259.1392167224028))
582.0ms
(+ (* (- (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z)))) (+ (- 1 z) 1)) (* (- 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) -1259.1392167224028))
555.0ms
(+ (* (- (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z)))) (+ (- 1 z) 1)) (* (- 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) -1259.1392167224028))

prune3.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes247.0ms

Accuracy

0% (0.5b remaining)

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

bsearch21.0ms

end0.0ms

sample44.3s

Algorithm
intervals