Average Error: 1.8 → 0.9
Time: 2.1m
Precision: 64
Internal Precision: 128
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \left(\sqrt{2} \cdot \sqrt{\pi}\right)\right)\right) \cdot \left(\left(\frac{\left(\sqrt{\left(\left(2 - z\right) \cdot 0.9999999999998099 + -1259.1392167224028\right) + \frac{676.5203681218851 \cdot \left(2 - z\right)}{1 - z}} \cdot \sqrt{\left(\left(2 - z\right) \cdot 0.9999999999998099 + -1259.1392167224028\right) + \frac{676.5203681218851 \cdot \left(2 - z\right)}{1 - z}}\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)}{\left(1 + \left(1 - z\right)\right) \cdot \left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right)} + \left(\frac{-176.6150291621406}{5 - \left(z + 1\right)} + \frac{771.3234287776531}{1 - \left(-2 + z\right)}\right)\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right) + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \frac{-0.13857109526572012}{7 - \left(z + 1\right)}\right)\right)\right)\]

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 flip-+0.6

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

  5. Applied frac-add1.0

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

  6. Simplified0.6

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

  8. Applied add-sqr-sqrt1.4

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

  10. Applied sqrt-prod0.9

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

  11. Final simplification0.9

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

Reproduce

herbie shell --seed 2019010 
(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: 2.0m)Debug log

sample1.6s

Algorithm
intervals

simplify134.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
134.0ms
(* (/ 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)))))

prune119.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize241.0ms

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))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
20×add-log-exp
20×*-un-lft-identity
18×frac-add
10×distribute-lft-out
10×flip-+
10×flip3-+
10×sum-log
4×add-cube-cbrt
4×add-exp-log
4×add-cbrt-cube
4×pow1
4×add-sqr-sqrt
3×+-commutative
2×associate-+l+
1×sqrt-prod
1×pow1/2
1×associate-+r+
Counts
4 → 66
Calls
4 calls:
Slowest
32.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
8.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
5.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
0.0ms
(sqrt (* 2 PI))

series120.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
66.0ms
(+ (+ (/ -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)))
25.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
0.0ms
(sqrt (* 2 PI))

simplify18.9s

Counts
49 → 76
Calls
49 calls:
Slowest
1.5s
(* (* (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)))))
1.5s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
1.4s
(* (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))))
1.3s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

prune4.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

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
(+ (/ 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))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
20×add-log-exp
20×*-un-lft-identity
18×frac-add
10×distribute-lft-out
10×flip-+
10×flip3-+
10×sum-log
4×add-cube-cbrt
4×add-exp-log
4×add-cbrt-cube
4×pow1
4×add-sqr-sqrt
3×+-commutative
2×associate-+r+
1×sqrt-prod
1×pow1/2
1×associate-+l+
Counts
4 → 66
Calls
4 calls:
Slowest
60.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
17.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
5.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
0.0ms
(sqrt (* 2 PI))

series114.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
46.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
44.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
24.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
0.0ms
(sqrt (* 2 PI))

simplify18.8s

Counts
49 → 76
Calls
49 calls:
Slowest
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)))))
1.6s
(* (* (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
(* (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))))
1.3s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

prune4.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize62.0ms

Local error

Found 4 expressions with local error:

2.6b
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
2.0b
(exp (log (+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))))
1.0b
(sqrt (* 2 PI))
1.0b
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
8×add-log-exp
6×add-cube-cbrt
6×add-sqr-sqrt
5×pow1
4×flip-+
4×add-exp-log
4×frac-add
4×exp-sum
4×add-cbrt-cube
4×flip3-+
4×exp-prod
4×log-prod
3×distribute-lft-out
3×exp-diff
3×log-div
2×sum-log
2×+-commutative
1×rem-exp-log
1×sqrt-prod
1×log-pow
1×pow1/2
1×associate-+r+
Counts
4 → 56
Calls
4 calls:
Slowest
24.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
6.0ms
(exp (log (+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))))
4.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
0.0ms
(sqrt (* 2 PI))

series92.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
37.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
28.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
27.0ms
(exp (log (+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))))
0.0ms
(sqrt (* 2 PI))

simplify4.5s

Counts
32 → 66
Calls
32 calls:
Slowest
640.0ms
(- (+ (* 4116.070392404628 (/ 1 (pow z 3))) (+ (* 1607.5101696843972 (/ 1 (pow z 2))) (* 594.7083996155126 (/ 1 z)))))
425.0ms
(* (- 1 z) (- (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
410.0ms
(exp (log (- (* (/ 771.3234287776531 (- 1 (+ z -2))) (/ 771.3234287776531 (- 1 (+ z -2)))) (* (/ -176.6150291621406 (- 5 (+ z 1))) (/ -176.6150291621406 (- 5 (+ z 1)))))))
272.0ms
(- (+ (* 4116.070392404628 (/ 1 (pow z 3))) (+ (* 1607.5101696843972 (/ 1 (pow z 2))) (* 594.7083996155126 (/ 1 z)))))
256.0ms
(+ (* (* 676.5203681218851 (- 2 z)) (+ (* (* (- 2 z) 0.9999999999998099) (* (- 2 z) 0.9999999999998099)) (- (* -1259.1392167224028 -1259.1392167224028) (* (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))) (* (- 1 z) (+ (pow (* (- 2 z) 0.9999999999998099) 3) (pow -1259.1392167224028 3))))

prune3.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
40×sqrt-div
24×flip-+
24×frac-add
24×flip3-+
16×*-un-lft-identity
16×frac-times
9×sqrt-prod
9×pow1
8×add-log-exp
8×add-cube-cbrt
8×add-sqr-sqrt
7×associate-*l*
7×associate-*r*
6×add-exp-log
6×add-cbrt-cube
5×pow1/2
4×distribute-lft-out
4×associate-*r/
4×associate-*l/
2×pow-prod-up
2×pow-prod-down
2×sum-log
2×associate-+r+
2×+-commutative
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×sqrt-unprod
1×pow-plus
1×rem-square-sqrt
1×pow2
Counts
4 → 95
Calls
4 calls:
Slowest
45.0ms
(* (sqrt (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))) (sqrt (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))))
26.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
23.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
1.0ms
(sqrt (* 2 PI))

series93.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
34.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
30.0ms
(* (sqrt (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))) (sqrt (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))))
29.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
0.0ms
(sqrt (* 2 PI))

simplify14.7s

Counts
87 → 105
Calls
87 calls:
Slowest
760.0ms
(* (* (* (sqrt (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))) (sqrt (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))) (sqrt (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))) (* (* (sqrt (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))) (sqrt (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))) (sqrt (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))))
563.0ms
(* (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)) (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))
458.0ms
(* (sqrt (+ (pow (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) 3) (pow (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028) 3))) (sqrt (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))))
453.0ms
(sqrt (* (- 1 z) (- (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))
447.0ms
(* (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)) (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))

prune6.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes649.0ms

Accuracy

0% (0.8b remaining)

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

bsearch10.0ms

end0.0ms

sample41.8s

Algorithm
intervals