Average Error: 1.8 → 0.6
Time: 2.3m
Precision: 64
Internal Precision: 128
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\frac{12.507343278686905}{5 - z} + \frac{-0.13857109526572012}{6 - z}\right)\right) + \left(\frac{\frac{676.5203681218851 \cdot \left(2 - z\right)}{1 - z} + \left(-1259.1392167224028 + 0.9999999999998099 \cdot \left(2 - z\right)\right)}{2 - z} + \frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {\left(\frac{771.3234287776531}{3 - z}\right)}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \frac{771.3234287776531}{3 - z}\right) + \frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}}\right)\right) \cdot \left(\frac{\frac{\pi}{\sin \left(\pi \cdot z\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \left({\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \sqrt{2 \cdot \pi}\right)\right)\]

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 flip3-+0.6

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

  6. Applied flip-+0.6

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

  7. Applied frac-add1.0

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

  8. Simplified0.6

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

  9. Simplified0.6

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

  10. Final simplification0.6

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

Reproduce

herbie shell --seed 2019016 
(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: 2.2m)Debug log

sample2.5s

Algorithm
intervals
Results
525×(pre true 80)
259×(body real 80)
158×(body exit 10240)
49×(body nan 1280)
34×(body nan 640)
15×(body nan 320)
5×(body nan 160)
5×(body nan 80)

simplify115.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
114.0ms
(* (/ 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)))))

prune78.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

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
(+ (/ 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))))

rewrite88.0ms

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
65.0ms
(+ (+ (/ -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))))
1.0ms
(sqrt (* 2 PI))

series108.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
56.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
27.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
24.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify19.2s

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

prune3.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize75.0ms

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
(pow (/ 771.3234287776531 (- 1 (+ z -2))) 3)
1.0b
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
18×add-log-exp
17×frac-add
9×distribute-lft-out
9×flip-+
9×flip3-+
9×sum-log
6×add-cube-cbrt
6×cube-prod
6×unpow-prod-down
6×add-sqr-sqrt
5×add-exp-log
5×add-cbrt-cube
5×pow1
4×associate-/r/
2×flip--
2×div-inv
2×flip3--
2×associate-+l+
2×+-commutative
1×rem-cube-cbrt
1×sqrt-prod
1×pow-exp
1×unpow3
1×pow1/2
1×pow-pow
1×associate-+r+
1×pow-to-exp
1×cube-mult
1×cube-div
Counts
4 → 79
Calls
4 calls:
Slowest
61.0ms
(+ (+ (/ -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)))
2.0ms
(pow (/ 771.3234287776531 (- 1 (+ z -2))) 3)
1.0ms
(sqrt (* 2 PI))

series133.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
69.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
32.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
32.0ms
(pow (/ 771.3234287776531 (- 1 (+ z -2))) 3)
0.0ms
(sqrt (* 2 PI))

simplify20.0s

Counts
60 → 89
Calls
60 calls:
Slowest
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))))
1.3s
(* (* (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)))))
1.3s
(+ (+ (/ -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))))

prune5.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize112.0ms

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
(pow (/ 771.3234287776531 (- 1 (+ z -2))) 3)
1.0b
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
18×add-log-exp
17×frac-add
9×distribute-lft-out
9×flip-+
9×flip3-+
9×sum-log
6×add-cube-cbrt
6×cube-prod
6×unpow-prod-down
6×add-sqr-sqrt
5×add-exp-log
5×add-cbrt-cube
5×pow1
4×associate-/r/
2×flip--
2×div-inv
2×flip3--
2×associate-+r+
2×+-commutative
1×rem-cube-cbrt
1×sqrt-prod
1×pow-exp
1×unpow3
1×pow1/2
1×pow-pow
1×associate-+l+
1×pow-to-exp
1×cube-mult
1×cube-div
Counts
4 → 79
Calls
4 calls:
Slowest
51.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
24.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
2.0ms
(pow (/ 771.3234287776531 (- 1 (+ z -2))) 3)
1.0ms
(sqrt (* 2 PI))

series90.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
41.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
29.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
19.0ms
(pow (/ 771.3234287776531 (- 1 (+ z -2))) 3)
0.0ms
(sqrt (* 2 PI))

simplify19.2s

Counts
61 → 89
Calls
61 calls:
Slowest
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))))
1.4s
(* (* (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)))))
1.3s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
1.3s
(* (* (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)))))

prune5.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize232.0ms

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 (* PI 2))
1.0b
(pow (/ 771.3234287776531 (- 3 z)) 3)
1.0b
(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
18×add-log-exp
17×frac-add
9×distribute-lft-out
9×flip-+
9×flip3-+
9×sum-log
6×add-cube-cbrt
6×cube-prod
6×unpow-prod-down
6×add-sqr-sqrt
5×add-exp-log
5×add-cbrt-cube
5×pow1
4×associate-/r/
2×flip--
2×div-inv
2×flip3--
2×associate-+r+
2×+-commutative
1×rem-cube-cbrt
1×sqrt-prod
1×pow-exp
1×unpow3
1×pow1/2
1×pow-pow
1×associate-+l+
1×pow-to-exp
1×cube-mult
1×cube-div
Counts
4 → 79
Calls
4 calls:
Slowest
31.0ms
(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))))
16.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
1.0ms
(pow (/ 771.3234287776531 (- 3 z)) 3)
0.0ms
(sqrt (* PI 2))

series111.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
44.0ms
(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))))
43.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
24.0ms
(pow (/ 771.3234287776531 (- 3 z)) 3)
0.0ms
(sqrt (* PI 2))

simplify8.5s

Counts
61 → 89
Calls
61 calls:
Slowest
618.0ms
(+ (* (+ (* 1.5056327351493116e-07 (- 7 z)) (* (- 8 z) 9.984369578019572e-06)) (+ (* (/ -0.13857109526572012 (- 6 z)) (/ -0.13857109526572012 (- 6 z))) (- (* (/ 12.507343278686905 (- 5 z)) (/ 12.507343278686905 (- 5 z))) (* (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))))) (* (* (- 8 z) (- 7 z)) (+ (pow (/ -0.13857109526572012 (- 6 z)) 3) (pow (/ 12.507343278686905 (- 5 z)) 3))))
549.0ms
(* (* (/ (/ PI (sin (* PI z))) (exp (+ (- 7 z) 0.5))) (* (sqrt (* PI 2)) (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))))) (+ (+ (* (/ (+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)) (- 2 z)) 1) (/ (+ (pow (/ -176.6150291621406 (- 4 z)) 3) (pow (/ 771.3234287776531 (- 3 z)) 3)) (+ (* (/ 771.3234287776531 (- 3 z)) (/ 771.3234287776531 (- 3 z))) (* (/ -176.6150291621406 (- 4 z)) (- (/ -176.6150291621406 (- 4 z)) (/ 771.3234287776531 (- 3 z))))))) (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))))))
414.0ms
(* (- 1 z) (- (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
338.0ms
(- (+ (* 24780115672.16207 (/ 1 (pow z 5))) (+ (* 458891030.9659644 (/ 1 (pow z 3))) (* 4130019278.693679 (/ 1 (pow z 4))))))
322.0ms
(* (- (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (* (/ -0.13857109526572012 (- 6 z)) (/ -0.13857109526572012 (- 6 z))) (- (* (/ 12.507343278686905 (- 5 z)) (/ 12.507343278686905 (- 5 z))) (* (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))))))

prune4.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes273.0ms

Accuracy

0% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch8.0ms

end0.0ms

sample43.3s

Algorithm
intervals
Results
15941×(pre true 80)
8086×(body real 80)
3925×(body exit 10240)
1511×(body nan 1280)
1205×(body nan 640)
619×(body nan 320)
300×(body nan 80)
295×(body nan 160)