Average Error: 1.8 → 0.7
Time: 3.2m
Precision: 64
Internal Precision: 128
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(1 + z\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right) + \left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(1 + z\right)}\right) + \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right)\right)\right) \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \sqrt[3]{\frac{{\left(\frac{1}{e} \cdot e^{z}\right)}^{3} \cdot {\left({\left(\left(6 + 0.5\right) + \left(1 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)}^{3}}{{\left(e^{6 + 0.5}\right)}^{3}}}\right)\]

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. Simplified0.7

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

  4. Applied add-cbrt-cube0.7

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \color{blue}{\sqrt[3]{\left(\frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}}}\right)\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\]

  5. Applied add-cbrt-cube0.7

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\color{blue}{\sqrt[3]{\left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right) \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}} \cdot \sqrt[3]{\left(\frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}}\right)\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\]

  6. Applied cbrt-unprod0.7

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \color{blue}{\sqrt[3]{\left(\left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right) \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right) \cdot \left(\left(\frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right)}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\]

  7. Simplified0.7

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \sqrt[3]{\color{blue}{{\left({\left(\left(1 - z\right) + \left(0.5 + 6\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)}^{3} \cdot {\left(\frac{\frac{1}{e} \cdot e^{z}}{e^{0.5 + 6}}\right)}^{3}}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\]
  8. Using strategy rm

  9. Applied cube-div0.7

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \sqrt[3]{{\left({\left(\left(1 - z\right) + \left(0.5 + 6\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)}^{3} \cdot \color{blue}{\frac{{\left(\frac{1}{e} \cdot e^{z}\right)}^{3}}{{\left(e^{0.5 + 6}\right)}^{3}}}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\]

  10. Applied associate-*r/0.7

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \sqrt[3]{\color{blue}{\frac{{\left({\left(\left(1 - z\right) + \left(0.5 + 6\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)}^{3} \cdot {\left(\frac{1}{e} \cdot e^{z}\right)}^{3}}{{\left(e^{0.5 + 6}\right)}^{3}}}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\]

  11. Final simplification0.7

    \[\leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(1 + z\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right) + \left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(1 + z\right)}\right) + \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right)\right)\right) \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \sqrt[3]{\frac{{\left(\frac{1}{e} \cdot e^{z}\right)}^{3} \cdot {\left({\left(\left(6 + 0.5\right) + \left(1 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)}^{3}}{{\left(e^{6 + 0.5}\right)}^{3}}}\right)\]

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(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: 3.2m)Debug log

sample1.8s

Algorithm
intervals

simplify116.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

116.0ms
(* (/ 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)))))

prune73.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize210.0ms

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 (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- (- 1 z) (- -6 0.5)))))
1.0b
(+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Counts
4 → 100
Calls

4 calls. Slowest were:

29.0ms
(* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- (- 1 z) (- -6 0.5)))))
7.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
6.0ms
(+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1))))

series143.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

79.0ms
(* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- (- 1 z) (- -6 0.5)))))
35.0ms
(+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1))))
29.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify20.5s

Counts
65 → 110
Calls

65 calls. Slowest were:

1.8s
(+ (* -0.13857109526572012 (- 6 (+ z 1))) (* (+ (- 1 z) 5) 12.507343278686905))
1.3s
(pow (+ (sqrt (- 1 z)) (sqrt (- -6 0.5))) (- (- 1 z) (- 1 0.5)))
1.1s
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))

prune5.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

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 (/ (* (/ 1 E) (exp z)) (exp (+ 0.5 6))) 3)
1.0b
(* (pow (pow (+ (- 1 z) (+ 0.5 6)) (- (- 1 z) (- 1 0.5))) 3) (pow (/ (* (/ 1 E) (exp z)) (exp (+ 0.5 6))) 3))

rewrite43.0ms

Algorithm
rewrite-expression-head
Counts
4 → 175
Calls

4 calls. Slowest were:

28.0ms
(* (pow (pow (+ (- 1 z) (+ 0.5 6)) (- (- 1 z) (- 1 0.5))) 3) (pow (/ (* (/ 1 E) (exp z)) (exp (+ 0.5 6))) 3))
7.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
5.0ms
(pow (/ (* (/ 1 E) (exp z)) (exp (+ 0.5 6))) 3)

series757.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

524.0ms
(* (pow (pow (+ (- 1 z) (+ 0.5 6)) (- (- 1 z) (- 1 0.5))) 3) (pow (/ (* (/ 1 E) (exp z)) (exp (+ 0.5 6))) 3))
200.0ms
(pow (/ (* (/ 1 E) (exp z)) (exp (+ 0.5 6))) 3)
33.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify55.7s

Counts
141 → 185
Calls

141 calls. Slowest were:

1.9s
(pow (pow (+ (- 1 z) (+ 0.5 6)) 1) 3)
1.6s
(pow (pow (+ (- 1 z) (+ 0.5 6)) 1) 3)
1.4s
(pow (pow (+ (- 1 z) (+ 0.5 6)) 1) 3)

prune10.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize96.0ms

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 E 3)
1.0b
(+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Counts
4 → 64
Calls

4 calls. Slowest were:

14.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
12.0ms
(+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1))))
1.0ms
(sqrt (* 2 PI))

series59.0ms

Counts
4 → 8
Calls

4 calls. Slowest were:

30.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
29.0ms
(+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1))))
0.0ms
(sqrt (* 2 PI))
0.0ms
(pow E 3)

simplify7.6s

Counts
25 → 72
Calls

25 calls. Slowest were:

1.6s
(+ (* -0.13857109526572012 (- 6 (+ z 1))) (* (+ (- 1 z) 5) 12.507343278686905))
756.0ms
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))
727.0ms
(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1 z)) 3)) (+ (- 1 z) 1)) (* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) -1259.1392167224028))

prune4.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

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 (* (/ 1 E) (exp z)) 3)
1.0b
(/ (* (pow (pow (+ (- 1 z) (+ 0.5 6)) (- (- 1 z) (- 1 0.5))) 3) (pow (* (/ 1 E) (exp z)) 3)) (pow (exp (+ 0.5 6)) 3))

rewrite49.0ms

Algorithm
rewrite-expression-head
Counts
4 → 159
Calls

4 calls. Slowest were:

23.0ms
(/ (* (pow (pow (+ (- 1 z) (+ 0.5 6)) (- (- 1 z) (- 1 0.5))) 3) (pow (* (/ 1 E) (exp z)) 3)) (pow (exp (+ 0.5 6)) 3))
19.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
3.0ms
(pow (* (/ 1 E) (exp z)) 3)

series631.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

548.0ms
(/ (* (pow (pow (+ (- 1 z) (+ 0.5 6)) (- (- 1 z) (- 1 0.5))) 3) (pow (* (/ 1 E) (exp z)) 3)) (pow (exp (+ 0.5 6)) 3))
52.0ms
(pow (* (/ 1 E) (exp z)) 3)
31.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify29.4s

Counts
136 → 169
Calls

136 calls. Slowest were:

1.1s
(/ (pow (pow (+ (- 1 z) (+ 0.5 6)) (- (- 1 z) (- 1 0.5))) 3) (pow (exp 0.5) 3))
993.0ms
(/ (pow (pow (+ (- 1 z) (+ 0.5 6)) (- (- 1 z) (- 1 0.5))) 3) (pow (exp 0.5) 3))
961.0ms
(/ (* (* (* (pow (pow (+ (- 1 z) (+ 0.5 6)) (- (- 1 z) (- 1 0.5))) 3) (pow (* (/ 1 E) (exp z)) 3)) (* (pow (pow (+ (- 1 z) (+ 0.5 6)) (- (- 1 z) (- 1 0.5))) 3) (pow (* (/ 1 E) (exp z)) 3))) (* (pow (pow (+ (- 1 z) (+ 0.5 6)) (- (- 1 z) (- 1 0.5))) 3) (pow (* (/ 1 E) (exp z)) 3))) (* (* (pow (exp (+ 0.5 6)) 3) (pow (exp (+ 0.5 6)) 3)) (pow (exp (+ 0.5 6)) 3)))

prune9.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes254.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch13.0ms

end0.0ms

sample43.2s

Algorithm
intervals