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

Error

Bits error versus z

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 simplification0.7

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

  4. Applied add-cbrt-cube0.7

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

  6. Applied flip--0.7

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

  7. Applied associate-/r/0.7

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

  8. Applied fma-def0.7

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

  9. Simplified0.7

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

  10. Final simplification0.7

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

Reproduce

herbie shell --seed 2018362 +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: 1.8m)Debug log

start2.3s

Algorithm
intervals

setup263.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize207.0ms

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
(* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- (- 1 z) (- -6 0.5)))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Counts
4 → 100
Calls

4 calls. Slowest were:

51.0ms
(* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- (- 1 z) (- -6 0.5)))))
21.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
10.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series175.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

110.0ms
(* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- (- 1 z) (- -6 0.5)))))
36.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
29.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify18.0s

Counts
65 → 110
Calls

65 calls. Slowest were:

1.5s
(pow (+ (sqrt (- 1 z)) (sqrt (- -6 0.5))) (- (- 1 z) (- 1 0.5)))
1.0s
(pow (- (- 1 z) (- -6 0.5)) (fma (sqrt (- 1 z)) (sqrt (- 1 z)) (- (* (sqrt (- 1 0.5)) (sqrt (- 1 0.5))))))
737.0ms
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))

prune8.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

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
(* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- (- 1 z) (- -6 0.5)))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Counts
4 → 100
Calls

4 calls. Slowest were:

33.0ms
(* (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)))
5.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series138.0ms

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
(+ (/ 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))

simplify18.2s

Counts
64 → 110
Calls

64 calls. Slowest were:

1.3s
(pow (+ (sqrt (- 1 z)) (sqrt (- -6 0.5))) (- (- 1 z) (- 1 0.5)))
1.0s
(pow (- (- 1 z) (- -6 0.5)) (fma (sqrt (- 1 z)) (sqrt (- 1 z)) (- (* (sqrt (- 1 0.5)) (sqrt (- 1 0.5))))))
826.0ms
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))

prune9.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

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
(fma (/ 771.3234287776531 (fma (- 2 z) (+ z -2) 1)) (+ 1 (+ z -2)) (/ -176.6150291621406 (- 5 (+ z 1))))
1.0b
(* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- (- 1 z) (- -6 0.5)))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Counts
4 → 89
Calls

4 calls. Slowest were:

40.0ms
(* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- (- 1 z) (- -6 0.5)))))
13.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
1.0ms
(sqrt (* 2 PI))

series191.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

109.0ms
(* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- (- 1 z) (- -6 0.5)))))
60.0ms
(fma (/ 771.3234287776531 (fma (- 2 z) (+ z -2) 1)) (+ 1 (+ z -2)) (/ -176.6150291621406 (- 5 (+ z 1))))
23.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify17.0s

Counts
57 → 99
Calls

57 calls. Slowest were:

1.3s
(pow (+ (sqrt (- 1 z)) (sqrt (- -6 0.5))) (- (- 1 z) (- 1 0.5)))
981.0ms
(pow (- (- 1 z) (- -6 0.5)) (fma (sqrt (- 1 z)) (sqrt (- 1 z)) (- (* (sqrt (- 1 0.5)) (sqrt (- 1 0.5))))))
839.0ms
(+ (* (+ (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))

prune9.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize57.0ms

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
(* (* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- 1 z)))) (exp (- -6 0.5)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Counts
4 → 87
Calls

4 calls. Slowest were:

36.0ms
(* (* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- 1 z)))) (exp (- -6 0.5)))
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))))

series256.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

195.0ms
(* (* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- 1 z)))) (exp (- -6 0.5)))
35.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
25.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify13.3s

Counts
56 → 97
Calls

56 calls. Slowest were:

901.0ms
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))
848.0ms
(+ (* (+ (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))
804.0ms
(* (* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) 1) (exp (- -6 0.5)))

prune7.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes755.0ms

Accuracy

0% (0.6b remaining)

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

bsearch18.0ms