Average Error: 1.8 → 0.6
Time: 3.1m
Precision: 64
Internal Precision: 128
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) + \left(\left(\left(\frac{-0.13857109526572012}{6 - z} + \frac{12.507343278686905}{5 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \left(\frac{771.3234287776531}{3 - z} + \frac{-176.6150291621406}{4 - z}\right)\right)\right)\right) \cdot \left(\left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \left(e^{-1 + z} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)}}{e^{6 + 0.5}}\right)\right)\]

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. Simplified0.7

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

  3. Simplified0.7

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

  5. Applied exp-sum0.7

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

  6. Applied *-un-lft-identity0.7

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

  7. Applied times-frac0.6

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

  8. Simplified0.6

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

  9. Simplified0.6

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

  10. Final simplification0.6

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

Reproduce

herbie shell --seed 2019022 +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: 3.0m)Debug log

sample1.1s

Algorithm
intervals
Results
589.0ms110×body10240exit
148.0ms42×body1280nan
137.0ms259×body80valid
106.0ms41×body640nan
35.0ms21×body320nan
11.0ms8×body160nan
11.0ms17×body80nan

simplify132.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
131.0ms
(* (/ 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)))))

prune99.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize180.0ms

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 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))
1.0b
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
20×add-log-exp
18×frac-add
13×fma-def
11×distribute-lft-out
10×flip-+
10×flip3-+
10×sum-log
7×add-cube-cbrt
7×add-sqr-sqrt
4×log1p-expm1-u
4×add-exp-log
4×add-cbrt-cube
4×pow1
4×expm1-log1p-u
3×+-commutative
2×associate-/r/
2×associate-+l+
1×flip--
1×div-inv
1×sqrt-prod
1×pow1/2
1×flip3--
1×associate-+r+
Counts
4 → 87
Calls
4 calls:
Slowest
41.0ms
(+ (+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))
13.0ms
(+ (+ 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))

series138.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
69.0ms
(+ (+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))
35.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
33.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify16.2s

Counts
57 → 97
Calls
57 calls:
Slowest
1.1s
(* (* (+ (- 1 z) 5) (- 6 (+ z 1))) (- (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))
804.0ms
(+ (* (+ (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))
753.0ms
(* (- (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))) (* (- 9 (+ z 1)) (- (- 1 z) -6)))
719.0ms
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))
705.0ms
(* (exp (+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1))))) (exp (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6)))))

prune4.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

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 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))
1.0b
(+ (+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
32×frac-add
30×add-log-exp
19×distribute-lft-out
17×sum-log
16×flip-+
16×flip3-+
11×fma-def
7×add-cube-cbrt
7×add-sqr-sqrt
4×log1p-expm1-u
4×add-exp-log
4×add-cbrt-cube
4×pow1
4×expm1-log1p-u
3×associate-+l+
3×+-commutative
2×associate-+r+
1×sqrt-prod
1×pow1/2
Counts
4 → 101
Calls
4 calls:
Slowest
63.0ms
(+ (+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))
54.0ms
(+ (+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))
6.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
1.0ms
(sqrt (* 2 PI))

series131.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
52.0ms
(+ (+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))
50.0ms
(+ (+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))
29.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify26.6s

Counts
78 → 111
Calls
78 calls:
Slowest
796.0ms
(* (* (exp (/ -0.13857109526572012 (+ (- 1 z) 5))) (exp (/ 12.507343278686905 (- 6 (+ z 1))))) (* (exp (/ 1.5056327351493116e-07 (- 9 (+ z 1)))) (exp (/ 9.984369578019572e-06 (- (- 1 z) -6)))))
780.0ms
(* (* (exp (/ -0.13857109526572012 (+ (- 1 z) 5))) (exp (/ 12.507343278686905 (- 6 (+ z 1))))) (* (exp (/ 1.5056327351493116e-07 (- 9 (+ z 1)))) (exp (/ 9.984369578019572e-06 (- (- 1 z) -6)))))
765.0ms
(* (* (+ (- 1 z) 5) (- 6 (+ z 1))) (- (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))
747.0ms
(* (* (+ (- 1 z) 5) (- 6 (+ z 1))) (- (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))
743.0ms
(+ (* (+ (pow (/ -0.13857109526572012 (+ (- 1 z) 5)) 3) (pow (/ 12.507343278686905 (- 6 (+ z 1))) 3)) (+ (* (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 1.5056327351493116e-07 (- 9 (+ z 1)))) (- (* (/ 9.984369578019572e-06 (- (- 1 z) -6)) (/ 9.984369578019572e-06 (- (- 1 z) -6))) (* (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6)))))) (* (+ (* (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ -0.13857109526572012 (+ (- 1 z) 5))) (- (* (/ 12.507343278686905 (- 6 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (* (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))))) (+ (pow (/ 1.5056327351493116e-07 (- 9 (+ z 1))) 3) (pow (/ 9.984369578019572e-06 (- (- 1 z) -6)) 3))))

prune6.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize150.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (* 2 PI))
1.0b
(+ (/ -176.6150291621406 (- 4 z)) (/ 771.3234287776531 (- 3 z)))
1.0b
(/ (pow (+ (- 1 z) (+ 6 0.5)) (- (- 1 z) (- 1 0.5))) (exp (+ (- 1 z) (+ 6 0.5))))
1.0b
(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
82×*-un-lft-identity
70×unpow-prod-up
68×add-cube-cbrt
68×add-sqr-sqrt
45×prod-diff
22×exp-sum
21×associate-/l*
20×unpow-prod-down
12×fma-def
10×associate--l+
10×sub-neg
8×add-log-exp
7×distribute-lft-out
6×add-exp-log
6×add-cbrt-cube
5×associate--r-
5×associate-/r/
4×log1p-expm1-u
4×associate-/r*
4×pow1
4×expm1-log1p-u
3×div-inv
3×div-exp
2×flip--
2×flip-+
2×frac-add
2×flip3--
2×flip3-+
2×sum-log
2×+-commutative
1×associate-/l/
1×pow-sub
1×sqrt-prod
1×associate-+l-
1×pow-exp
1×exp-diff
1×pow1/2
1×frac-2neg
1×clear-num
1×cbrt-undiv
1×pow-to-exp
Counts
4 → 180
Calls
4 calls:
Slowest
41.0ms
(/ (pow (+ (- 1 z) (+ 6 0.5)) (- (- 1 z) (- 1 0.5))) (exp (+ (- 1 z) (+ 6 0.5))))
10.0ms
(+ (/ -176.6150291621406 (- 4 z)) (/ 771.3234287776531 (- 3 z)))
5.0ms
(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))
1.0ms
(sqrt (* 2 PI))

series142.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
76.0ms
(/ (pow (+ (- 1 z) (+ 6 0.5)) (- (- 1 z) (- 1 0.5))) (exp (+ (- 1 z) (+ 6 0.5))))
38.0ms
(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))
28.0ms
(+ (/ -176.6150291621406 (- 4 z)) (/ 771.3234287776531 (- 3 z)))
0.0ms
(sqrt (* 2 PI))

simplify1.1m

Counts
225 → 190
Calls
225 calls:
Slowest
1.2s
(/ (pow 1 (- (- 1 z) (- 1 0.5))) 1)
1.2s
(/ (pow 1 (- (- 1 z) (- 1 0.5))) 1)
1.1s
(/ (sqrt (pow (+ (- 1 z) (+ 6 0.5)) (- (- 1 z) (- 1 0.5)))) (exp (+ 6 0.5)))
1.1s
(/ (pow (sqrt (+ (- 1 z) (+ 6 0.5))) (- (- 1 z) (- 1 0.5))) (exp (- 1 z)))
966.0ms
(/ (* (cbrt (pow (+ (- 1 z) (+ 6 0.5)) (- (- 1 z) (- 1 0.5)))) (cbrt (pow (+ (- 1 z) (+ 6 0.5)) (- (- 1 z) (- 1 0.5))))) 1)

prune9.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (* 2 PI))
1.0b
(+ (/ -176.6150291621406 (- 4 z)) (/ 771.3234287776531 (- 3 z)))
1.0b
(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))
1.0b
(+ (+ (/ -176.6150291621406 (- 4 z)) (/ 771.3234287776531 (- 3 z))) (+ (/ 676.5203681218851 (- 1 z)) 0.9999999999998099))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
16×fma-def
13×add-log-exp
10×frac-add
8×flip-+
8×flip3-+
7×add-cube-cbrt
7×add-sqr-sqrt
6×distribute-lft-out
5×sum-log
4×log1p-expm1-u
4×associate-/r/
4×add-exp-log
4×add-cbrt-cube
4×pow1
4×expm1-log1p-u
3×+-commutative
2×flip--
2×div-inv
2×flip3--
1×sqrt-prod
1×pow1/2
1×associate-+r+
1×associate-+l+
Counts
4 → 81
Calls
4 calls:
Slowest
63.0ms
(+ (+ (/ -176.6150291621406 (- 4 z)) (/ 771.3234287776531 (- 3 z))) (+ (/ 676.5203681218851 (- 1 z)) 0.9999999999998099))
9.0ms
(+ (/ -176.6150291621406 (- 4 z)) (/ 771.3234287776531 (- 3 z)))
9.0ms
(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))
1.0ms
(sqrt (* 2 PI))

series105.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
36.0ms
(+ (/ -176.6150291621406 (- 4 z)) (/ 771.3234287776531 (- 3 z)))
35.0ms
(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))
34.0ms
(+ (+ (/ -176.6150291621406 (- 4 z)) (/ 771.3234287776531 (- 3 z))) (+ (/ 676.5203681218851 (- 1 z)) 0.9999999999998099))
0.0ms
(sqrt (* 2 PI))

simplify5.8s

Counts
46 → 91
Calls
46 calls:
Slowest
453.0ms
(- (+ (* 4116.070392404628 (/ 1 (pow z 3))) (+ (* 1607.5101696843972 (/ 1 (pow z 2))) (* 594.7083996155126 (/ 1 z)))))
407.0ms
(* (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- (- 1 z) -6))) (+ (+ (+ (/ -176.6150291621406 (- 4 z)) (/ 771.3234287776531 (- 3 z))) (+ (/ 676.5203681218851 (- 1 z)) 0.9999999999998099)) (+ (/ -1259.1392167224028 (- 2 z)) (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))))) (* (* (exp (+ -1 z)) (/ (pow (+ (- 7 z) 0.5) (- 0.5 z)) (exp (+ 6 0.5)))) (* (sqrt (* 2 PI)) (/ PI (sin (* PI z))))))
349.0ms
(- (+ (* 4116.070392404628 (/ 1 (pow z 3))) (+ (* 1607.5101696843972 (/ 1 (pow z 2))) (* 594.7083996155126 (/ 1 z)))))
335.0ms
(* (- (/ -176.6150291621406 (- 4 z)) (/ 771.3234287776531 (- 3 z))) (+ (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1 z)) 0.9999999999998099))))
293.0ms
(- (+ (* 307.69502253760675 (/ 1 (pow z 3))) (+ (* 61.7052898218402 (/ 1 (pow z 2))) (* 12.368772183421186 (/ 1 z)))))

prune3.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes238.0ms

Accuracy

0% (0.6b remaining)

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

bsearch14.0ms

end0.0ms

sample41.0s

Algorithm
intervals
Results
22.8s3832×body10240exit
6.6s1504×body1280nan
6.0s8099×body80valid
3.4s1206×body640nan
1.3s643×body320nan
379.0ms319×body160nan
231.0ms301×body80nan
1.0ms1×body160valid