Average Error: 1.8 → 1.2
Time: 2.9m
Precision: 64
Internal Precision: 128
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\frac{1102.6408374891312 \cdot \sqrt{2}}{\frac{e^{7.5}}{z}} + \frac{263.38318698105144 \cdot \sqrt{2}}{e^{7.5} \cdot z}\right) \cdot \left(\sqrt{\pi} \cdot {\left({7.5}^{1.0}\right)}^{0.5}\right) + \left(\frac{43.89719783017523 \cdot \sqrt{2}}{\frac{e^{7.5}}{z}} \cdot \left(\sqrt{{\pi}^{5}} \cdot {\left({7.5}^{1.0}\right)}^{0.5}\right) + (\left(\frac{131.69159349052572 \cdot \sqrt{2}}{\frac{\frac{e^{7.5}}{z}}{\log 7.5 \cdot \log 7.5}}\right) \cdot \left(\sqrt{\pi} \cdot {\left({7.5}^{1.0}\right)}^{0.5}\right) + \left(\left(682.7204804053209 \cdot \frac{\sqrt{2}}{e^{7.5}}\right) \cdot \left(\sqrt{\pi} \cdot {\left({7.5}^{1.0}\right)}^{0.5}\right)\right))_*\right)\right) - (\left(\frac{263.38318698105144 \cdot \sqrt{2}}{\frac{e^{7.5}}{\log 7.5}}\right) \cdot \left(\sqrt{\pi} \cdot {\left({7.5}^{1.0}\right)}^{0.5}\right) + \left((682.7204804053209 \cdot \left(\left(\sqrt{\pi} \cdot {\left({7.5}^{1.0}\right)}^{0.5}\right) \cdot \left(\left(z \cdot \log 7.5\right) \cdot \frac{\sqrt{2}}{e^{7.5}}\right)\right) + \left(\frac{\sqrt{2} \cdot 65.84579674526286}{\frac{e^{7.5}}{z}} \cdot \left({\left(\frac{1}{{7.5}^{3.0}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right))_*\right))_*\]

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 simplification0.9

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

  3. Simplified0.9

    \[\leadsto \color{blue}{\left(\frac{\sqrt{2 \cdot \pi}}{e^{\left(7 - z\right) + 0.5}} \cdot {\left(\left(7 - z\right) + 0.5\right)}^{\left(0 - \left(z - 0.5\right)\right)}\right) \cdot (\left(\left(\left(\frac{-0.13857109526572012}{6 - z} + \frac{12.507343278686905}{5 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \left(\frac{-1259.1392167224028}{2 - z} + \frac{771.3234287776531}{3 - z}\right)\right)\right) \cdot \left(\frac{\pi}{\sin \left(z \cdot \pi\right)}\right) + \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right))_*}\]

  4. Taylor expanded around 0 1.2

    \[\leadsto \color{blue}{\left(263.38318698105144 \cdot \left(\frac{\sqrt{2}}{z \cdot e^{7.5}} \cdot \left({\left({7.5}^{1.0}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(1102.6408374891312 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{7.5}} \cdot \left({\left({7.5}^{1.0}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(131.69159349052572 \cdot \left(\frac{\sqrt{2} \cdot \left({\left(\log 7.5\right)}^{2} \cdot z\right)}{e^{7.5}} \cdot \left({\left({7.5}^{1.0}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(682.7204804053209 \cdot \left(\frac{\sqrt{2}}{e^{7.5}} \cdot \left({\left({7.5}^{1.0}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + 43.89719783017523 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{7.5}} \cdot \left({\left({7.5}^{1.0}\right)}^{0.5} \cdot \sqrt{{\pi}^{5}}\right)\right)\right)\right)\right)\right) - \left(263.38318698105144 \cdot \left(\frac{\sqrt{2} \cdot \log 7.5}{e^{7.5}} \cdot \left({\left({7.5}^{1.0}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(65.84579674526286 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{7.5}} \cdot \left({\left(\frac{1}{{7.5}^{3.0}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + 682.7204804053209 \cdot \left(\frac{\sqrt{2} \cdot \left(\log 7.5 \cdot z\right)}{e^{7.5}} \cdot \left({\left({7.5}^{1.0}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right)\right)\right)}\]

  5. Simplified1.2

    \[\leadsto \color{blue}{\left(\left(\frac{43.89719783017523 \cdot \sqrt{2}}{\frac{e^{7.5}}{z}} \cdot \left(\sqrt{{\pi}^{5}} \cdot {\left({7.5}^{1.0}\right)}^{0.5}\right) + (\left(\frac{131.69159349052572 \cdot \sqrt{2}}{\frac{\frac{e^{7.5}}{z}}{\log 7.5 \cdot \log 7.5}}\right) \cdot \left({\left({7.5}^{1.0}\right)}^{0.5} \cdot \sqrt{\pi}\right) + \left(\left(682.7204804053209 \cdot \frac{\sqrt{2}}{e^{7.5}}\right) \cdot \left({\left({7.5}^{1.0}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right))_*\right) + \left({\left({7.5}^{1.0}\right)}^{0.5} \cdot \sqrt{\pi}\right) \cdot \left(\frac{263.38318698105144 \cdot \sqrt{2}}{z \cdot e^{7.5}} + \frac{1102.6408374891312 \cdot \sqrt{2}}{\frac{e^{7.5}}{z}}\right)\right) - (\left(\frac{263.38318698105144 \cdot \sqrt{2}}{\frac{e^{7.5}}{\log 7.5}}\right) \cdot \left({\left({7.5}^{1.0}\right)}^{0.5} \cdot \sqrt{\pi}\right) + \left((682.7204804053209 \cdot \left(\left(\frac{\sqrt{2}}{e^{7.5}} \cdot \left(z \cdot \log 7.5\right)\right) \cdot \left({\left({7.5}^{1.0}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(\frac{65.84579674526286 \cdot \sqrt{2}}{\frac{e^{7.5}}{z}} \cdot \left({\left(\frac{1}{{7.5}^{3.0}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right))_*\right))_*}\]

  6. Final simplification1.2

    \[\leadsto \left(\left(\frac{1102.6408374891312 \cdot \sqrt{2}}{\frac{e^{7.5}}{z}} + \frac{263.38318698105144 \cdot \sqrt{2}}{e^{7.5} \cdot z}\right) \cdot \left(\sqrt{\pi} \cdot {\left({7.5}^{1.0}\right)}^{0.5}\right) + \left(\frac{43.89719783017523 \cdot \sqrt{2}}{\frac{e^{7.5}}{z}} \cdot \left(\sqrt{{\pi}^{5}} \cdot {\left({7.5}^{1.0}\right)}^{0.5}\right) + (\left(\frac{131.69159349052572 \cdot \sqrt{2}}{\frac{\frac{e^{7.5}}{z}}{\log 7.5 \cdot \log 7.5}}\right) \cdot \left(\sqrt{\pi} \cdot {\left({7.5}^{1.0}\right)}^{0.5}\right) + \left(\left(682.7204804053209 \cdot \frac{\sqrt{2}}{e^{7.5}}\right) \cdot \left(\sqrt{\pi} \cdot {\left({7.5}^{1.0}\right)}^{0.5}\right)\right))_*\right)\right) - (\left(\frac{263.38318698105144 \cdot \sqrt{2}}{\frac{e^{7.5}}{\log 7.5}}\right) \cdot \left(\sqrt{\pi} \cdot {\left({7.5}^{1.0}\right)}^{0.5}\right) + \left((682.7204804053209 \cdot \left(\left(\sqrt{\pi} \cdot {\left({7.5}^{1.0}\right)}^{0.5}\right) \cdot \left(\left(z \cdot \log 7.5\right) \cdot \frac{\sqrt{2}}{e^{7.5}}\right)\right) + \left(\frac{\sqrt{2} \cdot 65.84579674526286}{\frac{e^{7.5}}{z}} \cdot \left({\left(\frac{1}{{7.5}^{3.0}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right))_*\right))_*\]

Reproduce

herbie shell --seed 2018360 +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: 1.5m)Debug log

start2.6s

Algorithm
intervals

setup269.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize200.0ms

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
(* (* (sqrt (* 2 PI)) (pow (+ (- 8 (+ z 1)) 0.5) (- (- 1 z) (- 1 0.5)))) (/ 1 (exp (+ (- 8 (+ z 1)) 0.5))))
0.9b
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (+ (- 1 z) 7)) (/ 9.984369578019572e-06 (- 8 (+ z 1)))))

rewrite154.0ms

Algorithm
rewrite-expression-head
Counts
4 → 97
Calls

4 calls. Slowest were:

71.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (+ (- 1 z) 7)) (/ 9.984369578019572e-06 (- 8 (+ z 1)))))
66.0ms
(* (* (sqrt (* 2 PI)) (pow (+ (- 8 (+ z 1)) 0.5) (- (- 1 z) (- 1 0.5)))) (/ 1 (exp (+ (- 8 (+ z 1)) 0.5))))
14.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))

series264.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

187.0ms
(* (* (sqrt (* 2 PI)) (pow (+ (- 8 (+ z 1)) 0.5) (- (- 1 z) (- 1 0.5)))) (/ 1 (exp (+ (- 8 (+ z 1)) 0.5))))
55.0ms
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (+ (- 1 z) 7)) (/ 9.984369578019572e-06 (- 8 (+ z 1)))))
22.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify23.9s

Counts
71 → 107
Calls

71 calls. Slowest were:

1.0s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (+ (- 1 z) 7)) (/ 9.984369578019572e-06 (- 8 (+ z 1)))))
1.0s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (+ (- 1 z) 7)) (/ 9.984369578019572e-06 (- 8 (+ z 1)))))
1.0s
(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (+ (- 1 z) 7)) (/ 9.984369578019572e-06 (- 8 (+ z 1)))))

prune8.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize115.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (* 2 PI))
0.9b
(/ (sqrt (* 2 PI)) (exp (+ (- 7 z) 0.5)))
0.9b
(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))
0.9b
(* (* (/ (sqrt (* 2 PI)) (exp (+ (- 7 z) 0.5))) (pow (+ (- 7 z) 0.5) (- 0 (- z 0.5)))) (fma (+ (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ -176.6150291621406 (- 4 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z))))) (/ PI (sin (* z PI))) (* (+ (/ 9.984369578019572e-06 (- 7 z)) (/ 1.5056327351493116e-07 (- 8 z))) (/ PI (sin (* z PI))))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Counts
4 → 104
Calls

4 calls. Slowest were:

64.0ms
(* (* (/ (sqrt (* 2 PI)) (exp (+ (- 7 z) 0.5))) (pow (+ (- 7 z) 0.5) (- 0 (- z 0.5)))) (fma (+ (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ -176.6150291621406 (- 4 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z))))) (/ PI (sin (* z PI))) (* (+ (/ 9.984369578019572e-06 (- 7 z)) (/ 1.5056327351493116e-07 (- 8 z))) (/ PI (sin (* z PI))))))
15.0ms
(/ (sqrt (* 2 PI)) (exp (+ (- 7 z) 0.5)))
5.0ms
(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))

series504.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

387.0ms
(* (* (/ (sqrt (* 2 PI)) (exp (+ (- 7 z) 0.5))) (pow (+ (- 7 z) 0.5) (- 0 (- z 0.5)))) (fma (+ (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ -176.6150291621406 (- 4 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z))))) (/ PI (sin (* z PI))) (* (+ (/ 9.984369578019572e-06 (- 7 z)) (/ 1.5056327351493116e-07 (- 8 z))) (/ PI (sin (* z PI))))))
84.0ms
(/ (sqrt (* 2 PI)) (exp (+ (- 7 z) 0.5)))
33.0ms
(+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z)))
0.0ms
(sqrt (* 2 PI))

simplify11.0s

Counts
84 → 114
Calls

84 calls. Slowest were:

561.0ms
(+ (+ (log (/ (sqrt (* 2 PI)) (exp (+ (- 7 z) 0.5)))) (* (log (+ (- 7 z) 0.5)) (- 0 (- z 0.5)))) (log (fma (+ (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ -176.6150291621406 (- 4 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z))))) (/ PI (sin (* z PI))) (* (+ (/ 9.984369578019572e-06 (- 7 z)) (/ 1.5056327351493116e-07 (- 8 z))) (/ PI (sin (* z PI)))))))
543.0ms
(* (* (/ (* (* (sqrt (* 2 PI)) (sqrt (* 2 PI))) (sqrt (* 2 PI))) (* (* (exp (+ (- 7 z) 0.5)) (exp (+ (- 7 z) 0.5))) (exp (+ (- 7 z) 0.5)))) (* (* (pow (+ (- 7 z) 0.5) (- 0 (- z 0.5))) (pow (+ (- 7 z) 0.5) (- 0 (- z 0.5)))) (pow (+ (- 7 z) 0.5) (- 0 (- z 0.5))))) (* (* (fma (+ (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ -176.6150291621406 (- 4 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z))))) (/ PI (sin (* z PI))) (* (+ (/ 9.984369578019572e-06 (- 7 z)) (/ 1.5056327351493116e-07 (- 8 z))) (/ PI (sin (* z PI))))) (fma (+ (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ -176.6150291621406 (- 4 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z))))) (/ PI (sin (* z PI))) (* (+ (/ 9.984369578019572e-06 (- 7 z)) (/ 1.5056327351493116e-07 (- 8 z))) (/ PI (sin (* z PI)))))) (fma (+ (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ -176.6150291621406 (- 4 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z))))) (/ PI (sin (* z PI))) (* (+ (/ 9.984369578019572e-06 (- 7 z)) (/ 1.5056327351493116e-07 (- 8 z))) (/ PI (sin (* z PI)))))))
459.0ms
(+ (* 1/2 (* (/ (* (sqrt 2) (pow z 2)) (exp 7.5)) (sqrt PI))) (+ (* (/ (sqrt 2) (exp 7.5)) (sqrt PI)) (* (/ (* (sqrt 2) z) (exp 7.5)) (sqrt PI))))

prune8.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize199.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (* 682.7204804053209 (/ (sqrt 2) (exp 7.5))) (* (pow (pow 7.5 1.0) 0.5) (sqrt PI)))
1.0b
(/ (sqrt 2) (exp 7.5))
1.0b
(/ (sqrt 2) (exp 7.5))
1.0b
(* (pow (/ 1 (pow 7.5 3.0)) 0.5) (sqrt PI))

rewrite38.0ms

Algorithm
rewrite-expression-head
Counts
4 → 105
Calls

4 calls. Slowest were:

17.0ms
(* (* 682.7204804053209 (/ (sqrt 2) (exp 7.5))) (* (pow (pow 7.5 1.0) 0.5) (sqrt PI)))
10.0ms
(* (pow (/ 1 (pow 7.5 3.0)) 0.5) (sqrt PI))
5.0ms
(/ (sqrt 2) (exp 7.5))

series0.0ms

Counts
4 → 4
Calls

4 calls. Slowest were:

0.0ms
(* (* 682.7204804053209 (/ (sqrt 2) (exp 7.5))) (* (pow (pow 7.5 1.0) 0.5) (sqrt PI)))
0.0ms
(* (pow (/ 1 (pow 7.5 3.0)) 0.5) (sqrt PI))
0.0ms
(/ (sqrt 2) (exp 7.5))
0.0ms
(/ (sqrt 2) (exp 7.5))

simplify3.7s

Counts
79 → 109
Calls

79 calls. Slowest were:

426.0ms
(+ (log (* 682.7204804053209 (/ (sqrt 2) (exp 7.5)))) (+ (log (pow (pow 7.5 1.0) 0.5)) (log (sqrt PI))))
410.0ms
(+ (log (* 682.7204804053209 (/ (sqrt 2) (exp 7.5)))) (log (* (pow (pow 7.5 1.0) 0.5) (sqrt PI))))
407.0ms
(+ (log (* 682.7204804053209 (/ (sqrt 2) (exp 7.5)))) (+ (* (log (pow 7.5 1.0)) 0.5) (log (sqrt PI))))

prune9.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (* 2 PI))
1.0b
(sqrt (* 2 PI))
0.9b
(/ (sqrt (* 2 PI)) (exp (+ 7 (- 0.5 z))))
0.9b
(/ (sqrt (* 2 PI)) (exp (+ (- 7 z) 0.5)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Counts
4 → 100
Calls

4 calls. Slowest were:

22.0ms
(/ (sqrt (* 2 PI)) (exp (+ (- 7 z) 0.5)))
11.0ms
(/ (sqrt (* 2 PI)) (exp (+ 7 (- 0.5 z))))
1.0ms
(sqrt (* 2 PI))

series170.0ms

Counts
4 → 8
Calls

4 calls. Slowest were:

93.0ms
(/ (sqrt (* 2 PI)) (exp (+ 7 (- 0.5 z))))
77.0ms
(/ (sqrt (* 2 PI)) (exp (+ (- 7 z) 0.5)))
0.0ms
(sqrt (* 2 PI))
0.0ms
(sqrt (* 2 PI))

simplify7.7s

Counts
94 → 108
Calls

94 calls. Slowest were:

668.0ms
(+ (* (* (/ (sqrt (* 2 PI)) (exp (+ (- 7 z) 0.5))) (pow (+ (- 7 z) 0.5) (- 0 (- z 0.5)))) (* (+ (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ -176.6150291621406 (- 4 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z))))) (/ PI (sin (* z PI))))) (* (* (/ PI (sin (* z PI))) (/ (sqrt (* 2 PI)) (exp (+ 7 (- 0.5 z))))) (* (pow (+ 7 (- 0.5 z)) (- 0.5 z)) (+ (/ 9.984369578019572e-06 (- 7 z)) (/ 1.5056327351493116e-07 (- 8 z))))))
484.0ms
(+ (* (* (/ (sqrt (* 2 PI)) (exp (+ (- 7 z) 0.5))) (pow (+ (- 7 z) 0.5) (- 0 (- z 0.5)))) (* (+ (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ -176.6150291621406 (- 4 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z))))) (/ PI (sin (* z PI))))) (* (* (/ PI (sin (* z PI))) (/ (sqrt (* 2 PI)) (exp (+ 7 (- 0.5 z))))) (* (pow (+ 7 (- 0.5 z)) (- 0.5 z)) (+ (/ 9.984369578019572e-06 (- 7 z)) (/ 1.5056327351493116e-07 (- 8 z))))))
366.0ms
(+ (* 1/2 (* (/ (* (sqrt 2) (pow z 2)) (exp 7.5)) (sqrt PI))) (+ (* (/ (sqrt 2) (exp 7.5)) (sqrt PI)) (* (/ (* (sqrt 2) z) (exp 7.5)) (sqrt PI))))

prune9.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes482.0ms

Accuracy

0% (1.1b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 1.2b

bsearch11.0ms