Average Error: 1.8 → 0.7
Time: 2.0m
Precision: 64
Internal Precision: 128
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \frac{{\left(7.5 - z\right)}^{0.5}}{{\left(7.5 - z\right)}^{z} \cdot e^{7.5 - z}}\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \left(\frac{-176.6150291621406}{5 - \left(1 + z\right)} + \frac{771.3234287776531}{1 - \left(-2 + z\right)}\right)\right) + \left(\left(\frac{12.507343278686905}{6 - \left(1 + z\right)} + \frac{-0.13857109526572012}{5 + \left(1 - z\right)}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6} + \frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(1 + z\right)}\right)\right)\right)\]

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. Taylor expanded around inf 0.7

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \color{blue}{\frac{e^{\log \left(7.5 - z\right) \cdot \left(0.5 - z\right)}}{e^{7.5 - z}}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\]

  4. Simplified0.7

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \color{blue}{\frac{{\left(7.5 - z\right)}^{\left(0.5 - z\right)}}{e^{7.5 - z}}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\]
  5. Using strategy rm

  6. Applied pow-sub0.7

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \frac{\color{blue}{\frac{{\left(7.5 - z\right)}^{0.5}}{{\left(7.5 - z\right)}^{z}}}}{e^{7.5 - z}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\]

  7. Applied associate-/l/0.7

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \color{blue}{\frac{{\left(7.5 - z\right)}^{0.5}}{e^{7.5 - z} \cdot {\left(7.5 - z\right)}^{z}}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\]

  8. Final simplification0.7

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \frac{{\left(7.5 - z\right)}^{0.5}}{{\left(7.5 - z\right)}^{z} \cdot e^{7.5 - z}}\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \left(\frac{-176.6150291621406}{5 - \left(1 + z\right)} + \frac{771.3234287776531}{1 - \left(-2 + z\right)}\right)\right) + \left(\left(\frac{12.507343278686905}{6 - \left(1 + z\right)} + \frac{-0.13857109526572012}{5 + \left(1 - z\right)}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6} + \frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(1 + z\right)}\right)\right)\right)\]

Reproduce

herbie shell --seed 2019016 +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: 2.0m)Debug log

sample2.3s

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)

simplify173.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
173.0ms
(* (/ 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)))))

prune103.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize208.0ms

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)))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
22×associate-*l*
21×*-un-lft-identity
17×add-sqr-sqrt
15×add-cube-cbrt
14×unpow-prod-up
11×add-exp-log
9×prod-diff
9×fma-def
8×add-log-exp
6×prod-exp
6×add-cbrt-cube
5×associate-*r*
5×unpow-prod-down
4×log1p-expm1-u
4×pow1
4×expm1-log1p-u
3×flip-+
3×associate-/r/
3×frac-add
3×flip3-+
3×rec-exp
2×pow-sub
2×distribute-lft-out
2×div-inv
2×associate--l+
2×pow-exp
2×sub-neg
2×sum-log
2×+-commutative
2×pow-to-exp
1×difference-of-squares
1×associate--r-
1×distribute-lft-out--
1×flip--
1×cbrt-unprod
1×sqrt-prod
1×*-commutative
1×un-div-inv
1×associate-*r/
1×associate-*l/
1×exp-diff
1×pow1/2
1×flip3--
1×associate-+l+
1×frac-times
Counts
4 → 100
Calls
4 calls:
Slowest
51.0ms
(* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- (- 1 z) (- -6 0.5)))))
14.0ms
(+ (+ 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))

series158.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
114.0ms
(* (pow (- (- 1 z) (- -6 0.5)) (- (- 1 z) (- 1 0.5))) (/ 1 (exp (- (- 1 z) (- -6 0.5)))))
23.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
21.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify16.8s

Counts
65 → 110
Calls
65 calls:
Slowest
1.2s
(pow (+ (sqrt (- 1 z)) (sqrt (- -6 0.5))) (- (- 1 z) (- 1 0.5)))
900.0ms
(pow (- (- 1 z) (- -6 0.5)) (fma (sqrt (- 1 z)) (sqrt (- 1 z)) (- (* (sqrt (- 1 0.5)) (sqrt (- 1 0.5))))))
706.0ms
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))
688.0ms
(+ (* (+ (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))
635.0ms
(pow (- (- 1 z) (- -6 0.5)) (fma (sqrt (- 1 z)) (sqrt (- 1 z)) (- (* (cbrt (- 1 0.5)) (* (cbrt (- 1 0.5)) (cbrt (- 1 0.5)))))))

prune5.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

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 (- 7.5 z) (- 0.5 z)) (exp (- 7.5 z)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
31×*-un-lft-identity
27×add-cube-cbrt
27×add-sqr-sqrt
18×exp-sum
18×unpow-prod-down
15×sub-neg
12×unpow-prod-up
9×fma-def
8×add-log-exp
8×associate-/l*
6×add-exp-log
6×add-cbrt-cube
5×associate-/r*
4×log1p-expm1-u
4×pow1
4×expm1-log1p-u
3×flip-+
3×associate-/r/
3×frac-add
3×div-exp
3×flip3-+
2×distribute-lft-out
2×div-inv
2×sum-log
2×+-commutative
1×associate-/l/
1×pow-sub
1×flip--
1×sqrt-prod
1×pow-exp
1×exp-diff
1×pow1/2
1×flip3--
1×frac-2neg
1×clear-num
1×associate-+l+
1×cbrt-undiv
1×pow-to-exp
Counts
4 → 123
Calls
4 calls:
Slowest
14.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
13.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
6.0ms
(/ (pow (- 7.5 z) (- 0.5 z)) (exp (- 7.5 z)))
1.0ms
(sqrt (* 2 PI))

series135.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
82.0ms
(/ (pow (- 7.5 z) (- 0.5 z)) (exp (- 7.5 z)))
33.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
20.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify8.1s

Counts
125 → 133
Calls
125 calls:
Slowest
1.0s
(+ (* (+ (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))
666.0ms
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))
664.0ms
(* (* (* (/ PI (sin (* PI z))) (sqrt (* 2 PI))) (/ (pow (- 7.5 z) (- 0.5 z)) (exp (- 7.5 z)))) (+ (+ (+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1)))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))) (+ (+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))))
372.0ms
(- (+ (* 4116.070392404628 (/ 1 (pow z 3))) (+ (* 1607.5101696843972 (/ 1 (pow z 2))) (* 594.7083996155126 (/ 1 z)))))
344.0ms
(- (+ (* 4116.070392404628 (/ 1 (pow z 3))) (+ (* 1607.5101696843972 (/ 1 (pow z 2))) (* 594.7083996155126 (/ 1 z)))))

prune5.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

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 (- 7.5 z) 0.5) (* (exp (- 7.5 z)) (pow (- 7.5 z) z)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
21×add-exp-log
14×*-un-lft-identity
12×div-exp
10×add-cube-cbrt
10×add-sqr-sqrt
9×prod-exp
9×add-cbrt-cube
9×fma-def
8×add-log-exp
7×pow-exp
7×pow-to-exp
6×associate-/l*
6×times-frac
6×unpow-prod-down
4×log1p-expm1-u
4×pow1
4×expm1-log1p-u
3×flip-+
3×associate-/r/
3×frac-add
3×flip3-+
2×distribute-lft-out
2×div-inv
2×sum-log
2×+-commutative
2×cbrt-undiv
1×flip--
1×cbrt-unprod
1×sqrt-prod
1×associate-*l/
1×exp-diff
1×pow1/2
1×flip3--
1×frac-2neg
1×associate-/r*
1×clear-num
1×associate-+l+
Counts
4 → 92
Calls
4 calls:
Slowest
17.0ms
(/ (pow (- 7.5 z) 0.5) (* (exp (- 7.5 z)) (pow (- 7.5 z) z)))
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))))
1.0ms
(sqrt (* 2 PI))

series290.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
219.0ms
(/ (pow (- 7.5 z) 0.5) (* (exp (- 7.5 z)) (pow (- 7.5 z) z)))
37.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
34.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify8.9s

Counts
60 → 102
Calls
60 calls:
Slowest
733.0ms
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))
709.0ms
(+ (* (+ (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))
466.0ms
(- (+ (* 4116.070392404628 (/ 1 (pow z 3))) (+ (* 1607.5101696843972 (/ 1 (pow z 2))) (* 594.7083996155126 (/ 1 z)))))
370.0ms
(- (* (log (- 7.5 z)) 0.5) (+ (- 7.5 z) (log (pow (- 7.5 z) z))))
358.0ms
(- (* (log (- 7.5 z)) 0.5) (+ (- 7.5 z) (* (log (- 7.5 z)) z)))

prune5.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize50.0ms

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

rewrite60.0ms

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
42.0ms
(+ (+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))
11.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
5.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
1.0ms
(sqrt (* 2 PI))

series128.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
55.0ms
(+ (+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))
37.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
34.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify16.3s

Counts
58 → 97
Calls
58 calls:
Slowest
767.0ms
(* (* (+ (- 1 z) 5) (- 6 (+ z 1))) (- (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6))))
764.0ms
(* (* (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)))))
748.0ms
(* (exp (+ (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1))))) (exp (+ (/ 1.5056327351493116e-07 (- 9 (+ z 1))) (/ 9.984369578019572e-06 (- (- 1 z) -6)))))
745.0ms
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))
732.0ms
(* (- (/ -0.13857109526572012 (+ (- 1 z) 5)) (/ 12.507343278686905 (- 6 (+ z 1)))) (* (- 9 (+ z 1)) (- (- 1 z) -6)))

prune5.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes298.0ms

Accuracy

0% (0.6b remaining)

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

bsearch7.0ms

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)