Average Error: 14.0 → 14.0
Time: 45.7s
Precision: 64
Internal Precision: 128
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\sqrt[3]{\log \left(e^{1 - \left(\left(\frac{\left(\frac{-1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741\right) + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + \left(\frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot -0.284496736 + 0.254829592\right)\right) \cdot \frac{1}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left|x\right| \cdot \left(-\left|x\right|\right)}}\right) \cdot \left(\log \left(e^{1 - \left(\left(\frac{\left(\frac{-1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741\right) + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + \left(\frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot -0.284496736 + 0.254829592\right)\right) \cdot \frac{1}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left|x\right| \cdot \left(-\left|x\right|\right)}}\right) \cdot \log \left(e^{1 - \left(\left(\frac{\left(\frac{-1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741\right) + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + \left(\frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot -0.284496736 + 0.254829592\right)\right) \cdot \frac{1}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left|x\right| \cdot \left(-\left|x\right|\right)}}\right)\right)}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.0

    \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  2. Using strategy rm

  3. Applied distribute-rgt-in14.0

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \color{blue}{\left(-0.284496736 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|} + \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right) \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right)}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  4. Applied associate-+r+14.0

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \color{blue}{\left(\left(0.254829592 + -0.284496736 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) + \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right) \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right)}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  5. Simplified14.0

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(0.254829592 + -0.284496736 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) + \color{blue}{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + \left(\frac{-1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  6. Using strategy rm

  7. Applied add-log-exp14.0

    \[\leadsto \color{blue}{\log \left(e^{1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(0.254829592 + -0.284496736 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + \left(\frac{-1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)}\]
  8. Using strategy rm

  9. Applied add-cbrt-cube14.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\log \left(e^{1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(0.254829592 + -0.284496736 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + \left(\frac{-1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right) \cdot \log \left(e^{1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(0.254829592 + -0.284496736 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + \left(\frac{-1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)\right) \cdot \log \left(e^{1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(0.254829592 + -0.284496736 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + \left(\frac{-1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)}}\]

  10. Final simplification14.0

    \[\leadsto \sqrt[3]{\log \left(e^{1 - \left(\left(\frac{\left(\frac{-1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741\right) + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + \left(\frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot -0.284496736 + 0.254829592\right)\right) \cdot \frac{1}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left|x\right| \cdot \left(-\left|x\right|\right)}}\right) \cdot \left(\log \left(e^{1 - \left(\left(\frac{\left(\frac{-1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741\right) + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + \left(\frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot -0.284496736 + 0.254829592\right)\right) \cdot \frac{1}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left|x\right| \cdot \left(-\left|x\right|\right)}}\right) \cdot \log \left(e^{1 - \left(\left(\frac{\left(\frac{-1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741\right) + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + \left(\frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot -0.284496736 + 0.254829592\right)\right) \cdot \frac{1}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left|x\right| \cdot \left(-\left|x\right|\right)}}\right)\right)}\]

Reproduce

herbie shell --seed 2018360 
(FPCore (x)
  :name "Jmat.Real.erf"
  (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))

Details

Time bar (total: 38.1s)Debug log

start153.0ms

Algorithm
intervals

setup223.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.0b

localize58.0ms

Local error

Found 4 expressions with local error:

14.9b
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))
0.5b
(+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))
0.2b
(/ 1 (+ 1 (* 0.3275911 (fabs x))))
0.2b
(/ 1 (+ 1 (* 0.3275911 (fabs x))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
4 → 59
Calls

4 calls. Slowest were:

1.0ms
(+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))
1.0ms
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))
1.0ms
(/ 1 (+ 1 (* 0.3275911 (fabs x))))

series1.2s

Counts
4 → 12
Calls

4 calls. Slowest were:

980.0ms
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))
196.0ms
(+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))
19.0ms
(/ 1 (+ 1 (* 0.3275911 (fabs x))))
18.0ms
(/ 1 (+ 1 (* 0.3275911 (fabs x))))

simplify2.3s

Counts
26 → 71
Calls

26 calls. Slowest were:

419.0ms
(* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))) (/ 1 (+ 1 (* 0.3275911 (fabs x)))))
276.0ms
(* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))
270.0ms
(- (+ (* 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 4))) (+ (* 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 2))) 0.254829592)) (+ (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1))) (* 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 3)))))

prune2.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.9b

localize52.0ms

Local error

Found 4 expressions with local error:

14.9b
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))
0.4b
(/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911))))
0.2b
(/ 1.061405429 (+ 1 (* (fabs x) 0.3275911)))
0.2b
(/ 1 (+ 1 (* 0.3275911 (fabs x))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Counts
4 → 79
Calls

4 calls. Slowest were:

62.0ms
(/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911))))
1.0ms
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))
1.0ms
(/ 1 (+ 1 (* 0.3275911 (fabs x))))

series1.1s

Counts
4 → 12
Calls

4 calls. Slowest were:

952.0ms
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))
139.0ms
(/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911))))
29.0ms
(/ 1 (+ 1 (* 0.3275911 (fabs x))))
20.0ms
(/ 1.061405429 (+ 1 (* (fabs x) 0.3275911)))

simplify6.0s

Counts
50 → 91
Calls

50 calls. Slowest were:

459.0ms
(* (+ (* 1 1) (- (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)) (* 1 (* (fabs x) 0.3275911)))) (+ (* 1 1) (- (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)) (* 1 (* (fabs x) 0.3275911)))))
414.0ms
(* (- 1 (* (fabs x) 0.3275911)) (+ (* 1 1) (- (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)) (* 1 (* (fabs x) 0.3275911)))))
391.0ms
(/ (* (* (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741))) (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741))) (* (* (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (* (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911)))))

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.9b

localize10.0ms

Local error

Found 4 expressions with local error:

14.9b
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))
14.9b
(log (exp (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))))
0.4b
(/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911))))
0.2b
(/ 1.061405429 (+ 1 (* (fabs x) 0.3275911)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Counts
4 → 79
Calls

4 calls. Slowest were:

70.0ms
(/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911))))
3.0ms
(log (exp (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))))
1.0ms
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))

series2.0s

Counts
4 → 12
Calls

4 calls. Slowest were:

952.0ms
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))
885.0ms
(log (exp (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))))
168.0ms
(/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911))))
19.0ms
(/ 1.061405429 (+ 1 (* (fabs x) 0.3275911)))

simplify6.8s

Counts
53 → 91
Calls

53 calls. Slowest were:

490.0ms
(* (+ (* 1 1) (- (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)) (* 1 (* (fabs x) 0.3275911)))) (+ (* 1 1) (- (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)) (* 1 (* (fabs x) 0.3275911)))))
370.0ms
(/ (* (* (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741))) (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741))) (* (* (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (* (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911)))))
354.0ms
(* (- 1 (* (fabs x) 0.3275911)) (+ (* 1 1) (- (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)) (* 1 (* (fabs x) 0.3275911)))))

prune3.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.9b

localize33.0ms

Local error

Found 4 expressions with local error:

14.9b
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))
14.9b
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))
14.9b
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))
14.9b
(log (exp (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
4 → 51
Calls

4 calls. Slowest were:

5.0ms
(log (exp (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))))
3.0ms
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))
2.0ms
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))

series3.9s

Counts
4 → 12
Calls

4 calls. Slowest were:

1.1s
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))
965.0ms
(log (exp (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))))
958.0ms
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))
924.0ms
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))

simplify2.4s

Counts
21 → 63
Calls

21 calls. Slowest were:

174.0ms
(- (+ (* 1.453152027 (/ (exp (- (pow (fabs x) 2))) (pow (+ (* 0.3275911 (fabs x)) 1) 4))) (+ (* 0.284496736 (/ (exp (- (pow (fabs x) 2))) (pow (+ (* 0.3275911 (fabs x)) 1) 2))) 1)) (+ (* 1.061405429 (/ (exp (- (pow (fabs x) 2))) (pow (+ (* 0.3275911 (fabs x)) 1) 5))) (+ (* 1.421413741 (/ (exp (- (pow (fabs x) 2))) (pow (+ (* 0.3275911 (fabs x)) 1) 3))) (* 0.254829592 (/ (exp (- (pow (fabs x) 2))) (+ (* 0.3275911 (fabs x)) 1))))))
173.0ms
(- (+ (* 1.453152027 (/ (exp (- (pow (fabs x) 2))) (pow (+ (* 0.3275911 (fabs x)) 1) 4))) (+ (* 0.284496736 (/ (exp (- (pow (fabs x) 2))) (pow (+ (* 0.3275911 (fabs x)) 1) 2))) 1)) (+ (* 1.061405429 (/ (exp (- (pow (fabs x) 2))) (pow (+ (* 0.3275911 (fabs x)) 1) 5))) (+ (* 1.421413741 (/ (exp (- (pow (fabs x) 2))) (pow (+ (* 0.3275911 (fabs x)) 1) 3))) (* 0.254829592 (/ (exp (- (pow (fabs x) 2))) (+ (* 0.3275911 (fabs x)) 1))))))
160.0ms
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1 (+ 1 (* 0.3275911 (fabs x)))))) (/ (+ (/ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) (+ 1 (* (fabs x) 0.3275911))) (+ (/ -1.453152027 (+ 1 (* (fabs x) 0.3275911))) 1.421413741)) (* (+ 1 (* (fabs x) 0.3275911)) (+ 1 (* (fabs x) 0.3275911)))))) (exp (- (* (fabs x) (fabs x))))))

prune2.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.8b

regimes683.0ms

Accuracy

0% (0.0b remaining)

Error of 14.0b against oracle of 14.0b and baseline of 14.0b

bsearch10.0ms