Average Error: 13.7 → 13.7
Time: 29.7s
Precision: 64
Internal Precision: 128
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[e^{\log \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\sqrt[3]{\left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_* \cdot \frac{-1}{e^{\left|x\right| \cdot \left|x\right|}} + 1\right)}\]

Error

Bits error versus x

Derivation

  1. Initial program 13.7

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

  2. Simplified13.7

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

  4. Applied add-cbrt-cube13.7

    \[\leadsto (\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\color{blue}{\sqrt[3]{\left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*\]
  5. Using strategy rm

  6. Applied fma-udef13.7

    \[\leadsto \color{blue}{\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}} \cdot (\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\sqrt[3]{\left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_* + 1}\]
  7. Using strategy rm

  8. Applied add-exp-log13.7

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

  9. Final simplification13.7

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

Reproduce

herbie shell --seed 2019007 +o rules:numerics
(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: 28.0s)Debug log

sample79.0ms

Algorithm
intervals

simplify197.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

197.0ms
(- 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))))))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.8b

localize74.0ms

Local error

Found 4 expressions with local error:

13.8b
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)
0.4b
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))
0.1b
(/ 1.061405429 (fma 0.3275911 (fabs x) 1))
0.1b
(/ 1 (fma 0.3275911 (fabs x) 1))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
4 → 53
Calls

4 calls. Slowest were:

1.0ms
(/ 1 (fma 0.3275911 (fabs x) 1))
1.0ms
(/ 1.061405429 (fma 0.3275911 (fabs x) 1))
0.0ms
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)

series680.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

403.0ms
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)
214.0ms
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))
32.0ms
(/ 1.061405429 (fma 0.3275911 (fabs x) 1))
30.0ms
(/ 1 (fma 0.3275911 (fabs x) 1))

simplify1.5s

Counts
19 → 65
Calls

19 calls. Slowest were:

338.0ms
(- (+ (* 0.254829592 (/ 1 (+ (* 0.3275911 (fabs x)) 1))) (+ (* 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 5))) (* 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 3))))) (+ (* 0.284496736 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 2))) (* 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 4)))))
271.0ms
(- (+ (* 0.254829592 (/ 1 (+ (* 0.3275911 (fabs x)) 1))) (+ (* 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 5))) (* 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 3))))) (+ (* 0.284496736 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 2))) (* 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 4)))))
249.0ms
(- (+ (* 0.254829592 (/ 1 (+ (* 0.3275911 (fabs x)) 1))) (+ (* 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 5))) (* 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 3))))) (+ (* 0.284496736 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 2))) (* 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 4)))))

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.7b

localize57.0ms

Local error

Found 4 expressions with local error:

20.5b
(cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))))
13.8b
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)
0.4b
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))
0.1b
(* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Counts
4 → 66
Calls

4 calls. Slowest were:

12.0ms
(cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))))
7.0ms
(* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))
0.0ms
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)

series710.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

345.0ms
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)
233.0ms
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))
80.0ms
(cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))))
51.0ms
(* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))

simplify2.9s

Counts
36 → 78
Calls

36 calls. Slowest were:

314.0ms
(- (+ (* 0.254829592 (/ 1 (+ (* 0.3275911 (fabs x)) 1))) (+ (/ (cbrt 1.1957597040827896) (pow (+ (* 0.3275911 (fabs x)) 1) 5)) (* 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 3))))) (+ (* 0.284496736 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 2))) (* 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 4)))))
277.0ms
(/ 1.1265814847106739 (pow (+ (* 0.3275911 (fabs x)) 1) 2))
260.0ms
(- (+ (* 0.254829592 (/ 1 (+ (* 0.3275911 (fabs x)) 1))) (+ (/ (cbrt 1.1957597040827896) (pow (+ (* 0.3275911 (fabs x)) 1) 5)) (* 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 3))))) (+ (* 0.284496736 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 2))) (* 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 4)))))

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.7b

localize17.0ms

Local error

Found 4 expressions with local error:

20.5b
(cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))))
13.7b
(+ (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))) 1)
0.4b
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))
0.1b
(* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
4 → 71
Calls

4 calls. Slowest were:

7.0ms
(cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))))
5.0ms
(+ (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))) 1)
4.0ms
(* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))

series837.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

485.0ms
(+ (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))) 1)
268.0ms
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))
54.0ms
(cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))))
30.0ms
(* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))

simplify3.2s

Counts
39 → 83
Calls

39 calls. Slowest were:

293.0ms
(- (+ (* 0.254829592 (/ 1 (+ (* 0.3275911 (fabs x)) 1))) (+ (/ (cbrt 1.1957597040827896) (pow (+ (* 0.3275911 (fabs x)) 1) 5)) (* 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 3))))) (+ (* 0.284496736 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 2))) (* 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 4)))))
256.0ms
(- (+ (* 0.254829592 (/ 1 (+ (* 0.3275911 (fabs x)) 1))) (+ (/ (cbrt 1.1957597040827896) (pow (+ (* 0.3275911 (fabs x)) 1) 5)) (* 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 3))))) (+ (* 0.284496736 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 2))) (* 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 4)))))
254.0ms
(/ 1.1265814847106739 (pow (+ (* 0.3275911 (fabs x)) 1) 2))

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.7b

localize18.0ms

Local error

Found 4 expressions with local error:

20.5b
(cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))))
13.7b
(+ (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))) 1)
1.3b
(exp (log (+ (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))) 1)))
0.4b
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Counts
4 → 63
Calls

4 calls. Slowest were:

12.0ms
(cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))))
8.0ms
(exp (log (+ (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))) 1)))
7.0ms
(+ (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))) 1)

series1.1s

Counts
4 → 12
Calls

4 calls. Slowest were:

422.0ms
(exp (log (+ (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))) 1)))
397.0ms
(+ (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))) 1)
224.0ms
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))
67.0ms
(cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))))

simplify6.0s

Counts
33 → 75
Calls

33 calls. Slowest were:

951.0ms
(* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))))
553.0ms
(exp (log (* (cbrt (+ (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))) 1)) (cbrt (+ (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))) 1)))))
542.0ms
(exp (log (sqrt (+ (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (cbrt (* (* (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))) 1))))

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.7b

regimes518.0ms

Accuracy

0% (0.1b remaining)

Error of 13.7b against oracle of 13.7b and baseline of 13.7b

bsearch7.0ms

end0.0ms

sample3.6s

Algorithm
intervals