Average Error: 13.8 → 13.8
Time: 39.3s
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]{e^{\log \left((\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)_*\right)}} \cdot \left(\sqrt[3]{e^{\log \left((\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)_*\right)}} \cdot \sqrt[3]{e^{\log \left((\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)_*\right)}}\right)\]

Error

Bits error versus x

Derivation

  1. Initial program 13.8

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

  2. Initial simplification13.8

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

  4. Applied add-exp-log13.8

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

  6. Applied add-cube-cbrt13.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{e^{\log \left((\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)_*\right)}} \cdot \sqrt[3]{e^{\log \left((\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)_*\right)}}\right) \cdot \sqrt[3]{e^{\log \left((\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)_*\right)}}}\]

  7. Final simplification13.8

    \[\leadsto \sqrt[3]{e^{\log \left((\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)_*\right)}} \cdot \left(\sqrt[3]{e^{\log \left((\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)_*\right)}} \cdot \sqrt[3]{e^{\log \left((\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)_*\right)}}\right)\]

Reproduce

herbie shell --seed 2018362 +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: 31.3s)Debug log

start137.0ms

Algorithm
intervals

setup336.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.5b

localize66.0ms

Local error

Found 4 expressions with local error:

16.4b
(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)
0.5b
(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 (fma 0.3275911 (fabs x) 1))
0.1b
(/ 1 (fma 0.3275911 (fabs x) 1))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
4 → 56
Calls

4 calls. Slowest were:

1.0ms
(/ 1 (fma 0.3275911 (fabs x) 1))
1.0ms
(/ 1 (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)

series612.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

347.0ms
(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)
204.0ms
(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)))
31.0ms
(/ 1 (fma 0.3275911 (fabs x) 1))
30.0ms
(/ 1 (fma 0.3275911 (fabs x) 1))

simplify1.8s

Counts
20 → 68
Calls

20 calls. Slowest were:

420.0ms
(- (+ (* 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)))))
411.0ms
(- (+ (* 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)))))
319.0ms
(- (+ (* 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)))))

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.4b

localize19.0ms

Local error

Found 4 expressions with local error:

16.4b
(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)
1.5b
(exp (log (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)))
0.5b
(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 (fma 0.3275911 (fabs x) 1))

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
4 → 55
Calls

4 calls. Slowest were:

4.0ms
(exp (log (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)))
1.0ms
(/ 1 (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)

series965.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

371.0ms
(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)
359.0ms
(exp (log (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)))
217.0ms
(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)))
18.0ms
(/ 1 (fma 0.3275911 (fabs x) 1))

simplify4.1s

Counts
24 → 67
Calls

24 calls. Slowest were:

527.0ms
(exp (* (cbrt (log (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))) (cbrt (log (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)))))
464.0ms
(exp (log (* (cbrt (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)) (cbrt (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)))))
435.0ms
(- (+ (* 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)))))

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.4b

localize34.0ms

Local error

Found 4 expressions with local error:

16.4b
(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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)
1.5b
(exp (log (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)))
0.5b
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)))
0.3b
(cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
4 → 52
Calls

4 calls. Slowest were:

4.0ms
(exp (log (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)))
1.0ms
(cbrt (/ 1 (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)

series1.1s

Counts
4 → 12
Calls

4 calls. Slowest were:

370.0ms
(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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)
340.0ms
(exp (log (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)))
211.0ms
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)))
187.0ms
(cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))

simplify4.5s

Counts
25 → 64
Calls

25 calls. Slowest were:

553.0ms
(exp (log (* (cbrt (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)) (cbrt (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)))))
533.0ms
(exp (sqrt (log (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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))))
512.0ms
(exp (log (sqrt (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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))))

prune2.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.4b

localize10.0ms

Local error

Found 4 expressions with local error:

16.4b
(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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)
2.1b
(pow E (log (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)))
0.5b
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)))
0.3b
(cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
4 → 52
Calls

4 calls. Slowest were:

3.0ms
(pow E (log (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)))
1.0ms
(cbrt (/ 1 (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)

series1.8s

Counts
4 → 12
Calls

4 calls. Slowest were:

983.0ms
(pow E (log (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)))
409.0ms
(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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)
213.0ms
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)))
192.0ms
(cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))

simplify6.0s

Counts
24 → 64
Calls

24 calls. Slowest were:

583.0ms
(log (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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))
527.0ms
(sqrt (log (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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)))
501.0ms
(pow E (log (sqrt (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 (* (* (cbrt (/ 1 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 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))))

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.4b

regimes611.0ms

Accuracy

0% (0.1b remaining)

Error of 13.8b against oracle of 13.8b and baseline of 13.8b

bsearch7.0ms