Average Error: 15.2 → 0.8
Time: 11.3s
Precision: 64
Internal Precision: 128
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{1}{\frac{\sqrt[3]{a \cdot 2}}{\sqrt[3]{g}}}\]

Error

Bits error versus g

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.2

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  2. Using strategy rm

  3. Applied cbrt-div0.8

    \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.8

    \[\leadsto \frac{\color{blue}{1 \cdot \sqrt[3]{g}}}{\sqrt[3]{2 \cdot a}}\]

  6. Applied associate-/l*0.8

    \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}}\]

  7. Final simplification0.8

    \[\leadsto \frac{1}{\frac{\sqrt[3]{a \cdot 2}}{\sqrt[3]{g}}}\]

Reproduce

herbie shell --seed 2019008 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))

Details

Time bar (total: 9.9s)Debug log

sample51.0ms

Algorithm
intervals

simplify3.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

2.0ms
(cbrt (/ g (* 2 a)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize29.0ms

Local error

Found 1 expressions with local error:

17.1b
(cbrt (/ g (* 2 a)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 13
Calls

1 calls. Slowest were:

1.0ms
(cbrt (/ g (* 2 a)))

series129.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

129.0ms
(cbrt (/ g (* 2 a)))

simplify400.0ms

Counts
8 → 16
Calls

8 calls. Slowest were:

244.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
100.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))))
46.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))

prune138.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.6b
(cbrt (* 2 a))
0.6b
(cbrt g)
0.4b
(/ (cbrt g) (cbrt (* 2 a)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
3 → 48
Calls

3 calls. Slowest were:

3.0ms
(/ (cbrt g) (cbrt (* 2 a)))
0.0ms
(cbrt (* 2 a))
0.0ms
(cbrt g)

series741.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

310.0ms
(cbrt (* 2 a))
286.0ms
(cbrt g)
145.0ms
(/ (cbrt g) (cbrt (* 2 a)))

simplify496.0ms

Counts
42 → 57
Calls

42 calls. Slowest were:

139.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
137.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
37.0ms
(/ (exp (* 1/3 (- (log g) (log a)))) (cbrt 2))

prune518.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* 2 a))
0.6b
(cbrt g)
0.4b
(* (cbrt g) (/ 1 (cbrt (* 2 a))))
0.2b
(/ 1 (cbrt (* 2 a)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
4 → 56
Calls

4 calls. Slowest were:

9.0ms
(* (cbrt g) (/ 1 (cbrt (* 2 a))))
2.0ms
(/ 1 (cbrt (* 2 a)))
1.0ms
(cbrt (* 2 a))

series1.1s

Counts
4 → 12
Calls

4 calls. Slowest were:

369.0ms
(cbrt (* 2 a))
355.0ms
(/ 1 (cbrt (* 2 a)))
259.0ms
(cbrt g)
155.0ms
(* (cbrt g) (/ 1 (cbrt (* 2 a))))

simplify689.0ms

Counts
31 → 68
Calls

31 calls. Slowest were:

193.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
126.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
110.0ms
(* g (* (* (/ 1 (cbrt (* 2 a))) (/ 1 (cbrt (* 2 a)))) (/ 1 (cbrt (* 2 a)))))

prune647.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* 2 a))
0.6b
(cbrt g)
0.3b
(/ (cbrt (* 2 a)) (cbrt g))
0.3b
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
4 → 79
Calls

4 calls. Slowest were:

6.0ms
(/ (cbrt (* 2 a)) (cbrt g))
3.0ms
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))
1.0ms
(cbrt (* 2 a))

series956.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

335.0ms
(cbrt (* 2 a))
323.0ms
(cbrt g)
151.0ms
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))
147.0ms
(/ (cbrt (* 2 a)) (cbrt g))

simplify1.1s

Counts
63 → 91
Calls

63 calls. Slowest were:

215.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
194.0ms
(* (exp (* 1/3 (- (log (/ 1 g)) (log (/ 1 a))))) (cbrt 2))
171.0ms
(/ (* (cbrt -2) (exp (* 1/3 (- (log (/ -1 g)) (log (/ -1 a)))))) (cbrt -1))

prune893.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes291.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch2.0ms

end0.0ms

sample1.7s

Algorithm
intervals