Average Error: 15.3 → 0.9
Time: 12.4s
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 15.3

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

  3. Applied cbrt-div0.9

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

  5. Applied clear-num0.9

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

  6. Taylor expanded around 0 34.0

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

  7. Simplified0.9

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

  8. Final simplification0.9

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

Reproduce

herbie shell --seed 2019002 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))

Details

Time bar (total: 10.5s)Debug log

sample55.0ms

Algorithm
intervals

simplify5.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

5.0ms
(cbrt (/ g (* 2 a)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize18.0ms

Local error

Found 1 expressions with local error:

15.3b
(cbrt (/ g (* 2 a)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 13
Calls

1 calls. Slowest were:

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

series124.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

124.0ms
(cbrt (/ g (* 2 a)))

simplify429.0ms

Counts
8 → 16
Calls

8 calls. Slowest were:

197.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
176.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))))
48.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))

prune174.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.6b
(cbrt g)
0.5b
(cbrt (* 2 a))
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)

series764.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

316.0ms
(cbrt (* 2 a))
285.0ms
(cbrt g)
162.0ms
(/ (cbrt g) (cbrt (* 2 a)))

simplify560.0ms

Counts
42 → 57
Calls

42 calls. Slowest were:

199.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
124.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
38.0ms
(/ (exp (* 1/3 (- (log g) (log a)))) (cbrt 2))

prune602.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt g)
0.5b
(cbrt (* 2 a))
0.3b
(/ (cbrt (* 2 a)) (cbrt g))
0.3b
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
4 → 79
Calls

4 calls. Slowest were:

4.0ms
(/ (cbrt (* 2 a)) (cbrt g))
1.0ms
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))
1.0ms
(cbrt (* 2 a))

series990.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

340.0ms
(cbrt (* 2 a))
278.0ms
(cbrt g)
191.0ms
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))
181.0ms
(/ (cbrt (* 2 a)) (cbrt g))

simplify1.0s

Counts
63 → 91
Calls

63 calls. Slowest were:

192.0ms
(* (exp (* 1/3 (- (log (/ 1 g)) (log (/ 1 a))))) (cbrt 2))
175.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
146.0ms
(/ (* (cbrt -2) (exp (* 1/3 (- (log (/ -1 g)) (log (/ -1 a)))))) (cbrt -1))

prune880.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.0b

localize1.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt g)
0.5b
(cbrt (* 2 a))
0.3b
(/ (cbrt (* 2 a)) (cbrt g))
0.3b
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
4 → 79
Calls

4 calls. Slowest were:

3.0ms
(/ (cbrt (* 2 a)) (cbrt g))
1.0ms
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))
0.0ms
(cbrt (* 2 a))

series907.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

336.0ms
(cbrt (* 2 a))
281.0ms
(cbrt g)
160.0ms
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))
130.0ms
(/ (cbrt (* 2 a)) (cbrt g))

simplify1.1s

Counts
63 → 91
Calls

63 calls. Slowest were:

210.0ms
(* (exp (* 1/3 (- (log (/ 1 g)) (log (/ 1 a))))) (cbrt 2))
194.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
189.0ms
(/ (* (cbrt -2) (exp (* 1/3 (- (log (/ -1 g)) (log (/ -1 a)))))) (cbrt -1))

prune757.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.0b

regimes622.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch2.0ms

end0.0ms

sample1.5s

Algorithm
intervals