Average Error: 15.3 → 0.9
Time: 11.6s
Precision: 64
Internal Precision: 128
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}\]

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 div-inv15.3

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

  4. Applied cbrt-prod0.9

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

  5. Final simplification0.9

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

Reproduce

herbie shell --seed 2019005 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))

Details

Time bar (total: 10.0s)Debug log

sample82.0ms

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: 14.4b

localize18.0ms

Local error

Found 1 expressions with local error:

14.4b
(cbrt (/ g (* 2 a)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 13
Calls

1 calls. Slowest were:

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

series140.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

140.0ms
(cbrt (/ g (* 2 a)))

simplify365.0ms

Counts
8 → 16
Calls

8 calls. Slowest were:

193.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
114.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))))
49.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))

prune174.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
3 → 48
Calls

3 calls. Slowest were:

4.0ms
(/ (cbrt g) (cbrt (* 2 a)))
1.0ms
(cbrt (* 2 a))
0.0ms
(cbrt g)

series796.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

350.0ms
(cbrt (* 2 a))
257.0ms
(cbrt g)
189.0ms
(/ (cbrt g) (cbrt (* 2 a)))

simplify557.0ms

Counts
42 → 57
Calls

42 calls. Slowest were:

231.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
151.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
37.0ms
(/ (exp (* 1/3 (- (log g) (log a)))) (cbrt 2))

prune551.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
4 → 79
Calls

4 calls. Slowest were:

6.0ms
(/ (cbrt (* 2 a)) (cbrt g))
5.0ms
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))
1.0ms
(cbrt (* 2 a))

series950.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

315.0ms
(cbrt (* 2 a))
313.0ms
(cbrt g)
205.0ms
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))
117.0ms
(/ (cbrt (* 2 a)) (cbrt g))

simplify952.0ms

Counts
63 → 91
Calls

63 calls. Slowest were:

172.0ms
(/ (* (cbrt -2) (exp (* 1/3 (- (log (/ -1 g)) (log (/ -1 a)))))) (cbrt -1))
154.0ms
(* (exp (* 1/3 (- (log (/ 1 g)) (log (/ 1 a))))) (cbrt 2))
151.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))

prune924.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
4 → 56
Calls

4 calls. Slowest were:

7.0ms
(* (cbrt g) (/ 1 (cbrt (* 2 a))))
1.0ms
(/ 1 (cbrt (* 2 a)))
1.0ms
(cbrt (* 2 a))

series1.0s

Counts
4 → 12
Calls

4 calls. Slowest were:

375.0ms
(/ 1 (cbrt (* 2 a)))
281.0ms
(cbrt (* 2 a))
249.0ms
(cbrt g)
136.0ms
(* (cbrt g) (/ 1 (cbrt (* 2 a))))

simplify707.0ms

Counts
31 → 68
Calls

31 calls. Slowest were:

167.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
166.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
106.0ms
(* g (* (* (/ 1 (cbrt (* 2 a))) (/ 1 (cbrt (* 2 a)))) (/ 1 (cbrt (* 2 a)))))

prune698.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes374.0ms

Accuracy

0% (0.8b remaining)

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

bsearch2.0ms

end0.0ms

sample1.6s

Algorithm
intervals