Average Error: 15.1 → 0.9
Time: 11.1s
Precision: 64
Internal Precision: 128
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}\]

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 15.1

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  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 div-inv0.9

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

  6. Final simplification0.9

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

Reproduce

herbie shell --seed 2019007 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))

Details

Time bar (total: 9.3s)Debug log

sample48.0ms

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: 16.9b

localize15.0ms

Local error

Found 1 expressions with local error:

16.9b
(cbrt (/ g (* 2 a)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

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

series139.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

139.0ms
(cbrt (/ g (* 2 a)))

simplify467.0ms

Counts
8 → 18
Calls

8 calls. Slowest were:

192.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
177.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))))
82.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))

prune130.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
3 → 54
Calls

3 calls. Slowest were:

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

series828.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

354.0ms
(cbrt (* 2 a))
291.0ms
(cbrt g)
184.0ms
(/ (cbrt g) (cbrt (* 2 a)))

simplify569.0ms

Counts
42 → 63
Calls

42 calls. Slowest were:

181.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
155.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
37.0ms
(/ (exp (* 1/3 (- (log g) (log a)))) (cbrt 2))

prune476.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

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 → 64
Calls

4 calls. Slowest were:

6.0ms
(* (cbrt g) (/ 1 (cbrt (* 2 a))))
1.0ms
(/ 1 (cbrt (* 2 a)))
0.0ms
(cbrt (* 2 a))

series1.2s

Counts
4 → 12
Calls

4 calls. Slowest were:

398.0ms
(/ 1 (cbrt (* 2 a)))
335.0ms
(cbrt (* 2 a))
315.0ms
(cbrt g)
153.0ms
(* (cbrt g) (/ 1 (cbrt (* 2 a))))

simplify811.0ms

Counts
31 → 76
Calls

31 calls. Slowest were:

200.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
188.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
134.0ms
(* g (* (* (/ 1 (cbrt (* 2 a))) (/ 1 (cbrt (* 2 a)))) (/ 1 (cbrt (* 2 a)))))

prune688.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
3 → 50
Calls

3 calls. Slowest were:

4.0ms
(* (cbrt g) (cbrt (/ 1 (* 2 a))))
1.0ms
(cbrt (/ 1 (* 2 a)))
0.0ms
(cbrt g)

series737.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

327.0ms
(cbrt (/ 1 (* 2 a)))
273.0ms
(cbrt g)
137.0ms
(* (cbrt g) (cbrt (/ 1 (* 2 a))))

simplify665.0ms

Counts
28 → 59
Calls

28 calls. Slowest were:

213.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
159.0ms
(* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (* (cbrt -1) (cbrt -1/2)))
78.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))

prune465.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 0.0b

regimes527.0ms

Accuracy

0% (0.8b remaining)

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

bsearch1.0ms

end0.0ms

sample1.5s

Algorithm
intervals