Average Error: 15.0 → 0.9
Time: 10.8s
Precision: 64
Internal Precision: 128
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}\]

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 15.0

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

  3. Applied cbrt-div0.9

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

  4. Taylor expanded around 0 33.7

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

  5. Simplified0.9

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

  6. Final simplification0.9

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

Reproduce

herbie shell --seed 2019004 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))

Details

Time bar (total: 9.3s)Debug log

sample74.0ms

Algorithm
intervals

simplify5.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize17.0ms

Local error

Found 1 expressions with local error:

18.1b
(cbrt (/ g (* 2 a)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

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

series152.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

152.0ms
(cbrt (/ g (* 2 a)))

simplify485.0ms

Counts
8 → 18
Calls

8 calls. Slowest were:

223.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
211.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))))
43.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))

prune133.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite4.0ms

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)

series691.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

308.0ms
(cbrt (* 2 a))
245.0ms
(cbrt g)
138.0ms
(/ (cbrt g) (cbrt (* 2 a)))

simplify671.0ms

Counts
42 → 63
Calls

42 calls. Slowest were:

242.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
206.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
48.0ms
(/ (exp (* 1/3 (- (log g) (log a)))) (cbrt 2))

prune595.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.0b

localize1.0ms

Local error

Found 3 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
3 → 54
Calls

3 calls. Slowest were:

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

series807.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

333.0ms
(cbrt (* 2 a))
324.0ms
(cbrt g)
150.0ms
(/ (cbrt g) (cbrt (* 2 a)))

simplify591.0ms

Counts
42 → 63
Calls

42 calls. Slowest were:

181.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
177.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
50.0ms
(/ (exp (* 1/3 (- (log g) (log a)))) (cbrt 2))

prune627.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
3 → 50
Calls

3 calls. Slowest were:

8.0ms
(* (cbrt g) (cbrt (/ 1 (* 2 a))))
2.0ms
(cbrt (/ 1 (* 2 a)))
0.0ms
(cbrt g)

series770.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

323.0ms
(cbrt g)
306.0ms
(cbrt (/ 1 (* 2 a)))
141.0ms
(* (cbrt g) (cbrt (/ 1 (* 2 a))))

simplify558.0ms

Counts
28 → 59
Calls

28 calls. Slowest were:

197.0ms
(* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (* (cbrt -1) (cbrt -1/2)))
163.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
43.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))

prune481.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.0b

regimes582.0ms

Accuracy

0% (0.8b remaining)

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

bsearch1.0ms

end0.0ms

sample2.0s

Algorithm
intervals