Average Error: 15.3 → 0.9
Time: 12.8s
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 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))

Details

Time bar (total: 11.1s)Debug log

sample80.0ms

Algorithm
intervals

simplify3.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
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)))

simplify495.0ms

Counts
8 → 18
Calls

8 calls. Slowest were:

220.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
193.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))))
65.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))

prune149.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.6b
(cbrt g)
0.5b
(cbrt (* 2 a))
0.4b
(/ (cbrt g) (cbrt (* 2 a)))

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)

series800.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

316.0ms
(cbrt (* 2 a))
295.0ms
(cbrt g)
188.0ms
(/ (cbrt g) (cbrt (* 2 a)))

simplify629.0ms

Counts
42 → 63
Calls

42 calls. Slowest were:

230.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
163.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
44.0ms
(/ (exp (* 1/3 (- (log g) (log a)))) (cbrt 2))

prune563.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

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)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
4 → 87
Calls

4 calls. Slowest were:

7.0ms
(/ (cbrt (* 2 a)) (cbrt g))
3.0ms
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))
2.0ms
(cbrt (* 2 a))

series954.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

351.0ms
(cbrt (* 2 a))
285.0ms
(cbrt g)
160.0ms
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))
157.0ms
(/ (cbrt (* 2 a)) (cbrt g))

simplify1.1s

Counts
63 → 99
Calls

63 calls. Slowest were:

209.0ms
(* (exp (* 1/3 (- (log (/ 1 g)) (log (/ 1 a))))) (cbrt 2))
197.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
183.0ms
(/ (* (cbrt -2) (exp (* 1/3 (- (log (/ -1 g)) (log (/ -1 a)))))) (cbrt -1))

prune888.0ms

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)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
4 → 87
Calls

4 calls. Slowest were:

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

series927.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

349.0ms
(cbrt g)
293.0ms
(cbrt (* 2 a))
166.0ms
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))
119.0ms
(/ (cbrt (* 2 a)) (cbrt g))

simplify1.2s

Counts
63 → 99
Calls

63 calls. Slowest were:

249.0ms
(* (exp (* 1/3 (- (log (/ 1 g)) (log (/ 1 a))))) (cbrt 2))
182.0ms
(/ (* (cbrt -2) (exp (* 1/3 (- (log (/ -1 g)) (log (/ -1 a)))))) (cbrt -1))
178.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))

prune996.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.0b

regimes540.0ms

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