Average Error: 0.0 → 0.0
Time: 22.8s
Precision: 64
Internal Precision: 128
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[-\frac{n + f}{f - n}\]

Error

Bits error versus f

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]

  2. Final simplification0.0

    \[\leadsto -\frac{n + f}{f - n}\]

Reproduce

herbie shell --seed 2019016 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))

Details

Time bar (total: 22.5s)Debug log

sample100.0ms

Algorithm
intervals
Results
256×(pre true 80)
256×(body real 80)

simplify418.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
418.0ms
(/ (- (+ f n)) (- f n))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b
(/ (- (+ f n)) (- f n))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
24×add-cube-cbrt
24×*-un-lft-identity
24×add-sqr-sqrt
12×distribute-rgt-neg-in
12×distribute-lft-neg-in
10×associate-/l*
4×neg-mul-1
3×add-exp-log
3×add-cbrt-cube
3×associate-/r*
2×associate-/l/
2×distribute-neg-frac
2×associate-/r/
1×add-log-exp
1×flip--
1×div-inv
1×flip-+
1×distribute-frac-neg
1×div-exp
1×div-sub
1×flip3--
1×flip3-+
1×frac-2neg
1×clear-num
1×cbrt-undiv
1×pow1
1×neg-sub0
Counts
1 → 61
Calls
1 calls:
Slowest
10.0ms
(/ (- (+ f n)) (- f n))

series63.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
63.0ms
(/ (- (+ f n)) (- f n))

simplify1.1s

Counts
81 → 64
Calls
81 calls:
Slowest
168.0ms
(- (- (* f f) (* n n)))
117.0ms
(/ (* (* (- (+ f n)) (- (+ f n))) (- (+ f n))) (* (* (- f n) (- f n)) (- f n)))
56.0ms
(/ (- (* (cbrt (+ f n)) (cbrt (+ f n)))) (* (cbrt (- f n)) (cbrt (- f n))))
39.0ms
(/ (* (cbrt (- (+ f n))) (cbrt (- (+ f n)))) (* (cbrt (- f n)) (cbrt (- f n))))
32.0ms
(/ (* (cbrt (+ f n)) (cbrt (+ f n))) 1)

prune586.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (- (+ f n)) (/ 1 (- f n)))
0.0b
(/ 1 (- f n))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-*l*
7×add-cube-cbrt
7×add-exp-log
7×*-un-lft-identity
7×add-sqr-sqrt
6×associate-*r*
5×pow1
4×distribute-neg-frac
4×associate-/r/
4×add-cbrt-cube
3×distribute-rgt-neg-in
3×associate-/r*
3×distribute-lft-neg-in
2×add-log-exp
2×flip--
2×div-inv
2×flip-+
2×prod-exp
2×associate-*l/
2×flip3--
2×flip3-+
2×rec-exp
2×frac-times
1×inv-pow
1×pow-flip
1×cbrt-unprod
1×*-commutative
1×un-div-inv
1×associate-*r/
1×pow-prod-down
1×frac-2neg
1×neg-mul-1
1×clear-num
1×distribute-lft-neg-out
Counts
2 → 53
Calls
2 calls:
Slowest
10.0ms
(* (- (+ f n)) (/ 1 (- f n)))
2.0ms
(/ 1 (- f n))

series84.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
57.0ms
(* (- (+ f n)) (/ 1 (- f n)))
27.0ms
(/ 1 (- f n))

simplify1.8s

Counts
38 → 59
Calls
38 calls:
Slowest
434.0ms
(* (- (+ (pow f 3) (pow n 3))) (/ 1 (- f n)))
321.0ms
(* (+ (* f f) (- (* n n) (* f n))) (- f n))
222.0ms
(* (- (- (* f f) (* n n))) 1)
193.0ms
(* (- (+ f n)) (/ 1 (- f n)))
128.0ms
(* (* (* (- (+ f n)) (- (+ f n))) (- (+ f n))) (* (* (/ 1 (- f n)) (/ 1 (- f n))) (/ 1 (- f n))))

prune422.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ f n))
0.6b
(cbrt (+ f n))
0.6b
(cbrt (+ f n))
0.5b
(* (cbrt (+ f n)) (cbrt (+ f n)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
15×cbrt-prod
11×add-cube-cbrt
11×*-un-lft-identity
11×add-sqr-sqrt
9×flip-+
9×flip3-+
9×pow1
7×pow1/3
6×add-exp-log
6×associate-*l*
6×associate-*r*
4×add-log-exp
4×add-cbrt-cube
4×frac-times
2×pow-prod-up
2×associate-*r/
2×associate-*l/
2×pow-prod-down
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-plus
1×pow2
Counts
4 → 75
Calls
4 calls:
Slowest
10.0ms
(* (cbrt (+ f n)) (cbrt (+ f n)))
4.0ms
(cbrt (+ f n))
1.0ms
(cbrt (+ f n))
1.0ms
(cbrt (+ f n))

series672.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
207.0ms
(* (cbrt (+ f n)) (cbrt (+ f n)))
164.0ms
(cbrt (+ f n))
159.0ms
(cbrt (+ f n))
141.0ms
(cbrt (+ f n))

simplify1.6s

Counts
59 → 87
Calls
59 calls:
Slowest
223.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow n 2)) 1/3) f)) (pow n 1/3)) (* 1/9 (* (pow (/ 1 (pow n 5)) 1/3) (pow f 2))))
178.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow n 2)) 1/3) f)) (pow n 1/3)) (* 1/9 (* (pow (/ 1 (pow n 5)) 1/3) (pow f 2))))
161.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow n 2)) 1/3) f)) (pow n 1/3)) (* 1/9 (* (pow (/ 1 (pow n 5)) 1/3) (pow f 2))))
145.0ms
(- (+ (* 2/3 (* (pow (/ 1 n) 1/3) f)) (pow n 2/3)) (* 1/9 (* (pow (/ 1 (pow n 4)) 1/3) (pow f 2))))
115.0ms
(* (cbrt (+ (pow f 3) (pow n 3))) (cbrt (- (* f f) (* n n))))

prune818.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

33.2b
(* (* (- (+ f n)) (/ 1 (- (pow f 3) (pow n 3)))) (+ (* f f) (* (+ f n) n)))
11.0b
(* (- (+ f n)) (/ 1 (- (pow f 3) (pow n 3))))
5.0b
(- (pow f 3) (pow n 3))
1.4b
(+ (* f f) (* (+ f n) n))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
20×frac-times
16×distribute-neg-frac
16×flip-+
16×add-exp-log
16×flip3-+
14×associate-*l/
11×associate-*l*
11×add-cbrt-cube
11×*-un-lft-identity
11×pow1
11×add-sqr-sqrt
9×add-cube-cbrt
9×associate-*r*
8×add-log-exp
7×prod-exp
6×associate-*r/
4×cbrt-unprod
4×un-div-inv
4×pow-prod-down
3×distribute-rgt-neg-in
3×distribute-lft-neg-in
3×distribute-lft-neg-out
2×flip--
2×*-commutative
2×associate-/r/
2×flip3--
2×rec-exp
1×difference-of-squares
1×distribute-lft-out--
1×div-inv
1×diff-log
1×distribute-lft-in
1×sub-neg
1×sum-log
1×neg-mul-1
1×+-commutative
1×difference-cubes
1×distribute-rgt-in
Counts
4 → 103
Calls
4 calls:
Slowest
34.0ms
(* (* (- (+ f n)) (/ 1 (- (pow f 3) (pow n 3)))) (+ (* f f) (* (+ f n) n)))
8.0ms
(* (- (+ f n)) (/ 1 (- (pow f 3) (pow n 3))))
3.0ms
(- (pow f 3) (pow n 3))
2.0ms
(+ (* f f) (* (+ f n) n))

series166.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
72.0ms
(* (* (- (+ f n)) (/ 1 (- (pow f 3) (pow n 3)))) (+ (* f f) (* (+ f n) n)))
41.0ms
(- (pow f 3) (pow n 3))
36.0ms
(* (- (+ f n)) (/ 1 (- (pow f 3) (pow n 3))))
17.0ms
(+ (* f f) (* (+ f n) n))

simplify11.9s

Counts
91 → 115
Calls
91 calls:
Slowest
640.0ms
(* (- (pow f 3) (pow n 3)) (- (* f f) (* (+ f n) n)))
613.0ms
(* (* (+ (* f f) (- (* n n) (* f n))) (- (pow f 3) (pow n 3))) (- (* f f) (* (+ f n) n)))
562.0ms
(* (- (pow f 3) (pow n 3)) (- (* f f) (* (+ f n) n)))
550.0ms
(* (* (- (- (* f f) (* n n))) 1) (+ (* f f) (* (+ f n) n)))
492.0ms
(* (- (+ f n)) (- (* (* f f) (* f f)) (* (* (+ f n) n) (* (+ f n) n))))

prune1.4s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes95.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch2.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
8000×(pre true 80)
8000×(body real 80)