Average Error: 0.0 → 0.0
Time: 54.7s
Precision: 64
Internal Precision: 128
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[c \cdot i + \left(\left(z \cdot t + x \cdot y\right) + a \cdot b\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]

  2. Final simplification0.0

    \[\leadsto c \cdot i + \left(\left(z \cdot t + x \cdot y\right) + a \cdot b\right)\]

Reproduce

herbie shell --seed 2019022 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

Details

Time bar (total: 53.4s)Debug log

sample93.0ms

Algorithm
intervals
Results
63.0ms423×body80valid

simplify80.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
80.0ms
(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x y) (* z t)) (* a b))
0.0b
(+ (* x y) (* z t))
0.0b
(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
19×add-log-exp
10×sum-log
3×flip-+
3×add-cube-cbrt
3×add-exp-log
3×add-cbrt-cube
3×flip3-+
3×*-un-lft-identity
3×+-commutative
3×pow1
3×add-sqr-sqrt
2×associate-+l+
Counts
3 → 38
Calls
3 calls:
Slowest
47.0ms
(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))
16.0ms
(+ (+ (* x y) (* z t)) (* a b))
4.0ms
(+ (* x y) (* z t))

series369.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
288.0ms
(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))
50.0ms
(+ (+ (* x y) (* z t)) (* a b))
31.0ms
(+ (* x y) (* z t))

simplify633.0ms

Counts
17 → 47
Calls
17 calls:
Slowest
184.0ms
(* (* (* (exp (* x y)) (exp (* z t))) (exp (* a b))) (exp (* c i)))
158.0ms
(* (* (exp (+ (* x y) (* z t))) (exp (* a b))) (exp (* c i)))
115.0ms
(* (exp (+ (+ (* x y) (* z t)) (* a b))) (exp (* c i)))
48.0ms
(* (* (exp (* x y)) (exp (* z t))) (exp (* a b)))
44.0ms
(* (exp (+ (* x y) (* z t))) (exp (* a b)))

prune652.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.7b
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.7b
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.6b
(* (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))

rewrite121.0ms

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
71.0ms
(* (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
18.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
15.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
15.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

series675.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
226.0ms
(* (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
179.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
135.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
135.0ms
(cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

simplify8.3s

Counts
59 → 87
Calls
59 calls:
Slowest
772.0ms
(cbrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))
723.0ms
(cbrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))
713.0ms
(* (cbrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3))) (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
697.0ms
(* (cbrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3))) (cbrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3))))
692.0ms
(cbrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.3b
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.3b
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.3b
(* (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
0.0b
(+ (+ (* x y) (* z t)) (* a b))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-div
12×sqrt-prod
12×add-sqr-sqrt
10×add-cube-cbrt
10×*-un-lft-identity
9×add-log-exp
9×flip-+
9×flip3-+
9×pow1
6×add-exp-log
6×associate-*l*
6×associate-*r*
6×pow1/2
6×add-cbrt-cube
4×frac-times
3×sum-log
2×pow-prod-up
2×associate-*r/
2×associate-*l/
2×pow-prod-down
2×rem-sqrt-square
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×sqrt-unprod
1×pow-plus
1×rem-square-sqrt
1×associate-+l+
1×+-commutative
1×pow2
Counts
4 → 79
Calls
4 calls:
Slowest
80.0ms
(* (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
42.0ms
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
29.0ms
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
7.0ms
(+ (+ (* x y) (* z t)) (* a b))

series7.5s

Counts
4 → 12
Calls
4 calls:
Slowest
3.7s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
3.5s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
242.0ms
(* (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
44.0ms
(+ (+ (* x y) (* z t)) (* a b))

simplify5.9s

Counts
62 → 91
Calls
62 calls:
Slowest
760.0ms
(* (sqrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3))) (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
751.0ms
(sqrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))
711.0ms
(sqrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))
669.0ms
(* (sqrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3))) (sqrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3))))
169.0ms
(* (sqrt (- (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))) (* (* c i) (* c i)))) (sqrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3))))

prune1.6s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.3b
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.3b
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.3b
(* (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))) (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))))

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-div
27×sqrt-prod
16×add-sqr-sqrt
13×add-cube-cbrt
13×*-un-lft-identity
9×flip-+
9×associate-*l*
9×associate-*r*
9×flip3-+
9×pow1
7×pow1/2
6×add-exp-log
6×add-cbrt-cube
4×add-log-exp
4×frac-times
3×rem-sqrt-square
2×pow-prod-up
2×associate-*r/
2×associate-*l/
2×pow-prod-down
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×sqrt-unprod
1×pow-plus
1×rem-square-sqrt
1×pow2
Counts
4 → 86
Calls
4 calls:
Slowest
100.0ms
(* (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))) (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))))
60.0ms
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
52.0ms
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
45.0ms
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

series14.4s

Counts
4 → 12
Calls
4 calls:
Slowest
3.7s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
3.7s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
3.6s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
3.4s
(* (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))) (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))))

simplify6.0s

Counts
70 → 98
Calls
70 calls:
Slowest
676.0ms
(* (sqrt (sqrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))) (sqrt (sqrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))))
667.0ms
(sqrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))
651.0ms
(sqrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))
634.0ms
(sqrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))
619.0ms
(* (sqrt (sqrt (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)))) (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))))

prune1.7s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes1.4s

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.6s13866×body80valid