Average Error: 0.1 → 0.1
Time: 10.3s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[\left(d2 + \left(d3 + 3\right)\right) \cdot d1\]

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[d1 \cdot \left(\left(3 + d2\right) + d3\right)\]

Derivation

  1. Initial program 0.1

    \[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]

  2. Simplified0.1

    \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(3 + d3\right)\right)}\]

  3. Final simplification0.1

    \[\leadsto \left(d2 + \left(d3 + 3\right)\right) \cdot d1\]

Reproduce

herbie shell --seed 2019021 
(FPCore (d1 d2 d3)
  :name "FastMath test3"

  :herbie-target
  (* d1 (+ (+ 3 d2) d3))

  (+ (+ (* d1 3) (* d1 d2)) (* d1 d3)))

Details

Time bar (total: 9.6s)Debug log

sample29.0ms

Algorithm
intervals
Results
16.0ms312×body80valid
1.0ms5×body640valid
1.0ms4×body320valid
1.0ms2×body1280valid
0.0ms2×body160valid

simplify40.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
40.0ms
(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 1 expressions with local error:

0.0b
(* d1 (+ d2 (+ 3 d3)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
3×associate-*r*
2×add-cube-cbrt
2×associate-*r/
2×*-un-lft-identity
2×add-sqr-sqrt
1×add-log-exp
1×flip-+
1×*-commutative
1×add-exp-log
1×add-cbrt-cube
1×flip3-+
1×distribute-lft-in
1×pow1
1×distribute-rgt-in
Counts
1 → 15
Calls
1 calls:
Slowest
15.0ms
(* d1 (+ d2 (+ 3 d3)))

series29.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
29.0ms
(* d1 (+ d2 (+ 3 d3)))

simplify360.0ms

Counts
10 → 18
Calls
10 calls:
Slowest
170.0ms
(+ (* d2 d2) (- (* (+ 3 d3) (+ 3 d3)) (* d2 (+ 3 d3))))
47.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
45.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
23.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
20.0ms
(- d2 (+ 3 d3))

prune128.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* d2 d1) (* (+ 3 d3) d1))
0.0b
(* (+ 3 d3) d1)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
4×add-log-exp
3×add-cube-cbrt
3×associate-*l*
3×*-un-lft-identity
3×add-sqr-sqrt
2×flip-+
2×add-exp-log
2×associate-*l/
2×add-cbrt-cube
2×flip3-+
2×pow1
1×*-commutative
1×distribute-rgt-out
1×sum-log
1×+-commutative
Counts
2 → 25
Calls
2 calls:
Slowest
2.0ms
(+ (* d2 d1) (* (+ 3 d3) d1))
2.0ms
(* (+ 3 d3) d1)

series34.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
20.0ms
(+ (* d2 d1) (* (+ 3 d3) d1))
14.0ms
(* (+ 3 d3) d1)

simplify425.0ms

Counts
12 → 31
Calls
12 calls:
Slowest
140.0ms
(* (- (* 3 3) (* d3 d3)) d1)
116.0ms
(* (exp (* d2 d1)) (exp (* (+ 3 d3) d1)))
50.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
42.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
25.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))

prune269.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

9.6b
(/ (* (- 9 (* d3 d3)) d1) (- 3 d3))
2.7b
(* (- 9 (* d3 d3)) d1)
0.0b
(+ (* d2 d1) (/ (* (- 9 (* d3 d3)) d1) (- 3 d3)))
0.0b
(- 9 (* d3 d3))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
7×add-cube-cbrt
7×*-un-lft-identity
7×add-sqr-sqrt
6×add-log-exp
6×add-exp-log
6×add-cbrt-cube
4×flip--
4×associate-*l/
4×flip3--
4×pow1
3×associate-*l*
3×times-frac
3×associate-/r*
2×associate-/l/
2×associate-/r/
1×associate-/l*
1×div-inv
1×flip-+
1×*-commutative
1×div-exp
1×flip3-+
1×frac-2neg
1×sub-neg
1×sum-log
1×clear-num
1×+-commutative
1×cbrt-undiv
Counts
4 → 58
Calls
4 calls:
Slowest
10.0ms
(/ (* (- 9 (* d3 d3)) d1) (- 3 d3))
7.0ms
(+ (* d2 d1) (/ (* (- 9 (* d3 d3)) d1) (- 3 d3)))
5.0ms
(* (- 9 (* d3 d3)) d1)
1.0ms
(- 9 (* d3 d3))

series151.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
61.0ms
(+ (* d2 d1) (/ (* (- 9 (* d3 d3)) d1) (- 3 d3)))
47.0ms
(/ (* (- 9 (* d3 d3)) d1) (- 3 d3))
24.0ms
(- 9 (* d3 d3))
19.0ms
(* (- 9 (* d3 d3)) d1)

simplify1.7s

Counts
33 → 70
Calls
33 calls:
Slowest
284.0ms
(* (- (pow 9 3) (pow (* d3 d3) 3)) d1)
278.0ms
(* (- (pow 9 3) (pow (* d3 d3) 3)) d1)
206.0ms
(* (- (* 9 9) (* (* d3 d3) (* d3 d3))) d1)
197.0ms
(* (- (* 9 9) (* (* d3 d3) (* d3 d3))) d1)
112.0ms
(* (exp (* d2 d1)) (exp (/ (* (- 9 (* d3 d3)) d1) (- 3 d3))))

prune678.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

14.5b
(/ (* (+ (pow 3 3) (pow d3 3)) d1) (+ (* 3 3) (- (* d3 d3) (* 3 d3))))
3.1b
(* (+ (pow 3 3) (pow d3 3)) d1)
0.0b
(- (* d3 d3) (* 3 d3))
0.0b
(+ (* d2 d1) (/ (* (+ (pow 3 3) (pow d3 3)) d1) (+ (* 3 3) (- (* d3 d3) (* 3 d3)))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
8×add-log-exp
7×add-cube-cbrt
7×add-sqr-sqrt
6×add-exp-log
6×add-cbrt-cube
5×associate-*l*
4×flip-+
4×associate-*l/
4×flip3-+
4×pow1
3×times-frac
3×associate-/r*
2×associate-/l/
2×associate-/r/
1×associate-/l*
1×distribute-lft-out
1×flip--
1×div-inv
1×*-commutative
1×sum-cubes
1×div-exp
1×diff-log
1×distribute-rgt-out--
1×flip3--
1×frac-2neg
1×sub-neg
1×sum-log
1×clear-num
1×+-commutative
1×cbrt-undiv
Counts
4 → 62
Calls
4 calls:
Slowest
19.0ms
(+ (* d2 d1) (/ (* (+ (pow 3 3) (pow d3 3)) d1) (+ (* 3 3) (- (* d3 d3) (* 3 d3)))))
12.0ms
(/ (* (+ (pow 3 3) (pow d3 3)) d1) (+ (* 3 3) (- (* d3 d3) (* 3 d3))))
6.0ms
(* (+ (pow 3 3) (pow d3 3)) d1)
2.0ms
(- (* d3 d3) (* 3 d3))

series249.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(+ (* d2 d1) (/ (* (+ (pow 3 3) (pow d3 3)) d1) (+ (* 3 3) (- (* d3 d3) (* 3 d3)))))
39.0ms
(/ (* (+ (pow 3 3) (pow d3 3)) d1) (+ (* 3 3) (- (* d3 d3) (* 3 d3))))
37.0ms
(- (* d3 d3) (* 3 d3))
32.0ms
(* (+ (pow 3 3) (pow d3 3)) d1)

simplify3.2s

Counts
36 → 74
Calls
36 calls:
Slowest
385.0ms
(* (- (* (pow 3 3) (pow 3 3)) (* (pow d3 3) (pow d3 3))) d1)
384.0ms
(* (- (* (pow 3 3) (pow 3 3)) (* (pow d3 3) (pow d3 3))) d1)
376.0ms
(+ (* (* 3 3) (* 3 3)) (- (* (- (* d3 d3) (* 3 d3)) (- (* d3 d3) (* 3 d3))) (* (* 3 3) (- (* d3 d3) (* 3 d3)))))
371.0ms
(/ (* (* (* (+ (pow 3 3) (pow d3 3)) d1) (* (+ (pow 3 3) (pow d3 3)) d1)) (* (+ (pow 3 3) (pow d3 3)) d1)) (* (* (+ (* 3 3) (- (* d3 d3) (* 3 d3))) (+ (* 3 3) (- (* d3 d3) (* 3 d3)))) (+ (* 3 3) (- (* d3 d3) (* 3 d3)))))
221.0ms
(* (+ (pow (pow 3 3) 3) (pow (pow d3 3) 3)) d1)

prune898.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes112.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample1.1s

Algorithm
intervals
Results
745.0ms9540×body80valid
93.0ms213×body640valid
35.0ms85×body160valid
32.0ms93×body1280valid
31.0ms163×body320valid