Average Error: 0.0 → 0.0
Time: 5.8s
Precision: 64
Internal Precision: 128
\[d1 \cdot d2 + d1 \cdot d3\]
↓
\[d1 \cdot d2 + d3 \cdot d1\]

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

Original0.0
Target0.0
Herbie0.0
\[d1 \cdot \left(d2 + d3\right)\]

Derivation

  1. Initial program 0.0

    \[d1 \cdot d2 + d1 \cdot d3\]

  2. Final simplification0.0

    \[\leadsto d1 \cdot d2 + d3 \cdot d1\]

Reproduce

herbie shell --seed 2019016 
(FPCore (d1 d2 d3)
  :name "FastMath dist"

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

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

Details

Time bar (total: 5.4s)Debug log

sample51.0ms

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

simplify9.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
9.0ms
(+ (* d1 d2) (* d1 d3))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×distribute-lft-out
1×flip-+
1×add-cube-cbrt
1×add-exp-log
1×add-cbrt-cube
1×flip3-+
1×*-un-lft-identity
1×sum-log
1×+-commutative
1×pow1
1×add-sqr-sqrt
Counts
1 → 12
Calls
1 calls:
Slowest
4.0ms
(+ (* d1 d2) (* d1 d3))

series31.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
31.0ms
(+ (* d1 d2) (* d1 d3))

simplify58.0ms

Counts
5 → 15
Calls
5 calls:
Slowest
19.0ms
(* (exp (* d1 d2)) (exp (* d1 d3)))
18.0ms
(+ (* d3 d1) (* d2 d1))
9.0ms
(+ (* d2 d1) (* d3 d1))
9.0ms
(+ (* d3 d1) (* d2 d1))
2.0ms
(+ d2 d3)

prune167.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ d3 d2) d1)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
3×associate-*l*
2×add-cube-cbrt
2×associate-*l/
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×pow1
Counts
1 → 13
Calls
1 calls:
Slowest
5.0ms
(* (+ d3 d2) d1)

series25.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
25.0ms
(* (+ d3 d2) d1)

simplify370.0ms

Counts
7 → 16
Calls
7 calls:
Slowest
330.0ms
(* (- (* d3 d3) (* d2 d2)) d1)
24.0ms
(* (+ (pow d3 3) (pow d2 3)) d1)
4.0ms
(+ (* d2 d1) (* d3 d1))
4.0ms
(+ (* d2 d1) (* d3 d1))
4.0ms
(* (cbrt (+ d3 d2)) (cbrt (+ d3 d2)))

prune105.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

19.1b
(/ (* (- (* d3 d3) (* d2 d2)) d1) (- d3 d2))
6.6b
(* (- (* d3 d3) (* d2 d2)) d1)
2.4b
(- (* d3 d3) (* d2 d2))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
6×add-cube-cbrt
6×*-un-lft-identity
6×add-sqr-sqrt
5×add-log-exp
5×add-exp-log
5×add-cbrt-cube
4×flip--
4×associate-*l/
4×associate-*l*
4×flip3--
3×times-frac
3×associate-/r*
3×pow1
2×associate-/l/
2×difference-of-squares
2×associate-/r/
1×associate-/l*
1×div-inv
1×*-commutative
1×div-exp
1×diff-log
1×frac-2neg
1×sub-neg
1×clear-num
1×cbrt-undiv
Counts
3 → 50
Calls
3 calls:
Slowest
7.0ms
(/ (* (- (* d3 d3) (* d2 d2)) d1) (- d3 d2))
4.0ms
(* (- (* d3 d3) (* d2 d2)) d1)
2.0ms
(- (* d3 d3) (* d2 d2))

series95.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
42.0ms
(/ (* (- (* d3 d3) (* d2 d2)) d1) (- d3 d2))
33.0ms
(* (- (* d3 d3) (* d2 d2)) d1)
19.0ms
(- (* d3 d3) (* d2 d2))

simplify2.6s

Counts
33 → 59
Calls
33 calls:
Slowest
457.0ms
(* (- (* (* d3 d3) (* d3 d3)) (* (* d2 d2) (* d2 d2))) d1)
402.0ms
(* (- (* (* d3 d3) (* d3 d3)) (* (* d2 d2) (* d2 d2))) d1)
325.0ms
(* (- (pow (* d3 d3) 3) (pow (* d2 d2) 3)) d1)
271.0ms
(* (- (pow (* d3 d3) 3) (pow (* d2 d2) 3)) d1)
247.0ms
(- (log (* (- (* d3 d3) (* d2 d2)) d1)) (log (- d3 d2)))

prune464.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes159.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.1s

Algorithm
intervals
Results
10125×(pre true 80)
10125×(body real 80)