Average Error: 0.0 → 0.0
Time: 8.8s
Precision: 64
Internal Precision: 128
\[d1 \cdot d2 + d1 \cdot d3\]
↓
\[\left(d3 + d2\right) \cdot d1\]

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

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

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019022 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"

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

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

Details

Time bar (total: 8.5s)Debug log

sample38.0ms

Algorithm
intervals
Results
25.0ms333×body80valid

simplify10.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(+ (* d1 d2) (* d1 d3))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ d2 d3) d1)

rewrite3.0ms

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×log1p-expm1-u
1×flip-+
1×*-commutative
1×add-exp-log
1×add-cbrt-cube
1×flip3-+
1×pow1
1×expm1-log1p-u
Counts
1 → 15
Calls
1 calls:
Slowest
2.0ms
(* (+ d2 d3) d1)

series15.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
15.0ms
(* (+ d2 d3) d1)

simplify499.0ms

Counts
7 → 18
Calls
7 calls:
Slowest
465.0ms
(* (- (* d2 d2) (* d3 d3)) d1)
19.0ms
(* (+ (pow d2 3) (pow d3 3)) d1)
5.0ms
(+ (* d3 d1) (* d2 d1))
5.0ms
(+ (* d3 d1) (* d2 d1))
2.0ms
(* (cbrt (+ d2 d3)) (cbrt (+ d2 d3)))

prune121.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

1.9b
(cbrt (* (+ d2 d3) d1))
1.9b
(cbrt (* (+ d2 d3) d1))
1.9b
(cbrt (* (+ d2 d3) d1))
0.5b
(* (cbrt (* (+ d2 d3) d1)) (cbrt (* (+ d2 d3) d1)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*l/
18×cbrt-div
9×flip-+
9×flip3-+
9×pow1
7×pow1/3
6×add-cube-cbrt
6×add-exp-log
6×*-un-lft-identity
6×add-sqr-sqrt
5×cbrt-prod
4×add-log-exp
4×log1p-expm1-u
4×associate-*l*
4×associate-*r*
4×add-cbrt-cube
4×frac-times
4×expm1-log1p-u
2×pow-prod-up
2×associate-*r/
2×pow-prod-down
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-plus
1×pow2
Counts
4 → 73
Calls
4 calls:
Slowest
13.0ms
(* (cbrt (* (+ d2 d3) d1)) (cbrt (* (+ d2 d3) d1)))
2.0ms
(cbrt (* (+ d2 d3) d1))
1.0ms
(cbrt (* (+ d2 d3) d1))
1.0ms
(cbrt (* (+ d2 d3) d1))

series471.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(* (cbrt (* (+ d2 d3) d1)) (cbrt (* (+ d2 d3) d1)))
111.0ms
(cbrt (* (+ d2 d3) d1))
104.0ms
(cbrt (* (+ d2 d3) d1))
96.0ms
(cbrt (* (+ d2 d3) d1))

simplify3.6s

Counts
49 → 85
Calls
49 calls:
Slowest
246.0ms
(exp (* -1/3 (+ (* 2 (log (/ -1 d1))) (* 2 (log (/ -1 d2))))))
235.0ms
(exp (* -1/3 (+ (log (/ 1 d1)) (log (/ 1 d2)))))
235.0ms
(exp (* -1/3 (+ (log (/ 1 d1)) (log (/ 1 d2)))))
234.0ms
(exp (* -1/3 (+ (log (/ 1 d1)) (log (/ 1 d2)))))
179.0ms
(cbrt (* (- (* d2 d2) (* d3 d3)) d1))

prune595.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize5.0ms

Local error

Found 4 expressions with local error:

1.5b
(sqrt (* (+ d2 d3) d1))
1.5b
(sqrt (* (+ d2 d3) d1))
0.2b
(* (sqrt (* (+ d2 d3) d1)) (sqrt (* (+ d2 d3) d1)))
0.0b
(* (+ d2 d3) d1)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*l/
16×sqrt-div
9×flip-+
9×flip3-+
9×pow1
7×add-cube-cbrt
7×associate-*l*
7×*-un-lft-identity
7×add-sqr-sqrt
6×add-exp-log
6×pow1/2
6×add-cbrt-cube
4×add-log-exp
4×log1p-expm1-u
4×sqrt-prod
4×associate-*r*
4×frac-times
4×expm1-log1p-u
2×pow-prod-up
2×*-commutative
2×associate-*r/
2×pow-prod-down
1×cbrt-unprod
1×prod-exp
1×sqrt-unprod
1×pow-plus
1×rem-square-sqrt
1×pow2
Counts
4 → 77
Calls
4 calls:
Slowest
8.0ms
(* (sqrt (* (+ d2 d3) d1)) (sqrt (* (+ d2 d3) d1)))
2.0ms
(* (+ d2 d3) d1)
1.0ms
(sqrt (* (+ d2 d3) d1))
1.0ms
(sqrt (* (+ d2 d3) d1))

series133.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
53.0ms
(sqrt (* (+ d2 d3) d1))
51.0ms
(sqrt (* (+ d2 d3) d1))
15.0ms
(* (sqrt (* (+ d2 d3) d1)) (sqrt (* (+ d2 d3) d1)))
14.0ms
(* (+ d2 d3) d1)

simplify1.7s

Counts
52 → 89
Calls
52 calls:
Slowest
152.0ms
(* (* (* (sqrt (* (+ d2 d3) d1)) (sqrt (* (+ d2 d3) d1))) (sqrt (* (+ d2 d3) d1))) (* (* (sqrt (* (+ d2 d3) d1)) (sqrt (* (+ d2 d3) d1))) (sqrt (* (+ d2 d3) d1))))
140.0ms
(* (sqrt (* (- (* d2 d2) (* d3 d3)) d1)) (sqrt (* (+ (pow d2 3) (pow d3 3)) d1)))
139.0ms
(* (sqrt (* (+ (pow d2 3) (pow d3 3)) d1)) (sqrt (* (- (* d2 d2) (* d3 d3)) d1)))
123.0ms
(sqrt (* (- (* d2 d2) (* d3 d3)) d1))
121.0ms
(* (sqrt (* (- (* d2 d2) (* d3 d3)) d1)) (sqrt (* (- (* d2 d2) (* d3 d3)) d1)))

prune521.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes76.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample660.0ms

Algorithm
intervals
Results
522.0ms10104×body80valid