Average Error: 0.0 → 0.0
Time: 14.3s
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 2019018 
(FPCore (d1 d2 d3)
  :name "FastMath dist"

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

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

Details

Time bar (total: 13.9s)Debug log

sample20.0ms

Algorithm
intervals
Results
12.0ms307×body80valid

simplify5.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
5.0ms
(+ (* d1 d2) (* d1 d3))

prune14.0ms

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) (* d1 d3))

rewrite5.0ms

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))

simplify55.0ms

Counts
5 → 15
Calls
5 calls:
Slowest
19.0ms
(* (exp (* d1 d2)) (exp (* d1 d3)))
17.0ms
(+ (* d2 d1) (* d3 d1))
10.0ms
(+ (* d3 d1) (* d2 d1))
6.0ms
(+ (* d3 d1) (* d2 d1))
2.0ms
(+ d2 d3)

prune96.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ d3 d2) 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×flip-+
1×*-commutative
1×add-exp-log
1×add-cbrt-cube
1×flip3-+
1×pow1
Counts
1 → 13
Calls
1 calls:
Slowest
2.0ms
(* (+ d3 d2) d1)

series22.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
22.0ms
(* (+ d3 d2) d1)

simplify336.0ms

Counts
7 → 16
Calls
7 calls:
Slowest
300.0ms
(* (- (* d3 d3) (* d2 d2)) d1)
18.0ms
(* (+ (pow d3 3) (pow d2 3)) d1)
6.0ms
(* (cbrt (+ d3 d2)) (cbrt (+ d3 d2)))
5.0ms
(+ (* d2 d1) (* d3 d1))
5.0ms
(+ (* d2 d1) (* d3 d1))

prune100.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

4.2b
(cbrt (* (+ d3 d2) d1))
4.2b
(cbrt (* (+ d3 d2) d1))
4.2b
(cbrt (* (+ d3 d2) d1))
0.5b
(* (cbrt (* (+ d3 d2) d1)) (cbrt (* (+ d3 d2) d1)))

rewrite28.0ms

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×associate-*l*
4×associate-*r*
4×add-cbrt-cube
4×frac-times
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 → 65
Calls
4 calls:
Slowest
17.0ms
(* (cbrt (* (+ d3 d2) d1)) (cbrt (* (+ d3 d2) d1)))
3.0ms
(cbrt (* (+ d3 d2) d1))
3.0ms
(cbrt (* (+ d3 d2) d1))
3.0ms
(cbrt (* (+ d3 d2) d1))

series491.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
169.0ms
(* (cbrt (* (+ d3 d2) d1)) (cbrt (* (+ d3 d2) d1)))
134.0ms
(cbrt (* (+ d3 d2) d1))
97.0ms
(cbrt (* (+ d3 d2) d1))
90.0ms
(cbrt (* (+ d3 d2) d1))

simplify6.4s

Counts
49 → 77
Calls
49 calls:
Slowest
582.0ms
(- (+ (exp (* 1/3 (+ (* 2 (log d2)) (* 2 (log d1))))) (* 2/3 (* d3 (exp (* 1/3 (- (* 2 (log d1)) (log d2))))))) (* 1/9 (* (pow d3 2) (exp (* 1/3 (- (* 2 (log d1)) (* 4 (log d2))))))))
440.0ms
(* (* (+ d3 d2) d1) (* (+ d3 d2) d1))
413.0ms
(- (+ (exp (* 1/3 (+ (log d2) (log d1)))) (* 1/3 (* (exp (* 1/3 (- (log d1) (* 2 (log d2))))) d3))) (* 1/9 (* (pow d3 2) (exp (* 1/3 (- (log d1) (* 5 (log d2))))))))
385.0ms
(cbrt (* (- (* d3 d3) (* d2 d2)) d1))
354.0ms
(- (+ (exp (* 1/3 (+ (log d2) (log d1)))) (* 1/3 (* (exp (* 1/3 (- (log d1) (* 2 (log d2))))) d3))) (* 1/9 (* (pow d3 2) (exp (* 1/3 (- (log d1) (* 5 (log d2))))))))

prune686.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

4.2b
(cbrt (* (+ d3 d2) d1))
4.2b
(cbrt (* (+ d3 d2) d1))
4.2b
(cbrt (* (+ d3 d2) d1))
4.2b
(cbrt (* (+ d3 d2) d1))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-*l/
8×cbrt-div
4×add-log-exp
4×flip-+
4×add-cube-cbrt
4×add-exp-log
4×pow1/3
4×add-cbrt-cube
4×flip3-+
4×*-un-lft-identity
4×pow1
4×add-sqr-sqrt
4×cbrt-prod
Counts
4 → 44
Calls
4 calls:
Slowest
2.0ms
(cbrt (* (+ d3 d2) d1))
1.0ms
(cbrt (* (+ d3 d2) d1))
1.0ms
(cbrt (* (+ d3 d2) d1))
1.0ms
(cbrt (* (+ d3 d2) d1))

series421.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(cbrt (* (+ d3 d2) d1))
109.0ms
(cbrt (* (+ d3 d2) d1))
101.0ms
(cbrt (* (+ d3 d2) d1))
92.0ms
(cbrt (* (+ d3 d2) d1))

simplify3.7s

Counts
24 → 56
Calls
24 calls:
Slowest
297.0ms
(- (+ (exp (* 1/3 (+ (log d2) (log d1)))) (* 1/3 (* (exp (* 1/3 (- (log d1) (* 2 (log d2))))) d3))) (* 1/9 (* (pow d3 2) (exp (* 1/3 (- (log d1) (* 5 (log d2))))))))
281.0ms
(exp (* -1/3 (+ (log (/ 1 d1)) (log (/ 1 d3)))))
278.0ms
(- (+ (exp (* 1/3 (+ (log d2) (log d1)))) (* 1/3 (* (exp (* 1/3 (- (log d1) (* 2 (log d2))))) d3))) (* 1/9 (* (pow d3 2) (exp (* 1/3 (- (log d1) (* 5 (log d2))))))))
276.0ms
(exp (* -1/3 (+ (log (/ 1 d1)) (log (/ 1 d3)))))
272.0ms
(cbrt (* (- (* d3 d3) (* d2 d2)) d1))

prune610.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes140.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample716.0ms

Algorithm
intervals
Results
545.0ms9996×body80valid