Average Error: 0.0 → 0.0
Time: 19.5s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[\left(\left(d2 + 37\right) + d3\right) \cdot d1\]

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
\[d1 \cdot \left(\left(37 + d3\right) + d2\right)\]

Derivation

  1. Initial program 0.0

    \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(d3 + \left(d2 + 37\right)\right) \cdot d1}\]

  3. Final simplification0.0

    \[\leadsto \left(\left(d2 + 37\right) + d3\right) \cdot d1\]

Reproduce

herbie shell --seed 2019022 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"

  :herbie-target
  (* d1 (+ (+ 37 d3) d2))

  (+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32)))

Details

Time bar (total: 19.0s)Debug log

sample54.0ms

Algorithm
intervals
Results
39.0ms333×body80valid

simplify330.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
330.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ d3 (+ d2 37)) 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 37)) d1)

series27.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
27.0ms
(* (+ d3 (+ d2 37)) d1)

simplify846.0ms

Counts
7 → 16
Calls
7 calls:
Slowest
596.0ms
(* (+ (pow d3 3) (pow (+ d2 37) 3)) d1)
136.0ms
(* (- (* d3 d3) (* (+ d2 37) (+ d2 37))) d1)
40.0ms
(+ (* d3 d1) (+ (* d2 d1) (* 37 d1)))
24.0ms
(+ (* d3 d1) (+ (* d2 d1) (* 37 d1)))
23.0ms
(+ (* d3 d1) (+ (* d2 d1) (* 37 d1)))

prune102.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (* (+ d3 (+ d2 37)) d1))
0.5b
(cbrt (* (+ d3 (+ d2 37)) d1))
0.5b
(cbrt (* (+ d3 (+ d2 37)) d1))
0.5b
(* (cbrt (* (+ d3 (+ d2 37)) d1)) (cbrt (* (+ d3 (+ d2 37)) d1)))

rewrite27.0ms

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
16.0ms
(* (cbrt (* (+ d3 (+ d2 37)) d1)) (cbrt (* (+ d3 (+ d2 37)) d1)))
3.0ms
(cbrt (* (+ d3 (+ d2 37)) d1))
3.0ms
(cbrt (* (+ d3 (+ d2 37)) d1))
3.0ms
(cbrt (* (+ d3 (+ d2 37)) d1))

series651.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
199.0ms
(* (cbrt (* (+ d3 (+ d2 37)) d1)) (cbrt (* (+ d3 (+ d2 37)) d1)))
172.0ms
(cbrt (* (+ d3 (+ d2 37)) d1))
154.0ms
(cbrt (* (+ d3 (+ d2 37)) d1))
125.0ms
(cbrt (* (+ d3 (+ d2 37)) d1))

simplify7.6s

Counts
49 → 77
Calls
49 calls:
Slowest
496.0ms
(cbrt (* (+ (pow d3 3) (pow (+ d2 37) 3)) d1))
480.0ms
(* (* (+ d3 (+ d2 37)) d1) (* (+ d3 (+ d2 37)) d1))
465.0ms
(cbrt (* (+ (pow d3 3) (pow (+ d2 37) 3)) d1))
459.0ms
(cbrt (* (+ (pow d3 3) (pow (+ d2 37) 3)) d1))
420.0ms
(* (* (+ d3 (+ d2 37)) d1) (* (+ d3 (+ d2 37)) d1))

prune788.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (+ d3 (+ d2 37))) (* (sqrt (+ d3 (+ d2 37))) d1))
0.2b
(* (sqrt (+ d3 (+ d2 37))) d1)
0.0b
(sqrt (+ d3 (+ d2 37)))
0.0b
(sqrt (+ d3 (+ d2 37)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-div
12×sqrt-prod
12×associate-*l*
12×add-sqr-sqrt
10×add-cube-cbrt
10×associate-*l/
10×*-un-lft-identity
9×flip-+
9×flip3-+
6×add-exp-log
6×add-cbrt-cube
6×pow1
4×add-log-exp
4×frac-times
2×*-commutative
2×associate-*r/
2×pow1/2
2×rem-sqrt-square
1×cbrt-unprod
1×prod-exp
1×pow-prod-down
1×associate-*r*
Counts
4 → 70
Calls
4 calls:
Slowest
9.0ms
(* (sqrt (+ d3 (+ d2 37))) (* (sqrt (+ d3 (+ d2 37))) d1))
3.0ms
(* (sqrt (+ d3 (+ d2 37))) d1)
1.0ms
(sqrt (+ d3 (+ d2 37)))
1.0ms
(sqrt (+ d3 (+ d2 37)))

series136.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
61.0ms
(* (sqrt (+ d3 (+ d2 37))) d1)
28.0ms
(sqrt (+ d3 (+ d2 37)))
26.0ms
(* (sqrt (+ d3 (+ d2 37))) (* (sqrt (+ d3 (+ d2 37))) d1))
21.0ms
(sqrt (+ d3 (+ d2 37)))

simplify5.9s

Counts
51 → 82
Calls
51 calls:
Slowest
742.0ms
(* (* (* (sqrt (+ d3 (+ d2 37))) (sqrt (+ d3 (+ d2 37)))) (sqrt (+ d3 (+ d2 37)))) (* (* (* (sqrt (+ d3 (+ d2 37))) d1) (* (sqrt (+ d3 (+ d2 37))) d1)) (* (sqrt (+ d3 (+ d2 37))) d1)))
471.0ms
(sqrt (- (* d3 d3) (* (+ d2 37) (+ d2 37))))
462.0ms
(* (sqrt (- (* d3 d3) (* (+ d2 37) (+ d2 37)))) (* (sqrt (+ d3 (+ d2 37))) d1))
422.0ms
(* (sqrt (- (* d3 d3) (* (+ d2 37) (+ d2 37)))) d1)
376.0ms
(* (sqrt (+ (pow d3 3) (pow (+ d2 37) 3))) d1)

prune755.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes108.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.0s10070×body80valid
5.0ms16×body640valid
4.0ms13×body320valid
2.0ms4×body1280valid
1.0ms7×body160valid