Average Error: 0.0 → 0.0
Time: 11.9s
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 2019016 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"

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

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

Details

Time bar (total: 11.3s)Debug log

sample70.0ms

Algorithm
intervals
Results
330×(pre true 80)
329×(body real 80)
1×(body real 160)

simplify272.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
271.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ d3 (+ d2 37)) 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
3.0ms
(* (+ d3 (+ d2 37)) d1)

series17.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
17.0ms
(* (+ d3 (+ d2 37)) d1)

simplify918.0ms

Counts
7 → 16
Calls
7 calls:
Slowest
565.0ms
(* (+ (pow d3 3) (pow (+ d2 37) 3)) d1)
184.0ms
(* (- (* d3 d3) (* (+ d2 37) (+ d2 37))) d1)
49.0ms
(+ (* d3 d1) (+ (* d2 d1) (* 37 d1)))
47.0ms
(+ (* d3 d1) (+ (* d2 d1) (* 37 d1)))
46.0ms
(+ (* d3 d1) (+ (* d2 d1) (* 37 d1)))

prune125.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))
0.0b
(+ (* d1 d2) (* (+ d3 5) d1))
0.0b
(* (+ d3 5) d1)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
4×add-cube-cbrt
4×*-un-lft-identity
4×sum-log
4×add-sqr-sqrt
3×flip-+
3×add-exp-log
3×associate-*l*
3×add-cbrt-cube
3×flip3-+
3×pow1
2×associate-*l/
2×+-commutative
1×*-commutative
1×associate-+l+
Counts
3 → 37
Calls
3 calls:
Slowest
17.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))
5.0ms
(+ (* d1 d2) (* (+ d3 5) d1))
5.0ms
(* (+ d3 5) d1)

series77.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
29.0ms
(+ (* d1 d2) (* (+ d3 5) d1))
24.0ms
(* (+ d3 5) d1)
24.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))

simplify803.0ms

Counts
17 → 46
Calls
17 calls:
Slowest
130.0ms
(* (exp (+ (* d1 d2) (* (+ d3 5) d1))) (exp (* d1 32)))
123.0ms
(* (- (* d3 d3) (* 5 5)) d1)
120.0ms
(* (* (exp (* d1 d2)) (exp (* (+ d3 5) d1))) (exp (* d1 32)))
94.0ms
(* (exp (* d1 d2)) (exp (* (+ d3 5) d1)))
49.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))

prune400.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* (+ d3 5) d1))
0.6b
(cbrt (* (+ d3 5) d1))
0.6b
(cbrt (* (+ d3 5) d1))
0.5b
(* (cbrt (* (+ d3 5) d1)) (cbrt (* (+ d3 5) d1)))

rewrite25.0ms

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
14.0ms
(* (cbrt (* (+ d3 5) d1)) (cbrt (* (+ d3 5) d1)))
3.0ms
(cbrt (* (+ d3 5) d1))
3.0ms
(cbrt (* (+ d3 5) d1))
3.0ms
(cbrt (* (+ d3 5) d1))

series314.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(* (cbrt (* (+ d3 5) d1)) (cbrt (* (+ d3 5) d1)))
76.0ms
(cbrt (* (+ d3 5) d1))
74.0ms
(cbrt (* (+ d3 5) d1))
63.0ms
(cbrt (* (+ d3 5) d1))

simplify5.4s

Counts
49 → 77
Calls
49 calls:
Slowest
418.0ms
(- (+ (* 10/3 (/ (* (exp (* -1/3 (+ (* 2 (log (/ -1 d1))) (* 2 (log (/ -1 d3)))))) (pow (cbrt -1) 2)) d3)) (* (exp (* -1/3 (+ (* 2 (log (/ -1 d1))) (* 2 (log (/ -1 d3)))))) (pow (cbrt -1) 2))) (* 25/9 (/ (* (exp (* -1/3 (+ (* 2 (log (/ -1 d1))) (* 2 (log (/ -1 d3)))))) (pow (cbrt -1) 2)) (pow d3 2))))
401.0ms
(- (+ (* 1/15 (* d3 (exp (* 1/3 (+ (log 5) (log d1)))))) (exp (* 1/3 (+ (log 5) (log d1))))) (* 1/225 (* (pow d3 2) (exp (* 1/3 (+ (log 5) (log d1)))))))
385.0ms
(- (+ (exp (* 1/3 (+ (* 2 (log d1)) (log 25)))) (* 2/15 (* (exp (* 1/3 (+ (* 2 (log d1)) (log 25)))) d3))) (* 1/225 (* (exp (* 1/3 (+ (* 2 (log d1)) (log 25)))) (pow d3 2))))
362.0ms
(* (* (+ d3 5) d1) (* (+ d3 5) d1))
345.0ms
(- (+ (* 1/15 (* d3 (exp (* 1/3 (+ (log 5) (log d1)))))) (exp (* 1/3 (+ (log 5) (log d1))))) (* 1/225 (* (pow d3 2) (exp (* 1/3 (+ (log 5) (log d1)))))))

prune1.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes221.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
10138×(pre true 80)
10095×(body real 80)
17×(body real 640)
11×(body real 320)
8×(body real 1280)
7×(body real 160)