Average Error: 0.0 → 0.0
Time: 20.9s
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 2019008 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"

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

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

Details

Time bar (total: 20.2s)Debug log

sample37.0ms

Algorithm
intervals

simplify348.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

347.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 13
Calls

1 calls. Slowest were:

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

series16.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify812.0ms

Counts
7 → 16
Calls

7 calls. Slowest were:

575.0ms
(* (+ (pow d3 3) (pow (+ d2 37) 3)) d1)
120.0ms
(* (- (* d3 d3) (* (+ d2 37) (+ d2 37))) d1)
35.0ms
(+ (* d3 d1) (+ (* d2 d1) (* 37 d1)))

prune121.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Counts
3 → 37
Calls

3 calls. Slowest were:

17.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))
5.0ms
(+ (* d1 d2) (* (+ d3 5) d1))
5.0ms
(* (+ d3 5) d1)

series84.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

34.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))
27.0ms
(* (+ d3 5) d1)
22.0ms
(+ (* d1 d2) (* (+ d3 5) d1))

simplify867.0ms

Counts
17 → 46
Calls

17 calls. Slowest were:

154.0ms
(* (- (* d3 d3) (* 5 5)) d1)
152.0ms
(* (exp (+ (* d1 d2) (* (+ d3 5) d1))) (exp (* d1 32)))
149.0ms
(* (* (exp (* d1 d2)) (exp (* (+ d3 5) d1))) (exp (* d1 32)))

prune385.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

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)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

10.0ms
(* (cbrt (* (+ d3 5) d1)) (cbrt (* (+ d3 5) d1)))
2.0ms
(cbrt (* (+ d3 5) d1))
2.0ms
(cbrt (* (+ d3 5) d1))

series319.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

96.0ms
(cbrt (* (+ d3 5) d1))
84.0ms
(* (cbrt (* (+ d3 5) d1)) (cbrt (* (+ d3 5) d1)))
70.0ms
(cbrt (* (+ d3 5) d1))
70.0ms
(cbrt (* (+ d3 5) d1))

simplify5.8s

Counts
49 → 77
Calls

49 calls. Slowest were:

503.0ms
(cbrt (* (- (* d3 d3) (* 5 5)) d1))
415.0ms
(* (* (+ d3 5) d1) (* (+ d3 5) d1))
412.0ms
(- (+ (* 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)))))))

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

9.8b
(cbrt (* d1 (+ -25 (* d3 d3))))
9.8b
(cbrt (* d1 (+ -25 (* d3 d3))))
3.4b
(/ (* (cbrt (* d1 (+ -25 (* d3 d3)))) (cbrt (* d1 (+ -25 (* d3 d3))))) (* (cbrt (- d3 5)) (cbrt (- d3 5))))
2.9b
(* d1 (+ -25 (* d3 d3)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
4 → 74
Calls

4 calls. Slowest were:

12.0ms
(/ (* (cbrt (* d1 (+ -25 (* d3 d3)))) (cbrt (* d1 (+ -25 (* d3 d3))))) (* (cbrt (- d3 5)) (cbrt (- d3 5))))
1.0ms
(* d1 (+ -25 (* d3 d3)))
1.0ms
(cbrt (* d1 (+ -25 (* d3 d3))))

series517.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

183.0ms
(cbrt (* d1 (+ -25 (* d3 d3))))
178.0ms
(cbrt (* d1 (+ -25 (* d3 d3))))
114.0ms
(/ (* (cbrt (* d1 (+ -25 (* d3 d3)))) (cbrt (* d1 (+ -25 (* d3 d3))))) (* (cbrt (- d3 5)) (cbrt (- d3 5))))
42.0ms
(* d1 (+ -25 (* d3 d3)))

simplify6.1s

Counts
53 → 86
Calls

53 calls. Slowest were:

356.0ms
(- (exp (* -1/3 (+ (log (/ 1 d1)) (* 2 (log (/ 1 d3)))))) (* 25/3 (/ (exp (* -1/3 (+ (log (/ 1 d1)) (* 2 (log (/ 1 d3)))))) (pow d3 2))))
350.0ms
(- (exp (* -1/3 (+ (log (/ 1 d1)) (* 2 (log (/ 1 d3)))))) (* 25/3 (/ (exp (* -1/3 (+ (log (/ 1 d1)) (* 2 (log (/ 1 d3)))))) (pow d3 2))))
333.0ms
(- (+ (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))))

prune1.6s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes246.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.8s

Algorithm
intervals