Average Error: 0.2 → 0.0
Time: 8.0s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[\left(30 + d2\right) \cdot d1\]

Error

Bits error versus d1

Bits error versus d2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.0
\[d1 \cdot \left(30 + d2\right)\]

Derivation

  1. Initial program 0.2

    \[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]

  2. Initial simplification0.0

    \[\leadsto \left(d2 + 30\right) \cdot d1\]

  3. Final simplification0.0

    \[\leadsto \left(30 + d2\right) \cdot d1\]

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"

  :herbie-target
  (* d1 (+ 30 d2))

  (+ (+ (* d1 10) (* d1 d2)) (* d1 20)))

Details

Time bar (total: 5.9s)Debug log

start50.0ms

Algorithm
intervals

setup90.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ d2 30) d1)

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

3.0ms
(* (+ d2 30) d1)

series15.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

15.0ms
(* (+ d2 30) d1)

simplify381.0ms

Counts
7 → 18
Calls

7 calls. Slowest were:

316.0ms
(* (- (* d2 d2) (* 30 30)) d1)
27.0ms
(* (+ (pow d2 3) (pow 30 3)) d1)
11.0ms
(+ (* d2 d1) (* 30 d1))

prune145.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 2 expressions with local error:

9.3b
(/ (* (fma d2 d2 -900) d1) (- d2 30))
5.9b
(* (fma d2 d2 -900) d1)

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
2 → 36
Calls

2 calls. Slowest were:

11.0ms
(/ (* (fma d2 d2 -900) d1) (- d2 30))
5.0ms
(* (fma d2 d2 -900) d1)

series88.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

47.0ms
(/ (* (fma d2 d2 -900) d1) (- d2 30))
41.0ms
(* (fma d2 d2 -900) d1)

simplify318.0ms

Counts
22 → 42
Calls

22 calls. Slowest were:

129.0ms
(/ (* (* (* (fma d2 d2 -900) d1) (* (fma d2 d2 -900) d1)) (* (fma d2 d2 -900) d1)) (* (* (- d2 30) (- d2 30)) (- d2 30)))
60.0ms
(- (log (* (fma d2 d2 -900) d1)) (log (- d2 30)))
19.0ms
(+ (* d2 d2) (+ (* 30 30) (* d2 30)))

prune404.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

17.9b
(/ (fma (pow d2 3) d1 (* d1 27000)) (+ (* d2 d2) (- (* 30 30) (* d2 30))))
3.3b
(fma (pow d2 3) d1 (* d1 27000))
0.0b
(- (* 30 30) (* d2 30))
0.0b
(+ (* d2 d2) (- (* 30 30) (* d2 30)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Counts
4 → 77
Calls

4 calls. Slowest were:

18.0ms
(/ (fma (pow d2 3) d1 (* d1 27000)) (+ (* d2 d2) (- (* 30 30) (* d2 30))))
9.0ms
(+ (* d2 d2) (- (* 30 30) (* d2 30)))
4.0ms
(- (* 30 30) (* d2 30))

series118.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

71.0ms
(/ (fma (pow d2 3) d1 (* d1 27000)) (+ (* d2 d2) (- (* 30 30) (* d2 30))))
21.0ms
(fma (pow d2 3) d1 (* d1 27000))
16.0ms
(- (* 30 30) (* d2 30))
10.0ms
(+ (* d2 d2) (- (* 30 30) (* d2 30)))

simplify2.9s

Counts
49 → 89
Calls

49 calls. Slowest were:

323.0ms
(+ (* (* d2 d2) (* d2 d2)) (- (* (- (* 30 30) (* d2 30)) (- (* 30 30) (* d2 30))) (* (* d2 d2) (- (* 30 30) (* d2 30)))))
142.0ms
(/ (* (* (fma (pow d2 3) d1 (* d1 27000)) (fma (pow d2 3) d1 (* d1 27000))) (fma (pow d2 3) d1 (* d1 27000))) (* (* (+ (* d2 d2) (- (* 30 30) (* d2 30))) (+ (* d2 d2) (- (* 30 30) (* d2 30)))) (+ (* d2 d2) (- (* 30 30) (* d2 30)))))
134.0ms
(- (log (fma (pow d2 3) d1 (* d1 27000))) (log (+ (* d2 d2) (- (* 30 30) (* d2 30)))))

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes71.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms