Average Error: 61.8 → 0.3
Time: 4.9s
Precision: 64
Internal Precision: 128
\[\left(1 + t \cdot 2 \cdot 10^{-16}\right) \cdot \left(1 + t \cdot 2 \cdot 10^{-16}\right) + \left(-1 - 2 \cdot \left(t \cdot 2 \cdot 10^{-16}\right)\right)\]
↓
\[\left(\left(2 \cdot 10^{-16} \cdot t\right) \cdot t\right) \cdot 2 \cdot 10^{-16}\]

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original61.8
Target50.6
Herbie0.3
\[(\left(1 + t \cdot 2 \cdot 10^{-16}\right) \cdot \left(1 + t \cdot 2 \cdot 10^{-16}\right) + \left(-1 - 2 \cdot \left(t \cdot 2 \cdot 10^{-16}\right)\right))_*\]

Derivation

  1. Initial program 61.8

    \[\left(1 + t \cdot 2 \cdot 10^{-16}\right) \cdot \left(1 + t \cdot 2 \cdot 10^{-16}\right) + \left(-1 - 2 \cdot \left(t \cdot 2 \cdot 10^{-16}\right)\right)\]

  2. Simplified0.4

    \[\leadsto \color{blue}{\left(2 \cdot 10^{-16} \cdot t\right) \cdot \left(2 \cdot 10^{-16} \cdot t\right)}\]
  3. Using strategy rm

  4. Applied associate-*l*0.3

    \[\leadsto \color{blue}{2 \cdot 10^{-16} \cdot \left(t \cdot \left(2 \cdot 10^{-16} \cdot t\right)\right)}\]

  5. Final simplification0.3

    \[\leadsto \left(\left(2 \cdot 10^{-16} \cdot t\right) \cdot t\right) \cdot 2 \cdot 10^{-16}\]

Reproduce

herbie shell --seed 2019007 
(FPCore (t)
  :name "fma_test1"
  :pre (<= 0.9 t 1.1)

  :herbie-target
  (fma (+ 1 (* t 2e-16)) (+ 1 (* t 2e-16)) (- -1 (* 2 (* t 2e-16))))

  (+ (* (+ 1 (* t 2e-16)) (+ 1 (* t 2e-16))) (- -1 (* 2 (* t 2e-16)))))

Details

Time bar (total: 4.4s)Debug log

sample77.0ms

Algorithm
intervals

simplify1.1s

Counts
1 → 1
Calls

1 calls. Slowest were:

1.1s
(+ (* (+ 1 (* t 2e-16)) (+ 1 (* t 2e-16))) (- -1 (* 2 (* t 2e-16))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize6.0ms

Local error

Found 1 expressions with local error:

0.4b
(* (* 2e-16 t) (* 2e-16 t))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 16
Calls

1 calls. Slowest were:

3.0ms
(* (* 2e-16 t) (* 2e-16 t))

series15.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

15.0ms
(* (* 2e-16 t) (* 2e-16 t))

simplify544.0ms

Counts
9 → 19
Calls

9 calls. Slowest were:

497.0ms
(* (* (* (* 2e-16 t) (* 2e-16 t)) (* 2e-16 t)) (* (* (* 2e-16 t) (* 2e-16 t)) (* 2e-16 t)))
14.0ms
(+ (log (* 2e-16 t)) (log (* 2e-16 t)))
14.0ms
(* (* 2e-16 t) (* 2e-16 t))

prune86.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (* (* 2e-16 t) 2e-16) t)
0.2b
(* (* 2e-16 t) 2e-16)

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
2 → 18
Calls

2 calls. Slowest were:

11.0ms
(* (* (* 2e-16 t) 2e-16) t)
4.0ms
(* (* 2e-16 t) 2e-16)

series36.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

25.0ms
(* (* (* 2e-16 t) 2e-16) t)
11.0ms
(* (* 2e-16 t) 2e-16)

simplify17.0ms

Counts
7 → 24
Calls

7 calls. Slowest were:

4.0ms
(* 3.9999999999999997e-32 (pow t 2))
4.0ms
(* 3.9999999999999997e-32 (pow t 2))
3.0ms
(* 3.9999999999999997e-32 (pow t 2))

prune159.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b
(* 2e-16 (* t (* 2e-16 t)))
0.2b
(* t (* 2e-16 t))

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
2 → 18
Calls

2 calls. Slowest were:

4.0ms
(* 2e-16 (* t (* 2e-16 t)))
2.0ms
(* t (* 2e-16 t))

series34.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

20.0ms
(* 2e-16 (* t (* 2e-16 t)))
13.0ms
(* t (* 2e-16 t))

simplify32.0ms

Counts
7 → 24
Calls

7 calls. Slowest were:

7.0ms
(* 2e-16 (pow t 2))
6.0ms
(* 2e-16 (pow t 2))
6.0ms
(* 2e-16 (pow t 2))

prune117.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.2b
(* 3.9999999999999997e-32 (pow t 2))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 12
Calls

1 calls. Slowest were:

1.0ms
(* 3.9999999999999997e-32 (pow t 2))

series11.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

11.0ms
(* 3.9999999999999997e-32 (pow t 2))

simplify16.0ms

Counts
6 → 15
Calls

6 calls. Slowest were:

5.0ms
(* 3.9999999999999997e-32 (pow t 2))
3.0ms
(* 3.9999999999999997e-32 (pow t 2))
3.0ms
(* 3.9999999999999997e-32 (pow t 2))

prune64.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes25.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample2.0s

Algorithm
intervals