Average Error: 61.8 → 0.3
Time: 6.8s
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. Initial simplification0.4

    \[\leadsto \left(2 \cdot 10^{-16} \cdot t\right) \cdot \left(2 \cdot 10^{-16} \cdot t\right)\]
  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 2018365 
(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: 3.3s)Debug log

start95.0ms

Algorithm
intervals

setup1.5s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

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))

series13.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify825.0ms

Counts
9 → 19
Calls

9 calls. Slowest were:

750.0ms
(* (* (* (* 2e-16 t) (* 2e-16 t)) (* 2e-16 t)) (* (* (* 2e-16 t) (* 2e-16 t)) (* 2e-16 t)))
24.0ms
(+ (log (* 2e-16 t)) (log (* 2e-16 t)))
16.0ms
(* (* 2e-16 t) (* 2e-16 t))

prune191.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.3b
(* 3.9999999999999997e-32 (pow t 2))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 12
Calls

1 calls. Slowest were:

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

series19.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

18.0ms
(* 3.9999999999999997e-32 (pow t 2))

simplify15.0ms

Counts
6 → 15
Calls

6 calls. Slowest were:

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

prune129.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
2 → 18
Calls

2 calls. Slowest were:

5.0ms
(* 2e-16 (* t (* 2e-16 t)))
2.0ms
(* t (* 2e-16 t))

series43.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

22.0ms
(* 2e-16 (* t (* 2e-16 t)))
21.0ms
(* t (* 2e-16 t))

simplify32.0ms

Counts
7 → 24
Calls

7 calls. Slowest were:

7.0ms
(* 3.9999999999999997e-32 (pow t 2))
7.0ms
(* 3.9999999999999997e-32 (pow t 2))
3.0ms
(* 2e-16 (pow t 2))

prune208.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 9
Calls

1 calls. Slowest were:

5.0ms
(* (* 3.9999999999999997e-32 t) t)

series26.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

26.0ms
(* (* 3.9999999999999997e-32 t) t)

simplify25.0ms

Counts
3 → 12
Calls

3 calls. Slowest were:

9.0ms
(* 3.9999999999999997e-32 (pow t 2))
8.0ms
(* 3.9999999999999997e-32 (pow t 2))
7.0ms
(* 3.9999999999999997e-32 (pow t 2))

prune84.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms