Average Error: 0.0 → 0.0
Time: 13.6s
Precision: 64
Internal Precision: 128
\[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1\]
↓
\[(\left(d4 + d2\right) \cdot d1 + \left(\left(-d1\right) \cdot \left(d1 + d3\right)\right))_*\]

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Bits error versus d4

Target

Original0.0
Target0.0
Herbie0.0
\[d1 \cdot \left(\left(\left(d2 - d3\right) + d4\right) - d1\right)\]

Derivation

  1. Initial program 0.0

    \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1\]

  2. Simplified0.0

    \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - \left(d3 + d1\right)\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

    \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 + d4\right) + \left(-\left(d3 + d1\right)\right)\right)}\]

  5. Applied distribute-rgt-in0.0

    \[\leadsto \color{blue}{\left(d2 + d4\right) \cdot d1 + \left(-\left(d3 + d1\right)\right) \cdot d1}\]
  6. Using strategy rm

  7. Applied fma-def0.0

    \[\leadsto \color{blue}{(\left(d2 + d4\right) \cdot d1 + \left(\left(-\left(d3 + d1\right)\right) \cdot d1\right))_*}\]

  8. Final simplification0.0

    \[\leadsto (\left(d4 + d2\right) \cdot d1 + \left(\left(-d1\right) \cdot \left(d1 + d3\right)\right))_*\]

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"

  :herbie-target
  (* d1 (- (+ (- d2 d3) d4) d1))

  (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))

Details

Time bar (total: 13.1s)Debug log

sample69.0ms

Algorithm
intervals

simplify216.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

215.0ms
(- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 1 expressions with local error:

0.0b
(* d1 (- (+ d2 d4) (+ d3 d1)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
1 → 45
Calls

1 calls. Slowest were:

14.0ms
(* d1 (- (+ d2 d4) (+ d3 d1)))

series55.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

55.0ms
(* d1 (- (+ d2 d4) (+ d3 d1)))

simplify6.2s

Counts
38 → 48
Calls

38 calls. Slowest were:

492.0ms
(* (+ (* d2 d2) (- (* d4 d4) (* d2 d4))) (+ (* d3 d3) (- (* d1 d1) (* d3 d1))))
341.0ms
(* (fma (- (+ d3 d1)) 1 (* (+ d3 d1) 1)) d1)
322.0ms
(* (fma (- (+ d3 d1)) 1 (* (+ d3 d1) 1)) d1)

prune524.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* (+ d2 d4) d1) (* (- (+ d3 d1)) d1))
0.0b
(* (+ d2 d4) d1)

rewrite15.0ms

Algorithm
rewrite-expression-head
Counts
2 → 36
Calls

2 calls. Slowest were:

10.0ms
(+ (* (+ d2 d4) d1) (* (- (+ d3 d1)) d1))
4.0ms
(* (+ d2 d4) d1)

series86.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

64.0ms
(+ (* (+ d2 d4) d1) (* (- (+ d3 d1)) d1))
22.0ms
(* (+ d2 d4) d1)

simplify2.2s

Counts
23 → 42
Calls

23 calls. Slowest were:

450.0ms
(* (+ (* d2 d2) (- (* d4 d4) (* d2 d4))) (+ (* d3 d3) (- (* d1 d1) (* d3 d1))))
284.0ms
(* (exp (* (+ d2 d4) d1)) (exp (* (- (+ d3 d1)) d1)))
204.0ms
(* (- d2 d4) (+ (* d3 d3) (- (* d1 d1) (* d3 d1))))

prune454.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma (+ d2 d4) d1 (* (- (+ d3 d1)) d1))

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(fma (+ d2 d4) d1 (* (- (+ d3 d1)) d1))

series44.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

44.0ms
(fma (+ d2 d4) d1 (* (- (+ d3 d1)) d1))

simplify227.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

128.0ms
(- (* d4 d1) (+ (pow d1 2) (* d3 d1)))
98.0ms
(- (* d4 d1) (+ (pow d1 2) (* d3 d1)))
0.0ms
0

prune119.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma (- d1) (+ d1 d3) (* d4 d1))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(fma (- d1) (+ d1 d3) (* d4 d1))

series36.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

36.0ms
(fma (- d1) (+ d1 d3) (* d4 d1))

simplify470.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

169.0ms
(- (* d4 d1) (+ (pow d1 2) (* d3 d1)))
166.0ms
(- (* d4 d1) (+ (pow d1 2) (* d3 d1)))
133.0ms
(- (* d4 d1) (+ (pow d1 2) (* d3 d1)))

prune104.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes157.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample2.1s

Algorithm
intervals