Average Error: 0.2 → 0.0
Time: 5.4s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[\left(d2 + 30\right) \cdot d1\]

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

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

  3. Taylor expanded around inf 0.0

    \[\leadsto \color{blue}{d2 \cdot d1 + 30 \cdot d1}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{\left(30 + d2\right) \cdot d1}\]

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2018362 
(FPCore (d1 d2)
  :name "FastMath test2"

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

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

Details

Time bar (total: 3.2s)Debug log

start29.0ms

Algorithm
intervals

setup42.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b
(* d1 (+ 30 d2))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

1.0ms
(* d1 (+ 30 d2))

series22.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

22.0ms
(* d1 (+ 30 d2))

simplify112.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

83.0ms
(+ (* 30 30) (- (* d2 d2) (* 30 d2)))
5.0ms
(+ (* d2 d1) (* 30 d1))
5.0ms
(+ (* d2 d1) (* 30 d1))

prune163.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ 30 d2) d1)

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 13
Calls

1 calls. Slowest were:

4.0ms
(* (+ 30 d2) d1)

series17.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

17.0ms
(* (+ 30 d2) d1)

simplify195.0ms

Counts
7 → 16
Calls

7 calls. Slowest were:

143.0ms
(* (- (* 30 30) (* d2 d2)) d1)
19.0ms
(* (+ (pow 30 3) (pow d2 3)) d1)
10.0ms
(+ (* d2 d1) (* 30 d1))

prune140.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (* d1 30) (* d1 d2))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 12
Calls

1 calls. Slowest were:

2.0ms
(+ (* d1 30) (* d1 d2))

series19.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

19.0ms
(+ (* d1 30) (* d1 d2))

simplify25.0ms

Counts
5 → 15
Calls

5 calls. Slowest were:

10.0ms
(* (exp (* d1 30)) (exp (* d1 d2)))
5.0ms
(+ (* d2 d1) (* 30 d1))
5.0ms
(+ (* d2 d1) (* 30 d1))

prune114.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

8.2b
(/ (* (- 900 (* d2 d2)) d1) (- 30 d2))
3.8b
(* (- 900 (* d2 d2)) d1)

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
2 → 36
Calls

2 calls. Slowest were:

5.0ms
(/ (* (- 900 (* d2 d2)) d1) (- 30 d2))
2.0ms
(* (- 900 (* d2 d2)) d1)

series62.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

40.0ms
(/ (* (- 900 (* d2 d2)) d1) (- 30 d2))
22.0ms
(* (- 900 (* d2 d2)) d1)

simplify1.7s

Counts
26 → 42
Calls

26 calls. Slowest were:

392.0ms
(* (- (pow 900 3) (pow (* d2 d2) 3)) d1)
354.0ms
(* (- (pow 900 3) (pow (* d2 d2) 3)) d1)
253.0ms
(* (- (* 900 900) (* (* d2 d2) (* d2 d2))) d1)

prune474.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes84.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms