Average Error: 0.1 → 0.1
Time: 1.1m
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[\left(d2 + \left(d3 + 3\right)\right) \cdot d1\]

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[d1 \cdot \left(\left(3 + d2\right) + d3\right)\]

Derivation

  1. Initial program 0.1

    \[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]

  2. Simplified0.1

    \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(3 + d3\right)\right)}\]

  3. Final simplification0.1

    \[\leadsto \left(d2 + \left(d3 + 3\right)\right) \cdot d1\]

Reproduce

herbie shell --seed 2019007 
(FPCore (d1 d2 d3)
  :name "FastMath test3"

  :herbie-target
  (* d1 (+ (+ 3 d2) d3))

  (+ (+ (* d1 3) (* d1 d2)) (* d1 d3)))

Details

Time bar (total: 1.1m)Debug log

sample71.0ms

Algorithm
intervals

simplify61.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

61.0ms
(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b
(* d1 (+ d2 (+ 3 d3)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

2.0ms
(* d1 (+ d2 (+ 3 d3)))

series22.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

22.0ms
(* d1 (+ d2 (+ 3 d3)))

simplify350.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

174.0ms
(+ (* d2 d2) (- (* (+ 3 d3) (+ 3 d3)) (* d2 (+ 3 d3))))
48.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
36.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))

prune173.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (* d1 (sqrt (+ d2 (+ 3 d3)))) (sqrt (+ d2 (+ 3 d3))))
0.2b
(* d1 (sqrt (+ d2 (+ 3 d3))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Counts
2 → 42
Calls

2 calls. Slowest were:

16.0ms
(* (* d1 (sqrt (+ d2 (+ 3 d3)))) (sqrt (+ d2 (+ 3 d3))))
2.0ms
(* d1 (sqrt (+ d2 (+ 3 d3))))

series74.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

54.0ms
(* d1 (sqrt (+ d2 (+ 3 d3))))
19.0ms
(* (* d1 (sqrt (+ d2 (+ 3 d3)))) (sqrt (+ d2 (+ 3 d3))))

simplify3.4s

Counts
35 → 48
Calls

35 calls. Slowest were:

527.0ms
(* (* d1 (sqrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))) (sqrt (+ d2 (+ 3 d3))))
448.0ms
(* (* d1 (sqrt (+ (pow d2 3) (pow (+ 3 d3) 3)))) (sqrt (+ (pow d2 3) (pow (+ 3 d3) 3))))
287.0ms
(* (* d1 (sqrt (+ (pow d2 3) (pow (+ 3 d3) 3)))) (sqrt (+ d2 (+ 3 d3))))

prune505.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (sqrt (+ d2 (+ 3 d3)))) (cbrt (sqrt (+ d2 (+ 3 d3)))))
0.2b
(* (* (* d1 (* (cbrt (sqrt (+ d2 (+ 3 d3)))) (cbrt (sqrt (+ d2 (+ 3 d3)))))) (cbrt (sqrt (+ d2 (+ 3 d3))))) (sqrt (+ d2 (+ 3 d3))))
0.2b
(* (* d1 (* (cbrt (sqrt (+ d2 (+ 3 d3)))) (cbrt (sqrt (+ d2 (+ 3 d3)))))) (cbrt (sqrt (+ d2 (+ 3 d3)))))
0.2b
(* d1 (* (cbrt (sqrt (+ d2 (+ 3 d3)))) (cbrt (sqrt (+ d2 (+ 3 d3))))))

rewrite167.0ms

Algorithm
rewrite-expression-head
Counts
4 → 207
Calls

4 calls. Slowest were:

83.0ms
(* (* (* d1 (* (cbrt (sqrt (+ d2 (+ 3 d3)))) (cbrt (sqrt (+ d2 (+ 3 d3)))))) (cbrt (sqrt (+ d2 (+ 3 d3))))) (sqrt (+ d2 (+ 3 d3))))
42.0ms
(* (* d1 (* (cbrt (sqrt (+ d2 (+ 3 d3)))) (cbrt (sqrt (+ d2 (+ 3 d3)))))) (cbrt (sqrt (+ d2 (+ 3 d3)))))
18.0ms
(* d1 (* (cbrt (sqrt (+ d2 (+ 3 d3)))) (cbrt (sqrt (+ d2 (+ 3 d3))))))

series275.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

128.0ms
(* d1 (* (cbrt (sqrt (+ d2 (+ 3 d3)))) (cbrt (sqrt (+ d2 (+ 3 d3))))))
77.0ms
(* (cbrt (sqrt (+ d2 (+ 3 d3)))) (cbrt (sqrt (+ d2 (+ 3 d3)))))
49.0ms
(* (* d1 (* (cbrt (sqrt (+ d2 (+ 3 d3)))) (cbrt (sqrt (+ d2 (+ 3 d3)))))) (cbrt (sqrt (+ d2 (+ 3 d3)))))
20.0ms
(* (* (* d1 (* (cbrt (sqrt (+ d2 (+ 3 d3)))) (cbrt (sqrt (+ d2 (+ 3 d3)))))) (cbrt (sqrt (+ d2 (+ 3 d3))))) (sqrt (+ d2 (+ 3 d3))))

simplify45.4s

Counts
258 → 219
Calls

258 calls. Slowest were:

592.0ms
(* (* (* (cbrt (sqrt (+ (* d2 d2) (- (* (+ 3 d3) (+ 3 d3)) (* d2 (+ 3 d3)))))) (cbrt (sqrt (- d2 (+ 3 d3))))) (cbrt (sqrt (+ (* d2 d2) (- (* (+ 3 d3) (+ 3 d3)) (* d2 (+ 3 d3))))))) (sqrt (- d2 (+ 3 d3))))
538.0ms
(* (* d1 (* (cbrt (sqrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))) (cbrt (sqrt (+ d2 (+ 3 d3)))))) (cbrt (sqrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))))
523.0ms
(* (* (* d1 (* (cbrt (sqrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))) (cbrt (sqrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))))) (cbrt (sqrt (+ (pow d2 3) (pow (+ 3 d3) 3))))) (sqrt (+ d2 (+ 3 d3))))

prune4.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

15.2b
(/ (* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (- d2 (+ 3 d3)))
9.7b
(* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))
3.3b
(- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))
0.0b
(* (+ 3 d3) (+ 3 d3))

rewrite19.0ms

Algorithm
rewrite-expression-head
Counts
4 → 86
Calls

4 calls. Slowest were:

7.0ms
(/ (* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (- d2 (+ 3 d3)))
4.0ms
(* (+ 3 d3) (+ 3 d3))
4.0ms
(* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))

series221.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

101.0ms
(/ (* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))) (- d2 (+ 3 d3)))
78.0ms
(* d1 (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))
32.0ms
(- (* d2 d2) (* (+ 3 d3) (+ 3 d3)))
10.0ms
(* (+ 3 d3) (+ 3 d3))

simplify7.8s

Counts
67 → 98
Calls

67 calls. Slowest were:

650.0ms
(* (+ (* 3 3) (- (* d3 d3) (* 3 d3))) (+ (* 3 3) (- (* d3 d3) (* 3 d3))))
458.0ms
(* (- (* 3 3) (* d3 d3)) (+ 3 d3))
418.0ms
(cbrt (- (* d2 d2) (* (+ 3 d3) (+ 3 d3))))

prune1.0s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes153.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch1.0ms

end0.0ms

sample1.5s

Algorithm
intervals