Average Error: 0.1 → 0.1
Time: 14.8s
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. Initial simplification0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2018365 
(FPCore (d1 d2 d3)
  :name "FastMath test3"

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

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

Details

Time bar (total: 12.5s)Debug log

start87.0ms

Algorithm
intervals

setup60.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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:

1.0ms
(* d1 (+ d2 (+ 3 d3)))

series22.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify290.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

140.0ms
(+ (* d2 d2) (- (* (+ 3 d3) (+ 3 d3)) (* d2 (+ 3 d3))))
45.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))
25.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))

prune141.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

5.0ms
(+ (* d1 d2) (* d1 (+ 3 d3)))
2.0ms
(* d1 (+ 3 d3))

series63.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

35.0ms
(+ (* d1 d2) (* d1 (+ 3 d3)))
28.0ms
(* d1 (+ 3 d3))

simplify305.0ms

Counts
17 → 35
Calls

17 calls. Slowest were:

94.0ms
(* (exp (* d1 d2)) (exp (* d1 (+ 3 d3))))
72.0ms
(+ (* 3 3) (- (* d3 d3) (* 3 d3)))
27.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 3 d1)))

prune291.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* d1 (+ 3 d3)))
0.6b
(cbrt (* d1 (+ 3 d3)))
0.6b
(cbrt (* d1 (+ 3 d3)))
0.5b
(* (cbrt (* d1 (+ 3 d3))) (cbrt (* d1 (+ 3 d3))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

12.0ms
(* (cbrt (* d1 (+ 3 d3))) (cbrt (* d1 (+ 3 d3))))
2.0ms
(cbrt (* d1 (+ 3 d3)))
2.0ms
(cbrt (* d1 (+ 3 d3)))

series395.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

116.0ms
(cbrt (* d1 (+ 3 d3)))
105.0ms
(cbrt (* d1 (+ 3 d3)))
100.0ms
(* (cbrt (* d1 (+ 3 d3))) (cbrt (* d1 (+ 3 d3))))
73.0ms
(cbrt (* d1 (+ 3 d3)))

simplify5.9s

Counts
49 → 77
Calls

49 calls. Slowest were:

488.0ms
(- (+ (exp (* 1/3 (+ (log 9) (* 2 (log d1))))) (* 2/9 (* (exp (* 1/3 (+ (log 9) (* 2 (log d1))))) d3))) (* 1/81 (* (exp (* 1/3 (+ (log 9) (* 2 (log d1))))) (pow d3 2))))
462.0ms
(- (+ (/ (* (exp (* 1/3 (- (log -1) (+ (log (/ -1 d1)) (log (/ -1 d3)))))) (cbrt -1)) d3) (* (exp (* 1/3 (- (log -1) (+ (log (/ -1 d1)) (log (/ -1 d3)))))) (cbrt -1))) (/ (* (exp (* 1/3 (- (log -1) (+ (log (/ -1 d1)) (log (/ -1 d3)))))) (cbrt -1)) (pow d3 2)))
428.0ms
(- (+ (* 1/9 (* d3 (exp (* 1/3 (+ (log 3) (log d1)))))) (exp (* 1/3 (+ (log 3) (log d1))))) (* 1/81 (* (pow d3 2) (exp (* 1/3 (+ (log 3) (log d1)))))))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

6.7b
(/ (* d1 (- (* 3 3) (* d3 d3))) (- 3 d3))
6.2b
(* d1 (- (* 3 3) (* d3 d3)))
0.0b
(+ (* d1 d2) (/ (* d1 (- (* 3 3) (* d3 d3))) (- 3 d3)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Counts
3 → 52
Calls

3 calls. Slowest were:

8.0ms
(+ (* d1 d2) (/ (* d1 (- (* 3 3) (* d3 d3))) (- 3 d3)))
6.0ms
(/ (* d1 (- (* 3 3) (* d3 d3))) (- 3 d3))
6.0ms
(* d1 (- (* 3 3) (* d3 d3)))

series167.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

66.0ms
(+ (* d1 d2) (/ (* d1 (- (* 3 3) (* d3 d3))) (- 3 d3)))
58.0ms
(/ (* d1 (- (* 3 3) (* d3 d3))) (- 3 d3))
44.0ms
(* d1 (- (* 3 3) (* d3 d3)))

simplify2.7s

Counts
35 → 61
Calls

35 calls. Slowest were:

683.0ms
(/ (- (* 3 3) (* d3 d3)) (- 3 d3))
440.0ms
(* d1 (- (pow (* 3 3) 3) (pow (* d3 d3) 3)))
273.0ms
(* d1 (- (* (* 3 3) (* 3 3)) (* (* d3 d3) (* d3 d3))))

prune772.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes137.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms