Average Error: 0.2 → 0.0
Time: 16.6s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[\left(30 + d2\right) \cdot d1\]

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019018 
(FPCore (d1 d2)
  :name "FastMath test2"

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

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

Details

Time bar (total: 15.8s)Debug log

sample27.0ms

Algorithm
intervals
Results
15.0ms284×body80valid
1.0ms4×body1280valid
0.0ms1×body640valid

simplify41.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
41.0ms
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b
(* d1 (+ 30 d2))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
3×associate-*r*
2×add-cube-cbrt
2×associate-*r/
2×*-un-lft-identity
2×add-sqr-sqrt
1×add-log-exp
1×flip-+
1×*-commutative
1×add-exp-log
1×add-cbrt-cube
1×flip3-+
1×distribute-lft-in
1×pow1
1×distribute-rgt-in
Counts
1 → 15
Calls
1 calls:
Slowest
1.0ms
(* d1 (+ 30 d2))

series17.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
17.0ms
(* d1 (+ 30 d2))

simplify125.0ms

Counts
10 → 18
Calls
10 calls:
Slowest
86.0ms
(+ (* 30 30) (- (* d2 d2) (* 30 d2)))
10.0ms
(+ (* d2 d1) (* 30 d1))
9.0ms
(+ (* d2 d1) (* 30 d1))
9.0ms
(+ (* d2 d1) (* 30 d1))
3.0ms
(- 30 d2)

prune111.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

8.6b
(/ (* d1 (- (* 30 30) (* d2 d2))) (- 30 d2))
4.1b
(* d1 (- (* 30 30) (* d2 d2)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
5×add-cube-cbrt
5×*-un-lft-identity
5×add-sqr-sqrt
4×add-exp-log
4×associate-*r/
4×associate-*r*
4×add-cbrt-cube
3×flip--
3×flip3--
3×times-frac
3×associate-/r*
2×associate-/l/
2×add-log-exp
2×associate-/r/
2×distribute-lft-in
2×sub-neg
2×pow1
2×distribute-rgt-in
1×difference-of-squares
1×associate-/l*
1×div-inv
1×*-commutative
1×div-exp
1×frac-2neg
1×clear-num
1×cbrt-undiv
Counts
2 → 41
Calls
2 calls:
Slowest
6.0ms
(/ (* d1 (- (* 30 30) (* d2 d2))) (- 30 d2))
4.0ms
(* d1 (- (* 30 30) (* d2 d2)))

series96.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
51.0ms
(/ (* d1 (- (* 30 30) (* d2 d2))) (- 30 d2))
45.0ms
(* d1 (- (* 30 30) (* d2 d2)))

simplify2.1s

Counts
31 → 47
Calls
31 calls:
Slowest
482.0ms
(/ (- (* 30 30) (* d2 d2)) (- 30 d2))
295.0ms
(* d1 (- (pow (* 30 30) 3) (pow (* d2 d2) 3)))
236.0ms
(* d1 (- (* (* 30 30) (* 30 30)) (* (* d2 d2) (* d2 d2))))
228.0ms
(- (log (* d1 (- (* 30 30) (* d2 d2)))) (log (- 30 d2)))
161.0ms
(/ (- (* 30 30) (* d2 d2)) (sqrt (- 30 d2)))

prune323.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

15.1b
(/ (* d1 (+ (pow 30 3) (pow d2 3))) (+ 900 (* (- d2 30) d2)))
2.3b
(* d1 (+ (pow 30 3) (pow d2 3)))
0.0b
(* (- d2 30) d2)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-cube-cbrt
7×add-sqr-sqrt
5×add-exp-log
5×associate-*r*
5×add-cbrt-cube
4×associate-*r/
3×add-log-exp
3×flip-+
3×associate-*l*
3×times-frac
3×flip3-+
3×associate-/r*
3×pow1
2×associate-/l/
2×*-commutative
2×associate-/r/
2×associate-*l/
1×associate-/l*
1×distribute-lft-out
1×flip--
1×div-inv
1×sum-cubes
1×div-exp
1×flip3--
1×distribute-lft-in
1×frac-2neg
1×clear-num
1×cbrt-undiv
1×distribute-rgt-in
Counts
3 → 53
Calls
3 calls:
Slowest
9.0ms
(* d1 (+ (pow 30 3) (pow d2 3)))
7.0ms
(/ (* d1 (+ (pow 30 3) (pow d2 3))) (+ 900 (* (- d2 30) d2)))
5.0ms
(* (- d2 30) d2)

series189.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
110.0ms
(/ (* d1 (+ (pow 30 3) (pow d2 3))) (+ 900 (* (- d2 30) d2)))
60.0ms
(* d1 (+ (pow 30 3) (pow d2 3)))
19.0ms
(* (- d2 30) d2)

simplify2.5s

Counts
37 → 62
Calls
37 calls:
Slowest
398.0ms
(* d1 (- (* (pow 30 3) (pow 30 3)) (* (pow d2 3) (pow d2 3))))
367.0ms
(* d1 (+ (pow (pow 30 3) 3) (pow (pow d2 3) 3)))
304.0ms
(+ (* 900 900) (- (* (* (- d2 30) d2) (* (- d2 30) d2)) (* 900 (* (- d2 30) d2))))
287.0ms
(/ (* (* (* d1 (+ (pow 30 3) (pow d2 3))) (* d1 (+ (pow 30 3) (pow d2 3)))) (* d1 (+ (pow 30 3) (pow d2 3)))) (* (* (+ 900 (* (- d2 30) d2)) (+ 900 (* (- d2 30) d2))) (+ 900 (* (- d2 30) d2))))
278.0ms
(* (- (* d2 d2) (* 30 30)) d2)

prune625.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

12.6b
(* (/ d1 (sqrt (+ 900 (* (- d2 30) d2)))) (/ (+ 27000 (pow d2 3)) (sqrt (+ (* d2 (+ d2 -30)) 900))))
10.3b
(sqrt (+ 900 (* (- d2 30) d2)))
10.3b
(sqrt (+ (* d2 (+ d2 -30)) 900))
4.4b
(/ (+ 27000 (pow d2 3)) (sqrt (+ (* d2 (+ d2 -30)) 900)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×times-frac
35×add-cube-cbrt
35×*-un-lft-identity
27×sqrt-prod
24×associate-*r*
11×add-exp-log
11×add-cbrt-cube
10×sqrt-div
6×flip-+
6×associate-/r/
6×associate-*l*
6×flip3-+
6×associate-/r*
6×pow1
4×add-log-exp
3×associate-/l*
3×div-inv
2×associate-/l/
2×cbrt-unprod
2×prod-exp
2×div-exp
2×pow1/2
2×rem-sqrt-square
2×cbrt-undiv
1×*-commutative
1×associate-*r/
1×associate-*l/
1×pow-prod-down
1×frac-2neg
1×clear-num
1×frac-times
Counts
4 → 117
Calls
4 calls:
Slowest
22.0ms
(* (/ d1 (sqrt (+ 900 (* (- d2 30) d2)))) (/ (+ 27000 (pow d2 3)) (sqrt (+ (* d2 (+ d2 -30)) 900))))
11.0ms
(/ (+ 27000 (pow d2 3)) (sqrt (+ (* d2 (+ d2 -30)) 900)))
5.0ms
(sqrt (+ (* d2 (+ d2 -30)) 900))
1.0ms
(sqrt (+ 900 (* (- d2 30) d2)))

series188.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
97.0ms
(* (/ d1 (sqrt (+ 900 (* (- d2 30) d2)))) (/ (+ 27000 (pow d2 3)) (sqrt (+ (* d2 (+ d2 -30)) 900))))
41.0ms
(/ (+ 27000 (pow d2 3)) (sqrt (+ (* d2 (+ d2 -30)) 900)))
25.0ms
(sqrt (+ 900 (* (- d2 30) d2)))
24.0ms
(sqrt (+ (* d2 (+ d2 -30)) 900))

simplify6.3s

Counts
111 → 129
Calls
111 calls:
Slowest
464.0ms
(sqrt (+ (pow (* d2 (+ d2 -30)) 3) (pow 900 3)))
417.0ms
(/ (* (* (+ 27000 (pow d2 3)) (+ 27000 (pow d2 3))) (+ 27000 (pow d2 3))) (* (* (sqrt (+ (* d2 (+ d2 -30)) 900)) (sqrt (+ (* d2 (+ d2 -30)) 900))) (sqrt (+ (* d2 (+ d2 -30)) 900))))
338.0ms
(sqrt (+ (* (* d2 (+ d2 -30)) (* d2 (+ d2 -30))) (- (* 900 900) (* (* d2 (+ d2 -30)) 900))))
314.0ms
(sqrt (- (* (* d2 (+ d2 -30)) (* d2 (+ d2 -30))) (* 900 900)))
313.0ms
(sqrt (+ (* (* d2 (+ d2 -30)) (* d2 (+ d2 -30))) (- (* 900 900) (* (* d2 (+ d2 -30)) 900))))

prune1.9s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes75.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample961.0ms

Algorithm
intervals
Results
812.0ms8920×body80valid
19.0ms52×body1280valid
15.0ms45×body640valid
9.0ms34×body320valid
1.0ms6×body160valid