Average Error: 0.2 → 0.0
Time: 7.5s
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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019016 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"

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

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

Details

Time bar (total: 7.1s)Debug log

sample62.0ms

Algorithm
intervals
Results
296×(pre true 80)
293×(body real 80)
1×(body real 320)
1×(body real 640)
1×(body real 1280)

simplify83.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
83.0ms
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ d2 30) d1)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
3×associate-*l*
2×add-cube-cbrt
2×associate-*l/
2×*-un-lft-identity
2×add-sqr-sqrt
1×add-log-exp
1×log1p-expm1-u
1×flip-+
1×*-commutative
1×add-exp-log
1×add-cbrt-cube
1×flip3-+
1×pow1
1×expm1-log1p-u
Counts
1 → 15
Calls
1 calls:
Slowest
5.0ms
(* (+ d2 30) d1)

series24.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
24.0ms
(* (+ d2 30) d1)

simplify210.0ms

Counts
7 → 18
Calls
7 calls:
Slowest
165.0ms
(* (- (* d2 d2) (* 30 30)) d1)
20.0ms
(* (+ (pow d2 3) (pow 30 3)) d1)
6.0ms
(+ (* d2 d1) (* 30 d1))
6.0ms
(+ (* d2 d1) (* 30 d1))
6.0ms
(+ (* d2 d1) (* 30 d1))

prune119.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))
0.0b
(+ (* d1 10) (* d1 d2))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
9×add-log-exp
5×fma-def
4×distribute-lft-out
4×sum-log
3×add-cube-cbrt
3×*-un-lft-identity
3×add-sqr-sqrt
2×log1p-expm1-u
2×flip-+
2×add-exp-log
2×add-cbrt-cube
2×flip3-+
2×+-commutative
2×pow1
2×expm1-log1p-u
1×associate-+l+
Counts
2 → 35
Calls
2 calls:
Slowest
9.0ms
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))
2.0ms
(+ (* d1 10) (* d1 d2))

series47.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
28.0ms
(+ (* d1 10) (* d1 d2))
19.0ms
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))

simplify270.0ms

Counts
14 → 41
Calls
14 calls:
Slowest
99.0ms
(* (* (exp (* d1 10)) (exp (* d1 d2))) (exp (* d1 20)))
83.0ms
(* (exp (+ (* d1 10) (* d1 d2))) (exp (* d1 20)))
14.0ms
(* (cbrt (+ (* d1 10) (* d1 d2))) (cbrt (+ (* d1 10) (* d1 d2))))
13.0ms
(sqrt (+ (* d1 10) (* d1 d2)))
10.0ms
(* (exp (* d1 10)) (exp (* d1 d2)))

prune402.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 2 expressions with local error:

10.0b
(/ (* (fma d2 d2 -900) d1) (- d2 30))
4.0b
(* (fma d2 d2 -900) d1)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
5×add-cube-cbrt
5×*-un-lft-identity
5×add-sqr-sqrt
4×add-exp-log
4×add-cbrt-cube
3×associate-*l*
3×times-frac
3×associate-/r*
2×add-log-exp
2×log1p-expm1-u
2×associate-/r/
2×pow1
2×expm1-log1p-u
1×associate-/l*
1×flip--
1×div-inv
1×*-commutative
1×div-exp
1×flip3--
1×frac-2neg
1×clear-num
1×cbrt-undiv
Counts
2 → 36
Calls
2 calls:
Slowest
11.0ms
(/ (* (fma d2 d2 -900) d1) (- d2 30))
5.0ms
(* (fma d2 d2 -900) d1)

series87.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
48.0ms
(/ (* (fma d2 d2 -900) d1) (- d2 30))
39.0ms
(* (fma d2 d2 -900) d1)

simplify390.0ms

Counts
22 → 42
Calls
22 calls:
Slowest
114.0ms
(/ (* (* (* (fma d2 d2 -900) d1) (* (fma d2 d2 -900) d1)) (* (fma d2 d2 -900) d1)) (* (* (- d2 30) (- d2 30)) (- d2 30)))
54.0ms
(- (log (* (fma d2 d2 -900) d1)) (log (- d2 30)))
44.0ms
(+ (* d2 d2) (+ (* 30 30) (* d2 30)))
27.0ms
(- (* (pow d2 2) d1) (* 900 d1))
27.0ms
(- (* (pow d2 2) d1) (* 900 d1))

prune394.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize56.0ms

Local error

Found 3 expressions with local error:

15.9b
(/ (* (+ (pow d2 3) (pow 30 3)) d1) (+ (* d2 d2) (- (* 30 30) (* d2 30))))
4.0b
(* (+ (pow d2 3) (pow 30 3)) d1)
0.0b
(+ (* d2 d2) (- (* 30 30) (* d2 30)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
8×add-log-exp
8×*-un-lft-identity
6×add-cube-cbrt
6×add-sqr-sqrt
5×add-exp-log
5×associate-*l*
5×add-cbrt-cube
4×flip-+
4×associate-*l/
4×flip3-+
3×log1p-expm1-u
3×times-frac
3×associate-/r*
3×associate-+r+
3×pow1
3×expm1-log1p-u
2×associate-/l/
2×associate-/r/
2×sum-log
1×associate-/l*
1×distribute-lft-out
1×div-inv
1×*-commutative
1×sum-cubes
1×prod-diff
1×div-exp
1×diff-log
1×frac-2neg
1×fma-def
1×sub-neg
1×associate-+r-
1×clear-num
1×+-commutative
1×cbrt-undiv
Counts
3 → 61
Calls
3 calls:
Slowest
17.0ms
(/ (* (+ (pow d2 3) (pow 30 3)) d1) (+ (* d2 d2) (- (* 30 30) (* d2 30))))
7.0ms
(* (+ (pow d2 3) (pow 30 3)) d1)
5.0ms
(+ (* d2 d2) (- (* 30 30) (* d2 30)))

series98.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
62.0ms
(/ (* (+ (pow d2 3) (pow 30 3)) d1) (+ (* d2 d2) (- (* 30 30) (* d2 30))))
26.0ms
(* (+ (pow d2 3) (pow 30 3)) d1)
10.0ms
(+ (* d2 d2) (- (* 30 30) (* d2 30)))

simplify2.9s

Counts
36 → 70
Calls
36 calls:
Slowest
335.0ms
(* (+ (pow (pow d2 3) 3) (pow (pow 30 3) 3)) d1)
318.0ms
(* (+ (pow (pow d2 3) 3) (pow (pow 30 3) 3)) d1)
258.0ms
(+ (* (* d2 d2) (* d2 d2)) (- (* (- (* 30 30) (* d2 30)) (- (* 30 30) (* d2 30))) (* (* d2 d2) (- (* 30 30) (* d2 30)))))
226.0ms
(* (- (* (pow d2 3) (pow d2 3)) (* (pow 30 3) (pow 30 3))) d1)
212.0ms
(* (- (* (pow d2 3) (pow d2 3)) (* (pow 30 3) (pow 30 3))) d1)

prune644.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes158.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.0s

Algorithm
intervals
Results
9155×(pre true 80)
9027×(body real 80)
47×(body real 1280)
46×(body real 640)
21×(body real 320)
14×(body real 160)