Details

Time bar (total: 22.4s)

sample50.0ms

Algorithm
intervals
Results
31.0ms256×body80valid

simplify1.9s

Counts
1 → 1
Iterations
IterNodes
done5000
41857
3505
2152
162
029

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.9b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.1b
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
4.1b
(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
25.2b
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
38×*-un-lft-identity
31×times-frac
24×add-cube-cbrt
19×associate-*r*
11×add-cbrt-cube add-exp-log
7×distribute-lft-out-- difference-of-squares
6×pow1
5×associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* associate-*l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod fma-udef div-inv unswap-sqr associate-/l/
1×clear-num frac-2neg flip3-- div-sub pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 100
Calls
4 calls:
0.0ms
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
27.0ms
(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
45.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

series607.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
30.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
118.0ms
(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
405.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify1.9s

Counts
112 → 112
Iterations
IterNodes
done5001
21525
1458
0196

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
0.3b
(/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
3.8b
(* (- x 2.0) (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
25.2b
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (* (- x 2.0) (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
30×add-sqr-sqrt
24×*-un-lft-identity
21×add-cube-cbrt
20×times-frac add-cbrt-cube
14×associate-*r*
13×prod-exp
12×pow1
8×associate-*l* associate-*r/
7×cbrt-unprod
6×div-exp
4×expm1-log1p-u frac-times flip3-- pow-prod-down associate-*l/ log1p-expm1-u flip-- add-log-exp
3×cbrt-undiv rec-exp associate-/r* 1-exp associate-/l* unswap-sqr
2×un-div-inv *-commutative div-inv
1×clear-num frac-2neg fma-udef pow-flip distribute-lft-out-- inv-pow difference-of-squares
Counts
4 → 117
Calls
4 calls:
0.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
4.0ms
(/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
31.0ms
(* (- x 2.0) (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
48.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (* (- x 2.0) (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

series697.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
116.0ms
(/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
121.0ms
(* (- x 2.0) (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
410.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (* (- x 2.0) (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

simplify2.4s

Counts
129 → 129
Iterations
IterNodes
done5000
21630
1522
0222

prune964.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
0.1b
(/ (/ (* (+ x 2.0) (- x 2.0)) (fma x (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) 47.066876606)) (+ x 2.0))
23.8b
(/ (* (+ x 2.0) (- x 2.0)) (fma x (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) 47.066876606))
25.2b
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (/ (* (+ x 2.0) (- x 2.0)) (fma x (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) 47.066876606)) (+ x 2.0)))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
87×times-frac
71×*-un-lft-identity
46×add-sqr-sqrt
41×add-cube-cbrt
34×associate-*r*
32×add-cbrt-cube add-exp-log
15×distribute-lft-out
12×cbrt-undiv div-exp div-inv
9×associate-/l/
8×associate-/l*
7×associate-/r* prod-exp cbrt-unprod
6×pow1
5×flip3-+ flip-+
4×expm1-log1p-u frac-times associate-/r/ log1p-expm1-u add-log-exp
3×flip3-- associate-*l* associate-*r/ flip--
2×clear-num frac-2neg associate-*l/ unswap-sqr
1×pow-prod-down *-commutative fma-udef
Counts
4 → 160
Calls
4 calls:
1.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
44.0ms
(/ (/ (* (+ x 2.0) (- x 2.0)) (fma x (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) 47.066876606)) (+ x 2.0))
42.0ms
(/ (* (+ x 2.0) (- x 2.0)) (fma x (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) 47.066876606))
80.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (/ (* (+ x 2.0) (- x 2.0)) (fma x (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) 47.066876606)) (+ x 2.0)))

series587.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
111.0ms
(/ (/ (* (+ x 2.0) (- x 2.0)) (fma x (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) 47.066876606)) (+ x 2.0))
116.0ms
(/ (* (+ x 2.0) (- x 2.0)) (fma x (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) 47.066876606))
328.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (/ (* (+ x 2.0) (- x 2.0)) (fma x (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) 47.066876606)) (+ x 2.0)))

simplify2.7s

Counts
172 → 172
Iterations
IterNodes
done5001
23285
1800
0281

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize84.0ms

Local error

Found 4 expressions with local error:

7.4b
(sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
7.4b
(sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
15.1b
(* (- x 2.0) (sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
25.2b
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (* (* (- x 2.0) (sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
42×sqrt-prod
33×*-un-lft-identity times-frac
28×add-cube-cbrt
19×pow1
17×sqrt-div associate-*r*
15×add-cbrt-cube associate-*r/ add-exp-log
11×frac-times associate-*l/
8×associate-*l*
7×pow-prod-down prod-exp cbrt-unprod
6×rem-sqrt-square sqrt-pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×div-inv
2×pow1/2 *-commutative pow-flip inv-pow
1×distribute-lft-out-- difference-of-squares
Counts
4 → 137
Calls
4 calls:
4.0ms
(sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
3.0ms
(sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
30.0ms
(* (- x 2.0) (sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
200.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (* (* (- x 2.0) (sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

series876.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
155.0ms
(sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
200.0ms
(* (- x 2.0) (sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
377.0ms
(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (* (* (- x 2.0) (sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (sqrt (/ 1 (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

simplify2.0s

Counts
149 → 149
Iterations
IterNodes
done5000
21545
1583
0249

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes521.0ms

Accuracy

95.3% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 25.1b

bsearch336.0ms

Steps
ItersRangePoint
9
2.675449539496148e+31
2.5431457216642727e+36
2.133877352683456e+36
5
-8.732989020757522e+16
-2.781397284673614e+16
-6.373111573806196e+16

simplify13.0ms

Iterations
IterNodes
done46
146
037

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.7s8011×body80valid