Details

Time bar (total: 16.6s)

sample64.0ms

Algorithm
intervals
Results
30.0ms257×body80valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
02937
16230
215430
350230
4176630
done500030

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.9b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.6b
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
25.1b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
128×times-frac
96×add-sqr-sqrt *-un-lft-identity
68×add-cube-cbrt
16×associate-/r*
14×distribute-lft-out-- difference-of-squares
11×add-exp-log add-cbrt-cube
8×div-inv associate-/l*
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef associate-/l/
1×flip3-- div-sub associate-/r/ flip--
Counts
4 → 152
Calls
4 calls:
0.0ms
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
50.0ms
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
6.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series688.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
31.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
379.0ms
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
212.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify1.2s

Counts
164 → 164
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02637109
16606981
221376631
done50006626

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- x 2.0) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
0.0b
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
25.1b
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×times-frac
13×associate-*r*
11×add-exp-log add-cbrt-cube
6×pow1
5×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×cbrt-undiv frac-times flip3-- div-exp associate-*l/ prod-exp flip-- cbrt-unprod fma-udef div-inv unswap-sqr
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative distribute-lft-out-- difference-of-squares
Counts
4 → 89
Calls
4 calls:
43.0ms
(* (- x 2.0) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
1.0ms
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
10.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

series742.0ms

Counts
4 → 12
Calls
4 calls:
354.0ms
(* (- x 2.0) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
72.0ms
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
40.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
276.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

simplify1.3s

Counts
101 → 101
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01823108
14003061
213652727
done50002723

prune641.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
9.1b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
9.1b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
25.1b
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (* (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-/l*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp
1×frac-2neg prod-exp clear-num associate-/r* cbrt-unprod fma-udef div-inv
Counts
4 → 63
Calls
4 calls:
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
2.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
2.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
20.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (* (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))

series614.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
117.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
107.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
353.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (* (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))

simplify1.2s

Counts
75 → 75
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01222056
12541586
26451376
319471363
done50001361

prune494.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2.0 (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
0.3b
(/ x (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
25.1b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
25.1b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
168×times-frac
104×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
32×associate-/r*
18×add-exp-log add-cbrt-cube
12×div-inv associate-/l*
8×cbrt-undiv div-exp
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×associate-/r/
Counts
4 → 202
Calls
4 calls:
10.0ms
(/ 2.0 (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
19.0ms
(/ x (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
10.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
11.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series1.3s

Counts
4 → 12
Calls
4 calls:
359.0ms
(/ 2.0 (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
434.0ms
(/ x (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
266.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
263.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify1.3s

Counts
214 → 214
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03059434
16489271
220968705
done50008696

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes282.0ms

Accuracy

97.7% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 24.8b

bsearch315.0ms

Steps
ItersRangePoint
9
2.619665596277428e+42
5.643437391960611e+47
7.170111234031815e+44
6
-2.4520752562547516e+37
-1.7323537610041296e+36
-1.2340170654382657e+37

simplify29.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03458
13949
done3949

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.5s8015×body80valid