Details

Time bar (total: 29.9s)

sample82.0ms

Algorithm
intervals
Results
43.0ms258×body80valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
029731
162556
2154556
3512556
42165556
done5000556

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.1b
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
0.3b
(/ (- 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)))
20.8b
(/ (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))

rewrite36.0ms

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-cbrt-cube add-exp-log
8×div-inv associate-/l*
4×expm1-log1p-u pow1 cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×clear-num frac-2neg fma-udef associate-/l/
1×flip3-- div-sub associate-/r/ flip--
Counts
4 → 152
Calls
4 calls:
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.0ms
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
25.0ms
(/ (- 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)))
5.0ms
(/ (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))

series941.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
173.0ms
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
447.0ms
(/ (- 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)))
271.0ms
(/ (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))

simplify2.9s

Counts
164 → 164
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
0263125693
1730121184
23451119863
done5001119863

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.1b
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
0.1b
(/ 1 (/ (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)))
20.8b
(/ (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))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
17×add-exp-log
16×associate-/r*
11×add-cbrt-cube
8×div-exp
6×div-inv associate-/l*
5×pow1
4×expm1-log1p-u cbrt-undiv log1p-expm1-u add-log-exp
2×rec-exp clear-num frac-2neg 1-exp fma-udef
1×associate-/r/ pow-flip inv-pow
Counts
4 → 127
Calls
4 calls:
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.0ms
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
8.0ms
(/ 1 (/ (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)))
5.0ms
(/ (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))

series744.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
146.0ms
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
342.0ms
(/ 1 (/ (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)))
225.0ms
(/ (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))

simplify2.1s

Counts
139 → 139
Iterations

Useful iterations: done (2.1s)

IterNodesCost
021190957
147882253
2222681961
done500179504

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.1b
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
20.8b
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
3×associate-/r* fma-udef associate-/l*
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 59
Calls
4 calls:
0.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.0ms
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
7.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))

series500.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
28.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
102.0ms
(fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)
333.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))

simplify4.1s

Counts
71 → 71
Iterations

Useful iterations: done (4.1s)

IterNodesCost
012831738
124728449
272628157
3316528082
done500027827

prune719.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize100.0ms

Local error

Found 4 expressions with local error:

7.7b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
7.7b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
12.4b
(* (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) 1) (/ (sqrt (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)))
20.7b
(/ (sqrt (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))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
23×add-exp-log
22×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
8×pow1 div-exp
6×prod-exp associate-/l*
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×associate-/r* div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 1-exp
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 154
Calls
4 calls:
1.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
1.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
46.0ms
(* (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) 1) (/ (sqrt (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)))
5.0ms
(/ (sqrt (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))

series884.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
126.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
220.0ms
(* (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) 1) (/ (sqrt (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)))
432.0ms
(/ (sqrt (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))

simplify6.6s

Counts
166 → 166
Iterations

Useful iterations: 2 (1.8s)

IterNodesCost
0193109217
153897743
2494095586
done500195586

prune1.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes425.0ms

Accuracy

95.6% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 25.1b

bsearch231.0ms

Steps
ItersRangePoint
9
488997712.5877659
631776370996477.2
620615997107907.6
3
-6.376815652518718e+28
-5.267362834597857e+28
-6.307474851398664e+28

simplify12.0ms

Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0351035
143994
244994
done44994

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.6s8010×body80valid