Details

Time bar (total: 21.8s)

sample49.0ms

Algorithm
intervals
Results
20.0ms256×body80valid

simplify1.7s

Counts
1 → 1
Iterations
IterNodes
done5000
42165
3512
2154
162
029

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.4b

localize48.0ms

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)
3.3b
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
22.5b
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
104×add-sqr-sqrt *-un-lft-identity
72×add-cube-cbrt
26×associate-/r*
16×distribute-lft-out-- difference-of-squares
11×add-cbrt-cube add-exp-log associate-/r/
6×div-inv associate-/l*
5×flip3-- flip--
4×expm1-log1p-u pow1 cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×clear-num frac-2neg fma-udef
Counts
4 → 163
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)
18.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
38.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

series772.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
55.0ms
(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
155.0ms
(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
494.0ms
(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

simplify1.5s

Counts
175 → 175
Iterations
IterNodes
done5000
23509
1701
0296

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y)
0.1b
(fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
0.1b
(fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894)
22.7b
(/ (fma (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) x z) (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))

rewrite11.0ms

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 x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y)
0.0ms
(fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
0.0ms
(fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894)
8.0ms
(/ (fma (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) x z) (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))

series569.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y)
33.0ms
(fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
65.0ms
(fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894)
389.0ms
(/ (fma (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) x z) (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))

simplify1.8s

Counts
71 → 71
Iterations
IterNodes
done5000
32908
2696
1248
0131

prune727.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

6.8b
(sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))
6.8b
(sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))
15.3b
(/ (/ (fma (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))) (sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606)))
19.8b
(/ (fma (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-/l/
Counts
4 → 248
Calls
4 calls:
2.0ms
(sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))
2.0ms
(sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))
22.0ms
(/ (/ (fma (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))) (sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606)))
5.0ms
(/ (fma (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606)))

series1.2s

Counts
4 → 12
Calls
4 calls:
137.0ms
(sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))
187.0ms
(sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))
410.0ms
(/ (/ (fma (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))) (sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606)))
494.0ms
(/ (fma (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606)))

simplify1.5s

Counts
260 → 260
Iterations
IterNodes
done5000
23464
1729
0315

prune2.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894)
3.7b
(/ (fma (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) x z) (+ 2.0 x))
18.8b
(* (/ (* 1 (fma (- 2.0) 2.0 (pow x 2))) (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606)) (/ (fma (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) x z) (+ 2.0 x)))
22.1b
(/ (* 1 (fma (- 2.0) 2.0 (pow x 2))) (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
41×add-exp-log
39×*-un-lft-identity
32×add-cbrt-cube
31×times-frac
30×add-sqr-sqrt
25×add-cube-cbrt
18×associate-*r*
14×div-exp prod-exp
10×cbrt-undiv
9×cbrt-unprod
7×associate-/r* associate-*l* distribute-lft-out
6×pow1
4×expm1-log1p-u associate-/r/ log1p-expm1-u div-inv associate-/l* add-log-exp
3×1-exp
2×clear-num frac-2neg flip3-+ flip-+ unswap-sqr
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative fma-udef
Counts
4 → 124
Calls
4 calls:
0.0ms
(fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894)
16.0ms
(/ (fma (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) x z) (+ 2.0 x))
47.0ms
(* (/ (* 1 (fma (- 2.0) 2.0 (pow x 2))) (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606)) (/ (fma (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) x z) (+ 2.0 x)))
8.0ms
(/ (* 1 (fma (- 2.0) 2.0 (pow x 2))) (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))

series965.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894)
204.0ms
(/ (fma (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) x z) (+ 2.0 x))
573.0ms
(* (/ (* 1 (fma (- 2.0) 2.0 (pow x 2))) (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606)) (/ (fma (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) x z) (+ 2.0 x)))
147.0ms
(/ (* 1 (fma (- 2.0) 2.0 (pow x 2))) (fma x (fma x (fma (+ x 43.3400022514) x 263.505074721) 313.399215894) 47.066876606))

simplify2.3s

Counts
136 → 136
Iterations
IterNodes
done5001
23656
1647
0239

prune1.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes496.0ms

Accuracy

97.3% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 24.3b

bsearch404.0ms

Steps
ItersRangePoint
8
4.3244295128648204e+19
5.507951260787393e+23
5.4273741753551194e+23
9
-1.0536694575613961e+43
-1.1904368731341533e+38
-1.0087778421912963e+43

simplify6.0ms

Iterations
IterNodes
done45
245
144
036

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.8s8007×body80valid