Details

Time bar (total: 28.6s)

sample90.0ms

Algorithm
intervals
Results
43.0ms256×body80valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
02937
16230
215430
350230
4176630
done500030

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.2b

localize45.0ms

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)
0.3b
(/ (- 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)))
22.5b
(/ (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))

rewrite47.0ms

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 (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
28.0ms
(/ (- 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)))
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))

series711.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
30.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
399.0ms
(/ (- 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)))
244.0ms
(/ (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
164 → 164
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02667066
16596938
221356594
done50006585

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

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 x x (* 2.0 (+ 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)))
18.2b
(/ (- (pow x 3) (pow 2.0 3)) (* (fma x x (* 2.0 (+ 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))))
22.5b
(/ (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))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt
44×times-frac
42×*-un-lft-identity
32×difference-of-squares
28×associate-/l*
24×unpow-prod-down cube-prod
22×add-cube-cbrt
20×add-exp-log add-cbrt-cube
16×sqr-pow
13×associate-*r*
10×distribute-lft-out--
6×pow1 cbrt-undiv div-exp
4×expm1-log1p-u prod-exp associate-/r* cbrt-unprod log1p-expm1-u add-log-exp
3×associate-*l* div-inv
2×difference-cubes frac-2neg associate-*r/ clear-num associate-/l/ unswap-sqr
1×flip3-- div-sub pow-prod-down associate-/r/ *-commutative flip-- fma-udef
Counts
4 → 146
Calls
4 calls:
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
26.0ms
(* (fma x x (* 2.0 (+ 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)))
106.0ms
(/ (- (pow x 3) (pow 2.0 3)) (* (fma x x (* 2.0 (+ 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))

series1.1s

Counts
4 → 12
Calls
4 calls:
35.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
324.0ms
(* (fma x x (* 2.0 (+ 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)))
539.0ms
(/ (- (pow x 3) (pow 2.0 3)) (* (fma x x (* 2.0 (+ 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))))
238.0ms
(/ (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))

simplify1.4s

Counts
158 → 158
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02536698
15966590
226065897
done50025896

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow x 3) (pow 2.0 3)) (/ (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)))
0.2b
(/ 1 (fma x x (* 2.0 (+ x 2.0))))
18.3b
(* (/ 1 (fma x x (* 2.0 (+ x 2.0)))) (/ (- (pow x 3) (pow 2.0 3)) (/ (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))))
22.5b
(/ (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))

rewrite628.0ms

Algorithm
rewrite-expression-head
Rules
1151×times-frac
1090×add-sqr-sqrt
685×*-un-lft-identity
432×difference-of-squares
412×add-cube-cbrt
330×associate-*r*
324×unpow-prod-down cube-prod
216×sqr-pow
135×distribute-lft-out--
56×div-inv
54×add-exp-log
34×add-cbrt-cube
31×associate-/l*
27×difference-cubes
24×div-exp
19×associate-/r*
14×cbrt-undiv
13×associate-*l*
12×prod-exp
9×unswap-sqr
7×pow1
6×cbrt-unprod
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×associate-/r/ associate-/l/
1×frac-times flip3-- pow-flip div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- inv-pow
Counts
4 → 829
Calls
4 calls:
124.0ms
(/ (- (pow x 3) (pow 2.0 3)) (/ (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
(/ 1 (fma x x (* 2.0 (+ x 2.0))))
360.0ms
(* (/ 1 (fma x x (* 2.0 (+ x 2.0)))) (/ (- (pow x 3) (pow 2.0 3)) (/ (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))

series1.3s

Counts
4 → 12
Calls
4 calls:
421.0ms
(/ (- (pow x 3) (pow 2.0 3)) (/ (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)))
92.0ms
(/ 1 (fma x x (* 2.0 (+ x 2.0))))
557.0ms
(* (/ 1 (fma x x (* 2.0 (+ x 2.0)))) (/ (- (pow x 3) (pow 2.0 3)) (/ (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))))
250.0ms
(/ (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))

simplify2.3s

Counts
841 → 841
Iterations

Useful iterations: done (2.2s)

IterNodesCost
082946938
1249944862
done500142825

prune6.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

7.5b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
7.5b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
18.4b
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- x 2.0) (/ (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))))
22.4b
(/ (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))

rewrite234.0ms

Algorithm
rewrite-expression-head
Rules
277×times-frac
241×add-sqr-sqrt
174×*-un-lft-identity
122×add-cube-cbrt
115×associate-*r*
85×sqrt-prod
45×add-exp-log
27×add-cbrt-cube
22×associate-*l* distribute-lft-out-- difference-of-squares
20×unswap-sqr
19×div-exp
12×prod-exp
10×cbrt-undiv
8×pow1 div-inv
6×cbrt-unprod associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp 1-exp associate-/r*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r/ *-commutative
Counts
4 → 260
Calls
4 calls:
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))
185.0ms
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- x 2.0) (/ (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))))
15.0ms
(/ (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))

series1.2s

Counts
4 → 12
Calls
4 calls:
129.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
146.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
447.0ms
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- x 2.0) (/ (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))))
435.0ms
(/ (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))

simplify2.7s

Counts
272 → 272
Iterations

Useful iterations: done (2.7s)

IterNodesCost
037913471
1105812559
2346111029
done500111028

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes331.0ms

Accuracy

97.4% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 25.2b

bsearch576.0ms

Steps
ItersRangePoint
10
2.6969245666033035e+35
4.264445276026206e+51
4.185814178876574e+51
9
-5.504247016617868e+37
-3.1641101034949086e+31
-4.1468195884167556e+37

simplify11.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
04373
15264
done5264

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.8s8011×body80valid