Details

Time bar (total: 20.0s)

sample35.0ms

Algorithm
intervals
Results
15.0ms257×body80valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
02937
16230
215430
350230
4176630
done500030

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
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)))
24.2b
(/ (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))

rewrite38.0ms

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 4.16438922228 78.6994924154) x 137.519416416) x y)
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
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)))
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))

series616.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
30.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
316.0ms
(/ (- 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)))
203.0ms
(/ (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))

simplify1.0s

Counts
164 → 164
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02677079
16626951
221396605
done50006599

prune856.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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)))
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
22.1b
(/ (- (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))))
24.2b
(/ (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))

rewrite115.0ms

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:
14.0ms
(* (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)))
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
89.0ms
(/ (- (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))

series899.0ms

Counts
4 → 12
Calls
4 calls:
252.0ms
(* (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)))
29.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
414.0ms
(/ (- (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))))
203.0ms
(/ (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))

simplify1.1s

Counts
158 → 158
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02536698
15966590
226085897
done50005896

prune856.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

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)))
0.3b
(/ 1 (fma x x (* 2.0 (+ x 2.0))))
22.0b
(* (/ 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))))
24.2b
(/ (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))

rewrite406.0ms

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:
96.0ms
(/ (- (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))))
220.0ms
(* (/ 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))))
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))

series1.3s

Counts
4 → 12
Calls
4 calls:
335.0ms
(/ (- (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)))
67.0ms
(/ 1 (fma x x (* 2.0 (+ x 2.0))))
423.0ms
(* (/ 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))))
471.0ms
(/ (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))

simplify1.7s

Counts
841 → 841
Iterations

Useful iterations: done (1.6s)

IterNodesCost
082946938
1249944862
done500142825

prune3.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

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)))
0.3b
(/ 1 (fma x x (* 2.0 (+ x 2.0))))
22.0b
(* (/ 1 (fma x x (* 2.0 (+ x 2.0)))) (* 1 (/ (- (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)))))
24.2b
(/ (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))

rewrite294.0ms

Algorithm
rewrite-expression-head
Rules
586×times-frac
559×add-sqr-sqrt
363×*-un-lft-identity
224×difference-of-squares
223×add-cube-cbrt
168×unpow-prod-down cube-prod
114×add-exp-log
112×sqr-pow
70×distribute-lft-out--
52×prod-exp
45×add-cbrt-cube
44×div-exp
31×associate-/l*
30×div-inv
20×1-exp
19×associate-/r*
15×cbrt-undiv
14×difference-cubes cbrt-unprod
13×associate-*l*
10×pow1
8×rec-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*r/ pow-prod-down clear-num
2×associate-/l/
1×frac-times flip3-- pow-flip div-sub associate-*r* associate-*l/ associate-/r/ *-commutative flip-- inv-pow
Counts
4 → 510
Calls
4 calls:
94.0ms
(/ (- (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)))
5.0ms
(/ 1 (fma x x (* 2.0 (+ x 2.0))))
150.0ms
(* (/ 1 (fma x x (* 2.0 (+ x 2.0)))) (* 1 (/ (- (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
(/ (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:
349.0ms
(/ (- (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)))
74.0ms
(/ 1 (fma x x (* 2.0 (+ x 2.0))))
436.0ms
(* (/ 1 (fma x x (* 2.0 (+ x 2.0)))) (* 1 (/ (- (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)))))
214.0ms
(/ (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))

simplify908.0ms

Counts
522 → 522
Iterations

Useful iterations: done (863.0ms)

IterNodesCost
066731649
1169630220
done500128829

prune2.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes320.0ms

Accuracy

97.3% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 24.4b

bsearch307.0ms

Steps
ItersRangePoint
9
2.1557533500351985e+74
1.6770313419776726e+82
2.1846838672686284e+74
10
-5.613235761893359e+75
-6.487595383962257e+61
-6.944319865754395e+68

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04475
15464
done5464

end0.0ms

sample742.0ms

Algorithm
intervals
Results
501.0ms8010×body80valid