Details

Time bar (total: 9.9s)

sample32.0ms

Algorithm
intervals
Results
15.0ms257×body80valid

simplify480.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
02937
16230
215330
339030
4127230
done500030

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize22.0ms

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 (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
24.1b
(/ (* (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (- x 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
9×add-exp-log add-cbrt-cube
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-/r* fma-udef
2×cbrt-undiv associate-*r/ div-exp associate-/l/
1×flip3-- frac-2neg prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l*
Counts
4 → 55
Calls
4 calls:
0.0ms
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
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)
10.0ms
(/ (* (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (- x 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

series407.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
53.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
27.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
274.0ms
(/ (* (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (- x 2.0)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

simplify414.0ms

Counts
67 → 67
Iterations

Useful iterations: done (411.0ms)

IterNodesCost
01371539
13291508
211171262
done50001259

prune335.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(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)
3.1b
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
23.0b
(* (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
38×*-un-lft-identity
31×times-frac
24×add-cube-cbrt
19×associate-*r*
11×add-exp-log add-cbrt-cube
7×distribute-lft-out-- difference-of-squares
6×pow1
5×associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* associate-/r*
2×cbrt-undiv div-exp prod-exp cbrt-unprod fma-udef div-inv associate-/l/ unswap-sqr
1×flip3-- frac-2neg div-sub associate-*r/ pow-prod-down clear-num *-commutative flip--
Counts
4 → 100
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)
8.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
15.0ms
(* (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
26.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
90.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
281.0ms
(* (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify602.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (140.0ms)

IterNodesCost
01972962
14522901
217182609
done50002609

prune487.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

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))
14.3b
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
14.5b
(* (/ (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))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
20.1b
(/ (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)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
126×add-sqr-sqrt
108×times-frac
95×*-un-lft-identity
69×add-cube-cbrt
63×sqrt-prod
34×associate-*r*
22×associate-*l*
20×add-exp-log add-cbrt-cube
13×distribute-lft-out-- difference-of-squares
12×associate-/r*
9×unswap-sqr
8×associate-/l*
7×pow1
6×cbrt-undiv div-exp
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
2×frac-2neg clear-num associate-/l/
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 pow1/2 div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 201
Calls
4 calls:
1.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
10.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
37.0ms
(* (/ (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))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
3.0ms
(/ (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)))

series931.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
163.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
294.0ms
(* (/ (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))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
371.0ms
(/ (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)))

simplify1.1s

Counts
213 → 213
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02998963
17878520
230707595
done50017520

prune868.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

14.1b
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
14.1b
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
14.1b
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
21.1b
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (* (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×add-exp-log cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac pow1/3 associate-/l*
2×cbrt-undiv div-exp
1×frac-2neg prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 62
Calls
4 calls:
0.0ms
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
0.0ms
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
0.0ms
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
4.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (* (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))

series1.1s

Counts
4 → 12
Calls
4 calls:
157.0ms
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
157.0ms
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
153.0ms
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
641.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (* (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))

simplify954.0ms

Counts
74 → 74
Iterations

Useful iterations: 3 (309.0ms)

IterNodesCost
01272275
12902187
28311917
327271858
done50001858

prune415.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes226.0ms

Accuracy

97.5% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 25.0b

bsearch217.0ms

Steps
ItersRangePoint
10
1.176638228465725e+60
7.418644318783979e+71
4.542624288937221e+64
6
-2.817955795644209e+61
-2.1393564465797727e+60
-4.373221704574123e+60

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03458
13949
done3949

end0.0ms

sample701.0ms

Algorithm
intervals
Results
513.0ms8007×body80valid