Details

Time bar (total: 20.0s)

sample87.0ms

Algorithm
intervals
Results
50.0ms256×body80valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
02937
16230
215430
350230
4176630
done500030

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.1b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
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))

rewrite40.0ms

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 4.16438922228 78.6994924154) x 137.519416416)
1.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
27.0ms
(/ (- 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))

series769.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
54.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
403.0ms
(/ (- 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)))
256.0ms
(/ (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
164 → 164
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02667066
16596938
221366594
done50006585

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- x 2.0) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.1b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
22.5b
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×times-frac
13×associate-*r*
11×add-exp-log add-cbrt-cube
6×pow1
5×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×cbrt-undiv frac-times flip3-- div-exp associate-*l/ prod-exp flip-- cbrt-unprod fma-udef div-inv unswap-sqr
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative distribute-lft-out-- difference-of-squares
Counts
4 → 89
Calls
4 calls:
54.0ms
(* (- x 2.0) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
1.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
11.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

series850.0ms

Counts
4 → 12
Calls
4 calls:
397.0ms
(* (- x 2.0) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
44.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
73.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
337.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

simplify1.7s

Counts
101 → 101
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01853065
13993018
213662690
done50002682

prune765.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.1b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
2.1b
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
22.5b
(* (fma x (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) z) (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite60.0ms

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 x 4.16438922228 78.6994924154) x 137.519416416)
0.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
27.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
29.0ms
(* (fma x (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) z) (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

series671.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
54.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
132.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
448.0ms
(* (fma x (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) z) (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify1.3s

Counts
112 → 112
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01962949
14422888
214512598
done50002590

prune841.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.2b
(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
2.1b
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
22.3b
(/ (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
661×times-frac
380×add-sqr-sqrt *-un-lft-identity
288×add-cube-cbrt
46×distribute-lft-out-- difference-of-squares
37×div-inv
32×add-exp-log
27×associate-/l*
20×add-cbrt-cube
19×div-exp associate-/r*
10×cbrt-undiv
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp frac-2neg 1-exp div-sub clear-num associate-/l/
1×flip3-- pow-flip associate-/r/ flip-- fma-udef inv-pow
Counts
4 → 389
Calls
4 calls:
0.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
6.0ms
(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
30.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
34.0ms
(/ (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

series860.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
165.0ms
(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
136.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
494.0ms
(/ (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

simplify2.2s

Counts
401 → 401
Iterations

Useful iterations: done (2.2s)

IterNodesCost
058921563
1161720167
2398319301
done500119300

prune1.7s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes502.0ms

Accuracy

97.9% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 24.7b

bsearch477.0ms

Steps
ItersRangePoint
9
1.8328795043569038e+44
2.838659756671984e+50
2.2879431708269804e+47
10
-3.976749929960267e+79
-5.528985092060166e+69
-1.9144999724647918e+71

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03668
14354
done4354

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.8s8005×body80valid