Details

Time bar (total: 18.1s)

sample43.0ms

Algorithm
intervals
Results
22.0ms256×body80valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
02937
16230
215430
351330
4220730
done500130

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.2b

localize36.0ms

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)))
22.4b
(/ (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))

rewrite63.0ms

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)
39.0ms
(/ (- 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)))
9.0ms
(/ (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))

series784.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
39.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
417.0ms
(/ (- 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)))
247.0ms
(/ (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))

simplify1.5s

Counts
164 → 164
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02677079
17346973
234246615
done50006610

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 4 expressions with local error:

7.0b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
7.0b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
14.6b
(/ (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) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
19.7b
(/ (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)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×add-cube-cbrt *-un-lft-identity
150×sqrt-prod
28×associate-/r*
11×add-exp-log add-cbrt-cube
9×div-inv associate-/l*
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/r/
Counts
4 → 248
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))
21.0ms
(/ (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) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
9.0ms
(/ (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)))

series848.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
135.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
196.0ms
(/ (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) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
382.0ms
(/ (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)))

simplify535.0ms

Counts
260 → 260
Iterations

Useful iterations: done (513.0ms)

IterNodesCost
031316189
176415184
done500114719

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

7.0b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
7.0b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
20.0b
(* (/ 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))

rewrite180.0ms

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:
1.0ms
(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))
144.0ms
(* (/ 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))))
9.0ms
(/ (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))

series997.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
131.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
355.0ms
(* (/ 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))))
386.0ms
(/ (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))

simplify742.0ms

Counts
272 → 272
Iterations

Useful iterations: done (721.0ms)

IterNodesCost
037913471
1126812725
done500011728

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.4b
(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
1.9b
(/ (- 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)))

rewrite110.0ms

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 4.16438922228 78.6994924154) x 137.519416416)
8.0ms
(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
19.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
38.0ms
(/ (/ (- 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)))

series639.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
134.0ms
(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
122.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
340.0ms
(/ (/ (- 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)))

simplify1.2s

Counts
401 → 401
Iterations

Useful iterations: done (1.1s)

IterNodesCost
058721533
1187820491
done500119375

prune1.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.2b

regimes424.0ms

Accuracy

97% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 25.1b

bsearch271.0ms

Steps
ItersRangePoint
8
1.529063742838704e+38
5.064835482675284e+41
2.9657594637859867e+41
7
-1.725693211891992e+53
-5.553209047609446e+51
-2.2557635483334135e+52

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03673
14064
done4064

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.7s8009×body80valid