Details

Time bar (total: 29.6s)

sample92.0ms

Algorithm
intervals
Results
44.0ms256×body80valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
02937
16230
215430
351330
4220730
done500130

prune44.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.2b

localize76.0ms

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)
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)))
27.3b
(/ (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))

rewrite88.0ms

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:
1.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
62.0ms
(/ (- 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))

series1.3s

Counts
4 → 12
Calls
4 calls:
142.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
80.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
673.0ms
(/ (- 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)))
419.0ms
(/ (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))

simplify2.6s

Counts
164 → 164
Iterations

Useful iterations: done (2.6s)

IterNodesCost
02677079
17346973
234246615
done50006610

prune2.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize111.0ms

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)))
22.9b
(/ (- (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))))
27.3b
(/ (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))

rewrite244.0ms

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:
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
31.0ms
(* (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)))
189.0ms
(/ (- (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))))
13.0ms
(/ (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))

series1.6s

Counts
4 → 12
Calls
4 calls:
51.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
429.0ms
(* (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)))
734.0ms
(/ (- (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))))
349.0ms
(/ (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))

simplify2.8s

Counts
158 → 158
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02536698
16136594
230965903
done50015902

prune2.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

9.1b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
9.1b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
17.5b
(/ (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))))
23.5b
(/ (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)))

rewrite76.0ms

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:
3.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
3.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
29.0ms
(/ (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))))
12.0ms
(/ (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)))

series1.5s

Counts
4 → 12
Calls
4 calls:
189.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
189.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
349.0ms
(/ (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))))
750.0ms
(/ (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)))

simplify815.0ms

Counts
260 → 260
Iterations

Useful iterations: done (779.0ms)

IterNodesCost
031316189
176415184
done500114719

prune2.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize67.0ms

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)
3.3b
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
27.5b
(* (/ (- 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))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
38×*-un-lft-identity
31×times-frac
24×add-cube-cbrt
19×associate-*l*
11×add-exp-log add-cbrt-cube
7×distribute-lft-out-- difference-of-squares
6×pow1
5×associate-/l*
4×expm1-log1p-u fma-udef log1p-expm1-u add-log-exp
3×associate-*r* associate-/r*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-sub pow-prod-down associate-*l/ clear-num *-commutative flip--
Counts
4 → 102
Calls
4 calls:
1.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
32.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
68.0ms
(* (/ (- 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))

series1.0s

Counts
4 → 12
Calls
4 calls:
148.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
64.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
205.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
628.0ms
(* (/ (- 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))

simplify2.0s

Counts
114 → 114
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02033049
14793010
218462728
done50002721

prune1.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes521.0ms

Accuracy

96% (1.0b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 25.1b

bsearch515.0ms

Steps
ItersRangePoint
9
4.387960874763261e+27
8.737516579942584e+35
3.6858491050624058e+31
7
-1.5312203001569835e+19
-1.3073170848719158e+17
-1.4572255947977734e+19

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03458
13949
done3949

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.5s8013×body80valid