Details

Time bar (total: 18.6s)

sample95.0ms

Algorithm
intervals
Results
52.0ms256×body80valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
02937
16230
215430
350230
4176630
done500030

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.0b
(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)))
22.5b
(/ (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))

rewrite42.0ms

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 43.3400022514) x 263.505074721) x 313.399215894)
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
22.0ms
(/ (- 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))

series670.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
28.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
387.0ms
(/ (- 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)))
210.0ms
(/ (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))

simplify1.2s

Counts
164 → 164
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02667066
16596938
221356594
done50006585

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.0b
(* (- 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)))
0.0b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
22.4b
(/ (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))

rewrite63.0ms

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:
0.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
50.0ms
(* (- 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)))
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
8.0ms
(/ (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))

series1.1s

Counts
4 → 12
Calls
4 calls:
64.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
596.0ms
(* (- 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)))
28.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
378.0ms
(/ (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))

simplify1.1s

Counts
101 → 101
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01853065
13993018
213662690
done50012682

prune562.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize37.0ms

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))
7.5b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
14.1b
(* (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma x (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) z)))
22.4b
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma x (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) z))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
40×times-frac
36×add-cube-cbrt *-un-lft-identity
35×sqrt-prod
22×associate-*r*
11×add-exp-log add-cbrt-cube
8×pow1
6×associate-*l* associate-/l* unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp prod-exp cbrt-unprod div-inv
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 121
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))
37.0ms
(* (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma x (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) z)))
8.0ms
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma x (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) z))

series872.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
148.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
247.0ms
(* (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma x (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) z)))
347.0ms
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma x (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) z))

simplify2.2s

Counts
133 → 133
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01475074
13004497
28964075
329973967
done50003965

prune791.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.3b
(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
2.8b
(/ (- 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:
1.0ms
(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))
17.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
37.0ms
(/ (/ (- 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)))

series750.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
129.0ms
(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
127.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
444.0ms
(/ (/ (- 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)))

simplify2.0s

Counts
401 → 401
Iterations

Useful iterations: done (1.9s)

IterNodesCost
058721533
1161020137
2395319269
done500019268

prune1.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes300.0ms

Accuracy

97.3% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 24.9b

bsearch379.0ms

Steps
ItersRangePoint
9
2.0544205719112106e+24
3.3351947746546834e+30
3.2841517201888476e+30
7
-1.7458488000617126e+31
-2.6008056194933348e+29
-4.316916127649956e+30

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03458
13949
done3949

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.7s8009×body80valid