Details

Time bar (total: 14.0s)

sample38.0ms

Algorithm
intervals
Results
20.0ms256×body80valid

simplify994.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
02937
16230
215330
338330
4125130
done500030

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize26.0ms

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 (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (- x 2.0))
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
24.2b
(/ (* (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
24×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
11×add-exp-log distribute-rgt-in distribute-lft-in add-cbrt-cube
6×pow1
5×associate-*r*
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
3×times-frac associate-*l* associate-/r*
2×cbrt-undiv sub-neg flip3-- div-exp prod-exp flip-- cbrt-unprod fma-udef associate-/l/
1×frac-2neg pow-prod-down clear-num *-commutative div-inv associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 91
Calls
4 calls:
0.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
12.0ms
(* (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (- x 2.0))
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
11.0ms
(/ (* (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))

series579.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
162.0ms
(* (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (- x 2.0))
37.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
330.0ms
(/ (* (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))

simplify1.0s

Counts
103 → 103
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02192944
14712745
216312367
done50012349

prune483.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

6.8b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
14.1b
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
14.2b
(* (/ (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))))
19.4b
(/ (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)))

rewrite63.0ms

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)))
39.0ms
(* (/ (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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
119.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
190.0ms
(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
341.0ms
(* (/ (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))))
445.0ms
(/ (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 (1.1s)

IterNodesCost
02998963
17818490
224887595
done50007520

prune981.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

6.8b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
14.2b
(* (/ (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))) (/ (- (pow x 3) (pow 2.0 3)) (* (fma x x (* 2.0 (+ x 2.0))) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))))
19.4b
(/ (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)))
22.0b
(/ (- (pow x 3) (pow 2.0 3)) (* (fma x x (* 2.0 (+ x 2.0))) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
118×add-sqr-sqrt
88×times-frac
67×*-un-lft-identity
48×difference-of-squares
37×add-cube-cbrt
36×unpow-prod-down cube-prod
32×add-exp-log add-cbrt-cube
29×associate-*r*
28×associate-/l*
25×sqrt-prod
24×sqr-pow
22×associate-*l*
15×distribute-lft-out--
10×cbrt-undiv div-exp
9×prod-exp cbrt-unprod
7×pow1 associate-/r*
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×difference-cubes unswap-sqr
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 → 206
Calls
4 calls:
1.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
87.0ms
(* (/ (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))) (/ (- (pow x 3) (pow 2.0 3)) (* (fma x x (* 2.0 (+ 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)))
67.0ms
(/ (- (pow x 3) (pow 2.0 3)) (* (fma x x (* 2.0 (+ x 2.0))) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))

series1.3s

Counts
4 → 12
Calls
4 calls:
128.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
444.0ms
(* (/ (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))) (/ (- (pow x 3) (pow 2.0 3)) (* (fma x x (* 2.0 (+ x 2.0))) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))))
451.0ms
(/ (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)))
240.0ms
(/ (- (pow x 3) (pow 2.0 3)) (* (fma x x (* 2.0 (+ x 2.0))) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))

simplify1.7s

Counts
218 → 218
Iterations

Useful iterations: done (1.7s)

IterNodesCost
034910242
19089845
234708436
done50018361

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
1.6b
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
22.4b
(* (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)))

rewrite30.0ms

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 43.3400022514) x 263.505074721) x 313.399215894)
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
9.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
17.0ms
(* (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)))

series527.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
31.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
108.0ms
(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
340.0ms
(* (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)))

simplify899.0ms

Counts
112 → 112
Iterations

Useful iterations: done (894.0ms)

IterNodesCost
01962949
14472888
214492598
done50002591

prune491.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes242.0ms

Accuracy

97% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 24.7b

bsearch252.0ms

Steps
ItersRangePoint
6
1.5053965665246024e+46
7.029825254683234e+46
6.950586002949617e+46
10
-6.255829348918637e+62
-1.0452457700408589e+52
-5.0183641578968565e+54

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04386
15177
done5177

end0.0ms

sample661.0ms

Algorithm
intervals
Results
477.0ms8007×body80valid