Details

Time bar (total: 21.1s)

sample33.0ms

Algorithm
intervals
Results
15.0ms256×body80valid

simplify910.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
02937
16230
215330
338330
4125130
done500030

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (- x 2.0))
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)
28.7b
(/ (* (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))

rewrite25.0ms

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:
11.0ms
(* (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (- x 2.0))
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)
10.0ms
(/ (* (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))

series540.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(* (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (- x 2.0))
62.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
28.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
301.0ms
(/ (* (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
02202957
14782758
216322378
done50002360

prune446.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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)
2.5b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
27.7b
(/ (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) (- x 2.0)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
104×add-sqr-sqrt *-un-lft-identity
72×add-cube-cbrt
26×associate-/r*
16×distribute-lft-out-- difference-of-squares
11×add-exp-log associate-/r/ add-cbrt-cube
6×div-inv associate-/l*
5×flip3-- flip--
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef
Counts
4 → 163
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)
5.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
13.0ms
(/ (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) (- x 2.0)))

series509.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
35.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
101.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
312.0ms
(/ (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) (- x 2.0)))

simplify906.0ms

Counts
175 → 175
Iterations

Useful iterations: 2 (253.0ms)

IterNodesCost
02976972
16366816
222056516
done50016516

prune872.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
0.0b
(* (- 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)))
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
27.5b
(/ (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))

rewrite19.0ms

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 (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
14.0ms
(* (- 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)
2.0ms
(/ (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))

series684.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
323.0ms
(* (- 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)))
31.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
270.0ms
(/ (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
01863078
14063031
213772701
done50002698

prune507.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
3.3b
(/ (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) (- (pow x 3) (pow 2.0 3))))
24.1b
(/ (/ (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) (- (pow x 3) (pow 2.0 3)))) (+ (* x x) (+ (* 2.0 2.0) (* x 2.0))))
26.7b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- (pow x 3) (pow 2.0 3)))

rewrite380.0ms

Algorithm
rewrite-expression-head
Rules
3234×times-frac
2405×add-sqr-sqrt
1677×*-un-lft-identity
1157×add-cube-cbrt
832×difference-of-squares
624×unpow-prod-down cube-prod
416×sqr-pow
260×distribute-lft-out--
254×associate-/l*
109×associate-/r*
52×difference-cubes
41×associate-/r/
23×div-inv
20×add-exp-log add-cbrt-cube
17×flip3-- flip--
10×cbrt-undiv div-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×flip3-+ flip-+ fma-udef associate-/l/
Counts
4 → 1489
Calls
4 calls:
0.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
42.0ms
(/ (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) (- (pow x 3) (pow 2.0 3))))
125.0ms
(/ (/ (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) (- (pow x 3) (pow 2.0 3)))) (+ (* x x) (+ (* 2.0 2.0) (* x 2.0))))
29.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- (pow x 3) (pow 2.0 3)))

series869.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
322.0ms
(/ (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) (- (pow x 3) (pow 2.0 3))))
409.0ms
(/ (/ (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) (- (pow x 3) (pow 2.0 3)))) (+ (* x x) (+ (* 2.0 2.0) (* x 2.0))))
107.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (- (pow x 3) (pow 2.0 3)))

simplify3.5s

Counts
1501 → 1501
Iterations

Useful iterations: 1 (2.6s)

IterNodesCost
01611115134
13924105772
done5000105772

prune7.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes253.0ms

Accuracy

96.8% (0.8b remaining)

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

bsearch304.0ms

Steps
ItersRangePoint
10
9.05528890794319e+16
1.7496221259090696e+28
6.147426414162638e+26
7
-5.851033503887588e+26
-3.958357823763034e+24
-5.763344886008818e+26

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04985
15876
done5876

end0.0ms

sample662.0ms

Algorithm
intervals
Results
490.0ms8008×body80valid