Details

sample68.0ms

Algorithm

intervals

Results

42.0ms

256×

body

valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2165
3	512
2	154
1	62
0	29

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)
0.1b	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
1.4b	(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
24.9b	(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

rewrite32.0ms

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-cbrt-cube` `add-exp-log` `associate-/r/`
6×	`div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `fma-udef`

Counts

4 → 163

Calls

4 calls:

0.0ms	(fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)
0.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
9.0ms	(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
15.0ms	(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

series540.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)
28.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
97.0ms	(/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0))
351.0ms	(/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (- x 2.0)))

simplify2.1s

Counts

175 → 175

Iterations

Iter	Nodes
done	5001
2	3541
1	702
0	293

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

5.4b	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
5.4b	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
18.3b	(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
23.2b	(* (/ 1 (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

475×	`times-frac`
406×	`add-sqr-sqrt`
261×	`*-un-lft-identity`
175×	`add-cube-cbrt`
123×	`sqrt-prod`
114×	`add-exp-log`
113×	`associate-r`
71×	`associate-l`
67×	`div-exp`
44×	`unswap-sqr`
42×	`add-cbrt-cube`
30×	`prod-exp`
25×	`distribute-lft-out--` `difference-of-squares`
19×	`cbrt-undiv`
18×	`1-exp`
10×	`associate-/r/`
9×	`rec-exp` `cbrt-unprod` `div-inv`
8×	`pow1`
6×	`associate-/l*`
5×	`associate-/r*`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 368

Calls

4 calls:

2.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
2.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
12.0ms	(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
219.0ms	(* (/ 1 (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))))

series749.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
135.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
167.0ms	(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
341.0ms	(* (/ 1 (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) 1)) (/ (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))))

simplify2.0s

Counts

380 → 380

Iterations

Iter	Nodes
done	5001
1	1945
0	551

prune2.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize78.0ms

Local error

Found 4 expressions with local error:

5.4b	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
18.3b	(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
18.4b	(/ (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))
21.3b	(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

2196×	`times-frac`
1202×	`add-sqr-sqrt`
1201×	`*-un-lft-identity`
911×	`add-cube-cbrt`
711×	`sqrt-prod`
145×	`distribute-lft-out--` `difference-of-squares`
63×	`div-inv`
49×	`associate-/r/`
47×	`associate-/r*`
31×	`associate-/l*`
24×	`flip3--` `flip--`
20×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 985

Calls

4 calls:

2.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
19.0ms	(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
68.0ms	(/ (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))
9.0ms	(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

series1.2s

Counts

4 → 12

Calls

4 calls:

113.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
198.0ms	(/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0))
392.0ms	(/ (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (- x 2.0)))
505.0ms	(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify3.6s

Counts

997 → 997

Iterations

Iter	Nodes
done	5000
1	4054
0	1103

prune7.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize71.0ms

Local error

Found 4 expressions with local error:

5.4b	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
18.3b	(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
18.4b	(/ (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ 1 (/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
21.3b	(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite478.0ms

Algorithm

rewrite-expression-head

Rules

8762×	`times-frac`
4264×	`add-sqr-sqrt`
4263×	`*-un-lft-identity`
3421×	`add-cube-cbrt`
2040×	`sqrt-prod`
421×	`distribute-lft-out--` `difference-of-squares`
203×	`div-inv`
119×	`associate-/r*`
53×	`add-exp-log`
37×	`div-exp`
30×	`associate-/l*`
29×	`add-cbrt-cube`
24×	`associate-/r/`
17×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/l/`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `div-sub` `flip--`

Counts

4 → 2631

Calls

4 calls:

1.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
16.0ms	(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
110.0ms	(/ (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ 1 (/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
5.0ms	(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

series1.2s

Counts

4 → 12

Calls

4 calls:

127.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
207.0ms	(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
333.0ms	(/ (/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (/ 1 (/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
530.0ms	(/ (fma x (fma x (fma x (fma 4.16438922228 x 78.6994924154) 137.519416416) y) z) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify5.9s

Counts

2643 → 2643

Iterations

Iter	Nodes
done	5000
0	2811

prune22.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes476.0ms

Accuracy

98.2% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 25.3b

bsearch464.0ms

Steps

Iters	Range		Point
8	3.2078144529096677e+59	1.0208455540014498e+63	7.788614813457575e+59
10	-1.1249999356056908e+64	-5.854806215004893e+51	-2.3482240082525995e+55

simplify5.0ms

Iterations

Iter	Nodes
done	37
1	37
0	33

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.8s

8002×

body

valid