Details

sample85.0ms

Algorithm

intervals

Results

37.0ms

256×

body

valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1857
3	505
2	152
1	62
0	29

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
0.1b	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
3.1b	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
21.7b	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite76.0ms

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-cbrt-cube` `add-exp-log`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-sub` `pow-prod-down` `associate-r/` `-commutative` `flip--`

Counts

4 → 100

Calls

4 calls:

0.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
0.0ms	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
26.0ms	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
43.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
44.0ms	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
142.0ms	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
459.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify2.0s

Counts

112 → 112

Iterations

Iter	Nodes
done	5002
2	1525
1	458
0	196

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

6.8b	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
13.9b	(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
14.1b	(* (* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
18.1b	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
82×	`times-frac`
56×	`associate-r`
55×	`add-cube-cbrt`
50×	`add-exp-log`
47×	`sqrt-prod`
32×	`add-cbrt-cube`
22×	`prod-exp`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`pow1` `div-exp` `cbrt-unprod`
7×	`cbrt-undiv`
6×	`associate-/r*`
5×	`associate-/l*` `unswap-sqr`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `un-div-inv` `div-inv`
2×	`frac-times` `associate-l/` `-commutative` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-sub` `flip--`

Counts

4 → 190

Calls

4 calls:

1.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
27.0ms	(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
56.0ms	(* (* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
17.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

series1.2s

Counts

4 → 12

Calls

4 calls:

130.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
211.0ms	(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
346.0ms	(* (* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
525.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

simplify2.8s

Counts

202 → 202

Iterations

Iter	Nodes
done	5000
2	2765
1	879
0	316

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

6.8b	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
6.8b	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
18.1b	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
18.6b	(/ (* (* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (- x 2.0)) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`add-exp-log`
28×	`times-frac`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube` `sqrt-prod`
22×	`associate-r`
13×	`prod-exp`
10×	`div-exp`
8×	`pow1` `associate-/l/`
7×	`cbrt-unprod`
6×	`cbrt-undiv` `associate-/r` `associate-r/`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `un-div-inv` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `associate-l` `flip--`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-*l/` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `associate-/l`

Counts

4 → 122

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))
31.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
58.0ms	(/ (* (* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (- x 2.0)) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

series1.3s

Counts

4 → 12

Calls

4 calls:

127.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
139.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
620.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
407.0ms	(/ (* (* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (- x 2.0)) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify2.7s

Counts

134 → 134

Iterations

Iter	Nodes
done	5002
2	2049
1	595
0	227

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
0.1b	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
18.4b	(/ (- (* x x) (* 2.0 2.0)) (* (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (+ x 2.0)))
21.7b	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- (* x x) (* 2.0 2.0)) (* (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (+ x 2.0))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
10×	`associate-r`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`times-frac`
6×	`pow1`
5×	`prod-exp` `associate-*r/` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-/r/` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-l` `difference-of-squares`
2×	`flip3-+` `flip-+` `fma-udef` `div-inv` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `flip3--` `div-sub` `pow-prod-down` `-commutative` `flip--` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

0.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
0.0ms	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
23.0ms	(/ (- (* x x) (* 2.0 2.0)) (* (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (+ x 2.0)))
47.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- (* x x) (* 2.0 2.0)) (* (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (+ x 2.0))))

series793.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
64.0ms	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
160.0ms	(/ (- (* x x) (* 2.0 2.0)) (* (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (+ x 2.0)))
537.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- (* x x) (* 2.0 2.0)) (* (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606) (+ x 2.0))))

simplify2.5s

Counts

94 → 94

Iterations

Iter	Nodes
done	5004
2	2136
1	506
0	190

prune809.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes544.0ms

Accuracy

96.5% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 25.6b

bsearch500.0ms

Steps

Iters	Range		Point
10	1.892953091671697e+37	1.2896793512076026e+54	8.393327478259401e+40
8	-1.3439962295093205e+81	-4.4571909682776797e+76	-4.541305018061062e+76

simplify15.0ms

Iterations

Iter	Nodes
done	45
1	45
0	37

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.9s

8007×

body

valid