Details

sample50.0ms

Algorithm

intervals

Results

24.0ms

256×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.1b	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
2.8b	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
23.9b	(* (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)))

rewrite45.0ms

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 (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
14.0ms	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
27.0ms	(* (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)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
44.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
95.0ms	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
300.0ms	(* (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)))

simplify2.2s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1525
1	458
0	196

prune848.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.1b	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
2.8b	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
23.9b	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (log1p (expm1 (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

1.0ms	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
24.0ms	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
9.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (log1p (expm1 (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

series651.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
36.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
102.0ms	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
461.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (log1p (expm1 (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

simplify2.6s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
3	4190
2	1076
1	392
0	183

prune820.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize80.0ms

Local error

Found 4 expressions with local error:

16.3b	(cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
16.3b	(cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
16.3b	(cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
22.0b	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (* (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
15×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cbrt-cube`
10×	`prod-exp` `add-cube-cbrt`
9×	`cbrt-prod`
7×	`associate-r`
6×	`pow1`
5×	`times-frac`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp`
1×	`pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 75

Calls

4 calls:

1.0ms	(cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
1.0ms	(cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
1.0ms	(cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
45.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (* (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
190.0ms	(cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
181.0ms	(cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
815.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (* (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)) (cbrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

simplify3.3s

Counts

87 → 87

Iterations

Iter	Nodes
done	5000
3	4637
2	1128
1	371
0	156

prune953.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize163.0ms

Local error

Found 4 expressions with local error:

2.8b	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
23.9b	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (log1p (expm1 (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
23.9b	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (log1p (expm1 (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
23.9b	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (log1p (expm1 (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
20×	`add-cube-cbrt`
15×	`times-frac`
12×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-r` `associate-l`
5×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `div-inv` `flip--`

Counts

4 → 100

Calls

4 calls:

15.0ms	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
5.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (log1p (expm1 (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
5.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (log1p (expm1 (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
5.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (log1p (expm1 (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
426.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (log1p (expm1 (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
418.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (log1p (expm1 (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
428.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (log1p (expm1 (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))

simplify2.7s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
3	3799
2	943
1	339
0	153

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes647.0ms

Accuracy

95.9% (1.0b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 25.2b

bsearch388.0ms

Steps

Iters	Range		Point
9	6803.12139425764	1528168778729.1204	1498395052788.919
6	-2.3147063625104137e+31	-1.8713307606778553e+30	-1.9101382361175614e+31

simplify20.0ms

Iterations

Iter	Nodes
done	59
1	59
0	40

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.7s

8010×

body

valid