Details

sample32.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify309.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	9	19
1	19	18
2	39	18
3	77	18
4	128	18
5	184	18
6	211	18
7	216	18
done	216	18

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* (* y 4.0) y))
3.8b	(- (* x x) (* (* y 4.0) y))
28.6b	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `fma-udef` `div-inv`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma x x (* (* y 4.0) y))
9.0ms	(- (* x x) (* (* y 4.0) y))
44.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

series262.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(fma x x (* (* y 4.0) y))
66.0ms	(- (* x x) (* (* y 4.0) y))
138.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

simplify2.4s

Counts

67 → 67

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	94	1321
1	225	1289
2	782	1165
3	3081	1163
done	5000	1162

prune305.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* (* y 4.0) y))
1.3b	(fma x x (- (* (* y 4.0) y)))
28.6b	(/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma x x (* (* y 4.0) y))
0.0ms	(fma x x (- (* (* y 4.0) y)))
6.0ms	(/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y)))

series284.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(fma x x (* (* y 4.0) y))
92.0ms	(fma x x (- (* (* y 4.0) y)))
129.0ms	(/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y)))

simplify4.2s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	71	1123
1	121	1114
2	289	1005
3	953	1005
4	4561	1004
done	5000	1004

prune282.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))))
1.2b	(log1p (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))))
3.8b	(- (* x x) (* (* y 4.0) y))
28.6b	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log1p-udef` `expm1-log1p` `frac-2neg` `fma-neg` `diff-log` `div-sub` `log1p-expm1` `div-exp` `prod-diff` `clear-num` `div-inv` `expm1-udef`

Counts

4 → 70

Calls

4 calls:

0.0ms	(expm1 (log1p (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))))
1.0ms	(log1p (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))))
17.0ms	(- (* x x) (* (* y 4.0) y))
23.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

series869.0ms

Counts

4 → 12

Calls

4 calls:

372.0ms	(expm1 (log1p (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))))
273.0ms	(log1p (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))))
97.0ms	(- (* x x) (* (* y 4.0) y))
127.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

simplify2.9s

Counts

82 → 82

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	120	1748
1	266	1691
2	866	1505
3	3234	1501
done	5000	1500

prune415.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))))
0.5b	(expm1 (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))))
3.8b	(- (* x x) (* (* y 4.0) y))
28.6b	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`log1p-expm1-u`
4×	`pow1` `expm1-log1p-u`
3×	`associate-/r` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log1p-udef` `expm1-log1p` `frac-2neg` `fma-neg` `diff-log` `div-sub` `log1p-expm1` `div-exp` `prod-diff` `clear-num` `div-inv` `expm1-udef`

Counts

4 → 70

Calls

4 calls:

1.0ms	(log1p (expm1 (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))))
1.0ms	(expm1 (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))))
17.0ms	(- (* x x) (* (* y 4.0) y))
27.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(log1p (expm1 (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))))
139.0ms	(expm1 (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))))
79.0ms	(- (* x x) (* (* y 4.0) y))
110.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

simplify2.5s

Counts

82 → 82

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	113	1728
1	251	1671
2	811	1489
3	3100	1487
done	5001	1486

prune364.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.4b

regimes333.0ms

Accuracy

56.4% (13.4b remaining)

Error of 13.9b against oracle of 0.4b and baseline of 31.2b

bsearch308.0ms

Steps

Iters	Range		Point
9	9556.682540875734	15966983906.555069	98355.24381927797
9	4.924640387312937e-45	2.5480243600333034e-37	8.134021215145638e-38
9	1.5895540584967369e-59	9.417139633880594e-52	1.5753976874379915e-55
7	-4.0684965810982345e-160	-4.482309770999907e-162	-1.636890293131895e-160
10	-2.7913152028957945e+157	-7.954806027061161e+143	-4.75816735826197e+148

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	62
1	39	62
2	46	62
done	46	62

end0.0ms

sample826.0ms

Algorithm

intervals

Results

555.0ms

8000×

body

valid