Details

sample25.0ms

Algorithm

intervals

Results

10.0ms

335×

body

valid

simplify4.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (39.0ms)

Iter	Nodes	Cost
0	8	164
1	14	164
2	34	164
3	92	164
4	195	139
5	453	139
6	1169	139
7	2269	139
8	3328	139
done	5000	139

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (- y 1.0) z 1.0)
3.6b	(* x (fma (- y 1.0) z 1.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l` `fma-udef`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

0.0ms	(fma (- y 1.0) z 1.0)
6.0ms	(* x (fma (- y 1.0) z 1.0))

series115.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(fma (- y 1.0) z 1.0)
83.0ms	(* x (fma (- y 1.0) z 1.0))

simplify2.3s

Counts

38 → 38

Iterations

Useful iterations: 3 (500.0ms)

Iter	Nodes	Cost
0	54	7260
1	123	6984
2	323	6774
3	1388	6544
done	5015	6544

prune231.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.7b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* (- y 1.0) z) x) (* 1.0 x))
0.0b	(* (- y 1.0) z)
3.7b	(* (* (- y 1.0) z) x)

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity`
6×	`associate-r` `associate-l` `associate-*l/` `add-cube-cbrt`
5×	`add-log-exp`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`flip3--` `*-commutative` `flip--`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `distribute-rgt-out` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

45.0ms	(+ (* (* (- y 1.0) z) x) (* 1.0 x))
18.0ms	(* (- y 1.0) z)
56.0ms	(* (* (- y 1.0) z) x)

series194.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(+ (* (* (- y 1.0) z) x) (* 1.0 x))
50.0ms	(* (- y 1.0) z)
51.0ms	(* (* (- y 1.0) z) x)

simplify4.1s

Counts

70 → 70

Iterations

Useful iterations: 3 (2.4s)

Iter	Nodes	Cost
0	108	14515
1	290	12680
2	1011	11935
3	4521	11725
done	5000	11725

prune413.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (* z x))
2.2b	(fma (* z x) y (* 1.0 (- x (* z x))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
3×	`fma-neg` `prod-diff`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `fma-udef` `flip--`

Counts

2 → 31

Calls

2 calls:

9.0ms	(- x (* z x))
1.0ms	(fma (* z x) y (* 1.0 (- x (* z x))))

series150.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(- x (* z x))
90.0ms	(fma (* z x) y (* 1.0 (- x (* z x))))

simplify2.8s

Counts

37 → 37

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	62	7375
1	138	6844
2	473	6493
3	1970	6373
done	5008	5945

prune182.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma (* z x) y (* 1.0 (- x (* z x)))))
2.2b	(fma (* z x) y (* 1.0 (- x (* z x))))
2.2b	(fma (* z x) y (* 1.0 (- x (* z x))))
2.2b	(fma (* z x) y (* 1.0 (- x (* z x))))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (fma (* z x) y (* 1.0 (- x (* z x)))))
0.0ms	(fma (* z x) y (* 1.0 (- x (* z x))))
0.0ms	(fma (* z x) y (* 1.0 (- x (* z x))))
0.0ms	(fma (* z x) y (* 1.0 (- x (* z x))))

series491.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(cbrt (fma (* z x) y (* 1.0 (- x (* z x)))))
70.0ms	(fma (* z x) y (* 1.0 (- x (* z x))))
65.0ms	(fma (* z x) y (* 1.0 (- x (* z x))))
67.0ms	(fma (* z x) y (* 1.0 (- x (* z x))))

simplify2.4s

Counts

55 → 55

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	90	16371
1	206	15774
2	521	15214
3	1578	14820
done	5003	14462

prune314.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes287.0ms

Accuracy

95.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.6b

bsearch90.0ms

Steps

Iters	Range		Point
1	5.20815493831672e-22	5.686306980150838e-22	5.566768969692309e-22
9	-1.6605670889217131e-29	-9.492361916070632e-35	-1.6391887730651112e-29

simplify11.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	20	681
1	30	681
done	30	681

end0.0ms

sample1.2s

Algorithm

intervals

Results

461.0ms

10162×

body

valid