Details

sample133.0ms

Algorithm

intervals

Results

60.0ms	69×	body	1280	valid
26.0ms	43×	body	640	valid
21.0ms	30×	body	2560	valid
8.0ms	87×	body	80	valid
7.0ms	19×	body	320	valid
2.0ms	8×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	13
2	13
1	12
0	7

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.9b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1 x)
0.1b	(+ x (hypot 1 x))
2.0b	(log (+ x (hypot 1 x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
4×	`pow1` `log-prod` `add-exp-log`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `hypot-udef` `sum-log` `rem-log-exp` `log-pow`

Counts

3 → 47

Calls

3 calls:

0.0ms	(hypot 1 x)
4.0ms	(+ x (hypot 1 x))
3.0ms	(log (+ x (hypot 1 x)))

series305.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(hypot 1 x)
75.0ms	(+ x (hypot 1 x))
167.0ms	(log (+ x (hypot 1 x)))

simplify2.1s

Counts

56 → 56

Iterations

Iter	Nodes
4	4224
3	1536
2	601
1	244
0	108

prune464.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 3/40 (pow x 5) x)
0.1b	(* (* x x) x)
23.6b	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

0.0ms	(fma 3/40 (pow x 5) x)
14.0ms	(* (* x x) x)
0.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

series295.0ms

Counts

3 → 9

Calls

3 calls:

174.0ms	(fma 3/40 (pow x 5) x)
47.0ms	(* (* x x) x)
74.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

simplify2.3s

Counts

62 → 62

Iterations

Iter	Nodes
4	5515
3	1254
2	346
1	130
0	69

prune560.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

13.8b	(cbrt (fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x)))
23.6b	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))
23.6b	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))
23.6b	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

rewrite3.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 47

Calls

4 calls:

1.0ms	(cbrt (fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x)))
0.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))
0.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))
1.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

series467.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(cbrt (fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x)))
77.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))
74.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))
84.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

simplify4.8s

Counts

59 → 59

Iterations

Iter	Nodes
4	7928
3	1643
2	473
1	184
0	88

prune700.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

16.3b	(cbrt (pow x 7))
20.5b	(fma (cbrt (pow x 13)) 71/3240 (fma (cbrt (pow x 7)) -1/18 (cbrt x)))
23.6b	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))
23.6b	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

7×	`cbrt-prod`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `fma-udef`
1×	`pow1/3` `sqr-pow`

Counts

4 → 51

Calls

4 calls:

1.0ms	(cbrt (pow x 7))
0.0ms	(fma (cbrt (pow x 13)) 71/3240 (fma (cbrt (pow x 7)) -1/18 (cbrt x)))
0.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))
0.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

series1.5s

Counts

4 → 12

Calls

4 calls:

324.0ms	(cbrt (pow x 7))
1.1s	(fma (cbrt (pow x 13)) 71/3240 (fma (cbrt (pow x 7)) -1/18 (cbrt x)))
60.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))
76.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

simplify3.0s

Counts

63 → 63

Iterations

Iter	Nodes
4	7336
3	1900
2	573
1	218
0	111

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes124.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.3b

bsearch95.0ms

Steps

Iters	Range		Point
5	0.007518985586860445	0.025588075918097277	0.008689025353366112
8	-15521.296822102611	-0.2777104116290821	-1.0529948069434159

simplify10.0ms

Iterations

Iter	Nodes
2	35
1	35
0	30

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.4s	2374×	body	1280	valid
909.0ms	1539×	body	640	valid
546.0ms	790×	body	2560	valid
251.0ms	790×	body	320	valid
233.0ms	2131×	body	80	valid
139.0ms	376×	body	160	valid