Details

sample154.0ms

Algorithm

intervals

Results

75.0ms	81×	body	1280	valid
32.0ms	52×	body	640	valid
20.0ms	28×	body	2560	valid
9.0ms	22×	body	320	valid
6.0ms	62×	body	80	valid
2.0ms	11×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	11
2	11
1	10
0	7

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1 x)
0.9b	(+ x (hypot 1 x))
2.8b	(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)))

series321.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(hypot 1 x)
104.0ms	(+ x (hypot 1 x))
154.0ms	(log (+ x (hypot 1 x)))

simplify2.2s

Counts

56 → 56

Iterations

Iter	Nodes
4	4269
3	1489
2	592
1	243
0	108

prune473.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma -1/6 (* (* x x) x) x)
0.1b	(* (* x x) x)
19.7b	(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

rewrite20.0ms

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 -1/6 (* (* x x) x) x)
19.0ms	(* (* x x) x)
0.0ms	(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

series246.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(fma -1/6 (* (* x x) x) x)
55.0ms	(* (* x x) x)
79.0ms	(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

simplify2.9s

Counts

62 → 62

Iterations

Iter	Nodes
4	5740
3	1305
2	365
1	134
0	70

prune592.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (hypot 1 x))
0.3b	(cbrt (hypot 1 x))
2.8b	(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
12.4b	(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt (hypot 1 x))
1.0ms	(cbrt (hypot 1 x))
10.0ms	(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
10.0ms	(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))

series629.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt (hypot 1 x))
177.0ms	(cbrt (hypot 1 x))
177.0ms	(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
104.0ms	(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))

simplify1.2s

Counts

74 → 74

Iterations

Iter	Nodes
3	2305
2	838
1	314
0	134

prune659.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.8b	(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
15.3b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))

series897.0ms

Counts

4 → 12

Calls

4 calls:

344.0ms	(cbrt x)
238.0ms	(cbrt x)
169.0ms	(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
147.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))

simplify2.8s

Counts

66 → 66

Iterations

Iter	Nodes
4	3781
3	1152
2	432
1	186
0	93

prune731.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.0b

bsearch133.0ms

Steps

Iters	Range		Point
11	1.0334628320549359e-08	2.7368728718549235e+26	0.008829676865362644
9	-128555.04713805256	-0.18430940072566707	-1.0816386065582386

simplify6.0ms

Iterations

Iter	Nodes
2	35
1	35
0	33

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.9s	2338×	body	1280	valid
823.0ms	1571×	body	640	valid
515.0ms	2112×	body	80	valid
508.0ms	788×	body	2560	valid
228.0ms	800×	body	320	valid
68.0ms	391×	body	160	valid