Details

sample107.0ms

Algorithm

intervals

Results

44.0ms	65×	body	1280	valid
19.0ms	33×	body	2560	valid
19.0ms	46×	body	640	valid
7.0ms	30×	body	320	valid
4.0ms	68×	body	80	valid
2.0ms	14×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	11
2	11
1	10
0	7

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.4b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1 x)
0.9b	(+ x (hypot 1 x))
3.5b	(log (+ x (hypot 1 x)))

rewrite7.0ms

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` `log1p-expm1-u`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `hypot-udef` `sum-log` `rem-log-exp` `log-pow`

Counts

3 → 44

Calls

3 calls:

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

series390.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(hypot 1 x)
94.0ms	(+ x (hypot 1 x))
218.0ms	(log (+ x (hypot 1 x)))

simplify2.2s

Counts

53 → 53

Iterations

Iter	Nodes
4	4170
3	1483
2	591
1	240
0	105

prune375.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 5) 3/40 x)
0.1b	(* (* x x) x)
21.4b	(fma -1/6 (* (* x x) x) (fma (pow x 5) 3/40 x))

rewrite19.0ms

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` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

0.0ms	(fma (pow x 5) 3/40 x)
13.0ms	(* (* x x) x)
4.0ms	(fma -1/6 (* (* x x) x) (fma (pow x 5) 3/40 x))

series275.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(fma (pow x 5) 3/40 x)
41.0ms	(* (* x x) x)
61.0ms	(fma -1/6 (* (* x x) x) (fma (pow x 5) 3/40 x))

simplify2.8s

Counts

59 → 59

Iterations

Iter	Nodes
4	5499
3	1183
2	359
1	128
0	67

prune504.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ x (hypot 1 x))
3.5b	(log (+ x (hypot 1 x)))
3.5b	(log (+ x (hypot 1 x)))
3.5b	(log (+ x (hypot 1 x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`log-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`pow1` `add-exp-log`
6×	`log-div` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
3×	`fma-def` `rem-log-exp` `log-pow`
1×	`+-commutative` `sum-log`

Counts

4 → 68

Calls

4 calls:

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

series663.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ x (hypot 1 x))
196.0ms	(log (+ x (hypot 1 x)))
202.0ms	(log (+ x (hypot 1 x)))
174.0ms	(log (+ x (hypot 1 x)))

simplify2.0s

Counts

80 → 80

Iterations

Iter	Nodes
4	3879
3	1362
2	533
1	212
0	91

prune661.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1 x)
0.3b	(* (sqrt (hypot 1 x)) (sqrt (hypot 1 x)))
3.5b	(log (+ x (* (sqrt (hypot 1 x)) (sqrt (hypot 1 x)))))
7.5b	(+ x (* (sqrt (hypot 1 x)) (sqrt (hypot 1 x))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`pow1`
18×	`sqrt-prod`
14×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
7×	`add-exp-log`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod` `fma-def` `pow-prod-down` `pow-sqr`
2×	`log-div` `flip3-+` `flip-+`
1×	`pow2` `+-commutative` `hypot-udef` `sum-log` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

0.0ms	(hypot 1 x)
13.0ms	(* (sqrt (hypot 1 x)) (sqrt (hypot 1 x)))
2.0ms	(log (+ x (* (sqrt (hypot 1 x)) (sqrt (hypot 1 x)))))
4.0ms	(+ x (* (sqrt (hypot 1 x)) (sqrt (hypot 1 x))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(hypot 1 x)
85.0ms	(* (sqrt (hypot 1 x)) (sqrt (hypot 1 x)))
181.0ms	(log (+ x (* (sqrt (hypot 1 x)) (sqrt (hypot 1 x)))))
111.0ms	(+ x (* (sqrt (hypot 1 x)) (sqrt (hypot 1 x))))

simplify721.0ms

Counts

105 → 105

Iterations

Iter	Nodes
3	2016
2	834
1	332
0	147

prune1.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes56.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.0b

bsearch129.0ms

Steps

Iters	Range		Point
9	7.101228369635622e-07	0.9676876931049737	0.007683264102509549
10	-102.89153151738607	-2.897210331759478e-16	-1.0884602506497811

simplify22.0ms

Iterations

Iter	Nodes
2	35
1	35
0	31

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.9s	2242×	body	1280	valid
962.0ms	841×	body	2560	valid
895.0ms	1577×	body	640	valid
274.0ms	778×	body	320	valid
172.0ms	2188×	body	80	valid
97.0ms	374×	body	160	valid