Details

sample63.0ms

Algorithm

intervals

Results

21.0ms	198×	body	80	valid
9.0ms	18×	body	2560	valid
5.0ms	9×	body	5120	valid
4.0ms	12×	body	1280	valid
4.0ms	14×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify59.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	31
3	31
2	29
1	24
0	12

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize67.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.3b	(+ (hypot re im) re)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 45

Calls

3 calls:

1.0ms	(hypot re im)
16.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
25.0ms	(+ (hypot re im) re)

series571.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(hypot re im)
351.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
120.0ms	(+ (hypot re im) re)

simplify3.8s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	1405
2	487
1	190
0	89

prune832.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.0b

localize178.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(+ (hypot re im) re)
0.3b	(+ (hypot re im) re)
0.4b	(* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
26×	`add-sqr-sqrt` `sqrt-prod`
19×	`pow1`
14×	`add-cube-cbrt`
12×	`sqrt-div`
11×	`swap-sqr`
8×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`fma-def` `add-cbrt-cube` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`+-commutative` `sum-log` `associate-l/` `associate-r/`
1×	`pow2` `hypot-udef` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 112

Calls

4 calls:

2.0ms	(hypot re im)
26.0ms	(+ (hypot re im) re)
27.0ms	(+ (hypot re im) re)
107.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(hypot re im)
97.0ms	(+ (hypot re im) re)
95.0ms	(+ (hypot re im) re)
101.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re)))

simplify3.8s

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
3	1239
2	417
1	207
0	106

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.0b

localize253.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (hypot re im) re)
0.3b	(+ (hypot re im) re)
0.5b	(cbrt (+ (hypot re im) re))
0.5b	(cbrt (+ (hypot re im) re))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

12.0ms	(+ (hypot re im) re)
12.0ms	(+ (hypot re im) re)
8.0ms	(cbrt (+ (hypot re im) re))
9.0ms	(cbrt (+ (hypot re im) re))

series856.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(+ (hypot re im) re)
92.0ms	(+ (hypot re im) re)
340.0ms	(cbrt (+ (hypot re im) re))
338.0ms	(cbrt (+ (hypot re im) re))

simplify6.6s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
4	4229
3	1286
2	461
1	187
0	84

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.0b

localize109.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
7.9b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `fma-def` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 89

Calls

4 calls:

2.0ms	(hypot re im)
2.0ms	(hypot re im)
54.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
35.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series366.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(hypot re im)
98.0ms	(hypot re im)
104.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
90.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify3.7s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
3	1116
2	408
1	189
0	90

prune924.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.0b

regimes629.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	6065×	body	80	valid
452.0ms	648×	body	2560	valid
297.0ms	471×	body	1280	valid
189.0ms	294×	body	5120	valid
92.0ms	284×	body	640	valid
43.0ms	164×	body	320	valid
13.0ms	74×	body	160	valid