Details

sample93.0ms

Algorithm

intervals

Results

29.0ms	207×	body	80	valid
21.0ms	15×	body	1280	valid
16.0ms	19×	body	2560	valid
8.0ms	8×	body	5120	valid
2.0ms	4×	body	320	valid
2.0ms	3×	body	640	valid

simplify27.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	31
3	31
2	29
1	24
0	12

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.7b

localize28.0ms

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)

rewrite33.0ms

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` `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 → 42

Calls

3 calls:

0.0ms	(hypot re im)
24.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
8.0ms	(+ (hypot re im) re)

series451.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(hypot re im)
284.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
85.0ms	(+ (hypot re im) re)

simplify2.2s

Counts

51 → 51

Iterations

Iter	Nodes
4	3962
3	1315
2	472
1	186
0	86

prune426.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (hypot re im) re))
0.0b	(hypot re im)
0.3b	(+ (hypot re im) re)
0.4b	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`sqrt-prod`
10×	`add-cube-cbrt`
9×	`pow1`
7×	`associate-l`
6×	`add-cbrt-cube` `associate-r` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out`
2×	`associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `hypot-udef` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

4 → 81

Calls

4 calls:

4.0ms	(sqrt (+ (hypot re im) re))
0.0ms	(hypot re im)
4.0ms	(+ (hypot re im) re)
18.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

series613.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(sqrt (+ (hypot re im) re))
63.0ms	(hypot re im)
98.0ms	(+ (hypot re im) re)
276.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

simplify949.0ms

Counts

93 → 93

Iterations

Iter	Nodes
3	2071
2	784
1	306
0	135

prune916.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (hypot re im) re)) (cbrt (+ (hypot re im) re)))
0.5b	(cbrt (+ (hypot re im) re))
0.5b	(cbrt (+ (hypot re im) re))
0.5b	(cbrt (+ (hypot re im) re))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

28.0ms	(* (cbrt (+ (hypot re im) re)) (cbrt (+ (hypot re im) re)))
2.0ms	(cbrt (+ (hypot re im) re))
2.0ms	(cbrt (+ (hypot re im) re))
2.0ms	(cbrt (+ (hypot re im) re))

series863.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(* (cbrt (+ (hypot re im) re)) (cbrt (+ (hypot re im) re)))
221.0ms	(cbrt (+ (hypot re im) re))
238.0ms	(cbrt (+ (hypot re im) re))
173.0ms	(cbrt (+ (hypot re im) re))

simplify2.4s

Counts

115 → 115

Iterations

Iter	Nodes
4	4561
3	1814
2	750
1	315
0	140

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
12.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef` `sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

4 → 43

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
7.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series706.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(hypot re im)
75.0ms	(hypot re im)
342.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
228.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.2s

Counts

55 → 55

Iterations

Iter	Nodes
4	2926
3	1012
2	361
1	147
0	74

prune574.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.5b

regimes199.0ms

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 13.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	12
1	12
0	9

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.3s	5984×	body	80	valid
620.0ms	678×	body	2560	valid
405.0ms	519×	body	1280	valid
351.0ms	305×	body	5120	valid
223.0ms	276×	body	640	valid
60.0ms	163×	body	320	valid
18.0ms	75×	body	160	valid