Details

sample78.0ms

Algorithm

intervals

Results

22.0ms	193×	body	80	valid
20.0ms	27×	body	2560	valid
10.0ms	17×	body	1280	valid
8.0ms	8×	body	5120	valid
4.0ms	8×	body	640	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

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

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.1b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.2b	(+ (hypot re im) re)
0.2b	(sqrt (* (+ (hypot re im) re) 2.0))

rewrite23.0ms

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:

0.0ms	(hypot re im)
9.0ms	(+ (hypot re im) re)
13.0ms	(sqrt (* (+ (hypot re im) re) 2.0))

series444.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(hypot re im)
84.0ms	(+ (hypot re im) re)
292.0ms	(sqrt (* (+ (hypot re im) re) 2.0))

simplify2.5s

Counts

54 → 54

Iterations

Iter	Nodes
4	4000
3	1315
2	475
1	189
0	89

prune655.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.7b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.2b	(+ (hypot re im) re)
0.4b	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

0.0ms	(hypot re im)
5.0ms	(+ (hypot re im) re)
29.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

series426.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(hypot re im)
86.0ms	(+ (hypot re im) re)
275.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

simplify3.2s

Counts

74 → 74

Iterations

Iter	Nodes
4	4461
3	1585
2	607
1	249
0	113

prune849.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 12.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
7.0b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

0.0ms	(hypot re im)
22.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
18.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
17.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series509.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(hypot re im)
295.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
64.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
84.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify5.0s

Counts

106 → 106

Iterations

Iter	Nodes
4	5895
3	1897
2	735
1	286
0	133

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
0.5b	(* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))))
9.0b	(+ (* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))) re)

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
13.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
100.0ms	(* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))))
79.0ms	(+ (* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))) re)

series461.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt (hypot re im))
149.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
77.0ms	(* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))))
63.0ms	(+ (* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))) re)

simplify994.0ms

Counts

120 → 120

Iterations

Iter	Nodes
3	2153
2	871
1	334
0	151

prune1.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.7b

regimes234.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	12
1	12
0	9

end0.0ms

sample2.9s

Algorithm

intervals

Results

844.0ms	6072×	body	80	valid
715.0ms	281×	body	5120	valid
559.0ms	658×	body	2560	valid
351.0ms	493×	body	1280	valid
149.0ms	283×	body	640	valid
54.0ms	83×	body	160	valid
43.0ms	130×	body	320	valid