Details

sample84.0ms

Algorithm

intervals

Results

26.0ms	194×	body	80	valid
22.0ms	27×	body	2560	valid
10.0ms	16×	body	1280	valid
4.0ms	7×	body	640	valid
3.0ms	3×	body	5120	valid
2.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify70.0ms

Counts: 1 → 1

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.7b	(+ (hypot re im) re)
0.0b	(hypot re im)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))

rewrite11.0ms

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:

Slowest

6.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
4.0ms	(+ (hypot re im) re)
0.0ms	(hypot re im)

series404.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

254.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
89.0ms	(+ (hypot re im) re)
61.0ms	(hypot re im)

simplify1.7s

Counts: 54 → 54

prune609.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.6b

localize26.0ms

Local error

Found 4 expressions with local error:

8.5b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0b	(hypot re im)
0.0b	(hypot re im)

rewrite27.0ms

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:

Slowest

14.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
10.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.0ms	(hypot re im)
0.0ms	(hypot re im)

series292.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

85.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
74.0ms	(hypot re im)
71.0ms	(hypot re im)
63.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify1.4s

Counts: 101 → 101

prune1.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 13.6b

localize25.0ms

Local error

Found 4 expressions with local error:

9.4b	(+ (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) re)
0.3b	(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
0.3b	(* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
0.1b	(sqrt (sqrt (hypot re im)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

50×	`sqrt-pow1`
47×	`pow1`
43×	`sqrt-prod`
34×	`add-sqr-sqrt`
32×	`pow-prod-up`
28×	`pow1/2`
18×	`associate-r`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow-prod-down`
7×	`associate-l`
6×	`pow3` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`sqrt-unprod`
2×	`rem-sqrt-square` `pow-plus` `*-commutative`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 129

Calls

4 calls:

Slowest

46.0ms	(+ (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) re)
27.0ms	(* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
22.0ms	(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
2.0ms	(sqrt (sqrt (hypot re im)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

174.0ms	(sqrt (sqrt (hypot re im)))
166.0ms	(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
81.0ms	(+ (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) re)
77.0ms	(* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))

simplify926.0ms

Counts: 141 → 141

prune1.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.6b

localize49.0ms

Local error

Found 4 expressions with local error:

8.7b	(+ (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im)))))) re)
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.3b	(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`sqrt-prod`
15×	`pow1`
11×	`*-un-lft-identity` `sqrt-pow1` `add-cube-cbrt`
9×	`associate-r`
7×	`pow1/2`
6×	`cbrt-prod` `add-cbrt-cube` `associate-l` `add-exp-log` `pow-prod-up` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`pow-prod-down`
2×	`pow1/3` `pow3`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 89

Calls

4 calls:

Slowest

54.0ms	(+ (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im)))))) re)
25.0ms	(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))

series677.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

192.0ms	(+ (* (* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im)))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im)))))) re)
183.0ms	(* (sqrt (hypot re im)) (sqrt (sqrt (hypot re im))))
160.0ms	(cbrt (hypot re im))
142.0ms	(cbrt (hypot re im))

simplify2.0s

Counts: 101 → 101

prune1.8s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 13.5b

regimes325.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.9b and baseline of 13.1b

bsearch3.0ms

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	6040×	body	80	valid
566.0ms	659×	body	2560	valid
354.0ms	303×	body	5120	valid
327.0ms	499×	body	1280	valid
185.0ms	294×	body	640	valid
49.0ms	139×	body	320	valid
15.0ms	66×	body	160	valid