Details

sample219.0ms

Algorithm

intervals

Results

24.0ms	196×	body	80	valid
11.0ms	20×	body	2560	valid
9.0ms	11×	body	5120	valid
6.0ms	10×	body	640	valid
4.0ms	9×	body	1280	valid
2.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify140.0ms

Counts: 1 → 1

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.6b	(- (hypot re im) re)
0.2b	(sqrt (* (- (hypot re im) re) 2.0))
0.0b	(hypot re im)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow1`
5×	`add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3--` `sqrt-div` `associate-*l/` `flip--`
1×	`hypot-udef` `sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 56

Calls

3 calls:

Slowest

28.0ms	(sqrt (* (- (hypot re im) re) 2.0))
13.0ms	(- (hypot re im) re)
0.0ms	(hypot re im)

series690.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

463.0ms	(sqrt (* (- (hypot re im) re) 2.0))
147.0ms	(- (hypot re im) re)
79.0ms	(hypot re im)

simplify2.0s

Counts: 65 → 65

prune678.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.5b

localize23.0ms

Local error

Found 3 expressions with local error:

0.6b	(- (hypot re im) re)
0.4b	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
0.0b	(hypot re im)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`sqrt-prod`
9×	`prod-diff`
8×	`associate-l`
7×	`pow1`
6×	`associate-r`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`unswap-sqr`
3×	`expm1-log1p-u` `fma-neg` `pow-prod-down` `insert-posit16` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `associate-*l/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`hypot-udef` `sub-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 77

Calls

3 calls:

Slowest

33.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
10.0ms	(- (hypot re im) re)
0.0ms	(hypot re im)

series427.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

269.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
86.0ms	(- (hypot re im) re)
73.0ms	(hypot re im)

simplify2.5s

Counts: 86 → 86

prune951.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (hypot re im) re)
0.3b	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.2b	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
0.0b	(hypot re im)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
32×	`sqrt-prod`
23×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`associate-r`
16×	`pow1`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow-prod-down`
9×	`associate-l` `prod-diff`
6×	`associate-*l/` `add-log-exp` `unswap-sqr`
5×	`sqrt-pow1` `pow1/2`
4×	`expm1-log1p-u` `sqrt-div` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `sqrt-unprod` `flip--`
2×	`*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`hypot-udef` `sub-neg` `diff-log`

Counts

4 → 114

Calls

4 calls:

Slowest

60.0ms	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
21.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
17.0ms	(- (hypot re im) re)
0.0ms	(hypot re im)

series739.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

308.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
260.0ms	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
87.0ms	(- (hypot re im) re)
84.0ms	(hypot re im)

simplify1.6s

Counts: 126 → 126

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.5b

localize56.0ms

Local error

Found 4 expressions with local error:

9.8b	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3` `prod-diff`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 61

Calls

4 calls:

Slowest

47.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)
2.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))

series557.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

170.0ms	(cbrt (hypot re im))
153.0ms	(cbrt (hypot re im))
139.0ms	(cbrt (hypot re im))
95.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify1.1s

Counts: 73 → 73

prune954.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.5b

regimes166.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch2.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

960.0ms	693×	body	2560	valid
844.0ms	6049×	body	80	valid
289.0ms	477×	body	1280	valid
242.0ms	282×	body	5120	valid
138.0ms	264×	body	640	valid
70.0ms	149×	body	320	valid
16.0ms	86×	body	160	valid