Details

sample31.0ms

Algorithm

intervals

Results

9.0ms	190×	body	80	valid
5.0ms	27×	body	2560	valid
3.0ms	13×	body	5120	valid
2.0ms	12×	body	1280	valid
1.0ms	7×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	12	15
1	19	10
2	28	10
3	36	10
4	42	10
5	44	10
done	44	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite9.0ms

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×	`add-exp-log` `expm1-log1p-u` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `sqrt-pow1` `sqrt-div` `associate-*l/` `flip--`
1×	`sub-neg` `hypot-udef` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 53

Calls

3 calls:

4.0ms	(sqrt (* (- (hypot re im) re) 2.0))
0.0ms	(hypot re im)
4.0ms	(- (hypot re im) re)

series294.0ms

Counts

3 → 9

Calls

3 calls:

183.0ms	(sqrt (* (- (hypot re im) re) 2.0))
48.0ms	(hypot re im)
63.0ms	(- (hypot re im) re)

simplify2.8s

Counts

62 → 62

Iterations

Useful iterations: 3 (384.0ms)

Iter	Nodes	Cost
0	115	686
1	238	572
2	760	489
3	4109	434
done	5000	434

prune153.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(hypot re im)
0.0b	(hypot re im)
16.1b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`hypot-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 45

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
0.0ms	(hypot re im)
0.0ms	(hypot re im)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series326.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(sqrt (hypot re im))
50.0ms	(hypot re im)
45.0ms	(hypot re im)
144.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify844.0ms

Counts

57 → 57

Iterations

Useful iterations: done (842.0ms)

Iter	Nodes	Cost
0	69	452
1	131	360
2	373	314
3	1625	310
done	5001	307

prune198.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 13.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.1b	(sqrt (sqrt (hypot re im)))
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
16.1b	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

86×	`sqrt-prod`
54×	`add-sqr-sqrt`
40×	`sqrt-pow1`
31×	`pow1`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 129

Calls

4 calls:

1.0ms	(sqrt (sqrt (hypot re im)))
1.0ms	(sqrt (sqrt (hypot re im)))
12.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

series460.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(sqrt (sqrt (hypot re im)))
114.0ms	(sqrt (sqrt (hypot re im)))
87.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
147.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

simplify847.0ms

Counts

141 → 141

Iterations

Useful iterations: done (843.0ms)

Iter	Nodes	Cost
0	132	1875
1	255	1043
2	957	942
done	5001	938

prune307.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 13.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (pow (sqrt (sqrt (hypot re im))) 3)) (sqrt (sqrt (hypot re im))))
0.6b	(cbrt (pow (sqrt (sqrt (hypot re im))) 3))
0.7b	(pow (sqrt (sqrt (hypot re im))) 3)
16.1b	(fma (sqrt (hypot re im)) (* (cbrt (pow (sqrt (sqrt (hypot re im))) 3)) (sqrt (sqrt (hypot re im)))) (- re))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

108×	`sqrt-prod`
80×	`add-sqr-sqrt`
72×	`cbrt-prod`
36×	`unpow-prod-down` `cube-prod`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`associate-l` `unswap-sqr`
9×	`pow1` `associate-r`
7×	`add-exp-log`
6×	`add-cbrt-cube` `sqr-pow`
5×	`pow-pow`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow3`
2×	`pow1/2`
1×	`pow-to-exp` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `sqrt-pow2` `rem-cbrt-cube` `cbrt-unprod` `fma-udef` `rem-cube-cbrt`

Counts

4 → 163

Calls

4 calls:

25.0ms	(* (cbrt (pow (sqrt (sqrt (hypot re im))) 3)) (sqrt (sqrt (hypot re im))))
3.0ms	(cbrt (pow (sqrt (sqrt (hypot re im))) 3))
3.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
0.0ms	(fma (sqrt (hypot re im)) (* (cbrt (pow (sqrt (sqrt (hypot re im))) 3)) (sqrt (sqrt (hypot re im)))) (- re))

series487.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (cbrt (pow (sqrt (sqrt (hypot re im))) 3)) (sqrt (sqrt (hypot re im))))
112.0ms	(cbrt (pow (sqrt (sqrt (hypot re im))) 3))
137.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
146.0ms	(fma (sqrt (hypot re im)) (* (cbrt (pow (sqrt (sqrt (hypot re im))) 3)) (sqrt (sqrt (hypot re im)))) (- re))

simplify1.0s

Counts

175 → 175

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	187	3115
1	423	2132
2	1602	1600
done	5000	1597

prune372.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 13.1b

regimes66.0ms

Accuracy

0% (0.2b remaining)

Error of 13.2b against oracle of 13.0b and baseline of 13.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	11	10
done	11	10

end0.0ms

sample673.0ms

Algorithm

intervals

Results

199.0ms	6013×	body	80	valid
135.0ms	687×	body	2560	valid
76.0ms	495×	body	1280	valid
76.0ms	300×	body	5120	valid
33.0ms	256×	body	640	valid
14.0ms	157×	body	320	valid
6.0ms	92×	body	160	valid