Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	196×	body	80	valid
4.0ms	18×	body	2560	valid
3.0ms	11×	body	5120	valid
2.0ms	10×	body	1280	valid
1.0ms	9×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	12	15
1	19	10
2	28	10
3	35	10
4	41	10
5	43	10
done	43	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.0b	(hypot re im)
1.1b	(- (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)
3.0ms	(- (hypot re im) re)

series430.0ms

Counts

3 → 9

Calls

3 calls:

186.0ms	(sqrt (* (- (hypot re im) re) 2.0))
182.0ms	(hypot re im)
61.0ms	(- (hypot re im) re)

simplify2.0s

Counts

62 → 62

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	115	686
1	228	572
2	672	489
3	3524	434
done	5000	433

prune149.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.5b	(cbrt (hypot re im))
0.7b	(pow (cbrt (hypot re im)) 3)
10.1b	(- (pow (cbrt (hypot re im)) 3) re)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
54×	`prod-diff`
50×	`*-un-lft-identity`
48×	`add-cube-cbrt`
35×	`cbrt-prod`
32×	`unpow-prod-down` `cube-prod`
18×	`fma-neg`
6×	`add-log-exp` `difference-of-squares` `sqr-pow`
5×	`pow1` `add-exp-log` `cube-mult` `unpow3`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-unpow`
2×	`pow-pow` `pow1/3`
1×	`pow-to-exp` `sub-neg` `hypot-udef` `flip3--` `diff-log` `pow-exp` `flip--` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 148

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(cbrt (hypot re im))
2.0ms	(pow (cbrt (hypot re im)) 3)
22.0ms	(- (pow (cbrt (hypot re im)) 3) re)

series301.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot re im)
108.0ms	(cbrt (hypot re im))
88.0ms	(pow (cbrt (hypot re im)) 3)
61.0ms	(- (pow (cbrt (hypot re im)) 3) re)

simplify619.0ms

Counts

160 → 160

Iterations

Useful iterations: 2 (146.0ms)

Iter	Nodes	Cost
0	158	2671
1	301	1455
2	1009	1032
done	5001	1032

prune304.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 12.0b

localize13.0ms

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))
14.6b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
4×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `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)
2.0ms	(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))

series476.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot re im)
50.0ms	(hypot re im)
240.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
140.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify1.3s

Counts

55 → 55

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	76	577
1	151	419
2	430	358
3	1492	345
done	5000	343

prune205.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 12.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
14.6b	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (- re))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 78

Calls

4 calls:

0.0ms	(cbrt (hypot re im))
0.0ms	(cbrt (hypot re im))
6.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (- re))

series496.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(cbrt (hypot re im))
117.0ms	(cbrt (hypot re im))
123.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
145.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (- re))

simplify1.4s

Counts

90 → 90

Iterations

Useful iterations: 3 (427.0ms)

Iter	Nodes	Cost
0	99	1105
1	188	1029
2	601	845
3	2790	752
done	5001	752

prune326.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.0b

regimes122.0ms

Accuracy

0% (0.2b remaining)

Error of 13.3b against oracle of 13.1b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample688.0ms

Algorithm

intervals

Results

203.0ms	6006×	body	80	valid
143.0ms	691×	body	2560	valid
79.0ms	480×	body	1280	valid
75.0ms	314×	body	5120	valid
35.0ms	285×	body	640	valid
15.0ms	135×	body	320	valid
6.0ms	89×	body	160	valid