Details

sample119.0ms

Algorithm

intervals

Results

18.0ms	193×	body	80	valid
15.0ms	24×	body	2560	valid
5.0ms	11×	body	1280	valid
5.0ms	7×	body	5120	valid
3.0ms	9×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	3×	body	160	valid

simplify120.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	12	15
1	19	10
2	28	10
3	36	10
4	43	10
5	45	10
done	45	10

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.0b	(hypot re im)
1.5b	(- (hypot re im) re)

rewrite39.0ms

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:

19.0ms	(sqrt (* (- (hypot re im) re) 2.0))
0.0ms	(hypot re im)
15.0ms	(- (hypot re im) re)

series427.0ms

Counts

3 → 9

Calls

3 calls:

223.0ms	(sqrt (* (- (hypot re im) re) 2.0))
82.0ms	(hypot re im)
121.0ms	(- (hypot re im) re)

simplify3.3s

Counts

62 → 62

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	115	686
1	232	572
2	519	489
3	1765	434
done	5000	423

prune277.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
7.3b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`prod-diff` `pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 90

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
21.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
20.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series313.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(hypot re im)
85.0ms	(hypot re im)
55.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
91.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify4.0s

Counts

102 → 102

Iterations

Useful iterations: 4 (2.1s)

Iter	Nodes	Cost
0	108	1091
1	191	592
2	422	547
3	1164	523
4	3755	509
done	5000	509

prune414.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0b	(hypot re im)
0.0b	(hypot re im)
15.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite7.0ms

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:

5.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0ms	(hypot re im)
0.0ms	(hypot re im)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series700.0ms

Counts

4 → 12

Calls

4 calls:

337.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
70.0ms	(hypot re im)
74.0ms	(hypot re im)
219.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify4.5s

Counts

55 → 55

Iterations

Useful iterations: 4 (2.7s)

Iter	Nodes	Cost
0	76	577
1	151	419
2	397	358
3	1235	345
4	3563	343
done	5000	343

prune295.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.3b	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
0.7b	(pow (sqrt (sqrt (hypot re im))) 3)
11.7b	(- (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3)) re)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

97×	`sqrt-prod`
71×	`add-sqr-sqrt`
27×	`unpow-prod-down` `cube-prod`
24×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `unswap-sqr`
10×	`pow1` `add-exp-log`
9×	`associate-l`
8×	`sqrt-pow1`
7×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u`
3×	`pow-unpow` `prod-diff` `prod-exp`
2×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `unpow3` `pow-exp`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `*-commutative` `pow-prod-up` `sqrt-pow2` `flip--` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 153

Calls

4 calls:

2.0ms	(sqrt (sqrt (hypot re im)))
42.0ms	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
5.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
20.0ms	(- (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3)) re)

series558.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(sqrt (sqrt (hypot re im)))
64.0ms	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
212.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
96.0ms	(- (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3)) re)

simplify1.3s

Counts

165 → 165

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	174	2600
1	377	2193
2	1145	1508
done	5000	1343

prune502.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 13.7b

regimes150.0ms

Accuracy

0% (0.2b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.2s

Algorithm

intervals

Results

879.0ms	676×	body	2560	valid
524.0ms	6035×	body	80	valid
265.0ms	489×	body	1280	valid
188.0ms	291×	body	5120	valid
73.0ms	279×	body	640	valid
30.0ms	152×	body	320	valid
11.0ms	78×	body	160	valid