Details

sample127.0ms

Algorithm

intervals

Results

16.0ms	193×	body	80	valid
13.0ms	24×	body	2560	valid
4.0ms	11×	body	1280	valid
4.0ms	7×	body	5120	valid
3.0ms	9×	body	640	valid
2.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify114.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

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

localize14.0ms

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)

rewrite21.0ms

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:

10.0ms	(sqrt (* (- (hypot re im) re) 2.0))
0.0ms	(hypot re im)
9.0ms	(- (hypot re im) re)

series467.0ms

Counts

3 → 9

Calls

3 calls:

273.0ms	(sqrt (* (- (hypot re im) re) 2.0))
69.0ms	(hypot re im)
124.0ms	(- (hypot re im) re)

simplify2.6s

Counts

62 → 62

Iterations

Useful iterations: done (2.6s)

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

prune223.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.7b

localize14.0ms

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)

rewrite47.0ms

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)
18.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
26.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series262.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(hypot re im)
66.0ms	(hypot re im)
63.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
79.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify3.9s

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

prune415.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.7b

localize24.0ms

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))

rewrite13.0ms

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:

10.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
1.0ms	(hypot re im)
1.0ms	(hypot re im)
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series716.0ms

Counts

4 → 12

Calls

4 calls:

398.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
57.0ms	(hypot re im)
67.0ms	(hypot re im)
194.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify4.2s

Counts

55 → 55

Iterations

Useful iterations: 4 (2.5s)

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

prune271.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.7b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

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-l*` `unswap-sqr`
10×	`pow1` `add-exp-log`
9×	`associate-r`
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--` `pow-plus` `fma-neg` `diff-log` `*-commutative` `pow-prod-up` `sqrt-pow2` `flip--` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 154

Calls

4 calls:

3.0ms	(sqrt (sqrt (hypot re im)))
38.0ms	(* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im))))
6.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
20.0ms	(- (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))) re)

series604.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(sqrt (sqrt (hypot re im)))
94.0ms	(* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im))))
212.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
86.0ms	(- (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))) re)

simplify1.4s

Counts

166 → 166

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	172	2591
1	384	1733
2	1151	1491
done	5001	1331

prune490.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 13.7b

regimes134.0ms

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

sample2.0s

Algorithm

intervals

Results

871.0ms	6035×	body	80	valid
370.0ms	676×	body	2560	valid
149.0ms	489×	body	1280	valid
135.0ms	291×	body	5120	valid
84.0ms	78×	body	160	valid
77.0ms	152×	body	320	valid
69.0ms	279×	body	640	valid