Details

sample134.0ms

Algorithm

intervals

Results

20.0ms	193×	body	80	valid
11.0ms	20×	body	2560	valid
7.0ms	17×	body	1280	valid
6.0ms	9×	body	5120	valid
3.0ms	10×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify77.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (9.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite36.0ms

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:

17.0ms	(sqrt (* (- (hypot re im) re) 2.0))
0.0ms	(hypot re im)
15.0ms	(- (hypot re im) re)

series463.0ms

Counts

3 → 9

Calls

3 calls:

279.0ms	(sqrt (* (- (hypot re im) re) 2.0))
69.0ms	(hypot re im)
114.0ms	(- (hypot re im) re)

simplify2.8s

Counts

62 → 62

Iterations

Useful iterations: done (2.8s)

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

prune269.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
7.5b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
15×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`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×	`rem-sqrt-square`
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 → 100

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
17.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
28.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series410.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sqrt (hypot re im))
162.0ms	(sqrt (hypot re im))
58.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
69.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify5.1s

Counts

112 → 112

Iterations

Useful iterations: 4 (3.0s)

Iter	Nodes	Cost
0	124	1267
1	244	744
2	569	675
3	1551	643
4	4853	631
done	5000	631

prune391.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 13.6b

localize37.0ms

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))
0.8b	(pow (sqrt (sqrt (hypot re im))) 3)
11.4b	(- (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3)) re)

rewrite97.0ms

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)))
44.0ms	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
5.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
39.0ms	(- (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3)) re)

series522.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(sqrt (sqrt (hypot re im)))
60.0ms	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
180.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
85.0ms	(- (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3)) re)

simplify1.4s

Counts

165 → 165

Iterations

Useful iterations: done (1.3s)

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

prune482.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.8b	(pow (sqrt (sqrt (hypot re im))) 3)
12.1b	(- (* (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (* (sqrt (sqrt (cbrt (hypot re im)))) (pow (sqrt (sqrt (hypot re im))) 3))) re)

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

18×	`sqrt-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down` `cube-prod`
7×	`pow1`
6×	`cbrt-prod` `add-log-exp`
5×	`add-exp-log` `pow-pow` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u`
3×	`pow-unpow` `prod-diff`
2×	`pow1/2` `pow1/3`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `fma-neg` `diff-log` `unpow3` `pow-exp` `sqrt-pow2` `flip--` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 86

Calls

4 calls:

2.0ms	(cbrt (hypot re im))
2.0ms	(cbrt (hypot re im))
14.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
101.0ms	(- (* (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (* (sqrt (sqrt (cbrt (hypot re im)))) (pow (sqrt (sqrt (hypot re im))) 3))) re)

series606.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(cbrt (hypot re im))
177.0ms	(cbrt (hypot re im))
204.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
89.0ms	(- (* (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (* (sqrt (sqrt (cbrt (hypot re im)))) (pow (sqrt (sqrt (hypot re im))) 3))) re)

simplify1.1s

Counts

98 → 98

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	147	1489
1	333	1201
2	830	1074
done	5000	1066

prune660.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.6b

regimes184.0ms

Accuracy

0% (0.2b remaining)

Error of 13.1b against oracle of 12.9b and baseline of 13.1b

bsearch0.0ms

simplify3.0ms

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

1.1s	6054×	body	80	valid
290.0ms	691×	body	2560	valid
180.0ms	297×	body	5120	valid
148.0ms	457×	body	1280	valid
117.0ms	266×	body	640	valid
30.0ms	163×	body	320	valid
8.0ms	72×	body	160	valid