Details

sample118.0ms

Algorithm

intervals

Results

13.0ms	187×	body	80	valid
13.0ms	31×	body	2560	valid
4.0ms	13×	body	1280	valid
3.0ms	6×	body	5120	valid
2.0ms	11×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify106.0ms

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.0b	(hypot re im)
1.0b	(- (hypot re im) re)

rewrite57.0ms

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:

23.0ms	(sqrt (* (- (hypot re im) re) 2.0))
1.0ms	(hypot re im)
18.0ms	(- (hypot re im) re)

series502.0ms

Counts

3 → 9

Calls

3 calls:

314.0ms	(sqrt (* (- (hypot re im) re) 2.0))
84.0ms	(hypot re im)
104.0ms	(- (hypot re im) re)

simplify3.0s

Counts

62 → 62

Iterations

Useful iterations: done (3.0s)

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

prune222.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.0b

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)))
9.5b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite32.0ms

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)
14.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
15.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series328.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(hypot re im)
78.0ms	(hypot re im)
84.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
99.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify4.1s

Counts

102 → 102

Iterations

Useful iterations: 4 (2.3s)

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

prune333.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 15.0b

localize20.0ms

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)
11.0b	(- (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3)) re)

rewrite117.0ms

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:

5.0ms	(sqrt (sqrt (hypot re im)))
59.0ms	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
10.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
32.0ms	(- (* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3)) re)

series599.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(sqrt (sqrt (hypot re im)))
83.0ms	(* (sqrt (sqrt (hypot re im))) (pow (sqrt (sqrt (hypot re im))) 3))
224.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
88.0ms	(- (* (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

prune510.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 15.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(hypot re im)
0.0b	(hypot re im)
16.6b	(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))

series523.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(sqrt (hypot re im))
90.0ms	(hypot re im)
62.0ms	(hypot re im)
219.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify3.4s

Counts

57 → 57

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	69	452
1	131	360
2	294	314
3	778	310
4	2102	309
done	5000	302

prune276.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 15.0b

regimes140.0ms

Accuracy

0% (0.2b remaining)

Error of 13.7b against oracle of 13.5b and baseline of 13.7b

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

676.0ms	467×	body	1280	valid
547.0ms	5974×	body	80	valid
333.0ms	754×	body	2560	valid
171.0ms	273×	body	5120	valid
70.0ms	291×	body	640	valid
48.0ms	75×	body	160	valid
31.0ms	166×	body	320	valid