Details

sample150.0ms

Algorithm

intervals

Results

15.0ms	34×	body	2560	valid
14.0ms	168×	body	80	valid
10.0ms	16×	body	5120	valid
6.0ms	17×	body	1280	valid
4.0ms	12×	body	640	valid
2.0ms	4×	body	160	valid
1.0ms	5×	body	320	valid

simplify119.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (14.0ms)

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- (hypot re im) re) 2.0)
0.3b	(sqrt (* (- (hypot re im) re) 2.0))
0.6b	(- (hypot re im) re)

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`prod-diff`
8×	`pow1`
5×	`add-exp-log` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`associate-*l/`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `associate-r` `flip--` `log1p-expm1-u`
2×	`sqrt-pow1` `sqrt-div` `pow-prod-down` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `pow1/2` `diff-log` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 67

Calls

3 calls:

57.0ms	(* (- (hypot re im) re) 2.0)
19.0ms	(sqrt (* (- (hypot re im) re) 2.0))
16.0ms	(- (hypot re im) re)

series482.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(* (- (hypot re im) re) 2.0)
246.0ms	(sqrt (* (- (hypot re im) re) 2.0))
128.0ms	(- (hypot re im) re)

simplify891.0ms

Counts

76 → 76

Iterations

Useful iterations: done (885.0ms)

Iter	Nodes	Cost
0	134	879
1	302	771
2	1131	666
done	5001	640

prune302.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- (hypot re im) re))
0.4b	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
0.6b	(- (hypot re im) re)

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`sqrt-prod`
15×	`add-cube-cbrt`
9×	`prod-diff`
8×	`pow1` `associate-l`
6×	`associate-r`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`expm1-log1p-u` `flip3--` `sqrt-pow1` `pow1/2` `fma-neg` `pow-prod-down` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 83

Calls

3 calls:

20.0ms	(sqrt (- (hypot re im) re))
53.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
14.0ms	(- (hypot re im) re)

series569.0ms

Counts

3 → 9

Calls

3 calls:

210.0ms	(sqrt (- (hypot re im) re))
250.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
109.0ms	(- (hypot re im) re)

simplify1.1s

Counts

92 → 92

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	160	1139
1	363	1002
2	1407	903
done	5000	864

prune459.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (hypot re im) re))
0.2b	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
0.2b	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(- (hypot re im) re)

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
37×	`sqrt-prod`
26×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`associate-r`
17×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow-prod-down`
9×	`associate-l` `prod-diff`
6×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-*l/` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `flip3--` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg` `sqrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`*-commutative`
1×	`sub-neg` `rem-sqrt-square` `diff-log`

Counts

4 → 119

Calls

4 calls:

20.0ms	(sqrt (- (hypot re im) re))
41.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
116.0ms	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
14.0ms	(- (hypot re im) re)

series943.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(sqrt (- (hypot re im) re))
379.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
308.0ms	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
86.0ms	(- (hypot re im) re)

simplify2.1s

Counts

131 → 131

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	212	1873
1	533	1580
2	2739	1402
done	5000	1370

prune527.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (sqrt (+ (- (pow (cbrt (hypot re im)) 3) re) (+ (- re) re))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(cbrt (hypot re im))
0.7b	(pow (cbrt (hypot re im)) 3)
15.5b	(- (pow (cbrt (hypot re im)) 3) re)

rewrite707.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
54×	`prod-diff`
53×	`*-un-lft-identity`
51×	`add-cube-cbrt`
35×	`cbrt-prod`
32×	`unpow-prod-down` `cube-prod`
18×	`fma-neg`
13×	`pow1`
12×	`associate-*l/`
10×	`add-exp-log`
9×	`associate-r` `sqrt-prod` `add-cbrt-cube`
7×	`pow-prod-down`
6×	`sqrt-div` `add-log-exp` `difference-of-squares` `sqr-pow`
5×	`cube-mult` `unpow3`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `prod-exp` `flip--` `cbrt-unprod` `flip-+`
2×	`pow-pow` `pow1/3` `sqrt-unprod`
1×	`pow-to-exp` `sub-neg` `diff-log` `associate-l` `pow-exp` `*-commutative` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 173

Calls

4 calls:

643.0ms	(* (* (sqrt (+ (- (pow (cbrt (hypot re im)) 3) re) (+ (- re) re))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
1.0ms	(cbrt (hypot re im))
4.0ms	(pow (cbrt (hypot re im)) 3)
52.0ms	(- (pow (cbrt (hypot re im)) 3) re)

series724.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(* (* (sqrt (+ (- (pow (cbrt (hypot re im)) 3) re) (+ (- re) re))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
165.0ms	(cbrt (hypot re im))
158.0ms	(pow (cbrt (hypot re im)) 3)
102.0ms	(- (pow (cbrt (hypot re im)) 3) re)

simplify3.6s

Counts

185 → 185

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	270	3750
1	757	2271
2	4422	1652
done	5000	1651

prune629.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 18.1b

regimes233.0ms

Accuracy

0% (0.3b remaining)

Error of 14.0b against oracle of 13.7b and baseline of 14.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.4s

Algorithm

intervals

Results

636.0ms	292×	body	640	valid
500.0ms	5920×	body	80	valid
441.0ms	741×	body	2560	valid
198.0ms	497×	body	1280	valid
169.0ms	328×	body	5120	valid
83.0ms	141×	body	320	valid
10.0ms	81×	body	160	valid