Details

sample35.0ms

Algorithm

intervals

Results

12.0ms	198×	body	80	valid
6.0ms	25×	body	2560	valid
3.0ms	12×	body	1280	valid
2.0ms	10×	body	640	valid
2.0ms	5×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify20.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt`
4×	`pow1` `add-cube-cbrt`
3×	`add-exp-log` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `sqrt-div` `sum-log`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out`

Counts

3 → 38

Calls

3 calls:

18.0ms	(+ (* re re) (* im im))
74.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
9.0ms	(sqrt (+ (* re re) (* im im)))

series166.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ (* re re) (* im im))
71.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts: 47 → 47

prune226.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.0b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
31.2b	(sqrt (+ (* re re) (* im im)))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

79.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
35.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
17.0ms	(sqrt (+ (* re re) (* im im)))
16.0ms	(sqrt (+ (* re re) (* im im)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
70.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
65.0ms	(sqrt (+ (* re re) (* im im)))
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify824.0ms

Counts: 136 → 136

prune477.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.5b

localize43.0ms

Local error

Found 4 expressions with local error:

31.2b	(sqrt (+ (* re re) (* im im)))
32.2b	(cbrt (+ (* re re) (* im im)))
32.2b	(cbrt (+ (* re re) (* im im)))
32.2b	(cbrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

12.0ms	(sqrt (+ (* re re) (* im im)))
12.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(sqrt (+ (* re re) (* im im)))
121.0ms	(cbrt (+ (* re re) (* im im)))
141.0ms	(cbrt (+ (* re re) (* im im)))
137.0ms	(cbrt (+ (* re re) (* im im)))

simplify2.3s

Counts: 66 → 66

prune604.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.5b

localize37.0ms

Local error

Found 4 expressions with local error:

31.2b	(sqrt (+ (* re re) (* im im)))
32.2b	(cbrt (+ (* re re) (* im im)))
32.2b	(cbrt (+ (* re re) (* im im)))
32.2b	(cbrt (+ (* re re) (* im im)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

10.0ms	(sqrt (+ (* re re) (* im im)))
10.0ms	(cbrt (+ (* re re) (* im im)))
11.0ms	(cbrt (+ (* re re) (* im im)))
12.0ms	(cbrt (+ (* re re) (* im im)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (+ (* re re) (* im im)))
136.0ms	(cbrt (+ (* re re) (* im im)))
144.0ms	(cbrt (+ (* re re) (* im im)))
130.0ms	(cbrt (+ (* re re) (* im im)))

simplify2.1s

Counts: 66 → 66

prune607.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.5b

regimes341.0ms

Accuracy

53.9% (10.0b remaining)

Error of 27.9b against oracle of 17.9b and baseline of 39.6b

bsearch170.0ms

Steps

Iters	Range	Point
5	3.405487938897816e+124	7.120673724870613e+124	4.779501075464755e+124
7	1.5817682817464374e-173	6.441850365230505e-172	5.805113327902053e-173
9	-2.7933584181899312e-198	-3.0544378147195635e-207	-3.0502614519508694e-204

Iters

Range

Point

3.405487938897816e+124

7.120673724870613e+124

4.779501075464755e+124

1.5817682817464374e-173

6.441850365230505e-172

5.805113327902053e-173

-2.7933584181899312e-198

-3.0544378147195635e-207

-3.0502614519508694e-204

simplify918.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

704.0ms	738×	body	2560	valid
617.0ms	5995×	body	80	valid
193.0ms	498×	body	1280	valid
190.0ms	276×	body	5120	valid
80.0ms	277×	body	640	valid
29.0ms	147×	body	320	valid
9.0ms	69×	body	160	valid