Details

sample82.0ms

Algorithm

intervals

Results

23.0ms	189×	body	80	valid
15.0ms	20×	body	2560	valid
13.0ms	21×	body	1280	valid
9.0ms	10×	body	5120	valid
8.0ms	14×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	31
3	31
2	29
1	24
0	12

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.8b

localize49.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.0b	(hypot re im)
0.3b	(+ (hypot re im) re)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `*-un-lft-identity`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`+-commutative` `hypot-udef` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

3 → 45

Calls

3 calls:

6.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
0.0ms	(hypot re im)
5.0ms	(+ (hypot re im) re)

series462.0ms

Counts

3 → 9

Calls

3 calls:

282.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
84.0ms	(hypot re im)
96.0ms	(+ (hypot re im) re)

simplify2.6s

Counts

54 → 54

Iterations

Iter	Nodes
4	4081
3	1315
2	474
1	189
0	89

prune584.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ (hypot re im) re)) (cbrt (+ (hypot re im) re)))
0.4b	(cbrt (+ (hypot re im) re))
0.4b	(cbrt (+ (hypot re im) re))
0.4b	(cbrt (+ (hypot re im) re))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 107

Calls

4 calls:

36.0ms	(* (cbrt (+ (hypot re im) re)) (cbrt (+ (hypot re im) re)))
5.0ms	(cbrt (+ (hypot re im) re))
6.0ms	(cbrt (+ (hypot re im) re))
6.0ms	(cbrt (+ (hypot re im) re))

series856.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(* (cbrt (+ (hypot re im) re)) (cbrt (+ (hypot re im) re)))
229.0ms	(cbrt (+ (hypot re im) re))
207.0ms	(cbrt (+ (hypot re im) re))
229.0ms	(cbrt (+ (hypot re im) re))

simplify2.1s

Counts

119 → 119

Iterations

Iter	Nodes
4	4483
3	1762
2	736
1	317
0	142

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
10.5b	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 57

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
29.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series537.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt (hypot re im))
164.0ms	(cbrt (hypot re im))
139.0ms	(cbrt (hypot re im))
79.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify1.9s

Counts

69 → 69

Iterations

Iter	Nodes
4	3712
3	1168
2	408
1	152
0	65

prune782.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (sqrt (hypot re im)))
0.6b	(cbrt (sqrt (hypot re im)))
10.0b	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))) re)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 63

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (sqrt (hypot re im)))
1.0ms	(cbrt (sqrt (hypot re im)))
34.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))) re)

series590.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (hypot re im))
186.0ms	(cbrt (sqrt (hypot re im)))
189.0ms	(cbrt (sqrt (hypot re im)))
68.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))) re)

simplify938.0ms

Counts

75 → 75

Iterations

Iter	Nodes
3	2389
2	662
1	213
0	96

prune1.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.6b

regimes224.0ms

Accuracy

0% (0.3b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	12
1	12
0	9

end0.0ms

sample2.6s

Algorithm

intervals

Results

864.0ms	6062×	body	80	valid
830.0ms	650×	body	2560	valid
312.0ms	312×	body	5120	valid
241.0ms	450×	body	1280	valid
147.0ms	289×	body	640	valid
43.0ms	145×	body	320	valid
19.0ms	92×	body	160	valid