Details

sample28.0ms

Algorithm

intervals

Results

6.0ms	182×	body	80	valid
5.0ms	25×	body	2560	valid
3.0ms	22×	body	1280	valid
3.0ms	12×	body	5120	valid
1.0ms	8×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.0b	(+ (* re re) (* im im))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`pow1` `add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `fma-def` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `hypot-def` `distribute-lft-out`

Counts

4 → 67

Calls

4 calls:

26.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(+ (* re re) (* im im))
31.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
24.0ms	(+ (* re re) (* im im))
42.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
32.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	296	446
1	1086	401
2	3561	382
3	5001	381

prune214.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (hypot re im) re)))
0.8b	(+ (hypot re im) re)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

7.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
5.0ms	(+ (hypot re im) re)

series220.0ms

Counts

2 → 6

Calls

2 calls:

168.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
52.0ms	(+ (hypot re im) re)

simplify52.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	183	173
1	519	156
2	1741	150
3	5001	148

prune101.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
18.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
2×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

2 → 23

Calls

2 calls:

5.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series331.0ms

Counts

2 → 6

Calls

2 calls:

209.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
122.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify46.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	129	225
1	378	193
2	1445	178
3	5002	174

prune86.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))))
18.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
18.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
18.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `cbrt-prod` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`pow1/3` `sqrt-prod`

Counts

4 → 44

Calls

4 calls:

7.0ms	(cbrt (sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series657.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(cbrt (sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))))
124.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
121.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
121.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify88.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	217	510
1	720	448
2	3120	427
3	5001	419

prune229.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.2b

regimes124.0ms

Accuracy

16.9% (4.8b remaining)

Error of 12.2b against oracle of 7.4b and baseline of 13.2b

bsearch37.0ms

Steps

Iters	Range		Point
8	-1.3585418929568907e-114	-7.806801805986815e-118	-1.0698983567117504e-114

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	13
1	29	13
2	29	13

end0.0ms

sample708.0ms

Algorithm

intervals

Results

192.0ms	6044×	body	80	valid
144.0ms	735×	body	2560	valid
80.0ms	467×	body	1280	valid
65.0ms	284×	body	5120	valid
35.0ms	264×	body	640	valid
13.0ms	140×	body	320	valid
4.0ms	66×	body	160	valid