Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	189×	body	80	valid
5.0ms	27×	body	2560	valid
4.0ms	15×	body	5120	valid
2.0ms	11×	body	1280	valid
1.0ms	8×	body	640	valid
0.0ms	4×	body	160	valid
0.0ms	2×	body	320	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: 41.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
31.6b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series265.0ms

Counts

3 → 9

Calls

3 calls:

181.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	264	372
1	830	337
2	2660	322
3	5002	320

prune189.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.3b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (hypot re im) re)))
0.9b	(+ (hypot re im) re)

rewrite9.0ms

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:

5.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
3.0ms	(+ (hypot re im) re)

series253.0ms

Counts

2 → 6

Calls

2 calls:

197.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
56.0ms	(+ (hypot re im) re)

simplify49.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (46.0ms)

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

prune110.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (sqrt (* 2.0 (+ (hypot re im) re))))
0.2b	(sqrt (* 2.0 (+ (hypot re im) re)))
0.9b	(+ (hypot re im) re)
3.7b	(exp (log (sqrt (* 2.0 (+ (hypot re im) re)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

5.0ms	(log (sqrt (* 2.0 (+ (hypot re im) re))))
5.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
3.0ms	(+ (hypot re im) re)
7.0ms	(exp (log (sqrt (* 2.0 (+ (hypot re im) re)))))

series771.0ms

Counts

4 → 12

Calls

4 calls:

332.0ms	(log (sqrt (* 2.0 (+ (hypot re im) re))))
189.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
60.0ms	(+ (hypot re im) re)
191.0ms	(exp (log (sqrt (* 2.0 (+ (hypot re im) re)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	309	531
1	832	484
2	3111	461
3	5003	454

prune255.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
16.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite4.0ms

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:

3.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series387.0ms

Counts

2 → 6

Calls

2 calls:

243.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
143.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify47.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (43.0ms)

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

prune79.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.0b

regimes141.0ms

Accuracy

27.3% (4.0b remaining)

Error of 11.4b against oracle of 7.4b and baseline of 13.0b

bsearch50.0ms

Steps

Iters	Range		Point
8	-4.922636929833077e+106	-2.4504746634917517e+103	-1.545247932061966e+105

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	12
1	23	12

end0.0ms

sample682.0ms

Algorithm

intervals

Results

198.0ms	6051×	body	80	valid
139.0ms	715×	body	2560	valid
84.0ms	305×	body	5120	valid
73.0ms	440×	body	1280	valid
31.0ms	253×	body	640	valid
17.0ms	156×	body	320	valid
5.0ms	80×	body	160	valid