Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	189×	body	80	valid
5.0ms	27×	body	2560	valid
2.0ms	11×	body	1280	valid
1.0ms	12×	body	640	valid
1.0ms	6×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	4×	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: 38.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite78.0ms

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:

8.0ms	(+ (* re re) (* im im))
24.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
36.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (* re re) (* im im))
164.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
41.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify99.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (87.0ms)

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

prune213.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 8.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (hypot re im) re)))
0.0b	(hypot re im)
1.0b	(+ (hypot re im) re)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

11.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
0.0ms	(hypot re im)
6.0ms	(+ (hypot re im) re)

series272.0ms

Counts

3 → 9

Calls

3 calls:

176.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
46.0ms	(hypot re im)
50.0ms	(+ (hypot re im) re)

simplify54.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	196	197
1	536	180
2	1779	174
3	5002	172

prune137.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
0.0b	(hypot re im)
0.0b	(hypot re im)
16.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

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

series430.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
46.0ms	(hypot re im)
40.0ms	(hypot re im)
129.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify49.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	145	279
1	417	241
2	1510	226
3	5002	222

prune192.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.3b

localize15.0ms

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))
16.4b	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (sqrt (hypot re im)) re)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
0.0ms	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (sqrt (hypot re im)) re)

series439.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (hypot re im))
102.0ms	(cbrt (hypot re im))
102.0ms	(cbrt (hypot re im))
126.0ms	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (sqrt (hypot re im)) re)

simplify141.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (136.0ms)

Iter	Nodes	Cost
0	100	381
1	249	336
2	841	330
3	4138	294
4	5001	282

prune215.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.3b

regimes141.0ms

Accuracy

25.8% (4.3b remaining)

Error of 11.7b against oracle of 7.5b and baseline of 13.2b

bsearch39.0ms

Steps

Iters	Range		Point
7	-136035437490323.81	-2359205746464.0527	-16209155258582.346

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

sample687.0ms

Algorithm

intervals

Results

193.0ms	6027×	body	80	valid
131.0ms	712×	body	2560	valid
72.0ms	453×	body	1280	valid
71.0ms	306×	body	5120	valid
33.0ms	291×	body	640	valid
11.0ms	128×	body	320	valid
5.0ms	83×	body	160	valid