Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	193×	body	80	valid
3.0ms	18×	body	2560	valid
3.0ms	19×	body	1280	valid
2.0ms	7×	body	5120	valid
1.0ms	8×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	5×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 35.9b

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)))
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

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:

3.0ms	(+ (* re re) (* im im))
14.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
15.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
169.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
46.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
34.0ms	(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

prune407.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 5.8b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* 2.0 (+ (hypot re im) re)))
1.1b	(+ (hypot re im) re)

rewrite8.0ms

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:

0.0ms	(hypot re im)
4.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
3.0ms	(+ (hypot re im) re)

series283.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(hypot re im)
180.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
56.0ms	(+ (hypot re im) re)

simplify55.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (51.0ms)

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

prune135.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.0b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
15.3b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite4.0ms

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:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
2.0ms	(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)

series456.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot re im)
42.0ms	(hypot re im)
230.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
136.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify47.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (43.0ms)

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

prune190.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

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))
15.3b	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (sqrt (hypot re im)) re)

rewrite2.0ms

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:

0.0ms	(cbrt (hypot re im))
0.0ms	(cbrt (hypot re im))
0.0ms	(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)

series470.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt (hypot re im))
108.0ms	(cbrt (hypot re im))
109.0ms	(cbrt (hypot re im))
139.0ms	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (sqrt (hypot re im)) re)

simplify138.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (133.0ms)

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

prune228.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

regimes119.0ms

Accuracy

30.6% (4.4b remaining)

Error of 11.3b against oracle of 6.9b and baseline of 13.3b

bsearch30.0ms

Steps

Iters	Range		Point
5	-1.1060260739993621e-57	-4.156244049672509e-58	-4.940006105430029e-58

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample675.0ms

Algorithm

intervals

Results

203.0ms	6047×	body	80	valid
138.0ms	681×	body	2560	valid
76.0ms	483×	body	1280	valid
67.0ms	272×	body	5120	valid
36.0ms	286×	body	640	valid
13.0ms	144×	body	320	valid
5.0ms	87×	body	160	valid