Details

sample47.0ms

Algorithm

intervals

Results

16.0ms	192×	body	80	valid
9.0ms	24×	body	2560	valid
5.0ms	12×	body	5120	valid
5.0ms	15×	body	1280	valid
2.0ms	8×	body	640	valid
1.0ms	5×	body	320	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	8
1	28	8
2	36	8
3	44	8
4	46	8
5	46	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(- (sqrt (+ (* re re) (* im im))) re)
0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
8×	`pow1` `add-log-exp`
6×	`fma-neg`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `fma-def` `diff-log` `pow-prod-down` `sum-log` `hypot-def` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

3.0ms	(+ (* re re) (* im im))
21.0ms	(- (sqrt (+ (* re re) (* im im))) re)
29.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* re re) (* im im))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
167.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	342	834
1	1366	586
2	5002	533

prune227.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (hypot re im) re)
0.2b	(sqrt (* 2.0 (* 1 (- (hypot re im) re))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
8×	`pow1`
4×	`associate-*r/` `add-log-exp`
3×	`sqrt-pow1` `fma-neg` `pow-prod-down`
2×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
1×	`sub-neg` `pow1/2` `diff-log` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 44

Calls

2 calls:

5.0ms	(- (hypot re im) re)
27.0ms	(sqrt (* 2.0 (* 1 (- (hypot re im) re))))

series232.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (hypot re im) re)
178.0ms	(sqrt (* 2.0 (* 1 (- (hypot re im) re))))

simplify31.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	232	325
1	856	239
2	5002	235

prune118.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.6b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`sqrt-prod`
9×	`prod-diff`
8×	`associate-r`
6×	`pow1` `associate-l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`fma-neg` `pow-prod-down`
2×	`expm1-log1p-u` `flip3--` `sqrt-pow1` `pow1/2` `sqrt-div` `associate-*r/` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

2 → 64

Calls

2 calls:

3.0ms	(- (hypot re im) re)
13.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))

series240.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(- (hypot re im) re)
181.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))

simplify37.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	277	470
1	1061	382
2	5002	374

prune156.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (hypot re im) re)
0.2b	(* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re)))
0.2b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`pow1` `add-exp-log`
15×	`add-cube-cbrt`
13×	`sqrt-prod`
10×	`cbrt-prod` `associate-l` `add-cbrt-cube`
9×	`associate-r` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-*r/` `unswap-sqr`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `flip--` `log1p-expm1-u`
2×	`*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `diff-log`

Counts

3 → 92

Calls

3 calls:

3.0ms	(- (hypot re im) re)
17.0ms	(* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re)))
29.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re))))

series651.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(- (hypot re im) re)
403.0ms	(* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re)))
188.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re))))

simplify63.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	446	967
1	1860	755
2	5001	703

prune242.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.6b

regimes106.0ms

Accuracy

28.1% (4.3b remaining)

Error of 11.3b against oracle of 7.1b and baseline of 13.0b

bsearch56.0ms

Steps

Iters	Range		Point
6	0.00011468519908208964	0.0012055448239290207	0.00015530054912046227

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	35	14
2	35	14

end0.0ms

sample1.3s

Algorithm

intervals

Results

514.0ms	6072×	body	80	valid
258.0ms	677×	body	2560	valid
146.0ms	474×	body	1280	valid
124.0ms	282×	body	5120	valid
72.0ms	281×	body	640	valid
32.0ms	154×	body	320	valid
10.0ms	60×	body	160	valid