Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	196×	body	80	valid
4.0ms	20×	body	2560	valid
2.0ms	13×	body	1280	valid
1.0ms	6×	body	5120	valid
1.0ms	10×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	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: 36.6b

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)))
0.9b	(- (sqrt (+ (* re re) (* im im))) re)
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite61.0ms

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))
31.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
22.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
169.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	342	834
1	1366	586
2	5001	533

prune226.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.9b	(- (hypot re im) re)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

0.0ms	(hypot re im)
10.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
3.0ms	(- (hypot re im) re)

series281.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(hypot re im)
182.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
55.0ms	(- (hypot re im) re)

simplify47.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	283	345
1	1118	247
2	5001	236

prune157.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (* 2.0 (+ (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 0)))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.2b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`pow1`
22×	`sqrt-prod`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`sqrt-pow1`
10×	`pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `unswap-sqr`
3×	`prod-diff` `pow-sqr`
2×	`sqrt-div` `associate-*r/`
1×	`pow2` `sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `difference-of-squares`

Counts

4 → 100

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
20.0ms	(sqrt (* 2.0 (+ (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 0)))
9.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
5.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series366.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(sqrt (hypot re im))
180.0ms	(sqrt (* 2.0 (+ (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 0)))
44.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
58.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify68.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	393	617
1	1729	499
2	5001	485

prune252.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
9.0b	(- (* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) re)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`cbrt-prod` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`prod-diff` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`pow1/3`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `associate-r` `*-commutative` `flip--`

Counts

4 → 67

Calls

4 calls:

12.0ms	(* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))
0.0ms	(cbrt (hypot re im))
0.0ms	(cbrt (hypot re im))
12.0ms	(- (* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) re)

series460.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))
108.0ms	(cbrt (hypot re im))
111.0ms	(cbrt (hypot re im))
105.0ms	(- (* (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) re)

simplify41.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	288	748
1	1123	655
2	5001	645

prune277.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.6b

regimes105.0ms

Accuracy

35.6% (4.0b remaining)

Error of 11.5b against oracle of 7.5b and baseline of 13.7b

bsearch64.0ms

Steps

Iters	Range		Point
10	167712351607.73917	6.317567976138939e+21	9087940982052.582

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	14
1	33	14
2	33	14

end0.0ms

sample694.0ms

Algorithm

intervals

Results

206.0ms	5967×	body	80	valid
135.0ms	692×	body	2560	valid
84.0ms	514×	body	1280	valid
74.0ms	303×	body	5120	valid
39.0ms	288×	body	640	valid
17.0ms	151×	body	320	valid
5.0ms	85×	body	160	valid