Details

sample28.0ms

Algorithm

intervals

Results

6.0ms	182×	body	80	valid
4.0ms	21×	body	2560	valid
4.0ms	15×	body	5120	valid
3.0ms	22×	body	1280	valid
1.0ms	10×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	1×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

32.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
22.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series248.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify43.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	314	760
1	1192	522
2	5001	473

prune191.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.6b	(- (hypot re im) re)

rewrite17.0ms

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)))
5.0ms	(- (hypot re im) re)

series276.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(hypot re im)
178.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
54.0ms	(- (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

prune156.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re)) 0)))
18.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
4.0ms	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re)) 0)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

series535.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(sqrt (hypot re im))
83.0ms	(sqrt (hypot re im))
233.0ms	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re)) 0)))
137.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

simplify41.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	260	458
1	902	401
2	5002	379

prune232.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt (hypot re im)))
0.5b	(cbrt (sqrt (hypot re im)))
0.5b	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
17.9b	(fma (* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (cbrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (* -1 re))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

52×	`cbrt-prod`
42×	`add-sqr-sqrt`
26×	`sqrt-prod`
20×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `swap-sqr`
9×	`associate-r` `associate-l` `unswap-sqr`
8×	`pow1/3`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 100

Calls

4 calls:

1.0ms	(cbrt (sqrt (hypot re im)))
1.0ms	(cbrt (sqrt (hypot re im)))
9.0ms	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
0.0ms	(fma (* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (cbrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (* -1 re))

series469.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (sqrt (hypot re im)))
107.0ms	(cbrt (sqrt (hypot re im)))
109.0ms	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
141.0ms	(fma (* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (cbrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (* -1 re))

simplify107.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	208	1026
1	722	943
2	3411	868
3	5001	820

prune340.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.8b

regimes167.0ms

Accuracy

-17.7% (6.8b remaining)

Error of 14.2b against oracle of 7.4b and baseline of 13.2b

bsearch201.0ms

Steps

Iters	Range		Point
9	1.0963672838557836e+114	8.302175042271763e+120	3.3371304803298494e+120
10	1.7706522306460648e-167	8.676345970198339e-157	8.575500542659089e-157
9	-2.038197479000767e+61	-2.8729039666377685e+54	-8.34056697677881e+54
10	-1.8826421970161096e+123	-1.7180035749932514e+111	-4.1789077984601566e+114

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	41	34
1	48	34
2	54	14
3	57	14
4	63	14
5	74	14
6	81	14
7	82	14
8	82	14

end0.0ms

sample684.0ms

Algorithm

intervals

Results

206.0ms	6023×	body	80	valid
135.0ms	681×	body	2560	valid
80.0ms	487×	body	1280	valid
71.0ms	303×	body	5120	valid
39.0ms	281×	body	640	valid
14.0ms	151×	body	320	valid
5.0ms	74×	body	160	valid