Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	190×	body	80	valid
3.0ms	16×	body	2560	valid
2.0ms	15×	body	1280	valid
2.0ms	8×	body	5120	valid
2.0ms	14×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 38.8b

Counts

2 → 1

localize14.0ms

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)))
1.3b	(- (sqrt (+ (* re re) (* im im))) re)
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

108×	`*-un-lft-identity`
98×	`add-sqr-sqrt`
57×	`sqrt-prod`
33×	`prod-diff`
32×	`add-cube-cbrt`
30×	`associate-l` `distribute-lft-out`
26×	`hypot-def`
25×	`swap-sqr`
15×	`fma-def`
13×	`unswap-sqr`
12×	`*-commutative`
11×	`fma-neg`
9×	`associate-r`
8×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
3×	`rem-sqrt-square` `sqrt-pow1`
2×	`+-commutative` `flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `distribute-lft-out--`
1×	`sub-neg` `diff-log` `pow-prod-down` `sum-log`

Counts

4 → 173

Calls

4 calls:

16.0ms	(+ (* re re) (* im im))
35.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
21.0ms	(- (sqrt (+ (* re re) (* im im))) re)
17.0ms	(sqrt (+ (* re re) (* im im)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* re re) (* im im))
183.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
53.0ms	(- (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	388	1206
1	1485	822
2	5001	760

prune271.0ms

Filtered

185 candidates to 105 candidates (56.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	180	5	185
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	181	5	186

Merged error: 7.2b

Counts

186 → 5

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
14×	`sqrt-prod`
13×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow1`
5×	`associate-r` `add-log-exp`
3×	`add-exp-log` `expm1-log1p-u` `fma-neg` `associate-l` `add-cbrt-cube` `log1p-expm1-u`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `sqrt-div` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `hypot-udef` `pow1/2` `diff-log` `pow-prod-down` `*-commutative`

Counts

3 → 68

Calls

3 calls:

1.0ms	(hypot im re)
9.0ms	(sqrt (* 2.0 (- (hypot im re) re)))
4.0ms	(- (hypot im re) re)

series323.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(hypot im re)
212.0ms	(sqrt (* 2.0 (- (hypot im re) re)))
60.0ms	(- (hypot im re) re)

simplify38.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	322	460
1	1064	374
2	5002	369

prune152.0ms

Filtered

77 candidates to 59 candidates (76.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	74	8	82

Merged error: 7.1b

Counts

82 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot im re)
0.0b	(sqrt (* 2.0 (- (* (sqrt (hypot im re)) (sqrt (hypot im re))) re)))
0.5b	(* (sqrt (hypot im re)) (sqrt (hypot im re)))
9.6b	(- (* (sqrt (hypot im re)) (sqrt (hypot im re))) re)

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

201×	`add-sqr-sqrt`
131×	`sqrt-prod`
88×	`*-un-lft-identity`
87×	`prod-diff`
80×	`add-cube-cbrt`
48×	`swap-sqr`
46×	`associate-r`
35×	`associate-l`
30×	`unswap-sqr`
29×	`fma-neg`
22×	`pow1` `difference-of-squares`
10×	`sqrt-pow1`
9×	`pow1/2`
8×	`*-commutative`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-sqr`
2×	`rem-sqrt-square` `flip3--` `sqrt-div` `associate-*r/` `flip--`
1×	`pow2` `sub-neg` `hypot-udef` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `cbrt-unprod`

Counts

4 → 245

Calls

4 calls:

1.0ms	(hypot im re)
44.0ms	(sqrt (* 2.0 (- (* (sqrt (hypot im re)) (sqrt (hypot im re))) re)))
6.0ms	(* (sqrt (hypot im re)) (sqrt (hypot im re)))
18.0ms	(- (* (sqrt (hypot im re)) (sqrt (hypot im re))) re)

series388.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(hypot im re)
218.0ms	(sqrt (* 2.0 (- (* (sqrt (hypot im re)) (sqrt (hypot im re))) re)))
54.0ms	(* (sqrt (hypot im re)) (sqrt (hypot im re)))
62.0ms	(- (* (sqrt (hypot im re)) (sqrt (hypot im re))) re)

simplify74.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	530	2396
1	1711	1362
2	5002	1292

prune294.0ms

Filtered

257 candidates to 99 candidates (38.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	249	8	257
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	254	11	265

Merged error: 7.1b

Counts

265 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot im re))
0.5b	(cbrt (hypot im re))
0.5b	(cbrt (hypot im re))
11.3b	(- (* (sqrt (hypot im re)) (sqrt (* (* (cbrt (hypot im re)) (cbrt (hypot im re))) (cbrt (hypot im re))))) re)

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

1092×	`add-sqr-sqrt`
580×	`unswap-sqr`
534×	`sqrt-prod`
379×	`cbrt-prod`
333×	`prod-diff`
284×	`associate-r`
186×	`add-cube-cbrt` `*-un-lft-identity`
157×	`associate-l`
111×	`fma-neg`
84×	`swap-sqr`
41×	`difference-of-squares`
40×	`*-commutative`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 540

Calls

4 calls:

2.0ms	(cbrt (hypot im re))
1.0ms	(cbrt (hypot im re))
1.0ms	(cbrt (hypot im re))
77.0ms	(- (* (sqrt (hypot im re)) (sqrt (* (* (cbrt (hypot im re)) (cbrt (hypot im re))) (cbrt (hypot im re))))) re)

series438.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(cbrt (hypot im re))
126.0ms	(cbrt (hypot im re))
123.0ms	(cbrt (hypot im re))
66.0ms	(- (* (sqrt (hypot im re)) (sqrt (* (* (cbrt (hypot im re)) (cbrt (hypot im re))) (cbrt (hypot im re))))) re)

simplify153.0ms

Algorithm

egg-herbie

Counts

552 → 552

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	1010	12315
1	2509	9880
2	5001	7318

prune577.0ms

Filtered

552 candidates to 151 candidates (27.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	547	5	552
Fresh	5	4	9
Picked	1	0	1
Done	1	0	1
Total	554	9	563

Merged error: 7.1b

Counts

563 → 9

regimes147.0ms

Accuracy

47.5% (4.4b remaining)

Error of 11.9b against oracle of 7.5b and baseline of 15.8b

bsearch51.0ms

Steps

Iters	Range		Point
7	1.0482644148039984e-06	4.770996395318151e-05	1.2693065203045017e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	22
1	35	22
2	35	22

end0.0ms

sample660.0ms

Algorithm

intervals

Results

199.0ms	5986×	body	80	valid
128.0ms	695×	body	2560	valid
84.0ms	538×	body	1280	valid
60.0ms	264×	body	5120	valid
35.0ms	277×	body	640	valid
16.0ms	156×	body	320	valid
5.0ms	84×	body	160	valid