Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
5.0ms	25×	body	2560	valid
2.0ms	10×	body	5120	valid
2.0ms	13×	body	1280	valid
1.0ms	8×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	8

prune5.0ms

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: 36.1b

Counts

2 → 1

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)))
1.2b	(+ (sqrt (+ (* re re) (* im im))) re)
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
29×	`sqrt-prod`
26×	`fma-def` `hypot-def`
19×	`swap-sqr`
18×	`associate-l`
17×	`distribute-lft-out`
15×	`add-cube-cbrt`
13×	`unswap-sqr`
12×	`*-commutative`
8×	`pow1` `add-log-exp`
7×	`associate-r`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`+-commutative` `rem-sqrt-square` `sqrt-pow1`
2×	`pow1/2` `associate-*r/` `sum-log`
1×	`pow-prod-down`

Counts

4 → 135

Calls

4 calls:

16.0ms	(+ (* re re) (* im im))
25.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
20.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
16.0ms	(sqrt (+ (* re re) (* im im)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* re re) (* im im))
179.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify117.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	335	602
1	1228	559
2	4368	539
3	5001	537

prune250.0ms

Filtered

147 candidates to 101 candidates (68.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	142	5	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	5	148

Merged error: 8.8b

Counts

148 → 5

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (hypot re im) re)))
0.0b	(hypot re im)
1.2b	(+ (hypot re im) re)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`sqrt-prod`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`pow1`
5×	`add-log-exp`
4×	`associate-r`
3×	`add-exp-log` `expm1-log1p-u` `fma-def` `associate-l` `add-cbrt-cube` `log1p-expm1-u`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `hypot-udef` `pow1/2` `pow-prod-down` `sum-log` `*-commutative`

Counts

3 → 56

Calls

3 calls:

6.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
1.0ms	(hypot re im)
3.0ms	(+ (hypot re im) re)

series301.0ms

Counts

3 → 9

Calls

3 calls:

195.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
46.0ms	(hypot re im)
60.0ms	(+ (hypot re im) re)

simplify73.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	238	287
1	714	270
2	2651	262
3	5002	261

prune134.0ms

Filtered

65 candidates to 56 candidates (86.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	59	6	65
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	62	8	70

Merged error: 8.6b

Counts

70 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* (sqrt 2.0) (+ (hypot re im) re)))
0.3b	(* (sqrt (sqrt 2.0)) (sqrt (* (sqrt 2.0) (+ (hypot re im) re))))
0.3b	(* (sqrt 2.0) (+ (hypot re im) re))
1.2b	(+ (hypot re im) re)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-prod`
67×	`add-sqr-sqrt`
32×	`associate-r`
28×	`*-un-lft-identity`
27×	`associate-l`
26×	`unswap-sqr`
20×	`add-cube-cbrt`
16×	`pow1`
8×	`add-exp-log` `associate-*r/` `add-cbrt-cube`
7×	`pow-prod-down`
6×	`sqrt-pow1` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `sqrt-div` `*-commutative` `flip-+` `log1p-expm1-u` `distribute-lft-out`
3×	`+-commutative` `rem-sqrt-square` `fma-def` `pow1/2`
2×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `cbrt-unprod`
1×	`sqrt-unprod` `sum-log`

Counts

4 → 142

Calls

4 calls:

8.0ms	(sqrt (* (sqrt 2.0) (+ (hypot re im) re)))
16.0ms	(* (sqrt (sqrt 2.0)) (sqrt (* (sqrt 2.0) (+ (hypot re im) re))))
7.0ms	(* (sqrt 2.0) (+ (hypot re im) re))
3.0ms	(+ (hypot re im) re)

series600.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(sqrt (* (sqrt 2.0) (+ (hypot re im) re)))
196.0ms	(* (sqrt (sqrt 2.0)) (sqrt (* (sqrt 2.0) (+ (hypot re im) re))))
94.0ms	(* (sqrt 2.0) (+ (hypot re im) re))
60.0ms	(+ (hypot re im) re)

simplify59.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	408	1178
1	1731	1125
2	5001	1105

prune297.0ms

Filtered

154 candidates to 104 candidates (67.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	154	8	162

Merged error: 8.6b

Counts

162 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
13.4b	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
56×	`fma-def`
49×	`cbrt-prod`
36×	`associate-l`
30×	`unswap-sqr`
25×	`*-un-lft-identity`
19×	`add-cube-cbrt`
12×	`associate-r`
10×	`swap-sqr`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `*-commutative` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3` `distribute-lft-out`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 111

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
32.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series401.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt (hypot re im))
112.0ms	(cbrt (hypot re im))
111.0ms	(cbrt (hypot re im))
61.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify55.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	141	419
1	399	352
2	1356	309
3	5001	297

prune286.0ms

Filtered

123 candidates to 104 candidates (84.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	118	13	131

Merged error: 8.6b

Counts

131 → 13

regimes137.0ms

Accuracy

22.9% (4.6b remaining)

Error of 12.0b against oracle of 7.4b and baseline of 13.4b

bsearch41.0ms

Steps

Iters	Range		Point
6	-3.250294642428847e+155	-5.278913287823028e+154	-7.008560843419581e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample662.0ms

Algorithm

intervals

Results

194.0ms	6030×	body	80	valid
129.0ms	680×	body	2560	valid
87.0ms	522×	body	1280	valid
64.0ms	266×	body	5120	valid
35.0ms	268×	body	640	valid
14.0ms	155×	body	320	valid
5.0ms	79×	body	160	valid