Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	199×	body	80	valid
5.0ms	23×	body	2560	valid
2.0ms	9×	body	5120	valid
1.0ms	11×	body	640	valid
1.0ms	6×	body	1280	valid
1.0ms	6×	body	320	valid
0.0ms	2×	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

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: 38.1b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* re re) (* im im))
185.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
46.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify94.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	296	446
1	1086	401
2	3561	382
3	5001	381

prune239.0ms

Filtered

79 candidates to 69 candidates (87.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	74	5	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	5	80

Merged error: 6.7b

Counts

80 → 5

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
0.7b	(+ re (hypot re im))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1`
5×	`*-un-lft-identity`
4×	`associate-*r/` `add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def` `sqrt-pow1` `pow-prod-down`
2×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `pow1/2` `sum-log` `sqrt-prod` `distribute-lft-out`

Counts

2 → 33

Calls

2 calls:

6.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
4.0ms	(+ re (hypot re im))

series262.0ms

Counts

2 → 6

Calls

2 calls:

200.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
62.0ms	(+ re (hypot re im))

simplify85.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	194	185
1	791	167
2	3233	161
3	5001	161

prune120.0ms

Filtered

39 candidates to 34 candidates (87.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	38	6	44

Merged error: 6.4b

Counts

44 → 6

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ re (hypot re im)))
0.3b	(* (sqrt 2.0) (sqrt (+ re (hypot re im))))
0.7b	(+ re (hypot re im))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 71

Calls

3 calls:

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

series398.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(sqrt (+ re (hypot re im)))
199.0ms	(* (sqrt 2.0) (sqrt (+ re (hypot re im))))
61.0ms	(+ re (hypot re im))

simplify108.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	288	433
1	992	402
2	4306	387
3	5001	387

prune206.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	81	5	86

Merged error: 6.4b

Counts

86 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ re (hypot re im)))
0.2b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im)))))
0.3b	(* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im))))
0.7b	(+ re (hypot re im))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

35×	`sqrt-prod`
29×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`associate-l`
17×	`pow1`
14×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow-prod-down`
8×	`associate-r`
6×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-*r/` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `log1p-expm1-u`
3×	`fma-def` `sqrt-unprod` `distribute-lft-out`
2×	`*-commutative`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `hypot-def`

Counts

4 → 107

Calls

4 calls:

3.0ms	(sqrt (+ re (hypot re im)))
17.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im)))))
10.0ms	(* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im))))
3.0ms	(+ re (hypot re im))

series858.0ms

Counts

4 → 12

Calls

4 calls:

319.0ms	(sqrt (+ re (hypot re im)))
215.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im)))))
265.0ms	(* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im))))
58.0ms	(+ re (hypot re im))

simplify53.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	405	828
1	1591	742
2	5001	725

prune318.0ms

Filtered

119 candidates to 91 candidates (76.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	119	5	124

Merged error: 6.4b

Counts

124 → 5

regimes110.0ms

Accuracy

25.8% (4.4b remaining)

Error of 11.3b against oracle of 7.0b and baseline of 12.9b

bsearch61.0ms

Steps

Iters	Range		Point
9	-1.1334036948025617e+30	-2.3268372888139707e+24	-4.5768773392950057e+27

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample694.0ms

Algorithm

intervals

Results

212.0ms	6077×	body	80	valid
137.0ms	666×	body	2560	valid
80.0ms	293×	body	5120	valid
78.0ms	473×	body	1280	valid
37.0ms	288×	body	640	valid
13.0ms	129×	body	320	valid
5.0ms	74×	body	160	valid