Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	184×	body	80	valid
6.0ms	28×	body	2560	valid
3.0ms	16×	body	1280	valid
2.0ms	9×	body	5120	valid
1.0ms	11×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	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: 38.2b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt` `*-un-lft-identity`
57×	`sqrt-prod`
33×	`prod-diff`
26×	`add-cube-cbrt` `hypot-def`
25×	`distribute-lft-out`
23×	`associate-l`
20×	`swap-sqr`
12×	`unswap-sqr`
11×	`fma-neg` `*-commutative`
7×	`pow1`
6×	`associate-r`
5×	`add-log-exp`
4×	`sqrt-div` `difference-of-squares`
3×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `pow-prod-down` `flip-+`

Counts

3 → 140

Calls

3 calls:

34.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
21.0ms	(- (sqrt (+ (* re re) (* im im))) re)
20.0ms	(sqrt (+ (* re re) (* im im)))

series257.0ms

Counts

3 → 9

Calls

3 calls:

171.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	366	1122
1	1359	746
2	5001	689

prune250.0ms

Filtered

149 candidates to 79 candidates (53.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	144	5	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	5	150

Merged error: 8.1b

Counts

150 → 5

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* 2.0 (* 1 (- (hypot re im) re))))
1.0b	(- (hypot re im) re)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 83

Calls

3 calls:

1.0ms	(hypot re im)
17.0ms	(sqrt (* 2.0 (* 1 (- (hypot re im) re))))
6.0ms	(- (hypot re im) re)

series286.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(hypot re im)
186.0ms	(sqrt (* 2.0 (* 1 (- (hypot re im) re))))
56.0ms	(- (hypot re im) re)

simplify39.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	350	572
1	1225	465
2	5001	446

prune208.0ms

Filtered

92 candidates to 63 candidates (68.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	86	6	92
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	89	8	97

Merged error: 7.8b

Counts

97 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* (sqrt 2.0) (* 1 (- (hypot re im) re))))
0.2b	(* (sqrt (sqrt 2.0)) (sqrt (* (sqrt 2.0) (* 1 (- (hypot re im) re)))))
0.3b	(* (sqrt 2.0) (* 1 (- (hypot re im) re)))
1.0b	(- (hypot re im) re)

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

202×	`add-sqr-sqrt`
148×	`sqrt-prod`
100×	`unswap-sqr`
95×	`associate-r`
81×	`*-un-lft-identity`
56×	`add-cube-cbrt`
45×	`prod-diff`
44×	`distribute-rgt-in` `distribute-lft-in`
36×	`associate-l`
26×	`pow1`
14×	`associate-*r/` `pow-prod-down`
13×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`sqrt-pow1`
7×	`rem-sqrt-square` `*-commutative`
6×	`prod-exp` `add-log-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`pow1/2` `fma-neg`
1×	`sqrt-unprod` `diff-log` `1-exp`

Counts

4 → 260

Calls

4 calls:

21.0ms	(sqrt (* (sqrt 2.0) (* 1 (- (hypot re im) re))))
29.0ms	(* (sqrt (sqrt 2.0)) (sqrt (* (sqrt 2.0) (* 1 (- (hypot re im) re)))))
14.0ms	(* (sqrt 2.0) (* 1 (- (hypot re im) re)))
4.0ms	(- (hypot re im) re)

series608.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(sqrt (* (sqrt 2.0) (* 1 (- (hypot re im) re))))
191.0ms	(* (sqrt (sqrt 2.0)) (sqrt (* (sqrt 2.0) (* 1 (- (hypot re im) re)))))
98.0ms	(* (sqrt 2.0) (* 1 (- (hypot re im) re)))
64.0ms	(- (hypot re im) re)

simplify97.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	770	2799
1	2875	2341
2	5003	2309

prune525.0ms

Filtered

272 candidates to 138 candidates (50.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	269	3	272
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	274	6	280

Merged error: 7.8b

Counts

280 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 2.0) (hypot re im)) (* (sqrt 2.0) (- re)))))
0.4b	(* (sqrt 2.0) (hypot re im))
0.4b	(* (sqrt 2.0) (- re))
1.0b	(+ (* (sqrt 2.0) (hypot re im)) (* (sqrt 2.0) (- re)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-prod`
63×	`associate-l`
61×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`associate-r`
29×	`add-cube-cbrt`
28×	`distribute-lft-out`
16×	`fma-def`
12×	`pow1` `unswap-sqr`
10×	`add-exp-log` `add-cbrt-cube`
8×	`*-commutative`
6×	`add-log-exp`
5×	`distribute-rgt-neg-in` `pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `prod-exp` `distribute-rgt-neg-out` `cbrt-unprod`
2×	`distribute-rgt-out` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-unprod` `sqrt-div` `associate-*r/` `flip-+`
1×	`+-commutative` `neg-mul-1` `hypot-udef` `unsub-neg` `sum-log`

Counts

4 → 157

Calls

4 calls:

31.0ms	(* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 2.0) (hypot re im)) (* (sqrt 2.0) (- re)))))
5.0ms	(* (sqrt 2.0) (hypot re im))
6.0ms	(* (sqrt 2.0) (- re))
26.0ms	(+ (* (sqrt 2.0) (hypot re im)) (* (sqrt 2.0) (- re)))

series621.0ms

Counts

4 → 12

Calls

4 calls:

357.0ms	(* (sqrt (sqrt 2.0)) (sqrt (+ (* (sqrt 2.0) (hypot re im)) (* (sqrt 2.0) (- re)))))
96.0ms	(* (sqrt 2.0) (hypot re im))
47.0ms	(* (sqrt 2.0) (- re))
121.0ms	(+ (* (sqrt 2.0) (hypot re im)) (* (sqrt 2.0) (- re)))

simplify81.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	468	1126
1	2264	1039
2	5002	1020

prune429.0ms

Filtered

169 candidates to 115 candidates (68.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	165	4	169
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	169	6	175

Merged error: 7.8b

Counts

175 → 6

regimes101.0ms

Accuracy

22.4% (4.7b remaining)

Error of 12.1b against oracle of 7.4b and baseline of 13.5b

bsearch107.0ms

Steps

Iters	Range		Point
2	5.612059709364952e+140	6.1979150449352185e+140	5.685291626311235e+140
7	3.0152116158740813e+52	1.4121720889927557e+54	3.903092900167564e+52
7	61404.87568264329	1774840.6331059302	1755103.2713431905

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	40
1	68	40
2	69	40
3	69	40

end0.0ms

sample689.0ms

Algorithm

intervals

Results

212.0ms	6021×	body	80	valid
143.0ms	723×	body	2560	valid
77.0ms	479×	body	1280	valid
75.0ms	292×	body	5120	valid
34.0ms	273×	body	640	valid
14.0ms	144×	body	320	valid
4.0ms	68×	body	160	valid