Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	184×	body	80	valid
5.0ms	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)))

rewrite27.0ms

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:

14.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series263.0ms

Counts

3 → 9

Calls

3 calls:

176.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
46.0ms	(- (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify42.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

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

prune193.0ms

Filtered

83 candidates to 59 candidates (71.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	4	84

Merged error: 8.1b

Counts

84 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
1.0b	(- (hypot re im) re)

rewrite13.0ms

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:

1.0ms	(hypot re im)
7.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
4.0ms	(- (hypot re im) re)

series295.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(hypot re im)
188.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
62.0ms	(- (hypot re im) re)

simplify51.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	283	345
1	1118	247
2	5001	236

prune163.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	56	6	62
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	58	8	66

Merged error: 7.8b

Counts

66 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (- (hypot re im) re))
0.3b	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
1.0b	(- (hypot re im) re)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

1.0ms	(hypot re im)
4.0ms	(sqrt (- (hypot re im) re))
8.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
4.0ms	(- (hypot re im) re)

series430.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot re im)
127.0ms	(sqrt (- (hypot re im) re))
194.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
57.0ms	(- (hypot re im) re)

simplify43.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	348	614
1	1286	509
2	5002	488

prune257.0ms

Filtered

105 candidates to 78 candidates (74.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	106	7	113

Merged error: 7.8b

Counts

113 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`pow1`
18×	`add-exp-log` `sqrt-prod`
17×	`add-cube-cbrt`
11×	`add-cbrt-cube`
10×	`cbrt-prod` `associate-l`
9×	`associate-r` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`sqrt-div` `associate-*r/` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`*-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 111

Calls

4 calls:

4.0ms	(sqrt (- (hypot re im) re))
14.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re))))
9.0ms	(* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re)))
8.0ms	(- (hypot re im) re)

series811.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(sqrt (- (hypot re im) re))
198.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re))))
424.0ms	(* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re)))
62.0ms	(- (hypot re im) re)

simplify67.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	505	1087
1	2029	867
2	5001	818

prune327.0ms

Filtered

123 candidates to 88 candidates (71.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	123	7	130

Merged error: 7.8b

Counts

130 → 7

regimes103.0ms

Accuracy

22.7% (4.5b remaining)

Error of 11.9b against oracle of 7.4b and baseline of 13.3b

bsearch101.0ms

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	38	28
1	45	14
2	48	14
3	48	14

end0.0ms

sample677.0ms

Algorithm

intervals

Results

210.0ms	6021×	body	80	valid
137.0ms	723×	body	2560	valid
74.0ms	479×	body	1280	valid
68.0ms	292×	body	5120	valid
35.0ms	273×	body	640	valid
13.0ms	144×	body	320	valid
4.0ms	68×	body	160	valid