Details

sample28.0ms

Algorithm

intervals

Results

7.0ms	20×	body	2560	valid
6.0ms	199×	body	80	valid
2.0ms	10×	body	5120	valid
2.0ms	13×	body	1280	valid
1.0ms	9×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	1×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

11.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
15.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series263.0ms

Counts

3 → 9

Calls

3 calls:

179.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify76.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	264	372
1	830	337
2	2660	322
3	5002	320

prune186.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.4b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (* 1 (hypot re im)) re)))
0.4b	(+ (* 1 (hypot re im)) re)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

4.0ms	(sqrt (* 2.0 (+ (* 1 (hypot re im)) re)))
3.0ms	(+ (* 1 (hypot re im)) re)

series252.0ms

Counts

2 → 6

Calls

2 calls:

197.0ms	(sqrt (* 2.0 (+ (* 1 (hypot re im)) re)))
55.0ms	(+ (* 1 (hypot re im)) re)

simplify76.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	203	208
1	623	184
2	2642	176
3	5001	175

prune112.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ (* 1 (hypot re im)) re))
0.4b	(+ (* 1 (hypot re im)) re)
0.4b	(* (sqrt 2.0) (sqrt (+ (* 1 (hypot re im)) re)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`sqrt-prod`
11×	`*-un-lft-identity`
8×	`pow1` `add-cube-cbrt`
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` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `fma-def` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

3 → 68

Calls

3 calls:

4.0ms	(sqrt (+ (* 1 (hypot re im)) re))
3.0ms	(+ (* 1 (hypot re im)) re)
14.0ms	(* (sqrt 2.0) (sqrt (+ (* 1 (hypot re im)) re)))

series381.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(sqrt (+ (* 1 (hypot re im)) re))
62.0ms	(+ (* 1 (hypot re im)) re)
193.0ms	(* (sqrt 2.0) (sqrt (+ (* 1 (hypot re im)) re)))

simplify46.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	309	503
1	1095	448
2	5002	438

prune215.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (hypot re im) re)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `pow1/3`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 56

Calls

4 calls:

2.0ms	(+ (hypot re im) re)
0.0ms	(cbrt 2.0)
5.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)

series55.0ms

Counts

4 → 6

Calls

4 calls:

55.0ms	(+ (hypot re im) re)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (15.0ms)

Iter	Nodes	Cost
0	105	199
1	216	184
2	441	178
3	1063	177
4	3191	177
5	5001	177

prune211.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.3b

regimes180.0ms

Accuracy

2.3% (6.5b remaining)

Error of 13.8b against oracle of 7.3b and baseline of 14.0b

bsearch170.0ms

Steps

Iters	Range		Point
9	4.8628084908197105e+54	4.258838753023189e+61	2.963711736123439e+58
10	6.157903029658734e-17	1.6022175866244216e-06	1.1016319640223668e-07
7	-9.005634263921258e+27	-1.3211094853598534e+26	-1.0469681604918512e+27
7	-3.258679308852972e+154	-2.403665538206493e+152	-1.2115064360128906e+154

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	40	32
1	45	32
2	51	13
3	54	13
4	60	13
5	71	13
6	78	13
7	79	13
8	79	13

end0.0ms

sample673.0ms

Algorithm

intervals

Results

194.0ms	5930×	body	80	valid
128.0ms	686×	body	2560	valid
89.0ms	543×	body	1280	valid
79.0ms	318×	body	5120	valid
33.0ms	272×	body	640	valid
14.0ms	151×	body	320	valid
6.0ms	100×	body	160	valid