Details

sample31.0ms

Algorithm

intervals

Results

8.0ms	192×	body	80	valid
6.0ms	25×	body	2560	valid
3.0ms	18×	body	640	valid
2.0ms	8×	body	1280	valid
1.0ms	4×	body	5120	valid
1.0ms	9×	body	320	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 37.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
27.1b	(sqrt (+ (* re re) (* im im)))

rewrite65.0ms

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:

22.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
31.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
10.0ms	(sqrt (+ (* re re) (* im im)))

series237.0ms

Counts

3 → 9

Calls

3 calls:

163.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
40.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify75.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (70.0ms)

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

prune294.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.4b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

7.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
9.0ms	(+ (hypot re im) re)

series230.0ms

Counts

2 → 6

Calls

2 calls:

179.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
50.0ms	(+ (hypot re im) re)

simplify52.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	183	173
1	519	156
2	1741	150
3	5001	148

prune157.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
15.8b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
2×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

2 → 23

Calls

2 calls:

5.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series353.0ms

Counts

2 → 6

Calls

2 calls:

222.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
131.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify46.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	129	225
1	378	193
2	1445	178
3	5002	174

prune161.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.6b	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
15.5b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
11.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
0.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

series446.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (hypot re im))
102.0ms	(cbrt (hypot re im))
119.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
124.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

simplify111.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	164	530
1	621	474
2	3153	435
3	5002	423

prune487.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.3b

regimes538.0ms

Accuracy

3.5% (5.9b remaining)

Error of 13.4b against oracle of 7.4b and baseline of 13.6b

bsearch200.0ms

Steps

Iters	Range		Point
6	3.079568706737843e+117	3.0831907232232414e+118	9.324979180976782e+117
9	0.05496260612073811	15234496.061427226	4.133336329114142
10	-415.9104570848854	-2.5612855498029964e-09	-0.007674033058449952
7	-2.2138820721712034e+132	-9.063407043561957e+130	-1.173715694929761e+131

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	35	29
1	38	29
2	44	12
3	47	12
4	53	12
5	64	12
6	71	12
7	72	12
8	72	12

end0.0ms

sample853.0ms

Algorithm

intervals

Results

258.0ms	6004×	body	80	valid
176.0ms	677×	body	2560	valid
113.0ms	523×	body	1280	valid
90.0ms	262×	body	5120	valid
48.0ms	288×	body	640	valid
21.0ms	168×	body	320	valid
6.0ms	78×	body	160	valid