Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	208×	body	80	valid
4.0ms	20×	body	2560	valid
2.0ms	10×	body	5120	valid
2.0ms	10×	body	1280	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid

simplify10.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.0b	(+ (* re re) (* im im))
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
8×	`pow1` `add-log-exp`
6×	`fma-neg`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `fma-def` `diff-log` `pow-prod-down` `sum-log` `hypot-def` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

13.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(+ (* re re) (* im im))
8.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
28.0ms	(+ (* re re) (* im im))
50.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	342	834
1	1366	586
2	5001	533

prune235.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.4b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
5×	`pow1`
4×	`add-log-exp`
3×	`fma-neg`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `sqrt-div` `associate-*r/` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

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

series246.0ms

Counts

2 → 6

Calls

2 calls:

190.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
57.0ms	(- (hypot re im) re)

simplify45.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	273	321
1	1082	232
2	5001	228

prune116.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 4.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
12.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
5.0ms	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series557.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(sqrt (hypot re im))
86.0ms	(sqrt (hypot re im))
240.0ms	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
144.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify42.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	257	458
1	899	401
2	5001	379

prune218.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
12.0b	(fma (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (- re))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`pow1/3`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 64

Calls

4 calls:

6.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(fma (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (- re))

series515.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))
111.0ms	(cbrt (hypot re im))
114.0ms	(cbrt (hypot re im))
165.0ms	(fma (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (- re))

simplify39.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	291	636
1	1110	580
2	5001	566

prune320.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.4b

regimes72.0ms

Accuracy

22% (4.6b remaining)

Error of 11.9b against oracle of 7.3b and baseline of 13.1b

bsearch44.0ms

Steps

Iters	Range		Point
6	3.1824616164241624e+159	1.4236844560417313e+160	4.361595485786573e+159

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	14
1	33	14
2	33	14

end0.0ms

sample703.0ms

Algorithm

intervals

Results

213.0ms	6031×	body	80	valid
134.0ms	659×	body	2560	valid
81.0ms	471×	body	1280	valid
81.0ms	318×	body	5120	valid
37.0ms	286×	body	640	valid
15.0ms	156×	body	320	valid
5.0ms	79×	body	160	valid