Details

sample51.0ms

Algorithm

intervals

Results

17.0ms	187×	body	80	valid
9.0ms	23×	body	2560	valid
6.0ms	19×	body	1280	valid
6.0ms	12×	body	5120	valid
3.0ms	9×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	3×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
26.4b	(sqrt (+ (* re re) (* im im)))

rewrite64.0ms

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:

3.0ms	(+ (* re re) (* im im))
29.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
25.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
175.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (37.0ms)

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

prune243.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.0b	(hypot re im)
0.6b	(- (hypot re im) re)

rewrite16.0ms

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:

11.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.0ms	(hypot re im)
3.0ms	(- (hypot re im) re)

series296.0ms

Counts

3 → 9

Calls

3 calls:

190.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
45.0ms	(hypot re im)
61.0ms	(- (hypot re im) re)

simplify52.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (42.0ms)

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

prune160.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
12.8b	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3` `prod-diff`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 57

Calls

4 calls:

0.0ms	(cbrt (hypot re im))
0.0ms	(cbrt (hypot re im))
0.0ms	(cbrt (hypot re im))
14.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series401.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (hypot re im))
113.0ms	(cbrt (hypot re im))
114.0ms	(cbrt (hypot re im))
62.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify91.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	167	446
1	570	322
2	2968	294
3	5001	292

prune235.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))
11.6b	(- (* (* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
38×	`sqrt-prod`
24×	`cbrt-prod`
19×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
14×	`sqrt-pow1`
11×	`swap-sqr`
9×	`associate-r` `associate-l` `unswap-sqr`
8×	`pow1/2` `pow1/3`
6×	`add-exp-log` `pow-prod-up` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `pow-sqr` `log1p-expm1-u`
3×	`prod-diff`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 112

Calls

4 calls:

0.0ms	(cbrt (hypot re im))
0.0ms	(cbrt (hypot re im))
11.0ms	(* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))
103.0ms	(- (* (* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series407.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (hypot re im))
113.0ms	(cbrt (hypot re im))
114.0ms	(* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))
63.0ms	(- (* (* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify60.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	272	869
1	1213	668
2	5002	615

prune323.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.0b

regimes97.0ms

Accuracy

10.7% (4.9b remaining)

Error of 12.5b against oracle of 7.6b and baseline of 13.1b

bsearch81.0ms

Steps

Iters	Range		Point
11	2.8764294477061272e-176	1.9962584994272205e-147	1.9670001249123335e-147

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

sample1.4s

Algorithm

intervals

Results

542.0ms	6034×	body	80	valid
291.0ms	701×	body	2560	valid
156.0ms	462×	body	1280	valid
145.0ms	295×	body	5120	valid
80.0ms	296×	body	640	valid
30.0ms	141×	body	320	valid
11.0ms	71×	body	160	valid