Details

sample29.0ms

Algorithm

intervals

Results

7.0ms	196×	body	80	valid
7.0ms	18×	body	2560	valid
3.0ms	11×	body	5120	valid
2.0ms	10×	body	1280	valid
1.0ms	9×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	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: 38.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.1b	(- (sqrt (+ (* re re) (* im im))) re)
30.5b	(sqrt (+ (* re re) (* im im)))

rewrite58.0ms

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:

31.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
22.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series256.0ms

Counts

3 → 9

Calls

3 calls:

172.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (36.0ms)

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

prune191.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.4b

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)
1.1b	(- (hypot re im) re)

rewrite15.0ms

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:

10.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.0ms	(hypot re im)
3.0ms	(- (hypot re im) re)

series288.0ms

Counts

3 → 9

Calls

3 calls:

182.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
46.0ms	(hypot re im)
59.0ms	(- (hypot re im) re)

simplify47.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (42.0ms)

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

prune157.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (- (hypot re im) re))
1.1b	(- (hypot re im) re)
1.1b	(- (hypot re im) re)
1.1b	(- (hypot re im) re)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
5×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 101

Calls

4 calls:

2.0ms	(cbrt (- (hypot re im) re))
3.0ms	(- (hypot re im) re)
3.0ms	(- (hypot re im) re)
3.0ms	(- (hypot re im) re)

series330.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (- (hypot re im) re))
57.0ms	(- (hypot re im) re)
58.0ms	(- (hypot re im) re)
59.0ms	(- (hypot re im) re)

simplify112.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	226	736
1	690	507
2	3777	474
3	5001	444

prune332.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.3b

localize13.0ms

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)) (cbrt (hypot re im)))
10.6b	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

0.0ms	(cbrt (hypot re im))
0.0ms	(cbrt (hypot re im))
5.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
14.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series408.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(cbrt (hypot re im))
109.0ms	(cbrt (hypot re im))
120.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
60.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify42.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	247	660
1	1003	533
2	5001	476

prune278.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.3b

regimes72.0ms

Accuracy

32.9% (4.0b remaining)

Error of 11.4b against oracle of 7.3b and baseline of 13.3b

bsearch56.0ms

Steps

Iters	Range		Point
8	9.843787102234572e+98	1.5857372482503793e+103	2.8514934608649167e+100

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

sample682.0ms

Algorithm

intervals

Results

202.0ms	6006×	body	80	valid
138.0ms	691×	body	2560	valid
76.0ms	480×	body	1280	valid
76.0ms	314×	body	5120	valid
35.0ms	285×	body	640	valid
13.0ms	135×	body	320	valid
6.0ms	89×	body	160	valid