Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	189×	body	80	valid
4.0ms	24×	body	2560	valid
3.0ms	11×	body	5120	valid
2.0ms	16×	body	1280	valid
1.0ms	9×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	2×	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

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 40.3b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt` `*-un-lft-identity`
57×	`sqrt-prod`
33×	`prod-diff`
26×	`add-cube-cbrt` `hypot-def`
25×	`distribute-lft-out`
23×	`associate-l`
20×	`swap-sqr`
12×	`unswap-sqr`
11×	`fma-neg` `*-commutative`
7×	`pow1`
6×	`associate-r`
5×	`add-log-exp`
4×	`sqrt-div` `difference-of-squares`
3×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `pow-prod-down` `flip-+`

Counts

3 → 140

Calls

3 calls:

37.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
22.0ms	(- (sqrt (+ (* re re) (* im im))) re)
18.0ms	(sqrt (+ (* re re) (* im im)))

series271.0ms

Counts

3 → 9

Calls

3 calls:

180.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
53.0ms	(- (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	360	1122
1	1311	748
2	5001	689

prune208.0ms

Filtered

149 candidates to 79 candidates (47.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	144	5	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	5	150

Merged error: 7.8b

Counts

150 → 5

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
14×	`sqrt-prod`
13×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow1`
5×	`associate-r` `add-log-exp`
3×	`add-exp-log` `expm1-log1p-u` `fma-neg` `associate-l` `add-cbrt-cube` `log1p-expm1-u`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `sqrt-div` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `hypot-udef` `pow1/2` `diff-log` `pow-prod-down` `*-commutative`

Counts

3 → 68

Calls

3 calls:

10.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
1.0ms	(hypot re im)
4.0ms	(- (hypot re im) re)

series306.0ms

Counts

3 → 9

Calls

3 calls:

192.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
50.0ms	(hypot re im)
64.0ms	(- (hypot re im) re)

simplify37.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	273	437
1	918	343
2	5001	328

prune143.0ms

Filtered

77 candidates to 59 candidates (23.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	76	6	82

Merged error: 7.7b

Counts

82 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs (cbrt 2.0)) (sqrt (* (cbrt 2.0) (- (hypot re im) re))))
0.6b	(- (hypot re im) re)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`associate-r`
23×	`*-un-lft-identity`
21×	`sqrt-prod`
19×	`add-cube-cbrt`
11×	`cbrt-prod`
9×	`associate-l` `prod-diff`
8×	`unswap-sqr`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`fma-neg`
2×	`flip3--` `pow1/3` `sqrt-div` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `cbrt-unprod`

Counts

4 → 97

Calls

4 calls:

13.0ms	(* (fabs (cbrt 2.0)) (sqrt (* (cbrt 2.0) (- (hypot re im) re))))
4.0ms	(- (hypot re im) re)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)

series410.0ms

Counts

4 → 8

Calls

4 calls:

347.0ms	(* (fabs (cbrt 2.0)) (sqrt (* (cbrt 2.0) (- (hypot re im) re))))
63.0ms	(- (hypot re im) re)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	382	761
1	1505	654
2	5002	644

prune231.0ms

Filtered

105 candidates to 80 candidates (23.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	105	6	111

Merged error: 7.7b

Counts

111 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (cbrt (cbrt 2.0)) (cbrt (cbrt 2.0))) (cbrt (cbrt 2.0)))
1.0b	(cbrt (cbrt 2.0))
1.0b	(cbrt (cbrt 2.0))
1.0b	(cbrt (cbrt 2.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

207×	`cbrt-prod`
164×	`add-sqr-sqrt`
81×	`unswap-sqr`
50×	`associate-l`
26×	`add-cube-cbrt` `*-un-lft-identity`
23×	`pow1`
19×	`add-cbrt-cube`
18×	`swap-sqr` `associate-r` `cbrt-unprod`
12×	`pow1/3`
9×	`add-exp-log` `pow-prod-up`
6×	`pow-plus` `*-commutative`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `pow-sqr`
2×	`pow2` `pow3`

Counts

4 → 180

Calls

4 calls:

22.0ms	(* (* (cbrt (cbrt 2.0)) (cbrt (cbrt 2.0))) (cbrt (cbrt 2.0)))
2.0ms	(cbrt (cbrt 2.0))
2.0ms	(cbrt (cbrt 2.0))
2.0ms	(cbrt (cbrt 2.0))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(* (* (cbrt (cbrt 2.0)) (cbrt (cbrt 2.0))) (cbrt (cbrt 2.0)))
0.0ms	(cbrt (cbrt 2.0))
0.0ms	(cbrt (cbrt 2.0))
0.0ms	(cbrt (cbrt 2.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	281	1772
1	916	1522
2	5001	1310

prune387.0ms

Filtered

184 candidates to 114 candidates (38.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	184	6	190

Merged error: 7.7b

Counts

190 → 6

regimes134.0ms

Accuracy

25.2% (4.5b remaining)

Error of 11.7b against oracle of 7.2b and baseline of 13.2b

bsearch167.0ms

Steps

Iters	Range		Point
8	7.209797908640857e+154	6.66118297754639e+158	9.11944020096992e+157
9	3.0977499078117085e+118	1.5667647070445954e+126	1.1383524170048822e+124
9	1.5221618338087932e+67	2.3018138540721667e+76	3.315663193784861e+67

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	36	26
1	41	13
2	44	13
3	44	13

end0.0ms

sample679.0ms

Algorithm

intervals

Results

203.0ms	6026×	body	80	valid
137.0ms	696×	body	2560	valid
75.0ms	473×	body	1280	valid
69.0ms	296×	body	5120	valid
39.0ms	279×	body	640	valid
14.0ms	144×	body	320	valid
5.0ms	86×	body	160	valid